četvrtak, 15. kolovoza 2013.


Još jedno od dubokih pitanja na koje suradnici portala za treću kulturu Edge odgovaraju još dubljim i elegantnijim mislima. Pitanje za 2012. godinu bilo je: Koje je vaše najdraže, elegantno ili lijepo objašnjenje [svega]?

Mr. Brockman, the editor and publisher of Edge.org, asked the thinkers in his online science community to share their favorite “deep, elegant or beautiful” explanation. What sounds like a canned conversation starter at a dinner party of geeks ends up yielding a handy collection of 150 shortcuts to understanding how the world works. Elegance in this context means, as the evolutionary biologist Richard Dawkins writes, the “power to explain much while assuming little.” While some offerings can be incomprehensible (including the one entitled “Why Is Our World Comprehensible?”), others keep it simpler. Marcel Kinsbourne, a professor of psychology at the New School, describes how good ideas surface. Philip Campbell, editor in chief of Nature, tackles the beauty of sunrises. Among the things this book will teach you? How much you don’t know. - SUSANNAH MEADOWS

Scientists' greatest pleasure comes from theories that derive the solution to some deep puzzle from a small set of simple principles in a surprising way. These explanations are called "beautiful" or "elegant". Historical examples are Kepler's explanation of complex planetary motions as simple ellipses, Bohr's explanation of the periodic table of the elements in terms of electron shells, and Watson and Crick's double helix. Einstein famously said that he did not need experimental confirmation of his general theory of relativity because it "was so beautiful it had to be true."

Since this question is about explanation, answers may embrace scientific thinking in the broadest sense: as the most reliable way of gaining knowledge about anything, including other fields of inquiry such as philosophy, mathematics, economics, history, political theory, literary theory, or the human spirit. The only requirement is that some simple and non-obvious idea explain some diverse and complicated set of phenomena.

192 CONTRIBUTORS (128,500 words): Emanuel Derman, Nicholas Humphrey, Dylan Evans, Howard Gardner, Jeremy Berstein, Rudy Rucker, Michael Shermer, Nicholas Carr, Susam Blackmore, Scott Atran, David Christian, Andy Clark, Donald Hoffman, Derek Lowe, Roger Schank, Arnold Trehub, Timothy Taylor, Cliff Pickover, Ed Regis, Jared Diamond, Robert Provine, Richard Nisbett, Peter Woit, Haim Harari, Satyajit Das, Juan Enriquez, Jamshed Bharucha, Richard Foreman, Scott D. Sampson, Jonathan Gotschall, Keith Devlin, Clay Shirky, Steven Pinker, Gloria Origgi, Sean Carroll, Irene Pepperberg, Tor Nørretranders, Alan Alda, Jennifer Jacquet, George Dyson, Nigel Goldenfeld, Aubrey De Grey, Nassim Nicholas Taleb, George Church, Kevin Kelly, Stephen M. Kosslyn and Robin S. Rosenberg, Lawrence M. Krauss, James Croak, Armand Marie Leroi, Leonard Susskind, Douglas Rushkoff, Victoria Stodden, Daniel C. Dennett, Shing-tung Yau, Philip Campbell, Freeman Dyson, Mihaly Csikszentmihalyi, Martin Rees, Stanislas Dehaene, Samuel Arbesman, David Gelernter, Timothy D. Wilson, Judith Rich Harris, Samuel Barondes, Peter Atkins, Robert Kurzban, Todd C. Sacktor, Gerald Holton, Frank Wilczek,  Elizabeth Dunn, Eric J. Topol, Lee Smolin, Roger Highfield, Michael I. Norton, Richard Dawkins, Neil Gershenfeld, Alison Gopnik, Terrence J. Sejnowski, Rodney Brooks, Philip Zimbardo, Christopher Sykes, Nicholas A. Christakis, Marcel Kinsbourne, Thomas A. Bass, Randolph Nesse, Sherry Turkle, Gino Segre, Eric R. Kandel, Hugo Mercier, Beatrice Golomb, Benjamin Bergen, Alun Anderson, Alvy Ray Smith, Katinka Matson, Steve Giddings, Hans Ulrich Obrist, Gerd Gigerenzer , Gerald Smallberg, Paul Steinhardt, Adam Alter, Karl Sabbagh, David G. Myers, Lica DiBiase, Stuart Pimm, James J. O'Donnell, Albert-László Barabási, Simon Baron-Cohen, Charles Seife, Patrick Bateson, Carlo Rovelli, Jordan Pollack, Robert Sapolsky, Frank Tipler, Bruce Parker, Marcelo Gleiser, Richard Saul Wurman, Gary Klein, Ernst Pöppel, Evgeny Morozov, Gregory Benford, S. Abbas Raza, Rebecca Newberger Goldstein, Thomas Metzinger, David Haig, Melanie Swan, Laurence C. Smith, John C. Mather, Seth Lloyd, P. Murali Doriaswamy, Marti Hearst, Jon Kleinberg, Kai Krause, Joel Gold, Simone Schnall, Paul Saffo, Lisa Randall, Brian Eno, Giulio Boccaletti, Paul Bloom, Timo Hannay, Anthony Grayling, Matt Ridley, Doug Coupland, Amanda Gefter, Bruce Hood, Gregory Paul, Stephon Alexander, Bart Kosko, John Tooby, Stuart Kauffman, Barry C. Smith, John Naughton, Helen Fisher, Virginia Heffernan, Dimitar Sasselov, Eric Weinstein, Max Tegmark, PZ Myers, Andrew Lih, Christine Finn, Gregory Cochran, John McWhorter, Michael Vassar, Brian Knutson, Eduardo Salcedo-Albaran, Antony Garrett Lisi, Helena Cronin, Tania Lombrozo, Kevin Hand, Seirian Sumner, David Eagleman, Tim O'Reilly, Marco Iacoboni, Raphael Bousso, David Dalrymple, Emily Pronin, Dave Winer, Alanna Conner & Hazel Rose Markus, David Pizarro, Andrian Kreye, David Buss, Carl Zimmer, Stewart Brand, Anton Zeilinger, Carolyn Porco,  Dan Sperber, Mahzarin Banaji, V.S. Ramachandran, Nathan Myhrvold, Charles Simonyi, Richard Thaler, Andrei Linde

Professor, Financial Engineering, Columbia University; Principal, Prisma Capital Partners; Former Head, Quantitative Strategies Group, Equities Division, Goldman Sachs & Co.; Author, Models.Behaving.Badly
Sleep Is the Interest We Have to Pay on the Capital Which is Called In at Death
Sleep is the interest we have to pay on the capital which is called in at death; and the higher the rate
of interest and the more regularly it is paid, the further the date of redemption is postponed.
So wrote Arthur Schopenhauer, comparing life to finance in a universe that must keep its books balanced. At birth you receive a loan, consciousness and light borrowed from the void, leaving a hole in the emptiness. The hole will grow bigger each day. Nightly, by yielding temporarily to the darkness of sleep, you restore some of the emptiness and keep the hole from growing limitlessly. In the end you must pay back the principal, complete the void, and return the life originally lent you.
By focusing on the common periodic nature of sleep and interest payments, Schopenhauer extends the metaphor of borrowing to life itself. Life and consciousness are the principal, death is the final repayment, and sleep is la petite mort, the periodic little death that renews.

CEO and Managing Director, Intellectual Ventures; Co-Author (with Bill Gates), The Road Ahead; Author, Modernist Cuisine
The Scientific Method—An Explanation For Explanations
Humans are a story telling species. Throughout history we have told stories to each other and ourselves as one of the ways to understand the world around us. Every culture has its creation myth for how the universe came to be, but the stories do not stop at the big picture view; other stories discuss every aspect of the world around us. We humans are chatterboxes and we just can't resist telling a story about just about everything.
However compelling and entertaining these stories may be, they fall short of being explanations because in the end all they are is stories. For every story you can tell a different variation, or a different ending, without giving reason to choose between them. If you are skeptical or try to test the veracity of these stories you'll typically find most such stories wanting. One approach to this is forbid skeptical inquiry, branding it as heresy. This meme is so compelling that it was independently developed by cultures around the globes; it is the origin of religion—a set of stories about the world that must be accepted on faith, and never questioned.
Somewhere along the line a very different meme got started. Instead of forbidding inquiry into stories about the world people tried the other extreme of encouraging continual questioning. Stories about aspect of the world can be questioned skeptically, and tested with observations and experiments. If the story survives the tests then provisionally at least one can accept it as something more than a mere story; it is a theory that has real explanatory power. It will never be more than a provisional explanation—we can never let down our skeptical guard—but these provisional explanations can be very useful. We call this process of making and vetting stories the scientific method.
For me, the scientific method is the ultimate elegant explanation. Indeed it is the ultimate foundation for anything worthy of the name "explanation". It makes no sense to talk about explanations without having a process for deciding which are right and which are wrong, and in a broad sense that is what the scientific method is about. All of the other wonderful explanations celebrated here owe their origin and credibility to the process by which they are verified—the scientific method.
This seems quite obvious to us now, but it took many thousands of years for people to develop the scientific method to a point where they could use it to build useful theories about the world. It was not, a priori, obvious that such a method would work. At one extreme, creation myths discuss the origin of the universe, and for thousands of years one could take the position that this will never be more than a story—how can humans ever figure out something that complicated and distant in space and time? It would be a bold bet to say that people reasoning with the scientific method could solve that puzzle.
Well, it has taken us a while but by now enormous amounts are known about the composition of stars and galaxies and how the universe came to be. There are still gaps in our knowledge (and our skepticism will never stop), but we've made a lot of progress on cosmology and many other problems. Indeed we know more about the composition of distant stars than many questions about things here on earth. The scientific method has not conquered all great questions - other issues remain illusive, but the spirit of the scientific method is that one does shrink from the unknown. It is OK to say that we have no useful story for everything we are curious about, and we comfort ourselves that at some point in the future new explanations will fill the gaps in our current knowledge, as often raise new questions that highlight new gaps.
It's hard to overestimate the importance of the scientific method. Human culture contains much more than science—but science is the part that actually works—the rest is just stories. The rationally based inquiry the scientific method enables is what has given us science and technology and vastly different lifestyles than those of our hunter-gatherers ancestors. In some sense it is analogous to evolution. The sum of millions of small mutations separate us from single celled like blue-green algae. Each had to survive the test of selection and work better than the previous state in the sense of biological fitness. Human knowledge is the accumulation of millions of stories-that-work, each of which had to survive the test of the scientific method, matching observation and experiment more than the predecessors. Both evolution and science have taken us a long way, but looking forward it is clear that science will take us much farther.

Software Engineer, Computer Scientist, Entrepreneur, Philanthropist
Boscovich's Explanation Of Atomic Forces
A great example how a great deal of amazing insight can be gained from some very simple considerations is the explanation of atomic forces by the 18th century Jesuit polymath Roger Boscovich, who was born in Dubrovnik.
One of the great philosophical arguments at the time took place between the adherents of Descartes who—following Aristotle—thought that forces can only be the result of immediate contact and those who followed Newton and believed in his concept of force acting at a distance. Newton was the revolutionary here, but his opponents argued—with some justification—that "action at a distance" brought back into physics "occult" explanations that do not follow from the "clear and distinct" understanding that Descartes demanded. (In the following I am paraphrasing reference works.) Boscovich, a forceful advocate of the Newtonian point of view, turned the question around: Let's understand exactly what happens during the interaction that we would call immediate contact?
His arguments are very easy to understand and extremely convincing. Let's imagine two bodies, one of which is traveling at a speed of, say, 6 units, the other at a speed of 12 with the faster body catching up with the slower one along the same straight path. We imagine what transpires when the two bodies collide. By conservation of the "quantity of motion," both bodies should continue after collision along the same path, each with a speed of 9 units (in the case of inelastic collision, or in case of elastic collision for a brief period right after the collision)
But how did the velocity of the faster body come to be reduced from 12 to 9, and that of the slower body increased from 6 to 9? Clearly, the time interval for the change in velocities cannot be zero, for then, argued Boscovich, the instantaneous change in speed would violate the law of continuity. Furthermore, we would have to say that at the moment of impact, the speed of one body is simultaneously 12 and 9, which is patently absurd.
It is therefore necessary for the change in speed to take place in a small, yet finite, amount of time. But with this assumption, we arrive at yet another contradiction. Suppose, for example, that after a small interval of time, the speed of the faster body is 11, and that of the slower body is 7. But this would mean that they are not moving at the same velocity, and the front surface of the faster body would advance through the rear surface of the slower body, which is impossible because we have assumed that the bodies are impenetrable. It therefore becomes apparent that the interaction must take place immediately before the impact of the two bodies and that this interaction can only be a repulsive one because it is expressed in the slowing down of one body and the speeding up of the other.
Moreover, this argument is valid for arbitrary speeds, so one can no longer speak of definite dimensions for the particles that were until now thought of as impenetrable, namely, for the atoms. An atom should rather be viewed as a point source of force, with the force emanating from it acting in some complicated fashion that depends on distance.
According to Boscovich, when bodies are far apart, they act on each other through a force corresponding to the gravitational force, which is inversely proportional to the square of the distance. But with decreasing distance, this law must be modified because, in accordance with the above considerations, the force changes sign and must become a repulsive force. Boscovich even plotted fanciful traces of how the force should vary with distance in which the force changed sign several times, hinting to the existence of minima in the potential and the existence of stable bonds between the particles—the atoms.
With this idea Boscovich not only offered a new picture for interactions in place of the Aristotelian-Cartesian theory based on immediate contact, but also presaged our understanding of the structure of matter, especially that of solid bodies.

Father of Behavioral Economics; Director, Center for Decision Research, University of Chicago Graduate School of Business; Co-Author, Nudge
It is a fundamental principle of economics that a person is always better off if they have more alternatives to choose from. But this principle is wrong. There are cases when I can make myself better off by restricting my future choices and commit myself to a specific course of action.
The idea of commitment as a strategy is an ancient one. Odysseus famously had his crew tie him to the mast so he could listen to the Sirens' songs without falling into the temptation to steer the ship into the rocks. And he committed his crew to not listening by filling their ears with wax. Another classic is Cortés's decision to burn his ships upon arriving in Mexico, thus removing retreat as one of the options his crew could consider. But although the idea is an old one, we did not begin to understand its nuances until Nobel Laureate Thomas Schelling's wrote his 1956 masterpiece: "An Essay on Bargaining".
It is well known that thorny games such as the prisoner's dilemma can be solved if both players can credibly commit themselves to cooperating, but how can I convince you that I will cooperate when it is a dominant strategy for me to defect? (And, if you and I are game theorists, you know that I know that you know that I know that defecting is a dominant strategy.)
Schelling gives many examples of how this can be done, but here is my favorite. A Denver rehabilitation clinic whose clientele consisted of wealthy cocaine addicts, offered a "self-blackmail" strategy. Patient were offered an opportunity to write a self- incriminating letter that would be delivered if and only if the patient, who is tested on a random schedule, is found to have used cocaine. Most cocaine addicts will probably have no trouble thinking of something to write about, and will now have a very strong incentive to stay off drugs. They are committed.
Many of society's thorniest problems, from climate change to Middle East peace could be solved if the relevant parties could only find a way to commit themselves to some future course of action. They would be well advised to study Tom Schelling in order to figure out how to make that commitment.

Theoretical Physicist, Stanford; Father of Eternal Chaotic Inflation; Inaugural Winner, $3 million Fundamental Physics Prize
Why Is Our World Comprehensible?
"The most incomprehensible thing about the world is that it is comprehensible." This is one of the most famous quotes from Albert Einstein. "The fact that it is comprehensible is a miracle." Similarly, Eugene Wigner said that the unreasonable efficiency of mathematics is "a wonderful gift which we neither understand nor deserve." Thus we have a problem that may seem too metaphysical to be addressed in a meaningful way: Why do we live in a comprehensible universe with certain rules, which can be efficiently used for predicting our future?
One could always respond that God created the universe and made it simple enough so that we can comprehend it. This would match the words about a miracle and an undeserved gift. But shall we give up so easily? Let us consider several other questions of a similar type. Why is our universe so large? Why parallel lines do not intersect? Why different parts of the universe look so similar? For a long time such questions looked too metaphysical to be considered seriously. Now we know that inflationary cosmology provides a possible answer to all of these questions. Let us see whether it might help us again.
To understand the issue, consider some examples of an incomprehensible universe where mathematics would be inefficient. Here is the first one: Suppose the universe is in a state with the Planck density r ~ 1094 g/cm3. Quantum fluctuations of space-time in this regime are so large that all rulers are rapidly bending and shrinking in an unpredictable way. This happens faster than one could measure distance. All clocks are destroyed faster than one could measure time. All records about the previous events become erased, so one cannot remember anything and predict the future. The universe is incomprehensible for anybody living there, and the laws of mathematics cannot be efficiently used.
If the huge density example looks a bit extreme, rest assured that it is not. There are three basic types of universes: closed, open and flat. A typical closed universe created in the hot Big Bang would collapse in about 10-43 seconds, in a state with the Planck density. A typical open universe would grow so fast that formation of galaxies would be impossible, and our body would be instantly torn apart. Nobody would be able to live and comprehend the universe in either of these two cases. We can enjoy life in a flat or nearly flat universe, but this requires fine-tuning of initial conditions at the moment of the Big Bang with an incredible accuracy of about 10-60.
Recent developments in string theory, which is the most popular (though extremely complicated) candidate for the role of the theory of everything, reveal an even broader spectrum of possible but incomprehensible universes. According to the latest developments in string theory, we may have about 10500 (or more) choices of the possible state of the world surrounding us. All of these choices follow from the same string theory. However, the universes corresponding to each of these choices would look as if they were governed by different laws of physics; their common roots would be well hidden. Since there are so many different choices, some of them may describe the universe we live in. But most of these choices would lead to a universe where we would be unable to live and efficiently use mathematics and physics to predict the future.
At the time when Einstein and Wigner were trying to understand why our universe is comprehensible, everybody assumed that the universe is uniform and the laws of physics are the same everywhere. In this context, recent developments would only sharpen the formulation of the problem: We must be incredibly lucky to live in the universe where life is possible and the universe is comprehensible. This would indeed look like a miracle, like a "gift that we neither understand nor deserve." Can we do anything better than praying for a miracle?
During the last 30 years the way we think about our world changed profoundly. We found that inflation, the stage of an exponentially rapid expansion of the early universe, makes our part of the universe flat and extremely homogeneous. However, simultaneously with explaining why the observable part of the universe is so uniform, we also found that on a very large scale, well beyond the present visibility horizon of about 1010 light years, the universe becomes 100% non-uniform due to quantum effects amplified by inflation.
This means that instead of looking like an expanding spherically symmetric ball, our world looks like a multiverse, a collection of an incredibly large number of exponentially large bubbles. For (almost) all practical purposes, each of these bubbles looks like a separate universe. Different laws of the low energy physics operate inside each of these universes.
In some of these universes, quantum fluctuations are so large that any computations are impossible. Mathematics there is inefficient because predictions cannot be memorized and used. Lifetime of some of these universes is too short. Some other universes are long living but laws of physics there do not allow existence of anybody who could live sufficiently long to learn physics and mathematics.
Fortunately, among all possible parts of the multiverse there should be some exponentially large parts where we may live. But our life is possible only if the laws of physics operating in our part of the multiverse allow formation of stable, long-living structures capable of making computations. This implies existence of stable (mathematical) relations that can be used for long-term predictions. Rapid development of the human race was possible only because we live in the part of the multiverse where the long-term predictions are so useful and efficient that they allow us to survive in the hostile environment and win in the competition with other species.
To summarize, the inflationary multiverse consists of myriads of 'universes' with all possible laws of physics and mathematics operating in each of them. We can only live in those universes where the laws of physics allow our existence, which requires making reliable predictions. In other words, mathematicians and physicists can only live in those universes which are comprehensible and where the laws of mathematics are efficient.
One can easily dismiss everything that I just said as a wild speculation. It seems very intriguing, however, that in the context of the new cosmological paradigm, which was developed during the last 30 years, we might be able, for the first time, to approach one of the most complicated and mysterious problems which bothered some of the best scientists of the 20th century.

Neuroscientist; Professor & Director, Center for Brain and Cognition, UC, San Diego; Author, The Tell-Tale Brain
Genes , Claustrum, and Consciousness 
What's my favorite elegant idea? The elucidation of DNA's structure is surely the most obvious, but it bears repeating. I'll argue that the same strategy used to crack the genetic code might prove successful in cracking the "neural code" of consciousness and self. It's a long shot, but worth considering.
The ability to grasp analogies, and seeing the difference between deep and superficial ones, is a hallmark of many great scientists; Francis Crick and James Watson were no exception. Crick himself cautioned against the pursuit of elegance in biology, given that evolution proceeds happenstantially—"God is a hacker," he famously said, adding (according to my colleague Don Hoffman), "Many a young biologist has slit his own throat with Ockham's razor." Yet his own solution to the riddle of heredity ranks with natural selection as biology's most elegant discovery. Will a solution of similar elegance emerge for the problem of consciousness?
It is well known that Crick and Watson unraveled the double helical structure of the DNA molecule: two twisting complementary strands of nucleotides. Less well known is the chain of events culminating in this discovery.
First, Mendel's laws dictated that genes are particulate (a first approximation still held to be accurate). Then Thomas Morgan showed that fruit flies zapped with x-rays became mutants with punctate changes in their chromosomes, yielding the clear conclusion that the chromosomes are where the action is. Chromosomes are composed of histones and DNA; as early as 1928, the British bacteriologist Fred Griffith showed that a harmless species of bacterium, upon incubation with a heat-killed virulent species, actually changes into the virulent species! This was almost as startling as a pig walking into a room with a sheep and two sheep emerging. Later, Oswald Avery showed that DNA was the transformative principle here. In biology, knowledge of structure often leads to knowledge of function—one need look no further than the whole of medical history. Inspired by Griffith and Avery, Crick and Watson realized that the answer to the problem of heredity lay in the structure of DNA. Localization was critical, as, indeed, it may prove to be for brain function.
Crick and Watson didn't just describe DNA's structure, they explained its significance. They saw the analogy between the complementarity of molecular strands and the complementarity of parent and offspring—why pigs beget pigs and not sheep. At that moment modern biology was born.
I believe there are similar correlations between brain structure and mind function, between neurons and consciousness. I am stating the obvious here only because there are some philosophers, called "new mysterians," who believe the opposite. The erudite Colin McGinn has written, for instance, "The brain is only tangentially relevant to consciousness." ( There are many philosophers who would disagree, e.g. Churchland, Dennett, and Searle.)
After his triumph with heredity, Crick turned to what he called the "second great riddle" in biology—consciousness. There were many skeptics. I remember a seminar Crick was giving on consciousness at the Salk Institute here in La Jolla. He'd barely started when a gentleman in attendance raised a hand and said, "But Doctor Crick, you haven't even bothered to define the word consciousness before embarking on this." Crick's response was memorable: "I'd remind you that there was never a time in the history of biology when a bunch of us sat around the table and said, 'Let's first define what we mean by life.' We just went out there and discovered what it was—a double helix. We leave matters of semantic hygiene to you philosophers."
Crick did not, in my opinion, succeed in solving consciousness (whatever that might mean). Nonetheless, I believe he was headed in the right direction. He had been richly rewarded earlier in his career for grasping the analogy between biological complementarities, the notion that the structural logic of the molecule dictates the functional logic of heredity. Given his phenomenal success using the strategy of structure-function analogy, it is hardly surprising that he imported the same style of thinking to study consciousness. He and his colleague Christoff Koch did so by focusing on a relatively obscure structure called the claustrum.
The claustrum is a thin sheet of cells underlying the insular cortex of the brain, one on each hemisphere. It is histologically more homogeneous than most brain structures, and intriguingly, unlike most brain structures (which send and receive signals to and from a small subset of other structures), the claustrum is reciprocally connected with almost every cortical region. The structural and functional streamlining might ensure that, when waves of information come through the claustrum, its neurons will be exquisitely sensitive to the timing of the inputs.
What does this have to do with consciousness? Instead of focusing on pedantic philosophical issues, Crick and Koch began with their naïve intuitions. "Consciousness" has many attributes—continuity in time, a sense of agency or free will, recursiveness or "self-awareness," etc. But one attribute that stands out is subjective unity: you experience all your diverse sense impressions, thoughts, willed actions and memories as being a unity—not jittery or fragmented. This attribute of consciousness, with the accompanying sense of the immediate "present" or "here and now," is so obvious that we don't usually think about it; we regard it as axiomatic.
So a central feature of consciousness is its unity—and here is a brain structure that sends and receives signals to and from practically all other brain structures, including the right parietal (involved in polysensory convergence and embodiment) and anterior cingulate (involved in the experience of "free will"). Thus the claustrum seems to unify everything anatomically, and consciousness does so mentally. Crick and Koch recognized that this may not be a coincidence: the claustrum may be central to consciousness; indeed it may embody the idea of the " Cartesian theater" that's taboo among philosophers—or is at least the conductor of the orchestra. This is this kind of childlike reasoning that often leads to great discoveries. Obviously, such analogies don't replace rigorous science, but they're a good place to start. Crick and Koch may be right or wrong, but their idea is elegant. If they're right, they've paved the way to solving one of the great mysteries of biology. Even if they're wrong, students entering the field would do well to emulate their style. Crick has been right too often to ignore.
I visited him at his home in La Jolla in July of 2004. He saw me to the door as I was leaving and as we parted, gave me a sly, conspiratorial wink: "I think it's the claustrum, Rama; it's where the secret is." A week later he passed away.

Colombian philosopher
"We Are Dreaming Machines That Construct Virtual Models Of The Real World"
The most beautiful and elegant explanation should be as strong and overwhelming as a brick smashing your head; it should break your life in two. For instance, as a result of that explanation, you should realize that even if you are dreaming your brain is active doing what he does best: creating models of reality or, in fact, creating the reality where you live in.
Descartes was aware of this fact and that's why he concluded "I think, therefore I am", cogito ergo sum. You can think of yourself as walking on a park, but this could be just a vivid dream. Therefore, it's not possible to conclude anything about your existence based on the apparent fact of walking. However, if you are really walking on a park, or dreaming, you are thinking, therefore existing. Dreaming is so similar to waking, that you can't trust any sensory information as proof of your existence. You can only trust the fact of thinking or, in contemporary words, the fact that your brain is active.
Dreaming and waking are similar cognitive states, as Rodolfo Llinás says in his masterpiece "I of the vortex". The only difference is that while dreaming, your brain is not perceiving or representing the external reality, it is emulating it and providing self-generated inputs.
The explanation is also shocking in its consequence. While waking we are also dreaming, concludes Llinás: "The waking state is a dreamlike state (…) guided and shaped by the senses, whereas regular dreaming does not involve the senses at all".
In both cases our brain generates models of reality.
With this explanation very few entities—the brain and the matter of reality—are enough to remind us how we create what is usually defined as "reality": "The only reality that exists for us is already a virtual one (…). We are basically dreaming machines that construct virtual models of the real world", says Llinás.
This is not only a beautiful explanation because of the poetic fact that reality is self-generated while dreaming, and partially generated while waking. Is there anything more beautiful than understanding how to create reality?
This is not only an elegant explanation because it shows our minuscule and entirely representative place in the ontological and physical reality, in the huge amount of matter defined as universe.
This explanation is overwhelming in practical terms because as a philosopher and social scientist, I cannot explain the physical or the social reality without considering that we live and move in a model of reality. Including the representational, creative and even ontological role of the brain, is a naturalization project usually omitted as a result of hyper-positivism and scientific fragmentation. From Descartes to Llinás, form the understanding of galaxies to the understanding of crime, this explanation should be relevant in most scientific enterprises.

Neuroscientist; Professor of Psychiatry & Biobehavioral Sciences, David Geffen School of Medicine, UCLA; Author, Mirroring People
Like Attracts Like
The beauty of this explanation is twofold. First, it accounts for the complex organization of the cerebral cortex (the most recent evolutionary component of the brain) using a very simple rule. Second, it deals with scaling issues very well, and indeed it also accounts for a specific phenomenon in a widespread human behavior, imitation. It explains how neurons packed themselves in the cerebral cortex and how humans relate to each other. Not a small feat.
Let's start from the brain. The idea that neurons with similar properties cluster together is theoretically appealing, because it minimizes costs associated with transmission of information. This idea is also supported by empirical evidence (it does not always happen that a theoretically appealing idea is supported by empirical data, sadly). Indeed, more than a century of a variety of brain mapping techniques demonstrated the existence of 'visual cortex' (here we find neurons that respond to visual stimuli), 'auditory cortex' (here we find neurons that respond to sounds), 'somatosensory cortex' (here we find neurons that respond to touch), and so forth. When we zoom in and look in detail at each type of cortex, we also find that the 'like attracts like' principle works well. The brain forms topographic maps. For instance, let's look at the 'motor cortex' (here we find neurons that send signals to our muscles so that we can move our body, walk, grasp things, move the eyes and explore the space surrounding us, speak, and obviously type on a keyboard, as I am doing now). In the motor cortex there is a map of the body, with neurons sending signals to hand muscles clustering together and being separate from neurons sending signals to feet or face muscles. So far, so good.
In the motor cortex, however, we also find multiple maps for the same body part (for instance, the hand). Furthermore, these multiple maps are not adjacent. What is going here? It turns out that body parts are only one of the variables that are mapped by the motor cortex. Other important variables are, for instance, different types of coordinated actions and the space sector in which the action ends. The coordinated actions that are mapped by the motor cortex belong to a number of categories, most notably defensive actions (that is, actions to defend one's own body) hand to mouth actions (important to eat and drink!), manipulative actions (using skilled finger movements to manipulate objects). The problem here is that there are multiple dimensions that are mapped onto a two-dimensional entity (we can flatten the cerebral cortex and visualize it as a surface area). This problem needs to be solved with a process of dimensionality reduction. Computational studies have shown that algorithms that do dimensionality reduction while optimizing the similarity of neighboring points (our 'like attracts like' principle) produce maps that reproduce well the complex, somewhat fractured maps described by empirical studies of the motor cortex. Thus, the principle of 'like attracts like' seems working well even when multiple dimensions must be mapped onto a two-dimensional entity (our cerebral cortex).
Let's move to human behavior. Imitation in humans is widespread and often automatic. It is important for learning and transmission of culture. We tend to align our movements (and even words!) during social interactions without even realizing it. However, we don't imitate other people in an equal way. Perhaps not surprisingly, we tend to imitate more people that are like us. Soon after birth, infants prefer faces of their own race and respond more receptively to strangers of their own race. Adults make education and even career choices that are influenced by models of their own race. This is a phenomenon called self similarity bias. Since imitation increases liking, the self similarity bias most likely influences our social preferences too. We tend to imitate others that are like us, and by doing that, we tend to like those people even more. From neurons to people, the very simple principle of 'like attracts like' has a remarkable explanatory power. This is what an elegant scientific explanation is supposed to do. To explain a lot in a simple way.

Professor of Psychology, University of Texas, Austin; Coauthor: Why Women Have Sex; Author, The Dangerous Passion
Sexual Conflict Theory
A fascinating parallel has occurred in the history of the traditionally separate disciplines of evolutionary biology and psychology. Biologists historically viewed reproduction as an inherently cooperative venture. A male and female would couple for the shared goal of reproduction of mutual offspring. In psychology, romantic harmony was presumed to be the normal state. Major conflicts within romantic couples were and still are typically seen as signs of dysfunction. A radical reformulation embodied by sexual conflict theory changes these views.
Sexual conflict occurs whenever the reproductive interests of an individual male and individual female diverge, or more precisely when the "interests" of genes inhabiting individual male and female interactants diverge. Sexual conflict theory defines the many circumstances in which discord is predictable and entirely expected.
Consider deception on the mating market. If a man is pursuing a short-term mating strategy and the woman for whom he has sexual interest is pursuing a long-term mating strategy, conflict between these interactants is virtually inevitable. Men are known to feign long-term commitment, interest, or emotional involvement for the goal of casual sex, interfering with women's long-term mating strategy. Men's have evolved sophisticated strategies of sexual exploitation. Conversely, women sometimes present themselves as costless sexual opportunities, and then intercalate themselves into a man's mating mind to such a profound degree that he wakes up one morning and suddenly realizes that he can't live without her—one version of the ‘bait and switch' tactic in women's evolved arsenal.
Once coupled in a long-term romantic union, a man and a woman often still diverge in their evolutionary interests. A sexual infidelity by the woman might benefit her by securing superior genes for her progeny, an event that comes with catastrophic costs to her hapless partner who unknowingly devotes resources to a rival's child. From a woman's perspective, a man's infidelity risks the diversion of precious resources to rival women and their children. It poses the danger of losing the man's commitment entirely. Sexual infidelity, emotional infidelity, and resource infidelity are such common sources of sexual conflict that theorists have coined distinct phrases for each.
But all is not lost. As evolutionist Helena Cronin has eloquently noted, sexual conflict arises in the context of sexual cooperation. The evolutionary conditions for sexual cooperation are well-specified: When relationships are entirely monogamous; when there is zero probability of infidelity or defection; when the couple produces offspring together, the shared vehicles of their genetic cargo; and when joint resources cannot be differentially channeled, such as to one set of in-laws versus another.
These conditions are sometimes met, leading to great love and harmony between a man and a woman. The prevalence of deception, sexual coercion, stalking, intimate partner violence, murder, and the many forms of infidelity reveal that conflict between the sexes is ubiquitous. Sexual conflict theory, a logical consequence of modern evolutionary genetics, provides the most beautiful theoretical explanation for these darker sides of human sexual interaction.

Theoretical physicist
An Explanation of Fundamental Particle Physics That Doesn't Exist Yet
My favorite explanation is one that does not yet exist.
Research in fundamental particle physics has culminated in our current Standard Model of elementary particles. Using ever larger machines, we have been able to identify and determine the properties of a whole zoo of elementary particles. These properties present many interesting patterns. All the matter we see around us is composed of electrons and up and down quarks, interacting differently with photons of electromagnetism, W and Z bosons of the weak force, gluons of the strong force, and gravity, according to their different values and kinds of charges. Additionally, an interaction between a W and an electron produces an electron neutrino, and these neutrinos are now known to permeate space—flying through us in great quantities, interacting only weakly. A neutrino passing through the earth probably wouldn't even notice it was there. Together, the electron, electron neutrino, and up and down quarks constitute what is called the first generation of fermions. Using high energy particle colliders, physicists have been able to see even more particles. It turns out the first generation fermions have second and third generation partners, with identical charges to the first but larger masses. And nobody knows why. The second generation partner to the electron is called the muon, and the third generation partner is called the tau. Similarly, the down quark is partnered with the strange and bottom quarks, and the up quark has partners called the charm and top, with the top discovered in 1995. Last and least, the electron neutrinos are partnered with muon and tau neutrinos. All of these fermions have different masses, arising from their interaction with a theorized background Higgs field. Once again, nobody knows why there are three generations, or why these particles have the masses they do. The Standard Model, our best current description of fundamental physics, lacks a good explanation.
The dominant research program in high energy theoretical physics, string theory, has effectively given up on finding an explanation for why the particle masses are what they are. The current non-explanation is that they arise by accident, from the infinite landscape of theoretical possibilities. This is a cop out. If a theory can't provide a satisfying explanation of an important pattern in nature, it's time to consider a different theory. Of course, it is possible that the pattern of particle masses arose by chance, or some complicated evolution, as did the orbital distances of our solar system's planets. But, as experimental data accumulates, patterns either fade or sharpen, and in the newest data on particle masses an intriguing pattern is sharpening. The answer may come from the shy neutrino.
The masses of the three generations of fermions are described by their interaction with the Higgs field. In more detail, this is described by "mixing matrices," involving a collection of angles and phases. There is no clear, a priori reason why these angles and phases should take particular values, but they are of great consequence. In fact, a small difference in these phases determines the prevalence of matter over antimatter in our universe. Now, in the mixing matrix for the quarks, the three angles and one phase are all quite small, with no discernible pattern. But for neutrinos this is not the case. Before the turn of the 21st century it was not even clear that neutrinos mixed. Too few electron neutrinos seemed to be coming from the sun, but scientists weren't sure why. In the past few years our knowledge has improved immensely. From the combined effort of many experimental teams we now know that, to a remarkable degree of precision, the three angles for neutrinos have sin squared equal to 1/2, 1/3, and 0. We do need to consider the possibility of coincidence, but as random numbers go, these do not seem very random. In fact, this mixing corresponds to a "tribimaximal" matrix, related to the geometric symmetry group of the tetrahedron.
What is tetrahedral symmetry doing in the masses of neutrinos?! Nobody knows. But you can bet there will be a good explanation. It is likely that this explanation will come from mathematicians and physicists working closely with Lie groups. The most important lesson from the great success of Einstein's theory of General Relativity is that our universe is fundamentally geometric, and this idea has extended to the geometric description of known forces and particles using group theory. It seems natural that a complete explanation of the Standard Model, including why there are three generations of fermions and why they have the masses they do, will come from the geometry of group theory. This explanation does not yet exist, but when it does it will be deep, elegant, and beautiful—and it will be my favorite.

Professor of Theoretical Physics, Berkeley
My Favorite Annoying Elegant Explanation: Quantum Theory 
My favorite elegant explanations will already have been picked by others who turned in their homework early. Although I am a theoretical physicist, my choice could easily be Darwin. Closer to my area of expertise, there is General Relativity: Einstein's realization that free-fall is a property of space-time itself, which readily resolved a great mystery (why gravity acts in the same way on all bodies). So, in the interest of diversity, I will add a modifier and discuss my favorite annoying elegant explanation: quantum theory.
As explanations go, few are broader in applicability than the revolutionary framework of Quantum Mechanics, which was assembled in the first quarter of the 20th century. Why are atoms stable? Why do hot things glow? Why can I move my hand through air but not through a wall? What powers the sun? The strange workings of Quantum Mechanics are at the core of our remarkably precise and quantitative understanding of these and many other phenomena.
And strange they certainly are. An electron takes all paths between the two points at which it is observed, and it is meaningless to ask which path it actually took. We must accept that its momentum and position cannot both be known with arbitrary precision. For a while, we were even expected to believe that there are two different laws for time evolution: Schrödinger's equation governs unobserved systems, but the mysterious "collapse of the wave function" kicks in when a measurement is performed. The latter, with its unsettling implication that conscious observers might play a role in fundamental theory, has been supplanted, belatedly, by the notion of decoherence. The air and light in a room, which in classical theory would have little effect on a measuring apparatus, fundamentally alter the quantum-mechanical description of any object that is not carefully insulated from its environment. This, too, is strange. But do the calculation, and you will find that we used to call "wave function collapse" need not be postulated as a separate phenomenon. Rather, it emerges from
Schrödinger's equation, once we take the role of the environment into account.
Just because Quantum Mechanics is strange doesn't mean that it is wrong. The arbiter is Nature, and experiments have confirmed many of the most bizarre properties of this theory. Nor does Quantum Mechanics lack elegance: it is a rather simple framework with enormous explanatory power. What annoys me is this: we do not know for sure that Quantum Mechanics is wrong.
Many great theories in physics carry within them a seed of their demise. This seed is a beautiful thing. It hints at profound discoveries and conceptual revolutions still to come. One day, the beautiful explanation that has just transformed our view of the Universe will be supplanted by another, even deeper insight. Quantitatively, the new theory must reproduce all the experimental successes of the old one. But qualitatively, it is likely to rest on novel concepts, allowing for hitherto unimaginable questions to be asked and knowledge to be gained.
Newton, for instance, was troubled by the fact that his theory of gravitation allowed for instant communication across arbitrarily large distances. Einstein's theory of General Relativity fixed this problem, and as a byproduct, gave us dynamical spacetime, black holes, and an expanding universe that probably had a beginning.
General Relativity, in turn, is only a classical theory. It rests on a demonstrably false premise: that position and momentum can be known simultaneously. This may a good approximation for apples, planets, and galaxies: large objects, for which gravitational interactions tend to be much more important than for the tiny particles of the quantum world. But as a matter of principle, the theory is wrong. The seed is there. General Relativity cannot be the final word; it can only be an approximation to a more general Quantum Theory of Gravity.
But what about Quantum Mechanics itself? Where is its seed of destruction? Amazingly, it is not obvious that there is one. The very name of the great quest of theoretical physics—"quantizing General Relativity"—betrays an expectation that quantum theory will remain untouched by the unification we seek. String theory—in my view, by far the most successful, if incomplete, result of this quest—is strictly quantum mechanical, with no modifications whatsoever to the framework that was completed by Heisenberg, Schrödinger, and Dirac. In fact, the mathematical rigidity of Quantum Mechanics makes it difficult to conceive of any modifications, whether or not they are called for by observation.
Yet, there are subtle hints that Quantum Mechanics, too, will suffer the fate of its predecessors. The most intriguing, in my mind, is the role of time. In Quantum Mechanics, time is an essential evolution parameter. But in General Relativity, time is just one aspect of spacetime, a concept that we know breaks down at singularities deep inside black holes. Where time no longer makes sense, it is hard to see how Quantum Mechanics could still reign. As Quantum Mechanics surely spells trouble for General Relativity, the existence of singularities suggests that General Relativity may also spell trouble for Quantum Mechanics. It will be fascinating to watch this battle play out.

Journalist: Author, A Planet of Viruses; Science Ink: Tattoos of the Science Obsessed;
A Hot Young Earth: Unquestionably Beautiful and Stunningly Wrong
Around 4.567 billion years ago, a giant cloud of dust collapsed in on itself. At the center of the cloud our Sun began to burn, while the outlying dust grains began to stick together as they orbited the new star. Within a million years, those clumps of dust had become protoplanets. Within about 50 million years, our own planet had already reached about half its current size. As more protoplanets crashed into Earth, it continued to grow. All told, it may have taken another fifty million years to reach its full size—a time during which a Mars-sized planet crashed into it, leaving behind a token of its visit: our Moon.
The formation of the Earth commands our greatest powers of imagination. It is primordially magnificent. But elegant is not the word I'd use to describe the explanation I just sketched out. Scientists did not derive it from first principles. There is no equivalent of E=mc2 that predicts how the complex violence of the early Solar System produced a watery planet that could support life.
In fact, the only reason that we now know so much about how the Earth formed is because geologists freed themselves from a seductively elegant explanation that was foisted on them 150 years ago. It was unquestionably beautiful, and stunningly wrong.
The explanation was the work of one of the greatest physicists of the nineteenth century, William Thompson (a k a Lord Kelvin). Kelvin's accomplishments ranged from the concrete (figuring out how to lay a telegraph cable from Europe to America) to the abstract (the first and second laws of thermodynamics). Kelvin spent much of his career writing equations that could let him calculate how fast hot things got cold. Kelvin realized that he could use these equations to estimate how old the Earth is. "The mathematical theory on which these estimates are founded is very simple," Kelvin declared when he unveiled it in 1862.
At the time, scientists generally agreed that the Earth had started out as a ball of molten rock and had been cooling ever since. Such a birth would explain why rocks are hot at the bottom of mine shafts: the surface of the Earth was the first part to cool, and ever since, the remaining heat inside the planet has been flowing out into space. Kelvin reasoned that over time, the planet should steadily grow cooler. He used his equations to calculate how long it should take for a molten sphere of rock to cool to Earth's current temperature, with its observed rate of heat flow. His verdict was a brief 98 million years.
Geologists howled in protest. They didn't know how old the Earth was, but they thought in billions of years, not millions. Charles Darwin—who was a geologist first and then a biologist later—estimated that it had taken 300 million years for a valley in England to erode into its current shape. The Earth itself, Darwin argued, was far older. And later, when Darwin published his theory of evolution, he took it for granted that the Earth was inconceivably old. That luxury of time provided room for evolution to work slowly and imperceptibly.
Kelvin didn't care. His explanation was so elegant, so beautiful, so simple that it had to be right. It didn't matter how much trouble it caused for other scientists who would ignore thermodynamics. In fact, Kelvin made even more trouble for geologists when he took another look at his equations. He decided his first estimate had been too generous. The Earth might be only 10 million years old.
It turned out that Kelvin was wrong, but not because his equations were ugly or inelegant. They were flawless. The problem lay in the model of the Earth to which Kelvins applied his equations.
The story of Kelvin's refutation got a bit garbled in later years. Many people (myself included) have mistakenly claimed that his error stemmed from his ignorance of radioactivity. Radioactivity was only discovered in the early 1900s as physicists worked out quantum physics. The physicist Ernst Rutherford declared that the heat released as radioactive atom broke down inside the Earth kept it warmer than it would be otherwise. Thus a hot Earth did not have to be a young Earth.
It's true that radioactivity does give off heat, but there isn't enough inside the planet is to account for the heat flowing out of it. Instead, Kelvin's real mistake was assuming that the Earth was just a solid ball of rock. In reality, the rock flows like syrup, its heat lifting it up towards the crust, where it cools and then sinks back into the depths once more. This stirring of the Earth is what causes earthquakes, drives old crust down into the depths of the planet, and creates fresh crust at ocean ridges. It also drives heat up into the crust at a much greater rate than Kelvin envisioned.
That's not to say that radioactivity didn't have its own part to play in showing that Kelvin was wrong. Physicists realized that the tick-tock of radioactive decay created a clock that they could use to estimate the age of rocks with exquisite precision. Thus we can now say that the Earth is not just billions of years old, but 4.567 billion.
Elegance unquestionably plays a big part in the advancement of science. The mathematical simplicity of quantum physics is lovely to behold. But in the hands of geologists, quantum physics has brought to light the glorious, messy, and very inelegant history of our planet.

Co-Director of LSE's Centre for Philosophy of Natural and Social Science; Author, The Ant and the Peacock: Altruism and Sexual Selection from Darwin to Today
In The Beginning Is The Theory
Let's eavesdrop on an exchange between Charles Darwin and Karl Popper. Darwin, exasperated at the crass philosophy of science peddled by his critics, exclaims: "How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!" And, when the conversation turns to evolution, Popper observes: "All life is problem-solving … from the amoeba to Einstein, the growth of knowledge is always the same".
There is a confluence in their thinking. Though travelling by different pathways, they have arrived at the same insight. It is to do with the primacy and fundamental role of theories—of ideas, hypotheses, perspectives, views, dispositions and the like—in the acquisition and growth of knowledge. Darwin was right to stress that such primacy is needed 'if the observation is to be of any service'. But the role of a 'view' also goes far deeper. As Darwin knew, it is impossible to observe at all without some kind of view. If you are unconvinced, try this demonstration, one that Popper liked to use in lectures. "Observe!" Have you managed that? No. Because, of course, you need to know "Observe what?" All observation is in the light of some theory; all observation must be in the light of some theory. So all observation is theory-laden—not sometimes, not contingently, but always and necessarily.
This is not to depreciate observation, data, facts. On the contrary, it gives them their proper due. Only in the light of a theory, a problem, the quest for a solution, can they speak to us in revealing ways.
Thus the insight is immensely simple. But it has wide relevance and great potency. Hence its elegance and beauty.
Here are two examples, first from Darwin's realm then from Popper's.
• Consider the tedious but tenacious argument 'genes versus environment'. I'll take a well-studied case. Indigo buntings migrate annually over long distances. To solve the problem of navigation, natural selection equipped them with the ability to construct a mental compass by studying the stars in the night sky, boy-scout fashion, during their first few months of life. The fount of this spectacular adaptation is a rich source of information that natural selection, over evolutionary time, has packed into the birds' genes—in particular, information about the rotation of the stellar constellations. Thus buntings that migrate today can use the same instincts and the same environmental regularities to fashion the same precision-built instrument as did their long-dead ancestors.
And all adaptations work in this way. By providing the organism with innate information about the world, they open up resources for the organism to meet its own distinctive adaptive needs; thus natural selection creates the organism's own tailor-made, species-specific environment. And different adaptive problems therefore give rise to different environments; so different species, for example, have different environments.
Thus what constitutes an environment depends on the organism's adaptations. Without innate information, carried by the genes, specifying what constitutes an environment, no environments would exist. And thus environments, far from being separate from biology, autonomous and independent, are themselves in part fashioned by biology. Environment is therefore a biological issue, an issue that necessarily begins with biologically-stored information.
But aren't we anyway all interactionists now? No longer genes versus environment but gene—environment interaction? Yes, of course; interaction is what natural selection designed genes to do. Bunting genes are freighted with information about how to learn from stars because stars are as vital a part of a bunting's environment as is the egg in which it develops or the water that it drinks; buntings without stars are destined to be buntings without descendants. But interaction is not parity; the information must come first. Just try this parity test. Try specifying 'an' environment without first specifying whether it is the environment of a bunting or a human, a male or a female, an adaptation for bird navigation or for human language. The task is of course impossible; the specification must start from the information that is stored in adaptations.And here's another challenge to parity. Genes use environments for a purpose—self-replication. Environments, however, have no purposes; so they do not use genes. Thus bunting-genes are machines for converting stars into more bunting-genes; but stars are not machines for converting bunting-genes into more stars.
• The second example is to do with the notion of objectivity in science. Listen further to Darwin's complaint about misunderstandings over scientific observation: "How profoundly ignorant … [this critic] must be of the very soul of observation! About thirty years ago there was much talk that geologists ought only to observe and not theorize; and I well remember some one saying that at this rate a man might as well go into a gravel-pit and count the pebbles and describe the colours".
Nearly two hundred years later, variants of that thinking still stalk science. Consider the laudable, but now somewhat tarnished, initiative to establish evidence-based policy-making. What went wrong? All too often, objective evidence was taken to be data uncontaminated by the bias of a prior theory. But without 'the very soul' of a theory as guidance, what constitutes evidence? Objectivity isn't to do with stripping out all presuppositions. Indeed, the more that's considered to be possible or desirable, the more the undetected, un-criticised presuppositions and the less the objectivity. At worst, a desired but un-stated goal can be smuggled in at the outset. And the upshot? This well-meant approach is often justifiably derided as 'policy-based evidence-making'.
An egregious example from my own recent experience, which still has me reeling with dismay, was from a researcher on 'gender diversity' whose concern was discrimination against women in the professions. He proudly claimed that his research was absolutely free of any prior assumptions about male/female differences and that it was therefore entirely neutral and unbiased. If any patterns of differences emerged from the data, his neutral, unbiased assumption would be that they were the result of discrimination. So might he accept that evolved sex differences exist? Yes; if it were proven. And what might such a proof look like? Here he fell silent, at a loss—unsurprisingly, given that his 'neutral' hypotheses had comprehensively precluded such differences at the start. What irony that, in the purported interests of scientific objectivity, he ostensibly felt justified in clearing the decks of the entire wealth of current scientific findings.
The Darwin-Popper insight, in spite of its beauty, has yet to attract the admirers it deserves.

Researcher, MIT, Mind Machine Project
The Principle of Least Action
Nature is lazy. Scientific paradigms and "ultimate" visions of the universe come and go, but the idea of "least action" has remained remarkably unperturbed. From Newton's classical mechanics to Einstein's general relativity to Schrödinger's quantum field theory, every major theory has been reformulated with this single principle, by Euler, Hilbert, and Feynman, respectively. The reliability of this framework suggests a form for whatever the next major paradigm shift may be.
Action is a strange quantity, in the units of energy multiplied by time. A principle of least action does not explicitly specify what will happen, like an equation of motion does, but simply asserts that the action will be the least of any conceivable actions. In some sense, the universe is maximally efficient. To be precise, the action integrated over any interval of time is always minimal. Euler and Lagrange discovered that not only is this principle true, but one can derive all of Newtonian physics from it. The Newtonian worldview was often characterized as "clockwork," both because clockwork was an apt contemporary technology, and because of the crucially absolute measurement of time.
In Einstein's relativity, absolute time was no longer possible, and totally new equations of motion had to be written. Now we have to deal with four-dimensional spacetime, rather than the familiar three-dimensional space and the special dimension of time. At speeds much less than the speed of light, a first-order approximation can transform Einstein's equations into Newton's, yet the resemblance is hardly obvious. However, the principle of least action remains much the same, but with a difference that intuitively connects to the essence of Einstein's insight: instead of just integrating over time, we must integrate over space too, with the speed of light serving as a constant exchange rate between spatial and temporal units. The essence of relativity is not its well-known consequences—time dilation, length dilation, or even E=mc^2. Rather, it is the more intuitive idea that space and time are simply different ways of looking at the same thing. Much more complicated mathematics is needed to derive Einstein's equations from this principle, but the legendary mathematician David Hilbert was able to do it. Maxwell's theory of electromagnetism, too, can be derived from the least action principle by a generalization of operators. Even more remarkably, combining the least-action tweaks that lead to Einstein's and Maxwell's equations respectively produces modern relativistic electromagnetism.
By this point you may be imagining that practically any physical theory can be formulated using the principle of least action. But in fact, many cannot —for instance, an early attempt at quantum electrodynamics, put forth by Paul Dirac. Such theories tend to have other issues that preclude their practical use; under many conditions, Dirac's theory prescribed infinite energies (clearly a dramatic difference from experiment). Quantum electrodynamics was later "fixed" by Feynman, a feat for which he won the Nobel Prize. In his Nobel lecture, he mentioned that the initial confirmation he was on the right track was that his version, unlike Dirac's, could be formulated as a principle of least action.
I believe it's reasonable to expect it will be possible to explain the next major physical theory using the least action framework, whatever it may be. Perhaps it will benefit us as scientists to explore our theories within this framework, rather than attempting to guess at once the explicit equations, and leaving the inevitable least action derivation as an exercise for some enterprising mathematician to work out.
The essential idea of least action transcends even the deepest of theoretical physics, and enters the domain of metaphysics. Claude Shannon derived a formula to quantify uncertainty, which von Neumann pointed out was identical to the formula used in thermodynamics to compute entropy. Edwin Jaynes put forth an interpretation of thermodynamics, in which entropy simply is uncertainty, nothing more and nothing less. Although the formal mathematical underpinnings remain controversial, I find it very worthwhile, at least as an intuitive explanation. Jaynes' followers propose a profound connection between action and information, such that the principle of least action and the laws of thermodynamics both derive from basic symmetries of logic itself. We need only accept that all conceivable universes are equally likely, a principle of least information. Under this assumption, we can imagine a smooth spectrum from metaphysics to physics, from the omniverse to the multiverse to the universe, where the fundamental axis is information, and the only fundamental law is that you can never assume more than you know.
Starting from nothingness, or the absence of information, there is a flowering of possible refinements toward specifying a universe, one of which leads to our Big Bang, to particles, fields and spacetime, and ultimately to intelligent life. The reason that we had a long period of stellar, planetary and biological evolution is that this is the path to intelligent life, which required the least action. Imagine how much action it would take to create intelligence directly from nothing! Universes without intelligent life might require even less action, but there is nobody in those universes to wonder where they came from.
At least for me, the least action perspective explains all known physics as well as the origin of our universe, and that sure is deep and beautiful.

Founder, The Whole Earth Catalog; Co-founder, The Well; Co-Founder, The Long Now Foundation; Author, Whole Earth Discipline
Fitness Landscapes
The first time I saw a fitness landscape cartoon (in Garrett Hardin's Man And Nature, 1969), I knew it was giving me advice on how not to get stuck over-adapted—hence overspecialized—on some local peak of fitness, when whole mountain ranges of opportunity could be glimpsed in the distance, but getting to them involved venturing "downhill" into regions of lower fitness. I learned to distrust optimality.
Fitness landscapes (sometimes called "adaptive landscapes") keep turning up when people try to figure out how evolution or innovation works in a complex world. An important critique by Marvin Minsky and Seymour Papert of early optimism about artificial intelligence warned that seemingly intelligent agents would dumbly "hill climb" to local peaks of illusory optimality and get stuck there. Complexity theorist Stuart Kauffman used fitness landscapes to visualize his ideas about the "adjacent possible" in 1993 and 2000, and that led in turn to Steven Johnson's celebration of how the "adjacent possible" works for innovation in Where Good Ideas Come From.
The man behind the genius of fitness landscapes was the founding theorist of population genetics, Sewell Wright (1889-1988). In 1932 he came up with the landscape as a way to visualize and explain how biological populations escape the potential trap of a local peak by imagining what might drive their evolutionary "path" downhill from the peak toward other possibilities. Consider these six diagrams of his :

[Image credit: © Sewall Wright, The Role of Mutation, Inbreeding, Crossbreeding, and Selection in Evolution, Sixth International Congress of Genetics, Brooklyn, NY: Brooklyn Botanical Garden, 1932.]
The first two illustrate how low selection pressure or a high rate of mutation (which comes with small populations) can broaden the range of a species whereas intense selection pressure or a low mutation rate can severely limit a species to the very peak of local fitness. The third diagram shows what happens when the landscape itself shifts, and the population has to evolve to shift with it.
The bottom row explores how small populations respond to inbreeding by wandering ineffectively. The best mode of exploration Wright deemed the final diagram, showing how a species can divide into an array of races that interact with one another. That jostling crowd explores well, and it can respond to opportunity.
Fitness landscapes express so much so economically. There's no better way, for example, to show the different modes of evolution of a remote oceanic island and a continental jungle. The jungle is dense and "rugged" with steep peaks and valleys, isolating countless species on their tiny peaks of high specialization. The island, with its few species, is like a rolling landscape of gentle hills with species casually wandering over them, evolving into a whole array of Darwin's finches, say. The island creatures and plants "lazily" become defenseless against invaders from the mainland.
You realize that for each species, its landscape consists almost entirely of other species, all of them busy evolving right back. That's co-evolution. We are all each other's fitness landscapes.

Assistant Professor of Psychology, University of California
Realism And Other Metaphysical Half-Truths
The deepest, most elegant, and most beautiful explanations are the ones we find so overwhelmingly compelling that we don't even realize they're there. It can take years of philosophical training to recognize their presence and to evaluate their merits.
Consider the following three examples:
REALISM. We explain the success of our scientific theories by appeal to what philosophers call realism—the idea that they are more or less true. In other words, chemistry "works" because atoms actually exist, and hand washing prevents disease because there really are loitering pathogens.
OTHER MINDS. We explain why people act the way they do by positing that they have minds more or less like our own. We assume that they have feelings, beliefs, and desires, and that they are not (for instance) zombie automata that convincingly act as if they have minds. This requires an intuitive leap that engages the so-called "problem of other minds."
CAUSATION. We explain the predictable relationship between some events we call causes and others we call effects by appeal to a mysterious power called causation. Yet, as noted by 18th century philosopher David Hume, we never "discover anything but one event following another," and never directly observe "a force or power by which the cause operates, or any connexion between it and its supposed effect."
These explanations are at the core of humans' understanding of the world—of our intuitive metaphysics. They also illustrate the hallmarks of a satisfying explanation: they unify many disparate phenomena by appealing to a small number of core principles. In other words, they are broad but simple. Realism can explain the success of chemistry, but also of physics, zoology, and deep-sea ecology. A belief in other minds can help someone understand politics, their family, and Middlemarch. And assuming a world governed by orderly, causal relationships helps explain the predictable associations between the moon and the tides as well as that between caffeine consumption and sleeplessness.
Nonetheless, each explanation has come under serious attack at one point or another. Take realism, for example. While many of our current scientific theories are admittedly impressive, they come at the end of a long succession of failures: every past theory has been wrong. Ptolemy's astronomy had a good run, but then came the Copernican Revolution. Newtonian mechanics is truly impressive, but it was ultimately superseded by contemporary physics. Modesty and common sense suggest that like their predecessors, our current theories will eventually be overturned. But if they aren't true, why are they so effective? Intuitive realism is at best a metaphysical half-truth, albeit a pretty harmless one.
From these examples I draw two important lessons. First, the depth, elegance, and beauty of our intuitive metaphysical explanations can be a liability. These explanations are so broad and so simple that we let them operate in the background, constantly invoked but rarely scrutinized. As a result, most of us can't defend them and don't revise them. Metaphysical half-truths find a safe and happy home in most human minds.
Second, the depth, elegance, and beauty of our intuitive metaphysical explanations can make us appreciate them less rather than more. Like a constant hum, we forget that they are there. It follows that the explanations most often celebrated for their virtues—explanations such as natural selection and relativity—are importantly different from those that form the bedrock of intuitive beliefs. Celebrated explanations have the characteristics of the solution to a good murder-mystery. Where intuitive metaphysical explanations are easy to generate but hard to evaluate, scientific superstars like evolution are typically the reverse: hard to generate but easy to evaluate. We need philosophers like Hume to nudge us from complacency in the first case, and scientists like Darwin to advance science in the second.

Associate Professor of Psychology, Princeton University
Seeing Oneself in a Positive Light
Is there a single explanation that can account for all of human behavior? Of course not. But, I think there is one that does darn well. Human beings are motivated to see themselves in a positive light. We want, and need, to see ourselves as good, worthwhile, capable people. And fulfilling this motive can come at the expense of our being "rational actors." The motive to see oneself in a positive light is powerful, pervasive, and automatic. It can blind us to truths that would otherwise be obvious. For example, while we can readily recognize who among our friends and neighbors are bad drivers, and who among us is occasionally sexist or racist, most of us are deluded about the quality of our own driving and about our own susceptibility to sexist or racist behavior.
The motive to see oneself in a positive light can have profound effects. The work of Claude Steele and others shows that this motive can lead children who underperform in school to decide that academics are unimportant and not worth the effort, a conclusion that protects self-esteem but at a heavy price for the individual and society. More generally, when people fail to achieve on a certain dimension, they often disidentify from it in order to preserve a positive sense of self. That response can come at the expense of meeting one's rational best interest. It can cause some to drop out of school (after deciding that there are better things to do than "be a nerd"), and it can cause others to ignore morbid obesity (after deciding that other things are more important than "being skinny").
Another serious consequence of this motive involves prejudice and discrimination. A wide array of experiments in social psychology have demonstrated how members of different ethnic groups, different races, and even different bunks at summer camp see their "own kind" as better and more deserving than "outsiders" who belong to other groups—a perception that leads not only to ingroup favoritism but also to blatant discrimination against members of other groups. And, people are especially likely to discriminate when their own self-esteem has been threatened. For example, one study found that college students were especially likely to discriminate against a Jewish job applicant after they themselves had suffered a blow to their self-esteem; notably, their self-esteem recovered fully after the discrimination.
The motive to see oneself in a positive light is so fundamental to human psychology that it is a hallmark of mental health. Shelley Taylor and others have noted that mentally healthy people are "deluded" by positive illusions of themselves (and depressed people are sometimes more "realistic"). But, how many of us truly believe that this motive drives us? It is difficult to spot in ourselves because it operates quickly and automatically, covering its tracks before we detect it. As soon as we miss a shot in tennis, it is almost instantaneous that we generate a self-serving thought about the sun having been in our eyes. The automatic nature of this motive is perhaps best captured by the fact that we unconsciously prefer things that start with the same letter as our first initial (so people named Paul are likely to prefer pizza more than people named Harry, whereas Harrys are more likely to prefer hamburgers). Herein, though, lies the rub. I know a Lee who hates lettuce, and a Wendy who will not eat wheat. Both of them are better at tennis than they realize, and both take responsibility for a bad serve. Simple and elegant explanations only go so far when it comes to the complex and messy problem of human behavior.

Physicist, University of Vienna; Scientific Director, Institute of Quantum Optics and Quantum Information, Austrian Academy of Sciences; Author, Dance of the Photons: From Einstein to Quantum Teleportation
Einstein's Photons
My favorite deep, elegant and beautiful explanation is Albert Einstein's 1905 proposal that light consists of energy quanta, today called photons. Actually, it is little known, even among physicists, but extremely interesting how Einstein came to this position. It is often said that Einstein invented the concept to explain the photoelectric effect. Certainly, that is part of Einstein's 1905 publication, but only towards its end. The idea itself is much deeper, more elegant and, yes, more beautiful.
Imagine a closed container whose walls are at some temperature. The walls are glowing, and as they emit radiation, they also absorb radiation. After some time, there will be some sort of equilibrium distribution of radiation inside the container. This was already well known before Einstein. Max Planck had introduced the idea of quantization that explained the energy distribution of the radiation inside such a volume. Einstein went a step further. He studied how orderly the radiation is distributed inside such a container. For physicists, entropy is a measure of disorder.
To consider a simple example, it is much more probable that books, notes, pencils, photos, pens etc. are cluttered all over my desk than that they are well ordered forming a beautiful stack. Or, if we consider a million atoms inside a container, it is much more probable that they are more or less equally distributed all over the volume of the container than that they are all collected in one corner. In both cases, the first state is less orderly: when the atoms fill a larger volume they have a higher entropy than the second one mentioned. The Austrian physicist Ludwig Boltzmann had shown that the entropy of a system is a measure of how probable its state is.
Einstein then realized in his 1905 paper that the entropy of radiation (including light) changes in the same mathematical way with the volume as for atoms. In both cases, the entropy increases with the logarithm of that volume. For Einstein this could not just be a coincidence. Since we can understand the entropy of the gas because it consists of atoms, the radiation consists also of particles that he calls energy quanta.
Einstein immediately applied his idea for example to his well-known application of the photoelectric effect. But he also realizes very soon a fundamental conflict of the idea of energy quanta with the well-studied and observed phenomenon of interference.
The problem is simply how to understand the two-slit interference pattern. This is the phenomenon that, according to Richard Feynman, contains "the only mystery" of quantum physics. The challenge is very simple. When we have both slits open, we obtain bright and dark stripes on an observation screen, the interference fringes. When we have only one slit open, we get no stripes, no fringes, but a broad distribution of particles. This can easily be understood on the basis of the wave picture. Through each of the two slits, a wave passes, and they extinguish each other at some places of the observation screen and at others, they enforce each other. That way, we obtain dark and bright fringes.
But what to expect if the intensity is so low that only one particle at a time passes through the apparatus? Following Einstein's realist position, it would be natural to assume that the particle has to pass through either slit. We can still do the experiment by putting a photographic plate at the observation screen and sending many photons in, one at a time. After a long enough time, we look at the photographic plate. According to Einstein, if the particle passes through either slit, no fringes should appear, because, simply speaking, how should the individual particle know whether the other slit, the one it does not pass through, is open or not. This was indeed Einstein's opinion, and he suggested that the fringes only appear if many particles go through at the same time, and somehow interact with each other such that they make up the interference pattern.
Today, we know that the pattern even arises if we have such low intensities that only one, say, photon per second passes through the whole apparatus. If we wait long enough and look at the distribution of all of them, we get the interference pattern. The modern explanation is that the interference pattern only arises if there is no information present anywhere in the Universe through which slit the particle passes. But even as Einstein was wrong here, his idea of the energy quanta of light, today called photons pointed far into the future.
In a letter to his friend Habicht in the same year of 1905, the miraculous year where he also wrote his Special Theory of Relativity, he called the paper proposing particles of light "revolutionary". As far as is known, this was the only work of his that he ever called revolutionary. And therefore it is quite fitting that the Nobel Prize was given to him for the discovery of particles of light. This was the Nobel Prize of 1921. That the situation was not as clear a few years before is witnessed by a famous letter signed by Planck, Nernst, Rubens and Warburg, suggesting Einstein for membership in the Prussian Academy of Sciences in 1913. They wrote: "the fact that he (Einstein) occasionally went too far should not be held too strongly against him. Not even in the exact natural sciences can there be progress without occasional speculation." Einstein's deep, elegant and beautiful explanation of the entropy of radiation, proposing particles of light in 1905, is a strong case in point for the usefulness of occasional speculation.

Planetary Scientist and Astrobiologist, NASA Jet Propulsion Laboratory, California Institute of Technology
On Oceans and Airport Security
It may sound odd, but for as much as I loathe airport security lines, I must admit that while I'm standing there, stripped down and denuded of metal, waiting to go through the doorway, part of my mind wanders to oceans that likely exist on distant worlds in our solar system.
These oceans exist today and are sheltered beneath the icy shells that cover worlds like Europa, Ganymede, and Callisto (moons of Jupiter), and Enceladus and Titan (moons of Saturn). The oceans within these worlds are liquid water (H2O), just as we know and love it here on Earth, and they have likely been in existence for much of the history of the solar system (about 4.6 billion years). The total volume of liquid water contained within these oceans is at least 20 times that found here on Earth.
From the standpoint of our search for life beyond Earth, these oceans are prime real estate for a second origin of life and the evolution of extraterrestrial ecosystems.
But how do we know these oceans exist? The moons are covered in ice and thus we can't just look down with a spacecraft and see the liquid water.
That's where the airport security comes into play. You see, when you walk through an airport security door you're walking through a rapidly changing magnetic field. The laws of physics dictate that if you put a conducting material in a changing magnetic field electric currents will arise and those electric currents will then create a secondary magnetic field. This secondary field is often referred to as the induced magnetic field because it is induced by the primary field of the doorway. Also contained within the doorway are detectors that can sense when an induced field is present. When these sensors detect an induced field, the alarm goes off, and you get whisked over to the 'special' search line.
The same basic principle, the same fundamental physics, is largely responsible for our knowledge of oceans on some of these distant worlds. Jupiter's moon Europa provides a good example. Back in the late 1990's the NASA's Galileo spacecraft made several flybys of Europa and the magnetic field sensors on the spacecraft detected that Europa does not have a strong internal field of its own, instead it has an induced magnetic field that is created as a result of Jupiter's strong background magnetic field. In other words, the alarm went off.
But in order for the alarm to go off there needed to be a conductor. And for Europa the data indicated that the conducting layer must be near the surface. Other lines of evidence had already shown that the outer ~150 km of Europa was water, but those datasets could not help distinguish between solid ice water and liquid water. With the magnetic field data, however, ice doesn't work—it's not a good conductor. Liquid water with salts dissolved in it, similar to our ocean, does work. A salty ocean is needed to explain the data. The best fits to the data indicate that Europa has an outer ice shell of about 10 km in thickness, beneath which lies a global ocean of about ~100 km in depth. Beneath that is a rocky seafloor that may be teeming with hydrothermal vents and bizarre other-wordly organisms.
So, the next time your in airport security and get frustrated by that disorganized person in front of you who can't seem to get it through their head that their belt, wallet, and watch will all set off the alarm, just take a deep breathe and think of the possibly habitable distant oceans we now know of thanks to the same beautiful physics that's driving you nuts as you try to reach your departing plane.

Blogging and RSS Software Pioneer; Editor, Scripting News Weblog
What Time Is It? 
A few years ago, I heard said only old-fashioned folk wear watches. But I thought I would always wear a watch. Today I don't wear a watch.
How do I find the time? Either I do without or I keep my eyes fixed on a screen that has the time in the upper-right corner. It's gotten so that I resent that reality doesn't dispay the time in the upper-right corner. 

Planetary Scientist; Cassini Imaging Team Leader; Director, CICLOPS, Space Science Institute, Boulder, Colorado
The Inductive Economy of An Elegant Idea
An elegant and beautiful explanation is, to me, one that corrals a herd of seemingly unrelated facts within a single unifying concept. In our explorations of the worlds, including our own, that orbit the Sun, and in our attempts to find from these efforts what is special and what is commonplace about our own planet, I can think of two examples of this.
The first is an idea that was originally offered in the 1912 but met with such extreme hostility from the scientific establishment—not an unusual response, by the way, to an original idea—that it wasn't generally accepted until 50 years later. By that time, the sheer weight of evidence supporting it became so overwhelming that the notion was rendered irrefutable. And that notion was plate tectonics.
It could be said that the first indications of plate motions, though of course not recognized as such at the time, came from the observations of the early explorers, like Magellan, who noticed the puzzle-like fit of the continents, Africa and South America, for instance, on their maps. Fast forward to the early 20th century…Alfred Wegener, a German geophysicist, proposes movement of the continents (continental drift), to explain this hand-in-glove fit. Having no explanation, however, for how the continents could actually move, he was laughed out of the room.
But the evidence continued to mount: fossils, rock types, ancient climates were shown to be similar within widely separated geographical regions, like the east coast of South America and the west coast of Africa. Studies of magnetized rocks, which if stationary will always indicate a consistent direction to the north magnetic pole regardless where on the globe they form, indicated that either the north pole location varied throughout time or that the rocks themselves were not formed where they are found today. Finally, by the 1960s, it was clear that many of the Earth's presently active geological phenomena, such as the strongest earthquakes and volcanoes, were found within distinct, sinuous belts that wrapped around the planet and carved the Earth's surface into distinct bounded regions. Furthermore, studies of rocks on the floors of the Earth's oceans revealed an alternating north-up/north-down magnetic striping pattern that could only be explained by the upwelling of molten lava from below, creating new oceanic floor, and the consequent spreading of the old floor, pushing the continents farther apart with time. We now know that the tectonic forces driving the motions of the Earth's crustal plates arise from the convective upwelling and downwelling currents of molten rock in the Earth's mantle that drag around the solid plates sitting atop them.
In the end, the notion that bits of the Earth's surface can drift over time is a glorious example of a simple, efficient and even elegant idea that was eventually proven correct yet so radical for its time, it was scorned.
The second is more or less an extraterrestrial version of the same. In an historic mission not unlike Homer's Odyssey, two identical spacecraft—Voyager I and II—spent the 1980s touring the planetary systems of Jupiter, Saturn, Uranus and Neptune. And the images they returned provided humanity its first detailed views of these planets and the moons and rings surrounding them.
Jupiter was the gateway planet, the first of the four encountered, and it was there that we learned just how complex and presently active other planetary bodies could be. Along with the stunningly active moon, Io, which sported at the time about 9 large volcanic eruptions, Voyager imaged the surface of Jupiter's icy moon, Europa. Just a bit smaller than our own Moon, Europa's surface was clearly young, rather free of craters, and scored with a complex pattern of cracks and fractures that were cycloidal in shape and continuous, with many 'loops', like the scales on a fish. From these discoveries and others, it was inferred that Europa might have a thin crust overlying either warm, soft ice or perhaps even liquid water, though how the fracture pattern came to look the way it does was a mystery. The idea of a sub-surface ocean was enticing for the implicit possibility of a habitable zone for extraterrestrial life.
A follow-on spacecraft, Galileo, arrived at Jupiter in 1995 and before too long got an even better look at Europa's cracked ice shell and its cycloidal fractures. It became clear to researchers at the University of Arizona's Lunar and Planetary Lab that the cycloidal fractures, and even their detailed characteristics, like the shapes of the cycloidal segments, and the existence of, the distance between, and orientations of the cusps, could all be explained by the stresses across the moon's thin ice shell created by the tides raised on it by Jupiter. Europa's distance to Jupiter varies over the course of its orbit because of gravitational resonances with the other Jovian moons. And that varying separation causes the magnitude and direction of the tidal stresses on its surface to change. Under these conditions, if a crack in the thin ice shell is initiated at any location by these stresses, then that crack will propagate across the surface over the course of a Europan day and will take the shape of a cycloid. This will continue, day in and day out, scoring the surface of Europa in the manner that we find it today. Furthermore, tidal stresses would be inadequate to affect these kinds of changes to the moon's surface if its ice shell did not overlie a liquid ocean…an exciting possibility by anyone's measure.
And so, a whole array of features on the surface of one of Jupiter's most fascinating moons, the enormous complexity of the patterns they form, and the implication of a subterranean liquid water ocean in which extraterrestrial life might have taken hold, were explained and supported with one very simple, very easily demonstrated, and very elegant idea….an idea which itself, like that of plate tectonics, exemplifies the great beauty and economy derivable from logical induction, one of humankind's most demonstrably powerful intellectual devices.

Senior Lecturer in Behavioural Biology School, University of Bristol
Help, I need somebody!
I play this game with my kids. It's a 'guess-who' game: Think of an animal, person, object and then try to describe it to another person without giving away the real identity. The other person has to guess what/who you are. You have to get in character and tell a story: What do you do, how do you feel, what do you think and want?
Let's have a go. Read the character scenarios below and see if you can guess who/what they are.
"It's just not fair! Mum says I'm getting in the way, I'm a lay-about and she can't afford for me to stay with her any more. But I like being in a big family, and I don't want to leave. Mum says that if I am to stay home, we'd need some kind of 'glue' to keep us from drifting apart. Glue is costly and she says she hasn't the energy to make it since she's busy making babies. But then I had this brilliant idea: how aboutImake the glue using a bit of cell wall (mum won't mind), add some glycoproteins (they're a bit sticky, so I have to promise mum I'll wash my hands afterwards) and bingo! Job done: we've got ourselves a nice cosy extracellular matrix! I'm happy doing the bulk of the work, so long as mum keeps giving me more siblings. I suggested this to mum last night, and guess what? She said yes! But she also said I'm out the door if I don't keep up my side of the bargain: no free-riders…."
Who am I?
"I am a uni-cell becoming multicellular. If I group with my relatives then someone needs to pay the cost of keeping us together—the extracellular matrix. I don't mind paying that cost if I benefit from the replication of my own genes through my relatives."
Ok, that was a tough one. Try this one:
"I'm probably what you'd call the 'maternal type'. I like having babies, and I seem to be pretty good at it. I love them all equally, obviously. Damn hard work though, especially since their father didn't stick around. I can't see my latest babies surviving unless I get some help around the place. So I said to my oldest the other day, fancy helping your old Ma out? Here's the deal: you go find some food whilst I squeeze out a few more siblings for you. Remember, kid, I'm doing this for you—all these siblings will pay off in the long run. One day, some of them will be Mas just like me, and you'll be reaping in the benefits from them long after you and I are gone. This way you don't ever have to worry about sex, men or any of that sperm stuff. Your old Ma's got everything you need, right here. All you have to do is feed us, and clear out the mess!"
Who am I?
"I am an insect becoming a society. If I nest alone I have to find food which means leaving my young unprotected. If some of my grown-up children stay home and help me, they can go out foraging whilst I stay home to protect the young. I can have even more babies this way, which my children love as this means more and more of their genes are passed on through their siblings. Anyway, it's a pretty tough world out there right now for youngsters; it's much less risky to stay at home."
"I could also be a gene becoming a genome, or a prokaryote becoming an eukaryote. I am part of the same, fundamental event in evolution's playground. I am the evolution of helping and cooperation. I am the major transition that shapes all levels of biological complexity. The reason I happen is because I help others like me, and we settle on a division of labour. I don't help because, paradoxically, I benefit. My secret? I'm selective: I like to help relatives because they end up also helping me, by passing on our shared genes. I've embraced the transition from autonomy to cooperation. And it feels good!"
The evolution of cooperation and helping behaviour is a beautiful and simple explanation of how nature got complex, diverse and wonderful. It's not restricted to the charismatic Meerkats, or fluffy bumble-bees. It is a general phenomenon which generates the biological hierarchies that characterise the natural world. Groups of individuals (genes, prokaryotes, single-celled and multicellular organisms) that could previously replicate independently, form a new, collective individual that can only replicate as a whole.
Hamilton's 1964 inclusive fitness theory is an elegant and simple explanation why sociality evolves. It was more recently formalised conceptually as unified framework to explain the evolution of major transitions to biological complexity in general (e.g. Bourke's 2011 Principles of Social Evolution). Entities cooperate because it increases their fitness—their chance of passing on genes to the next generation. Beneficiaries get enhanced personal reproduction; helpers benefit from the propagation of the genes they share with the relatives they help. But the conditions need to be right: the benefits must outweigh the costs and this sum is affected by the options available to independent replicating entities before they commit to their higher-level collective. Ecology and environment play a role, as well as kinship. The resulting division of labour is the fundamental basis to societal living, uniting genes into genomes, mitochondria with prokaryotes to produce eukaryotes, unicellular organisms into multicellular ones, and solitary animals into eusocieties. This satisfyingly simple explanation makes the complexities of the world less mysterious, but no less wonderful.
If only adults indulged a bit more in children's games, perhaps we'd stumble across simple explanations for the complexities of life more often.

Cultural psychologist, writer, and consultant
Davis-Brack Professor in the Behavioral Sciences, Stanford University; Co-Editor, Doing Race: 21 Essays for the 21st Century
You Think, Therefore I Am
"I think, therefore I am." Cogito ergo sum. Remember this elegant and deep idea from René Descartes' Principles of Philosophy? The fact that a person is contemplating whether she exists, Descartes argued, is proof that she, indeed, actually does exist. With this single statement, Descartes knit together two central ideas of Western philosophy: 1) thinking is powerful, and 2) individuals play a big role in creating their own I's—that is, their psyches, minds, souls, or selves.
Most of us learn "the cogito" at some point during our formal education. Yet far fewer of us study an equally deep and elegant idea from social psychology: Other people's thinking likewise powerfully shapes the I's that we are. Indeed, in many situations, other people's thinking has a bigger impact on our own thoughts, feelings, and actions than do the thoughts we conjure while philosophizing alone.
In other words, much of the time, "You think, therefore I am." For better and for worse.
An everyday instance of how your thinking affects other people's being is the Pygmalion effect. Psychologists Robert Rosenthal and Lenore Jacobson captured this effect in a classic 1963 study. After giving an IQ test to elementary school students, the researchers told the teachers which students would be "academic spurters" because of their allegedly high IQs. In reality, these students' IQs were no higher than those of the "normal" students. At the end of the school year, the researchers found that the "spurters'" had attained better grades and higher IQs than the "normals." The reason? Teachers had expected more from the spurters, and thus given them more time, attention, and care. And the conclusion? Expect more from students, and get better results.
A less sanguine example of how much our thoughts affect other people's I's is stereotype threat. Stereotypes are clouds of attitudes, beliefs, and expectations that follow around a group of people. A stereotype in the air over African Americans is that they are bad at school. Women labor under the stereotype that they suck at math.
As social psychologist Claude Steele and others have demonstrated in hundreds of studies, when researchers conjure these stereotypes—even subtly, by, say, asking people to write down their race or gender before taking a test—students from the stereotyped groups score lower than the stereotype-free group. But when researchers do not mention other people's negative views, the stereotyped groups meet or even exceed their competition. The researchers show that students under stereotype threat are so anxious about confirming the stereotype that they choke on the test. With repeated failures, they seek their fortunes in other domains. In this tragic way, other people's thoughts deform the I's of promising students.
As the planet gets smaller and hotter, knowing that "You think, therefore I am" could help us more readily understand how we affect our neighbours and how our neighbours affect us. Not acknowledging how much we impact each other, in contrast, could lead us to repeat the same mistakes.

Social and Cognitive Scientist; CEU Budapest and CNRS Paris; Co-author (with Deirdre Wilson), Meaning and Relevance
Eratosthenes' measurement of the Earth's circumference
Eratosthenes (276-195 BCE), the head of the famous Library of Alexandria in Ptolemaic Egypt, made ground-breaking contributions to mathematics, astronomy, geography, and history. He also argued against dividing humankind into Greeks and 'Barbarians'. What he is remembered for however is having provided the first correct measurement of the circumference of the Earth (a story well told in Nicholas Nicastro's recent book, Circumference). How did he do it?
Eratosthenes had heard that, every year, on a single day at noon, the Sun shone directly to the bottom of an open well in the town of Syene (now Aswan). This meant that the Sun was then at the zenith. For that, Syene had to be on the Tropic of Cancer and the day had to be the Summer solstice (our June 21). He knew how long it took caravans to travel from Alexandria to Syene and, on that basis, estimated the distance between the two cities to be 5014 stades. He assumed that Syene was due south on the same meridian as Alexandria. Actually, in this he was slightly mistaken—Syene is somewhat to the east of Alexandria—, and also in assuming that Syene was right on the Tropic; but, serendipitously, the effect of these two mistakes cancelled one another. He understood that the Sun was far enough to treat as parallel its rays that reach the Earth. When the Sun was at the zenith in Syene, it had to be south of the zenith in the more northern Alexandria. By how much? He measured the length of the shadow cast by an obelisk located in front of the Library (says the story—or cast by some other, more convenient vertical object), and, even without trigonometry that had yet to be developed, he could determine that the Sun was at an angle of 7.2 degrees south of the zenith. That very angle, he understood, measured the curvature of the Earth between Alexandria and Syene (see the figure). Since 7.2 degrees is a fiftieth of 360 degrees, Eratosthenes could then, by multiplying the distance between Alexandria and Syene by 50, calculate the circumference of the Earth. The result, 252,000 stades, is 1% shy of the modern measurement of 40,008 km.

Eratosthenes brought together apparently unrelated pieces of evidence—the pace of caravans, the Sun shining to the bottom of a well, the length of the shadow of an obelisk—, assumptions—the sphericity of the Earth, its distance from the Sun—, and mathematical tools to measure a circumference that he could only imagine but neither see nor survey. His result is simple and compelling: the way he reached it epitomizes human intelligence at its best.
Was Eratosthenes thinking concretely about the circumference of the earth (in the way he might have been thinking concretely about the distance from the Library to the Palace in Alexandria)? I believe not. He was thinking rather about a challenge posed by the quite different estimates of the circumference of the Earth that had been offered by other scholars at the time. He was thinking about various mathematical principles and tools that could be brought to bear on the issue. He was thinking of the evidential use that could be made of sundry observations and reports. He was aiming at finding a clear and compelling solution, a convincing argument. In other terms, he was thinking about representations—theories, conjectures, reports—, and looking for a novel and insightful way to put them together. In doing so, he was inspired by others, and aiming at others. His intellectual feat only makes sense as a particularly remarkable link in a social-cultural chain of mental and public events. To me, it is a stunning illustration not just of human individual intelligence but also and above all of the powers of socially and culturally extended minds.

Neuroscientist, Baylor College of Medicine; Author, Incognito: The Secret Lives of the Brain
Ceaseless Reinvention Leads To Overlapping Solutions
The elegance of the brain lies in its inelegance.
For centuries, neuroscience attempted to neatly assign labels to the various parts of the brain: this is the area for language, this one for morality, this for tool use, color detection, face recognition, and so on. This search for an orderly brain map started off as a viable endeavor, but turned out to be misguided.
The deep and beautiful trick of the brain is more interesting: it possesses multiple, overlapping ways of dealing with the world. It is a machine built of conflicting parts. It is a representative democracy that functions by competition among parties who all believe they know the right way to solve the problem.
As a result, we can get mad at ourselves, argue with ourselves, curse at ourselves and contract with ourselves. We can feel conflicted. These sorts of neural battles lie behind marital infidelity, relapses into addiction, cheating on diets, breaking of New Year's resolutions—all situations in which some parts of a person want one thing and other parts another.
These are things which modern machines simply do not do. Your car cannot be conflicted about which way to turn: it has one steering wheel commanded by only one driver, and it follows directions without complaint. Brains, on the other hand, can be of two minds, and often many more. We don't know whether to turn toward the cake or away from it, because there are several sets of hands on the steering wheel of behavior.
Take memory. Under normal circumstances, memories of daily events are consolidated by an area of the brain called the hippocampus. But in frightening situations—such as a car accident or a robbery—another area, the amygdala, also lays down memories along an independent, secondary memory track. Amygdala memories have a different quality to them: they are difficult to erase and they can return in "flash-bulb" fashion—a common description of rape victims and war veterans. In other words, there is more than one way to lay down memory. We're not talking about memories of different events, but different memories of the same event. The unfolding story appears to be that there may be even more than two factions involved, all writing down information and later competing to tell the story. The unity of memory is an illusion.
And consider the different systems involved in decision making: some are fast, automatic and below the surface of conscious awareness; others are slow, cognitive, and conscious. And there's no reason to assume there are only two systems; there may well be a spectrum. Some networks in the brain are implicated in long-term decisions, others in short-term impulses (and there may be a fleet of medium-term biases as well).
Attention, also, has also recently come to be understood as the end result of multiple, competing networks, some for focused, dedicated attention to a specific task, and others for monitoring broadly (vigilance). They are always locked in competition to steer the actions of the organism.
Even basic sensory functions—like the detection of motion—appear now to have been reinvented multiple times by evolution. This provides the perfect substrate for a neural democracy.
On a larger anatomical scale, the two hemispheres of the brain, left and right, can be understood as overlapping systems that compete. We know this from patients whose hemispheres are disconnected: they essentially function with two independent brains. For example, put a pencil in each hand, and they can simultaneously draw incompatible figures such as a circle and a triangle. The two hemispheres function differently in the domains of language, abstract thinking, story construction, inference, memory, gambling strategies, and so on. The two halves constitute a team of rivals: agents with the same goals but slightly different ways of going about it.
To my mind, this elegant solution to the mysteries of the brain should change the goal for aspiring neuroscientists. Instead of spending years advocating for one's favorite solution, the mission should evolve into elucidating the different overlapping solutions: how they compete, how the union is held together, and what happens when things fall apart.
Part of the importance of discovering elegant solutions is capitalizing on them. The neural democracy model may be just the thing to dislodge artificial intelligence. We human programmers still approach a problem by assuming there's a best way to solve it, or that there's a way it should be solved. But evolution does not solve a problem and then check it off the list. Instead, it ceaselessly reinvents programs, each with overlapping and competing approaches. The lesson is to abandon the question "what's the most clever way to solve that problem?" in favor of "are there multiple, overlapping ways to solve that problem?" This will be the starting point in ushering in a fruitful new age of elegantly inelegant computational devices.

Psychologist, Cornell University
How The Availability Of Some Plants And Animals Can Explain Thousands Of Years Of Human History
One of the most elegant explanations I have encountered in the social sciences comes courtesy of Jared Diamond, and is outlined in his wonderful book "Guns, Germs, and Steel." Diamond attempts to answer an enormously complex and historically controversial question—why certain societies achieved such historical dominance over others—by appealing to a set of very basic differences in the physical environments from which these societies emerged (such as differences in the availability of plants and animals suitable for domestication).
These differences, Diamond argues, gave rise to a number of specific advantages (such as greater immunity to disease) that were directly responsible for the historical success of some societies.
I'm not an expert in this domain, and I accept that Diamond's explanation might be completely misguided. Yet the appeal to such basic mechanisms in order to explain such a wide set of complex observations is so deeply satisfying that I hope he is right.

Psychologist; Richard Clarke Cabot Professor of Social Ethics, Department of Psychology, Harvard University
Bounded Rationality As An Explanation For Many of Our Ills
Explanations that are extraordinary, both analytically and aesthetically, share among others, these properties: (a) they are often simpler compared to what was received wisdom, (b) they point to the more true cause as being some place quite removed from the phenomenon, and (c) they make you wish so much that you had come upon the explanation yourself.
Those of us who attempt to understand the mind, have a unique limitation to confront: the object that is the knower is also the known. The mind is the thing doing the explaining; the mind is also the thing to be explained. Distance from one's own mind, distance from attachments to the specialness of one's species or tribe, getting away from introspection and intuition (not as hypothesis generators but as answers and explanations) are all especially hard to achieve when what we seek to do is explain our own minds and those of others of our kind.
For this reason, my candidate for the most deeply satisfying explanation of recent decades is the idea of bounded rationality. The idea that human beings are smart by comparison to other species, but not smart enough by their own standards including behaving in line with basic axioms of rationality is a now a well-honed observation with deep empirical foundation in the form of discoveries in support.
Herbert Simon put one stake in the ground through the study of information processing and AI, showing that both people and organizations follow principles of behavior such as "satisficing" that constrain them to decent but not the best decisions. The second stake was placed by Kahneman and Tversky, who showed the stunning ways in even experts are error-prone—with consequences for not only their own health and happiness but that of their societies broadly.
Together the view of human nature that evolved over the past four decades has systematically changed the explanation for who we are and why we do what we do. We are error-prone in the unique ways in which we are, the explanation goes, not because we have malign intent, but because of the evolutionary basis of our mental architecture, the manner in which we remember and learn information, the way in which we are affected by those around us and so on. The reason we are boundedly rational is because the information space in which we must do our work is large compared to the capacities we have, including severe limits on conscious awareness, the ability to be able to control behavior, and to act in line even with our own intentions.
From these bounds on rationality generally, we can look also at the compromise of ethical standards—again the story is the same; that it is not intention to harm that's the problem. Rather the explanation lies in such sources are the manner in which some information plays a disproportionate role in decision making, the ability to generalize or overgeneralize, and the commonness of wrong doing that typify daily life. These are the more potent causes of the ethical failures of individuals and institutions.
The idea that bad outcomes result from limited minds that cannot store, compute and adapt to the demands of the environment is a radically different explanation of our capacities and thereby our nature. It's elegance and beauty comes from it placing the emphasis on the ordinary and the invisible rather than on specialness and malign motives. This seems not so dissimilar from another shift in explanation from god to natural section and it is likely to be equally resisted.

Associate Professor of Psychology and Neuroscience; Stanford University
Expected Value (and beyond)
To make the best choices, we face the impossible task of evaluating the future. Until the invention of "expected value," people lacked a simple way to quantify the value of an uncertain future event. Expected value was famously hit upon in a 1654 correspondence between polymaths Blaise Pascal and Pierre de Fermat. Pascal had enlisted Fermat to help find a mathematical solution to the "problem of points:" namely, how can a jackpot be divided between two gamblers when their game is interrupted before they learn of its final outcome?
A gamble's value obviously depends upon how much one can win. But Pascal and Fermat further concluded that a gamble's value also should be weighted by the likelihood of a win. Thus, expected value is computed as a potential event's magnitude multiplied by its probability (thus, in the case of a single gamble "x," E(x) = x*p). This formula is now so common that it is taken for granted. But I remember a fundamental shift in my worldview after my first encounter with expected value—as if an impending fork in the road transformed into a broad landscape of potentials, whose hills and valleys were defined by goodness and likelihood. This open view of all possible outcomes implies optimal choice—to maximize expected value, simply head for the highest hill. Thus, expected value is both elegant in its computation and deep in its implications for choice.
Even today, expected value forms the backbone of dominant theories of choice in fields including economics and psychology. More recent replacements have mainly tweaked the key ingredients of expected value—adding a curve to the magnitude component (in the case of Expected Utility), or flattening the probability component (in the case of Prospect Theory). But beyond its longevity, what amazes me most about this seventeenth century innovation is that the brain may faithfully represent something like it. Specifically, not only does activity in mesolimbic circuits appear to correlate with expected value before the outcome of a gamble is revealed, but this activity can be used to predict diverse choices—ranging from what to buy, to which investment to make, to whom to trust.
Thus, expected value is beautiful in its simplicity and utility—and almost true. Like any good scientific theory, expected value is not only quantifiable, but also falsifiable. As it turns out, people don't always maximize expected value. Sometimes they let potential losses overshadow gains or disregard probability (as highlighted by Prospect Theory). These quirks of choice suggest that while expected value may prescribe how people should choose, it does not always describe what people do choose. On the neuroimaging front, emerging evidence suggests that while subcortical regions of the mesolimbic circuit are more sensitive to magnitude, cortical regions (i.e., the medial prefrontal cortex) more heavily weight probability. By implication, people who have suffered prefrontal damage (e.g., due to injury, illness, or age) may be more seduced by attractive but unlikely offers (e.g., lottery jackpots).
Indeed, thinking about probability seems more complex and effortful than thinking about magnitude—requiring one not only to consider the next best thing, but also the one after that, and after that, and so on. Neuroimaging findings suggest that more recently evolved parts of the prefrontal cortex allow us not to "be here now"—but instead to transport ourselves into the uncertain future. Mental and neural evidence for differentiating magnitude and probability suggest a limit on the explanatory power of expected value. To some, this limit paradoxically makes expected value all the more intriguing. Scientists often love explanations more for the questions they raise than the questions they answer.

Founder and CEO of O Reilly Media, Inc.
Pascal's Wager
In 1661 or 1162, in his Pensees, philosopher and mathematician Blaise Pascal articulated what would come to be known as Pascal's Wager, the question of whether or not to believe in God, in the face of the failure of reason and science to provide a definitive answer.
"You must wager. It is not optional. You are embarked. Which will you choose then?...You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is."
While this proposition of Pascal's is clothed in obscure religious language and on a religious topic, it is a significant and early expression of decision theory. And, stripped of its particulars, it provides a simple and effective way to reason about contemporary problems like climate change.
We don't need to be 100% sure that the worst fears of climate scientists are correct in order to act. All we need to think about are the consequences of being wrong.
Let's assume for a moment that there is no human-caused climate change, or that the consequences are not dire, and we've made big investments to avert it. What's the worst that happens? In order to deal with climate change:
1. We've made major investments in renewable energy. This is an urgent issue even in the absence of global warming, as the IEA has now revised the date of "peak oil" to 2020, only 11 years from now.
2. We've invested in a potent new source of jobs.
3. We've improved our national security by reducing our dependence on oil from hostile or unstable regions.
4. We've mitigated the enormous "off the books" economic losses from pollution. (China recently estimated these losses as 10% of GDP.) We currently subsidize fossil fuels in dozens of ways, by allowing power companies, auto companies, and others to keep environmental costs "off the books," by funding the infrastructure for autos at public expense while demanding that railroads build their own infrastructure, and so on.
5. We've renewed our industrial base, investing in new industries rather than propping up old ones. Climate critics like Bjorn Lomborg like to cite the cost of dealing with global warming. But the costs are similar to the "costs" incurred by record companies in the switch to digital music distribution, or the costs to newspapers implicit in the rise of the web. That is, they are costs to existing industries, but ignore the opportunities for new industries that exploit the new technology. I have yet to see a convincing case made that the costs of dealing with climate change aren't principally the costs of protecting old industries.
By contrast, let's assume that the climate skeptics are wrong. We face the displacement of millions of people, droughts, floods and other extreme weather, species loss, and economic harm that will make us long for the good old days of the current financial industry meltdown.
Climate change really is a modern version of Pascal's wager. On one side, the worst outcome is that we've built a more robust economy. On the other side, the worst outcome really is hell. In short, we do better if we believe in climate change and act on that belief, even if we turned out to be wrong.
But I digress. The illustration has become the entire argument. Pascal's wager is not just for mathematicians, nor for the religiously inclined. It is a useful tool for any thinking person.

Editor, The Feuilleton (Arts and Essays), of the German Daily Newspaper, Sueddeutsche Zeitung, Munich
Subjective Environment
Explanations tend to be at their most elegant, when science distills the meanderings of philosophy into fact. I was looking for explanations for an observation, when I came across the theory of "Umwelt" versus "Umfeld" (vaguely environment versus surroundings) by the Estonian biologist and forefather of biosemiotics Jakob von Uexküll. According to his definition "Umwelt" is the subjective environment as perceived and impacted by an organism, while "Umfeld" is the objective environment which encompasses and impacts all organisms in it's realm.
My observation had been a mere notion of the major difference between my native Europe and America, my adopted continent for a couple of decades. In Europe the present is perceived as the end point of history. In America the present is perceived as the beginning of the future. Philosophy or history, I hoped, would have an explanation for such a fundamental yet simple difference. Both can deliver parts of an explanation of course. The different paths the histories of ideas and the histories of the countries have taken just in the past 200 years are astounding.
Uexküll's definition of the subjective environment as published in his book Umwelt und Innnenwelt der Tiere (Environments and inner worlds of animals, published 1909 in the language of his German exile) puts both philosophy and history into perspective and context though. Distrusting theories he always wanted ideas to persist in nature. Putting his idea of the subjective environment to the test in the Indian Ocean, the Atlantic and the Mediterranean. He observed simple creatures like sea anemones, sea urchins and crustaceans. His most famous example to explain his theory was the tick though. Here he found a creature whose perception and actions could be defined by three parameters each. Ticks perceive their surroundings by the directions of up and down, by warm and cold and the presence or absence of butyric acid. Their actions to survive and procreate are crawling, waiting and gripping.
This model lead him not only to define environment as a subjective notion. He found the perception of time for any organism as subjective as the perception of space, defined by the very perceptions and actions that create the organism's subjective environment. If subjective time is defined by the experiences and actions of an organism, the context of a continent's history with its myriads of parameters turns philosophy and history into mere factors in a complex environment of collective perception. Now there was an elegant explanation for a rather simple observation. Making it even more elegant is the notion that in the context of a continent's evolution geography, climate, food and culture will weigh in as factors of the perception of the subjective environment and time as well, making it impossible to prove or disprove the explanation scientifically. Having rendered philosophy to just one of many parameters it thus reduces its efforts to discredit Jakob von Uexküll's definition of the subjective environment to mere meanderings.

Professor of Biological Sciences, Physics, Astronomy, University of Calgary; Author, Reinventing the Sacred
Demonstration That Cell Types Are Dynamical Attractors
The human body has, by histological criteria, some 285 cell types. Familiar examples are skin cells, liver cells, nerve cells, muscle cells. But the human embryo starts as a single fertilized egg, the zygote, and in the process call ontogeny the zygote divides about 50 times to create the new born baby, not only with 285 cell types, but the intricate morphology of the human. Developmental biology is the study of these processes.
The process by which the zygote gives rise to different cell types is called cell differentiation.
By the 1950s, using protein separation techniques such as gel electrophoresis, it became clear that different cell types manufactured their own specific set of proteins. For example, only red blood cells make the protein hemoglobin. By then genetic work had convinced all biologists that genes were like beads lined up single file on chromosomes. The emerging hypothesis of the day was "one gene makes one protein". If so, different cells had different active subsets of the total complement of human genes on the diverse chromosomes. The active genes would be making their specific proteins.
By 1953 Watson and Crick established the structure of DNA, the race was on to discover the genetic code, soon worked out, by which the sequence of nucleotide bases in a gene encodes a corresponding messenger RNA, which was then translated, according to the soon known genetic code, into proteins by a host of protein enzymes and the RNA ribosome.
These brilliant results, the core of molecular biology, left hanging the deep question: How do different cell types manage to have different subsets of the full set of human genes active in the corresponding cell type?
Two superb French microbiologists, F. Jacob and J. Monod in 1961 made the first experimental breakthrough using the bacterium E. coli. They showed that, adjacent to the gene encoding a protein called beta galactosidase, a small "operator" DNA sequence, "O", bound a "repressor protein", "R". When R was bound to O, the adjacent gene for beta galactosidase could not be copied into its messenger RNA. In short, genes and their products could turn one another "on" and "off".
By 1963 these two authors cracked, it seemed, the central problem of how 285 cell types with the same genes could possibly have different patterns of gene activity in the 285 cell types. Jacob and Monod proposed that two genes, A and B, which turned one another "off", ie "repressed" one another, could have two "steady states of gene activity: 1) A "on" B "off"; 2) A "off" B "on".
In brief, by imagining a very simple "genetic circuit" where A and B repress one another, the genetic circuit, like an electronic circuit, could have two different steady state patterns of gene activity, each corresponding to one of two cell types, the first making A protein, the second making B protein.
In principle, Jacob and Monod had cracked the problem of cell differentiation: how cells with the same genes could exhibit diverse and unique patterns of gene activities.
I was entering biology at that time, with a background studying neural circuits and logic. It was clear to most biologists that some huge genetic network among the then thought 100,000 human genes somehow controlled cell differentiation in ontogeny. My question was an odd one: Did evolution have to struggle hard to evolve very specific genetic networks to support ontogeny, or, I hoped, were there huge classes, or "ensembles" of networks that as a total class, behaved with sufficient self-organized order to account for major features of ontogeny?
To explore this, I invented "random Boolean networks", a set of N "light bulbs", each receiving regulatory inputs from K light bulbs, and turing on and off according to some logical, or Boolean rule. Such networks have the property of having a generalization of the Jacob and Monod "A "on" B "off" versus A "off B "on", property. These two patterns are called "attractors", for reasons I make clear in a moment.
I studied networks with up to 10,000 light bulb model genes, each with K = 2 inputs, and sampled the class or ensemble of N = 10,000 K = 2 possible networks by assigning the 2 inputs to each model gene at random and the logical, or Boolean, rule to that gene at random from the 16 logical functions of two inputs. It turned out that such networks followed a sequence of states, like a stream, and settled down to a cycle of states, like a stream reaching a lake. Many streams, or trajectories, typically flowed into each "state cycle" attractor, called an "attractor" because the state cycle lake attracts a set of trajectories to flow into it. More each network had many such state cycle lake attractors.
The obvious hypothesis was that each attractor corresponded to a cell type.
On this hypothesis, differentiation was a process in which a signal, or chemical noise, induced a cell to leave one attractor, and reach a state that flowed along a trajectory that flowed to another attractor cell type.
This remained a mere hypothesis until a decade ago, a brilliant biologist, Dr. Sui Huang, used a mild leukemic cell line, HL60. He used two different chemical perturbations, All Trans Retinoic Acid and DMSO, to treat two sets of HL60 cells. At regular intervals, Huang used the technique of gene arrays to sample the activities of 12,000 genes. He showed, wonderfully, that under the two chemical treatments, HL60 followed two divergent then convergent "stream-trajectory" pathways in the patterns of activity of 12,000 genes, both of which ended up on the same pattern, corresponding to a normal polymorphoneuterophil blood cell.
Huang's powerful result remains the best evidence that cell types are indeed attractors.. If this is true, it should be possible to perturb the gene activities of cell types to control their differentiation into desired cell types.

Biologist; Associate Professor, University of Minnesota, Morris
Everything Is The Way It Is Because It Got That Way
There is no denying that the central concept of modern biology is evolution, but I'm afraid I was a victim of the American public school system, and I went through twelve years of education without once hearing any mention of the 'controversial' E word. We dissected cats, we memorized globs of taxonomy, we regurgitated extremely elementary fragments of biochemistry on exams, but we were not given any framework to make sense of it all (one reason I care very much about science education now is that mine was so poor).
The situation wasn't much better in college. There, evolution was universally assumed, but there was no remedial introduction to the topic—it was sink or swim, and determined not to drown, I sought out context, anything that would help me understand all these facts my instructors expected me to know. I found it in a used bookstore, a book that I selected because it wasn't too thick and daunting, and because when I skimmed it, it was clearly written, unlike all the massive dense and opaque reference books my classes foisted on me. It was John Tyler Bonner's On Development: The Biology of Form, and it blew my mind, and also warped me permanently to see biology through the lens of development.
The first thing the book taught me wasn't an explanation, which was something of a relief; my classes were just full of explanations already. Bonner's book is about questions, good questions, some of which had answers and others are just hanging there ripely. For instance, how is biological form defined by genetics? It's the implicit question in the title, but the book just refined the questions that we need to answer in order to explain the problem! Or maybe that is an important explanation at a different level; science isn't the body of facts archived in our books and papers, it's the path we follow to acquire new knowledge.
Bonner also led me to D'Arcy Wentworth Thompson and his classic book, On Growth and Form, which provided my favorite aphorism for a scientific view of the universe, "Everything is the way it is because it got that way"—it's a subtle way of emphasizing the importance of process and history in understanding why everything is the way it is. You simply cannot grasp the concepts of science if your approach is to dissect the details in a static snapshot of its current state; your only hope is to understand the underlying mechanisms that generate that state, and how it came to be. The necessity of that understanding is implicit in developmental biology, where all we do is study the process of change in the developing embryo, but I also found it essential as well in genetics, comparative physiology, anatomy, biochemistry...and of course, it is paramount in evolutionary biology.
So my most fundamental explanation is a mode of thinking: to understand how something works, you must first understand how it got that way.

Science Writer; Founding chairman of the International Centre for Life; Author, The Rational Optimist
Life Is a Digital Code
It's hard now to recall just how mysterious life was on the morning of 28 February and just how much that had changed by lunchtime. Look back at all the answers to the question "what is life?" from before that and you get a taste of just how we, as a species, floundered. Life consisted of three-dimensional objects of specificity and complexity (mainly proteins). And it copied itself with accuracy. How? How do you set about making a copy of a three-dimensional object? How to do you grow it and develop it in a predictable way? This is the one scientific question where absolutely nobody came close to guessing the answer. Erwin Schrodinger had a stab, but fell back on quantum mechanics, which was irrelevant. True, he used the phrase "aperiodic crystal" and if you are generous you can see that as a prediction of a linear code, but I think that's stretching generosity.
Indeed, the problem had just got even more baffling thanks to the realization that DNA played a crucial role—and DNA was monotonously simple. All the explanations of life before 28 Feb 1953 are hand-waving waffle and might as well speak of protoplasm and vital sparks for all the insights they gave.
Then came the double helix and the immediate understanding that, as Crick wrote to his son a few weeks later, "some sort of code"—digital, linear two-dimensional, combinatorially infinite and instantly self-replicating—was all the explanation you needed. Here's part of Francis Crick's letter, 17 March 1953:
"My Dear Michael,
Jim Watson and I have probably made a most important discovery...Now we believe that the DNA is a code. That is, the order of the bases (the letters) makes one gene different from another gene (just as one page pf print is different from another). You can see how Nature makes copies of the genes. Because if the two chains unwind into two separate chains, and if each chain makes another chain come together on it, then because A always goes with T, and G with C, we shall get two copies where we had one before. In other words, we think we have found the basic copying mechanismby which life comes from life...You can understand we are excited."
Never has a mystery seemed more baffling in the morning and an explanation more obvious in the afternoon.

Writer, Artist, Designer; Author, Generation A
One Concidence; Two Deja Vues
I take comfort in the fact that there are two human moments that seem to be doled out equally and democratically within the human condition—and that there is no satisfying ultimate explanation for either. One is coincidence, the other is déja vu. It doesn't matter if you're Queen Elizabeth, one of the thirty-three miners rescued in Chile, a South Korean housewife or a migrant herder in Zimbabwe—in the span of 365 days you will pretty much have two déja vus as well as one coincidence that makes you stop and say, "Wow, that was a coincidence."
The thing about coincidence is that when you imagine the umpteen trillions of coincidences that can happen at any given moment, the fact is, that in practice, coincidences almost never do occur. Coincidences are actually so rare that when they do occur they are, in fact memorable. This suggests to me that the universe is designed to ward of coincidence whenever possible—the universe hates coincidence—I don't know why—it just seems to be true. So when a coincidence happens, that coincidence had to work awfully hard to escape the system. There's a message there. What is it? Look. Look harder. Mathematicians perhaps have a theorem for this, and if they do, it might, by default be a theorem for something larger than what they think it is.
What's both eerie and interesting to me about déja vus is that they occur almost like metronomes throughout our lives, about one every six months, a poetic timekeeping device that, at the very least, reminds us we are alive. I can safely assume that my thirteen year old niece, Stephen Hawking and someone working in a Beijing luggage-making factory each experience two déja vus a year. Not one. Not three. Two.
The underlying biodynamics of déja vus is probably ascribable to some sort of tingling neurons in a certain part of the brain, yet this doesn't tell us why they exist. They seem to me to be a signal from larger point of view that wants to remind us that our lives are distinct, that they have meaning, and that they occur throughout a span of time. We are important, and what makes us valuable to the universe is our sentience and our curse and blessing of perpetual self-awareness.

Professor & Director, Institute of Philosophy School of Advanced Study University of London
Lemons are Fast
When asked to put lemons on a scale between fast and slow almost everyone says 'fast', and we have no idea why. Maybe human brains are just built to respond that way. Probably. But how does that help? It's an explanation of sorts but it seems to be a stopping point when we wanted to know more. This leads us to ask what we want from an explanation: one that's right, or one that satisfies us? Things that were once self-evident are now known to be false. A straight line is obviously the shortest distance between two points until we think that space is curved. What satisfies our way of thinking need not reflect reality. Why expect a simple theory of a complex world?
Wittgenstein had interesting things to say about what we want from explanations and he knew different things could serve. Sometimes we just need more information; sometimes, we need to examine a mechanism, like a valve, or a pulley, to understand how it works; while sometimes what we need is a way of seeing something familiar in a new light, to see it as it really is. He also knew there were times when explanations won't do. 'To the man who has lost in love', he asks, 'what will help him? An explanation?' The question clearly invites the answer, no.
So what of the near universal response to the seemingly meaningless question of whether lemons are fast or slow? To be told that our brains are simply built to respond that way doesn't satisfy us. But it's precisely when an explanation leaves us short that it spurs us to greater effort.
It's the start of the story, not the end. For the obvious next question to ask is why are human brains built this way? What purpose could it serve? And here the phenomenon of automatic associations may give us a deep clue about the way the mind works because it's symptomatic of what we call cross-modal correspondences: non-arbitrary associations between features in one sense modality with features in another.
There are cross-modal correspondences between taste and shape, between sound and vision, between hearing and smell, many of which are being investigated by neuroscientist Charles Spence and philosopher Ophelia Deroy. These unexpected connections are reliable and shared, unlike cases of synaesthesia, which are idiosyncratic—though individually consistent. And the reason we make these connections in the brain is to give us multiple fixes on objects in the environment that we can both hear and see. It also allows us to communicate elusive aspects of our experience.
We often say that tastes are hard to describe, but when we realise that we can change vocabulary and talk about a taste as round or sharp new possibilities open up. Musical notes are high or low; sour tastes are high, and bitter notes low. Smells can have low notes and high notes. You can feel low, or be incredibly high. This switching of vocabularies allows us to utilise well-understood sensory modalities to map various possibilities of experience.
Advertisers know this intuitively and exploit cross-modal correspondences between abstract shapes and particular products, or between sounds and sights. Angular shapes conjure up carbonated water not still, while an ice cream called 'Frisch' would be thought creamier than one called 'Frosch'. Notice, too, how many successful companies have names starting with the /k/ sound, and how few with /s/. These associations set up expectations in the mind that not only help us perceive but may shape our experiences.
And it is not just vocabularies that we use. In his nineteenth century tract on the Psychology of Architecture, Heinrich Wofflin tells us that it's because we have bodies, and are subject to gravity, bending and balance, that we can appreciate the shape of buildings, and columns, by feeling an empathy for their weight and strain. Physical forms possess a character only because we possess a body.
This idea has led to recent insights into aesthetic appreciation in the work of Chris McManus at UCL. Like all good explanations it spawns more explanations and further insights. It's another example of how we use the interaction of sensory information to shape our perceptions and help us to understand and respond to the world around us. Like all good explanations it spawns more explanations and further insights. So the fact that we all think that lemons are fast may be a big part of the reason why we are so smart.

Associate Professor of Journalism, Annenberg School for Journalism; Author, The Wikipedia Revolution
"Information Is The Resolution Of Uncertainty"
Nearly everything we enjoy in the digital age hinges on this one idea, yet few people know about its originator or the foundations of this simple, elegant theory of information.
Einstein is well rooted in popular culture as the developer of the theory of relativity. Watson and Crick are associated with the visual spectacle of DNA's double helix structure.
How many know that the information age was not the creation of Gates or Jobs but of Claude Shannon in 1948?
The brilliant mathematician, geneticist and cryptanalyst formulated what would become information theory in the aftermath of World War II, when it was apparent it was not just a war of steel and bullets.
If World War I was the first mechanized war, the second war could be considered the first struggle based around communication technologies. Combat in the Pacific and Atlantic theaters were as much a battle of information as they were about guns, ships and planes.
Consider the advances of the era that transformed the way wars were fought.
Unlike previous conflicts, there was heavy utilization of radio communication among military forces. This quick remote coordination quickly pushed the war to all corners of the globe. Because of this, the field of cryptography advanced quickly in order to keep messages secret and hidden from adversaries. Also, for the first time in combat, radar was used to strategically detect and track aircraft, thereby surpassing conventional visual capabilities that ended on the horizon.
One researcher, Claude Shannon, was working on the problem of anti-aircraft targeting and designing fire-control systems to work directly with radar. How could you determine the current, and future position of enemy aircraft's flight path, so you could properly time artillery fire to shoot it down? The radar information about plane position was a breakthrough, but "noisy" in that it provided an approximation of its location, but not precisely enough to be immediately useful.
After the war, this inspired Shannon and many others to think about the nature of filtering and propagating information, whether it was radar signals, voice for a phone call, or video for television.
He knew that noise was the enemy of communication, so any way to store and transmit information that rejected noise was of particular interest to his employer, Bell Laboratories, the research arm of the mid-century American telephone monopoly.
Shannon considered communication "the most mathematical of the engineering sciences," and turned his intellectual sights towards this problem. Having worked on the intricacies of Vannevar Bush's differential analyzer analog computer in his early days at MIT, and with a mathematics-heavy Ph.D. thesis on the "Algebra for Theoretical Genetics," Shannon was particularly well-suited to understanding the fundamentals of handling information using knowledge from a variety of disciplines.
By 1948 he had formed his central, simple and powerful thesis:
Information is the resolution of uncertainty.
As long as something can be relayed that resolves uncertainty, that is the fundamental nature of information. While this sounds surprisingly obvious, it was an important point, given how many different languages people speak and how one utterance could be meaningful to one person, and unintelligible to another. Until Shannon's theory was formulated, it was not known how to compensate for these types of "psychological factors" appropriately. Shannon built on the work of fellow researchers Ralph Hartley and Harry Nyquist to reveal that coding and symbols were the key to resolving whether two sides of a communication had a common understanding of the uncertainty being resolved.
Shannon then considered: what was the simplest resolution of uncertainty?
To him, it was the flip of the coin—heads or tails, yes or no—as an event with only two outcomes. Shannon concluded that any type of information, then, could be encoded as a series of fundamental yes or no answers. Today, we know these answers as bits of digital information—ones and zeroes—that represent everything from email text, digital photos, compact disc music or high definition video.
That any and all information could be represented and coded in discrete bits not just approximately, but perfectly, without noise or error was a breakthrough which astonished even his brilliant peers at academic institutions and Bell Laboratories who previously thought it was unthinkable to have a simple universal theory of information.
The compact disc, the first ubiquitous digital encoding system for the average consumer, showed the legacy of Shannon's work to the masses in 1982. It provides perfect reproduction of sound by dividing each second of musical audio waves into 44,100 slices (samples), and recording the height of each slice in digital numbers (quantization). Higher sampling rates and finer quantization raise the quality of the sound. Converting this digital stream back to audible analog sound using modern circuitry allowed for consistent high fidelity versus the generation loss people were accustomed to in analog systems, such as compact cassette.
Similar digital approaches have been used for images and video, so that today we enjoy a universe of MP3, DVDs, HDTV, AVCHD multimedia files that can be stored, transmitted and copied without any loss of quality.
Shannon became a professor at MIT, and over the years students of Shannon went on to be the builders of many major breakthroughs of the information age, including digital modems, computer graphics, data compression, artificial intelligence and digital wireless communication.
But without a sensational origin myth, bombastic personality or iconic tongue-wagging photo, Shannon's contribution is largely unknown to today's digital users.
Shannon was a humble man and intellectual wanderlust who shunned public speaking or granting interviews. He once remarked, "After I had found answers, it was always painful to publish, which is where you get the acclaim. Many things I have done and never written up at all. Too lazy, I guess."
Shannon was perhaps lazy to publish, but he was not a lazy thinker. Later in life, he occupied himself with puzzles he found personally interesting—designing a Rubik's cube solving device and modeling the mathematics of juggling.
The 20th century was a remarkable scientific age, where the fundamental building blocks of matter, life and information were all revealed in interconnected areas of research centered around mathematics. The ability to manipulate atomic and genetic structures found in nature have provided breakthroughs in the fields of energy and medical research. Less expected was discovering the fundamental nature of communication. Information theory as a novel, original and "unthinkable" discovery has completely transformed nearly every aspect of our lives to digital, from how we work, live, love and socialize.
Beautiful, elegant and deeply powerful.

Consultant, New Scientist; Founding Editor, CultureLab"
Structural Realism
Structural realism—in its metaphysical version, championed by the philosopher of science James Ladyman—is the deepest explanation I know, because it serves as a kind of meta-explanation, one that explains the nature of reality and the nature of scientific explanations.
The idea behind structural realism is pretty simple: the world isn't made of things, it's made of mathematical relationships, or structure. A mathematical structure is a set of isomorphic elements, each of which can be perfectly mapped onto the next. To give a trivial example, the numbers 25 and 52 share the same mathematical structure.
When the philosopher John Worrall first introduced structural realism (though he attributes it to physicist Henri Poincaré), he was trying to explain something puzzling: how was it possible that a scientific theory that would later turn out to be wrong could still manage to make accurate predictions? Take Newtonian gravity. Newton said that gravity was a force that masses exert on one another from a distance. That idea was overthrown by Einstein, who showed that gravity was the curvature of spacetime. Given how wrong Newton was about gravity, it seems almost miraculous that he was able to accurately predict the motions of the planets.
Thankfully, we don't have to resort to miracles. Newton may have gotten the physical interpretation of gravity wrong, but he got a piece of the math right. That's why, at weak masses and small velocities, Einstein's equations reduce to Newton's. The problem, Worrall pointed out, was that we mistook an interpretation of the theory for the theory itself. The fact is, in physics, theories are sets of equations, and nothing more. "Quantum field theory" is a group of mathematical structures. "Electrons" are little stories we tell ourselves.
These days, believing in the reality of objects—of physical things like particles, fields, forces, even spacetime geometries—can quickly lead to profound existential crises.
Quantum theory, for instance, strips particles of any sense of "thingness". One electron is not merely similar to another, all electrons are exactly the same. Electrons have no inherent identity—a fact that makes quantum statistics drastically different from the classical kind. Anyone who believes that an electron is a "thing" in its own right is bound to lose big in a quantum casino.
Meanwhile, all of nature's fundamental forces, including electromagnetism and the nuclear forces that operate deep in the cores of atoms, are described by gauge theory, which shows that forces aren't physical things in the world, but discrepancies in different descriptions of the world, in different observers' points of view. Gravity is a gauge force too, which means you can make it blink out of existence just by changing your frame of reference. In fact, that was Einstein's "happiest thought": a person in freefall can't feel their weight. It's often said that you can't disobey the law of gravity, but the truth is you can take it out with a simple coordinate change.
Recent advances in theoretical physics have only made the situation worse. The holographic principle tells us that our four-dimensional spacetime and everything in it is exactly equivalent to physics taking place on the two-dimensional boundary of the universe. Neither description is more "real" than the other—one can be perfectly mapped onto the other with no loss of information. When we try to believe that spacetime is really four-dimensional or really has a particular geometry, the holographic principle pulls the rug out from under us.
The physical nature of reality has been further eroded by M-theory, the theory that many physicists believe can unite general relativity and quantum mechanics. M-theory encompasses five versions of string theory (plus one non-stringy theory known as supergravity) all of which are related by mathematical maps called dualities. What looks like a strong interaction in one theory looks like a weak interaction in another. What look like eleven dimensions in one theory look like ten in another. Big can look like small, strings can look like particles. Virtually any object you can think of will be transformed into something totally different as you move from one theory to the next—and yet, somehow, all of the theories are equally true.
This reality crisis has grown so dire that Stephen Hawking has called for a kind of philosophical surrender, a white flag he terms "model-dependent realism", which basically says that while our theoretical models offer possible descriptions of the world, we'll simply never know the true reality that lies beneath. Perhaps there is no reality at all.
But structural realism offers a way out. An explanation. A reality. The only catch is that it's not made of physical objects. Then again, our theories never said it was. Electrons aren't real, but the mathematical structure of quantum field theory is. Gauge forces aren't real, but the symmetry groups that describe them are. The dimensions, geometries and even strings described by any given string theory aren't real—what's real are the mathematical maps that transform one string theory into another.
Of course, it's only human to want to interpret mathematical structure. There's a reason that "42" is hardly a satisfying answer to life, the universe and everything. We want to know what the world is really like, but we want it in a form that fits our intuitions. A form that means something. And for our narrative-driven brains, meaning comes in the form of stories, stories about things. I doubt we'll ever stop telling stories about how the universe works, and I, for one, am glad. We just have to remember not to mistake the stories for reality.
Structural realism forces us to radically revise the way we think about the universe. But it also provides a powerful explanation for some of the most mystifying aspects of physics. Without it, we'd have to give up on the notion that scientific theories can ever tell us how the world really is. And that, in my humble opinion, makes it a pretty beautiful explanation.

Academic; Newspaper Columnist; Vice-President, Wolfson College; Author, From Gutenberg to Zuckerberg: what you really need to know about the Internet
Flocking Behaviour In Birds
My favourite explanation is Craig Reynold's suggestion (first published in 1986, I think) that flocking behaviour in birds can be explained by assuming that each bird follows three simple rules—separation (don't crowd your neighbours), alignment (steer towards the average heading of your neighbours) and cohesion (steer towards the average position of your neighbours). The idea that such complex behaviour can be accounted for in such a breathtakingly simple way is, well, just beautiful.

Archaeologist, Journalist; Author, Artifacts
Dirt Is Matter Out of Place
I admire this explanation of cultural relativity, by the anthropologist Mary Douglas, for its clean lines and tidiness. I like its beautiful simplicity, the way it illuminates dark corners of misreading, how it limelights the counter-conventional. Poking about in the dirt is exciting, and irreverent. It is about talking what is out of bounds and making it relevant. Douglas's explanation of 'dirt' makes us question the very boundaries we are pushing.

Director of the Bristol Cognitive Development Centre in the Experimental Psychology Department at the University of Bristol; Author, The Self-Illusion
Complexity Out of Simplicity
As a scientist dealing with complex behavioral and cognitive processes, my deep and elegant explanation comes not from psychology (which is rarely elegant) but from the mathematics of physics. For my money, Fourier's theorem has all the simplicity and yet more power than other familiar explanations in science. Stated simply, any complex pattern, whether in time or space, can be described as a series of overlapping sine waves of multiple frequencies and various amplitudes.
I first encountered Fourier's theorem when I was a Ph.D. student in Cambridge working on visual development. There, I met Fergus Campbell who in the 1960's had demonstrated that not only was Fourier theorem an elegant way of analyzing complex visual patterns, but it was also biologically plausible. This insight was later to become a cornerstone of various computational models of vision. But why restrict the analysis to vision?
In effect, any complex physical event can be reduced to the mathematical simplicity of sine waves. It doesn't matter whether it is Van Gogh's Starry Night, Mozart's Requiem, Chanel's No. 5, Rodin's Thinker or a Waldorf salad. Any complex pattern in the environment can be translated into neural patterns that in turn, can be decomposed into the multitude of sine wave activity arising from the output of populations of neurons.
Maybe I have some physics envy, but to quote Lord Kelvin, "Fourier's theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." You don't get much higher praise than that.

Biological Anthropologist, Rutgers University; Author, Why Him? Why Her? How to Find and Keep Lasting Love
To me, epigenetics is the most monumental explanation to emerge in the social and biological sciences since Darwin proposed his theories of Natural Selection and Sexual Selection. Over 2,500 articles, many scientific meetings, the formation of the San Diego Epigenome Center as well as other institutes, a five-year Epigenomics Program launched in 2008 by the National Institutes of Health, and many other institutions, academic forums and people are now devoted to this new field. Although epigenetics has been defined in several ways, all are based in the central concept that environmental forces can affect gene behavior, either turning genes on or off. As an anthropologist untrained in advanced genetics, I won't attempt to explain the processes involved, although two basic mechanisms are known: one involves molecules known as methyl-groups that latch on to DNA to suppress and silence gene expression; the other involves molecules known as acetyl-groups which activate and enhance gene expression.
The consequences of epigenetic mechanisms are likely to be phenomenal. Scientists now hypothesize that epigenetic factors play a role in the etiology of many diseases, conditions and human variations—from cancers, to clinical depression and mental illnesses, to human behavioral and cultural variations.
Take the Moroccan Amazighs or Berbers, people with highly similar genetic profiles who now reside in three different environments: some roam the deserts as nomads; some farm the mountain slopes; some live in the towns and cities along the Moroccan coast. And depending on where they live, up to one-third of their genes are differentially expressed, reports researcher Youssef Idaghdour.
 For example, among the urbanites, some genes in the respiratory system are switched on—perhaps, Idaghdour suggests, to counteract their new vulnerability to asthma and bronchitis in these smoggy surroundings. Idaghdour and his colleague Greg Gibson, propose that epigenetic mechanisms have altered the expression of many genes in these three Berber populations, producing their population differences.
 Psychiatrists, psychologists and therapists have long been preoccupied with our childhood experiences, specifically how these sculpt our adult attitudes and behaviors. Yet they have focused on how the brain integrates and remembers these occurrences. Epigenetic studies provide a different explanation.
As an example, mother rats that spend more time licking and grooming their young during the first week after birth produce infants who later become better adjusted adults. And researcher Moshe Szyf proposes that this behavioral adjustment occurs because epigenetic mechanisms are triggered during this "critical period," producing a more active version of a gene that encodes a specific protein. Then this protein, via complex pathways, sets up a feedback loop in the hippocampus of the brain—enabling these rats to cope more efficiently with stress.
These behavioral modifications remain stable through adulthood. However, Szyf notes that when specific chemicals were injected into the adult rat's brain to alter these epigenetic processes and suppress this gene expression, well-adjusted rats became anxious and frightened. And when different chemicals are injected to trigger epigenetic processes that enhance the expression of this gene instead, fearful adult rats (that had received little maternal care in infancy) became more relaxed.
 Genes hold the instructions; epigenetic factors direct how those instructions are carried out. And as we age, scientists report, these epigenetic processes continue to modify and build who we are. Fifty-year-old twins, for example, show three times more epigenetic modifications than do three-year-old twins; and twins reared apart show more epigenetic alterations than those who grow up together. Epigenetic investigations are proving that genes are not destiny; but neither is the environment—even in people.
Shelley Taylor has shown this. Studying an allele (genetic variant) in the serotonin system, she and colleagues were able to demonstrate that the symptoms of depression are visible only when this allele is expressed in combination with specific environmental conditions. Moreover, Taylor maintains that individuals growing up in unstable households are likely to suffer all their lives with depression, anxiety, specific cancers, heart disease, diabetes or obesity. Epigenetics at work? Probably.
 Even more remarkable, some epigenetic instructions are passed from one generation to the next. Trans-generational epigenetic modifications are now documented in plants and fungi, and have been suggested in mice. Genes are like the keys on a piano; epigenetic processes direct how these keys are played—modifying the tune, even passing these modifications to future generations. Indeed, in 2010, scientists wrote in Science magazine that epigenetic systems are now regarded as "heritable, self-perpetuating and reversible."
 If epigenetic mechanisms can not only modulate our intellectual and physical capacities, but also pass these alterations to our descendants, epigenetics has immense and profound implications for the origin, evolution and future of life on earth. In coming decades scientists studying epigenetics may come to understand how myriad environmental forces impact our health and longevity in specific ways, find cures for many human diseases and conditions, and explain intricate variations in human personality.
The 18th century philosopher, John Locke, was convinced that the human mind is an empty slate upon which the environment inscribes personality. With equal self-assurance, others have been convinced that genes orchestrate our development, illnesses and life styles. Yet social scientists had failed for decades to explain the mechanisms governing behavioral variations between twins, family members and culture groups. And biological scientists had failed to pinpoint the genetic foundations of many mental illnesses and complex diseases. The central mechanism to explain these complex issues has been found.
 I am hardly the first to hail this new field of biology as revolutionary—the fundamental process by which nature and nurture interact. But to me as an anthropologist long trying to take a middle road in a scientific discipline intractably immersed in nature-versus-nurture warfare, epigenetics is the missing link.

Artist; Composer; Recording Producer: U2, Coldplay, Talking Heads, Paul Simon; Recording Artist
The Limits Of Intuition
We sometimes tend to think that ideas and feelings arising from our intuitions are intrinsically superior to those achieved by reason and logic. Intuition—the 'gut'—becomes deified as the Noble Savage of the mind, fearlessly cutting through the pedantry of reason. Artists, working from intuition much of the time, are especially prone to this belief. A couple of experiences have made me more sceptical.
The first is a question that Wittgenstein used to pose to his students. It goes like this: you have a ribbon which you want to tie round the centre of the Earth (let's assume it to be a perfect sphere). Unfortunately you've tied the ribbon a bit too loose: it's a meter too long. The question is this: if you could distribute the resulting slack—the extra meter—evenly round the planet so the ribbon hovered just above the surface, how far above the surface would it be?
Most people's intuitions lead them to an answer in the region of a minute fraction of a millimeter. The actual answer is almost 16 cms. In my experience only two sorts of people intuitively get close to this: mathematicians and dressmakers. I still find it rather astonishing: in fact when I heard it as an art student I spent most of one evening calculating and recalculating it because my intuition was screaming incredulity.
Not many years later, at the Exploratorium in San Francisco, I had another shock-to-the-intuition. I saw for the first time a computer demonstration of John Conway's Life. For those of you who don't know it, it's a simple grid with dots that are acted on according to an equally simple, and totally deterministic, set of rules. The rules decide which dots will live, die or be born in the next step. There are no tricks, no creative stuff, just the rules. The whole system is so transparent that there should be no surprises at all, but in fact there are plenty: the complexity and 'organic-ness' of the evolution of the dot-patterns completely beggars prediction. You change the position of one dot at the start, and the whole story turns out wildly differently. You tweak one of the rules a tiny bit, and there's an explosion of growth or instant armageddon. You just have no (intuitive) way of guessing which it's going to be.
These two examples elegantly demonstrate the following to me:
a) 'Deterministic' doesn't mean 'predictable',
b) we aren't good at intuiting the interaction of simple rules with initial conditions (and the bigger point here is that the human brain may be intrinsically limited in its ability to intuit certain things—like quantum physics and probability, for example), and
c) intuition is not a quasi-mystical voice from outside ourselves speaking through us, but a sort of quick-and-dirty processing of our prior experience (which is why dressmakers get it when the rest of us don't). That processing tool sometimes produces incredibly impressive results at astonishing speed, but it's worth reminding ourselves now and again that it can also be totally wrong.

Consultant; Adaptive Optics and Adjunct Professor of Anthropology, University of Utah; Co-author, The Ten Thousand Year Explosion
Germs Cause Disease
The germ theory of disease has been very successful, particularly if you care about practical payoffs, like staying alive. It explains how disease can rapidly spread to large numbers of people (exponential growth), why there are so many different diseases (distinct pathogen species), and why some kind of contact (sometimes indirect) is required for disease transmission.
In modern language, most disease syndromes turn out to be caused by tiny self-replicating machines whose genetic interests are not closely aligned with ours.
In fact, germ theory has been so successful that it almost seems uninteresting. Once we understood the causes of cholera and pneumonia and syphilis, we got rid of them, at least in the wealthier countries. Now we're at the point where people resist the means of victory—vaccination for example—because they no longer remember the threat.
It is still worth studying—not just to fight the next plague, but also because it has been a major factor in human history and human evolution. You can't really understand Cortez without smallpox or Keats without tuberculosis. The past is another country—don't drink the water.
It may well explain patterns that we aren't even supposed to see, let alone understand. For example, human intelligence was, until very recently, ineffective at addressing problems causing by microparasites, as William McNeill pointed out in Plagues and Peoples. Those invisible enemies played a major role in determining human biological fitness—more so in some places than others. Consider the implications.
Lastly, when you leaf through a massively illustrated book on tropical diseases and gaze upon an advanced case of elephantiasis, or someone with crusted scabies, you realize that any theory that explains that much ugliness just has to be true.

Independent Researcher; Author, The Princeton Field Guide of Dinosaurs
Birds Are The Direct Descendents Of Dinosaurs
The most graceful example of an elegant scientific idea in one of my fields of expertise is the idea is that dinosaurs were tachyenergetic, that they were endotherms with the high internal energy production and high aerobic exercise capacity typical of birds and mammals that can sustain long periods of intense activity. Although it is not dependent upon it, high powered dinosaurs blends in with the hypothesis that birds are the direct descendents of dinosaurs, that birds literally are flying dinosaurs, much as bats are flying mammals.
 It cannot be overemphasized how much sense the above makes, and how it has revolutionized a big chunk of our understanding of evolution and 230 millions years of earth history relative to what was thought from the mid 1800s to the 1960s. Until then it was generally presumed that dinosaurs were a dead end collection of bradyenergetic reptiles that could achieve high levels of activity for only brief bursts; even walking at 5 mph requires high respiratory capacity beyond that of reptiles who must plod along at a mph or so if they are moving a long distance. Birds were seen as a distinct and feathery group in which energy inefficiency evolved in order to power flight.
Although the latter hypothesis was not inherently illogical, it was divergent from the evolution of bats in which high aerobic capacity was already present in their furry ancestors.
I first learned of "warm-blooded" dinosaurs in my senior year of high school via a blurb in Smithsonian Magazine about Robert Bakker's article in Nature in the summer of 1972. As soon as I read it, it just clicked. I had been illustrating dinosaurs in accord with the reptilian consensus, but it was a bad fit because dinosaurs are so obviously constructed like birds and mammals, not crocs and lizards. About the same time John Ostrom, who also had a hand in discovering dinosaur endothermy, was presenting the evidence that birds are aerial versions of avepod dinosaurs—a concept so obvious that should have become the dominant thesis back in the 1800s.
For a quarter century the hypotheses was highly controversial—the one regarding dinosaur metabolics especially so—and some of the first justifications were flawed. But the evidence has piled up. Growth rings in dinosaur bones show they grew at the fast pace not achievable by reptiles, their trackways show they walked at steady speeds too high for bradyaerobes, many small dinosaurs were feathery, and polar dinosaurs, birds and mammals were living through blizzardy Mesozoic winters that excluded ectotherms.
 Because of the dinorevolution our understanding of the evolution of the animals that dominated the continents is far closer to the truth than it was. Energy efficient amphibians and reptiles dominated the continents for only 70 million years in the later portion of the Paleozoic, the era that had begun with trilobites and nothing on land. For the last 270 million years higher power albeit less energy efficient tachyenergy has reigned supreme on land, starting with protomammalian therapsids near the end of the Paleozoic. When therapsids went belly up early in the Mesozoic (the survivors of the group being the then all small mammals) they were not replaced by lower power dinosaurs for the next 150 million years, but by dinosaurs that quickly took aerobic exercise capacity to even greater levels.
The unusual avian respiratory complex is so effective that some birds fly as high as airliners, but the system did not evolve for flight. That's because the skeletal apparatus for operating air sac ventilated lungs first developed in flightless avepod dinosaurs for terrestrial purposes (some but by no means all offer low global oxygen levels as the selective factor). So the basics of avian energetics appeared in predacious dinosaurs, and only later were used to achieve powered flight. Rather like how internal combustion engines happened to make powered human flight practical, rather than being developed to do so.

National Correspondent, Yahoo News; Ph.D., English, Harvard
Back To The Beginning, The Mere Word
Richard Rorty's transformation of "survival of the fittest" to "whatever survives survives" is not in itself my favorite explanation, though I find it immensely satisfying, but it enacts a wholesome return to language away from the most rococo fantasies of science. In this case, a statement that looks to describe history and biology—controversially, no less—drops into a foundational locution, a tautology. Back to the beginning, the mere Word. Anytime an explanation, for anything, returns us to language, and its dynamics, I'm satisfied. Exhilarated.

Physicist, Atmospheric and Oceanic Scientist; Partner, McKinsey & Company
Fooled By Habits
"Caron non ti crucciare: Vuolsi così colà dove si puote ciò che si vuole, e più non dimandare" ("Charon, do not torment yourself: It is so willed where will and power are one, and ask no more") says Virgil to old Charon, justifiably alarmed by the mortal Dante and his inflated sense of entitlement in attempting to cross the Acheron. And so with that explanation they go on, Virgil and his literary pupil in tow. Or rather they would if Dante didn't decide to faint right there and then, as so often happens during his journey through the great poem.
Explanations are seldom as effective as Virgil's, although arguably they can be somewhat more scientific.I suppose I could have chosen any number of elegant scientific theories, but in truth it is a practitioner's explanation rather than that of a theorist, that I find most compelling. My preferred explanation is actually this: that our own habits tend to distort our perception of our own body and its movement.
Have you ever recorded your own voice, listened to it, and wondered how on earth you never realized you sounded like that? Well, the same is true for movement. Often we don't move the way we think we do.
Start by asking someone some basic questions about their anatomy. For example, ask them where is the joint that attaches their arm to the rest of their skeleton. They will likely point to their shoulder. But, functionally, the clavicle—the "collar bone"—is part of the arm and can move with it. In that sense the arm attaches to the rest of the skeleton at the top of the sternum. Ask them to point to the top of their spine, where their head sits. They will likely indicate some point in the middle of their neck. But the top of the first vertebra, the atlas, actually sits more or less at the height of the tip of their nose or the middle of the ear.
The problem is not just having the wrong mental picture of one's anatomy: the problem is being in the habit of moving as if it that were the right one. As it turns out, most of the time we operate our bodies much in the same way that someone without a driving license would operate a car: with difficulty and often hurting ourselves in the process.
One of the people who famously made this observation was a somewhat eccentric Tasmanian actor by the name of F. M. Alexander, around the turn of the last century. Alexander was essentially an empiricist. The story goes that he lost his voice while reciting Shakespeare. After visiting a number of specialists, who could not figure out what in the world was wrong with him, he eventually concluded that the problem must be something he was doing.
What followed was an impressive exercise in solipsistic sublimation: Alexander spent three years observing himself in a three-way mirror, trying to find out what was wrong. Finally he noticed something: When he would declaim verse, he had an almost imperceptible habit of tensing the back of his neck. Could that small tension, unnoticed up to then, possibly explain the loss of voice? It turned out that it did. Alexander continued to observe and explore, and through this process learnt to recognize and retrain his own movement and the use of his body. His voice returned.
To be fair, the study of the body and its movement has a long and illustrious history, from Muybridge onwards. But the realization that our own perception of it may be inaccurate has practical implications that run deep into our capacity to express ourselves.
This point is familiar to performing artists. Playing the key of a piano requires applying a pressure equivalent to about seventy grams, an almost insignificant weight for a human body a thousand times that. Yet most pianists know well the physical exhaustion that can come with playing. Not only their movement fails to achieve efficiency or effectiveness, but it often does not even reflect what they believe to be doing. Not surprisingly, a substantial part of modern piano training consists of inhibiting habitual behavior, in the hopes of achieving Rubinstein's famous effortlessness.
Musicians are not the only ones for whom the idea of retraining one's proprioception is important. For example, our posture and movement communicate plenty of information to those who see us. When wanting to "stand tall", we push our chests out, lift our chin and face. But we fail to notice that this results in a contraction of the neck muscles and therefore a significant shortening of the back, achieving exactly the opposite result. Actors know this well, and have a long tradition of studying the use of the body, recognizing and inhibiting such habits: you cannot control what to communicate through your posture and movement, if you are already busy communicating existing habits. This insight is, alas, true for most of us.
We are fascinated by the natural world as conceptualized in our elegant explanations, yet the single thing we spend the most time doing—using our body—is rarely the subject of extensive analytical consideration. Simple insights of practitioners like Alexander have depth and meaning because they remind us that analytical observation can tell us a lot, not just about the extraordinary, but also about the ordinary in our daily lives.

Linguist; Cultural Commentator; Senior Fellow, Manhattan Institute; Author, Doing Our Own Thing
How Do You Get From A Lobster To A Cat?
Did you ever notice that the "vein" you are told, for some reason, to remove from shrimp before eating them doesn't seem to ooze anything you'd be inclined to call blood? Doesn't the slime seem more like some sort of alimentary waste? That's because it is. In shrimp, you can get at the digestive system right through its back because that's where it is. The heart's up there too, and this is the way it is in arthropods, the animal phylum that includes crustaceans and insects. Meanwhile, if you were interested in finding the shrimp's main nerve highway, you'd find it running down along its bottom side.
That feels backwards to us, because we're chordates, another big animal phylum. Chordates have the spinal nerve running down the back, with the gut and heart up in front. It's as if our body plans were mirror images of arthropods', and this is a microcosm of a general split between larger classes: arthropods are among the protostomes, with the guts on the back, as opposed to the deuterostomes that we chordates are among, with the guts up front.
Biologists have noticed this since auld lang sine, with naturalist Étienne Geoffroy Saint-Hilaire famously turning a dissected lobster upside down and showing that as such, its innards' arrangement resembled ours. The question was how things got this way, especially as Darwin's natural selection theory became accepted. How could one get step-by-step from guts on the back and the spinal chord up front to the reverse situation? More to the point, why would this be evolutionarily advantageous, which is the only reason we assume it would happen at all?
Short of imagining that the nerve chord glommed upward and took over the gut and a new gut spontaneously developed down below because it was "needed"—this was actually entertained for a while by one venturesome thinker—the best biologists could do for a long time was suppose that the arthropod plan and the chordate plan were alternative pathways of evolution from some primordial creature. It must have just been a matter of the roll of the dice coming out differently one time than the next one, they thought.
Not only was this boring—the problem was that molecular biology started making it ever clearer that arthropods and chordates trace back to the same basic body plan in a good amount of detail. The shrimp's little segments are generated by the same basic genes that create our vertebral column, and so on. Which leads to the old question again—how do you get from a lobster to a cat? Biologists are converging upon an answer that combines elegance with a touch of mystery while occasioning a scintilla of humility in the bargain.
Namely, what is increasingly thought to have happened is that some early worm-like aquatic creature with the arthropod-style body plan started swimming upside-down. Creatures can do that: brine shrimp, today, for example (remember those "sea monkeys"?). Often it's because a creature's coloring is different on the top than the bottom, and having the top color face down makes them harder for predators to see. That is, there would have been evolutionary advantage to such a creature gradually turning upside down forever.
But what this would mean is that in this creature, the spinal chord was up and the guts were down. In itself, that's perhaps cute, maybe a little sad, but little more. But—suppose this little worm then evolved into today's chordates? It's hardly a stretch, given that the most primitive chordates actually are wormish, only vaguely piscine things called lancelets. And of course, if you were moved to rip one open you'd see that nerve chord on the back, not the front.
Molecular biology is quickly showing exactly how developing organisms can be signaled either to develop a shrimp-like or a cat-like body plan along these lines. There even seems to be a "missing link"—there are rather vile, smelly bottom-feeding critters called acorn worms that have nerve chords on the back and on the front, and guts that seem on their way to moving on down.
So—the reason we humans have a backbone is not because it's somehow better to have a spinal column to break a fall backwards or anything of the sort. Roll the dice again and we could be bipedals with spinal columns running down our fronts like zippers and the guts carried in the back (it actually doesn't sound half bad). And beyond this, this explanation of what's called dorsoventral inversion is yet more evidence of how under natural selection, such awesome variety can emerge in unbroken fashion from such humble beginnings. And finally, it's hard not to be heartened by a scientific explanation that early adopters, like Geoffroy-St. Hilaire, were ridiculed for espousing.
Quite often when preparing shrimp, tearing open a lobster, contemplating what it would be like to be forced to dissect an acorn worm, patting my cat on the belly, or giving someone a hug, I think a bit about the fact that all of those bodies are built on the same plan, except that the cats' and the huggees' bodies are the legacy of, of all things, some worm swimming the wrong way up in a Precambrian Ocean over 550 million years ago. It has always struck me as rather gorgeous.

Associate Professor of Physics and Astronomy, Dartmouth College
The Gravitational Harmony of Quantum Fields
These three terms are all interconnected in my head. While I was about to quit Grad school in theoretical physics, I stumbled across a quantum field theory book on a classmate's desk which, upon reading the introduction, enticed me to finish up. Let me paraphrase the beginning of the book's intro: "The new paradigm of physics describes the totality of nature as an ensemble vibrating fields that interact with each other… in that sense the universe is like an orchestra and we are a result of eons of harmonies, rhythm and improvisation" (I added in the improvisation part). It helped that I was also a student of jazz theory at the time.
As I continued to study quantum field theory over the years (and now teach the subject), I am amazed at the concise parallels between the quantum field paradigm of nature, music and improvisation. Connected to this theme is one of the coolest things I've learned; an idea that was pioneered by a true master in quantum field theory, Leonard Parker. The basic idea is that when we combine Einstein's discovery that the gravitational force arises from the curving of spacetime with the field paradigm of matter we get a very neat physical effect—which underlies Stephen Hawking's information loss paradox and the emergence of matter from the early universe that is devoid of stars and galaxies.
Last month I had the pleasure to finally meet Parker at the University of Wisconsin, Milwaukee. After a seminar on gravitational wave physics, Leonard took me to his office and revealed the pioneering calculations in his PhD dissertation, which established the study of quantum fields in curved spacetime—I'll refer to the effect as the Parker Process.
In quantum field theory, we can think of all matter as a field (similar to the electromagnetic field) that permeates a large region of space. A useful picture is to imagine a smooth blanket of magnetic fields that fills our entire galaxy (which is actually true). Likewise the electron also has a field that can be distributed across regions of space. At this stage, the field is "classical", since it is a smooth, continuous distribution.
To speak of a quantized field means that we can imagine that if the field vibrates, only discrete bundles (quanta) of vibration are allowed, like an individual musical note on a guitar. The quanta of the field are identified with the creation (or annihilation) of a particle. Quantum field theory has new features that classical field theories lack; perhaps the most important one is the notion of the vacuum. The vacuum is a situation where no particles exist, but one can "disturb" the vacuum and create particles by "exciting" the field (usually with an interaction). It is important to know that the vacuum depends on the space-time location of an observer who can measure no particles.
On the other hand we know from General relativity, space-time is curved and observers don't see the same curvature at different places in general. What Parker realized was that in space-times of cosmological interest, such our expanding universe that Hubble discovered, that existed in a state of zero particles would create particles at a later time due to the very expansion of the space. We can think of this effect occurring because of the wave-like nature of particles (a quantum effect).
The quantum matter fields that live in the vacuum also interact with the expanding space-time field (the gravitational field). The expansion acts on the vacuum in a manner that "squeezes" particle quanta out of the vacuum. It is this quantum-field effect, which is used to explain the seeds of stars, and galaxies that now exist in the universe. Similarly, when black holes evaporate, the space-time also becomes time-dependent and particles are created, but this time as a thermal bath of matter/radiation. This physical feature of quantum fields in curved spaces raise the philosophical questions about the observer dependence of particles or the lack of them.
As you read these words, don't try to imagine some strange observer in some far region of the universe that will swear that you don't exist; and don't blame it on Leonard.

Professor of Astronomy, Harvard University; Director, Harvard Origins of Life Initiative; Author, The Life of Super-Earths
Frames of Reference
Deep and elegant explanations relate to natural or social phenomena and the observer often has no place in them. As a young student I was fascinated to understand how frames of reference work, i.e., to learn what it means to be an observer.
The reference frame concept is central in physics and astronomy. For example, the study of flows relies most often on two basic frames: one in which the flow is described as it moves through space, called an Eulerian frame, and another—called a Lagrangian frame, which moves with the flow, stretching and bending as it goes. The equations of motion in the Eulerian frame seemed intuitively obvious to me, but I felt exhilarated when I understood the same flow described by equations in the Lagrangian frame.
It is beautiful: let's think of a flow of water—a winding river. You are perched on a hill by the riverbank observing the water flow marked by a multitude of floating tree leaves. The banks of the river, the details of the surroundings—they provide a natural coordinate system, just as you would on a geographical map—you could almost create a mental image of fixed criss crossing lines—your frame of reference. The river flow of water moves through that fixed map: you are able to describe the twists and turns of the currents and their changing speed, all thanks to this fixed Eulerian frame of reference, named after Leonhard Euler (1707-1783).
It turns out that you could describe the flow with equal success if, instead of standing safely on the top of the hill, you plunged into the river and floated downstream, observing the whirling motions of the tree leaves all around you. Your frame of reference—the one named after Joseph-Louis Lagrange (1736-1813), is no longer fixed; instead you are describing all motions as relative to you and to each other. Your description of the flow will match exactly the description you achieved by observing from the hill, although the mathematical equations appear unrecognizably different.
To younger me, back then, the transformation between the two frames looked like magic. It was not deep perhaps, but it was elegant, and extremely helpful. However, it was also just the easy start of a journey—a journey that would pull the old frames of reference out from under me. It started with the naïve unmoving Earth as the absolute frame of Aristotle, soon to be rejected and replaced by Galileo with a frame of reference in which motion is not absolute—oh, how I loved floating with Lagrange down Euler's river!, only to be unsettled again by the special relativity of Einstein and trying to comprehend the loss of simultaneity. And a loss it was.
A fundamental shift in our frame of reference, especially the one that defines our place in the world, affects deeply each and every one of us personally. We live and learn, the next generation is born into the new with no attachment to the old. In science it is easy. Human frames of reference go beyond mathematics, physics, and astronomy. Do we know how to transform between human frames of reference successfully? Are they more often than not "Lagrangian" and relative? Perhaps we could take a cue from science and find an elegant solution. Or at least—an elegant explanation.

Brooks and Suzanne Ragen Professor of Psychology, Yale University; Author, How Pleasure Works
Everything Is The Way It Is Because It Got That Way
This aphorism is attributed to the biologist and classicist D'Arcy Thompson, and it's an elegant summary of how Thompson sought to explain the shapes of things, from jellyfish to sand dunes to elephant tusks. I saw this quoted first in an Edge discussion by Daniel Dennett, who made the point that this insight applies to explanation more generally—all sciences are, to at least some extent, historical sciences.
I think it's a perfect motto for my own field of developmental psychology. Every adult mind has two histories. There is evolution. Few would doubt that some of the most elegant and persuasive explanations in psychology appeal to the constructive process of natural selection. And there is development—how our minds unfold over time, the processes of maturation and learning.
While evolutionary explanations work best for explaining what humans share, development can sometimes capture how we differ. This can be obvious: Nobody is surprised to hear that adults who are fluent in Korean have usually been exposed to Korean when they were children or that adults who practice Judaism have usually been raised as Jews. But other developmental explanations are rather interesting.
There is evidence that an adult's inability to see in stereo is due to poor vision during a critical period in childhood. Some have argued that the self-confidence of adult males is influenced by how young they were when they reached puberty (because of the boost in status caused by being bigger, even if temporarily, than their peers). It's been claimed that smarter adults are more likely to be firstborns (because later children find themselves in environments that are, on average, less intellectually sophisticated). Creative adults are more likely to be later-borns (because they were forced to find their own distinctive niches.) Romantic attachments in adults are influenced by their relationships as children with their parents. A man's pain-sensitivity later in life is influenced by whether or not he was circumcised as a baby.
With the exception of the stereo-vision example, I don't know if any of these explanations are true. But they are elegant and non-obvious, and some of them verge on beautiful.

President, Singularity Institute
We're Apes
Phylogenetically, and in terms of their ecological niche and morphology, apes are less similar to small monkeys than to paleolithic humans. Therefore, absent evidence to the contrary, we should expect that we can predict ape behavior better by looking at paleolithic human behavior than by looking at monkey behavior. This is a testable claim. Naive subjects can try to predict ape behavior by using different pools of evidence, information about either monkeys or paleolithic humans. The amount that one can know about a by observing b is correlated to the amount one can know about b by observing a. This consideration really should narrow the range of hypotheses we consider when speculating upon our innate behavior. If all other apes and monkeys possess a feature, including 'innate behavior' in so far as 'innate behavior' is a valid conceptual construct, we probably also possess that feature.
It may not be much, as a theory of psychology, but it's a start.
While making some correct predictions, this model certainly has its failures. Some of these failures seem relatively unthreatening. For instance, because we eat far less fruit than most monkeys or apes do, we tend to have much lower concentrations of vitamin C in our blood than do other primates. We can explain this difference easily because we can conceive of a clear difference between the concepts 'innate biochemistry' and 'biochemistry'. Other theoretical failures are more perplexing. One might speculate that paleolithic humans lack thick body hair because they use fire. Some day, differences between preserved Habilus and Erectus tissues might even partially confirm this, but one then has to ask why they and Sapiens but no other apes can use fire. Habitat is surely somewhat relevant, as most apes live in very heavily wooded locations, which present difficulties in the use of fire. Other apes also possess generally inferior tool-using abilities when compared to Habilus, Erectus or Sapiens. Most distressing, paleolithic humans tend to produce a much larger range of vocalizations than do other primates, a behavior that seems more typically birdlike.

Information Scientist and Professor of Electrical Engineering and Law, the University of Southern California; Author, Noise
Why The Sun Still Shines
One of the deepest explanations has to be why the sun still shines—and thus why the sun has not long since burned out as do the fires of everyday life. That had to worry some of the sun gazers of old as they watched campfires and forest fires burn through their life cycles. It worried the nineteenth-century scientists who knew that gravity alone could not account for the likely long life of the sun.
It sure worried me when I first thought about it as a child.
The explanation of hydrogen atoms fusing into helium was little comfort. It came at the height of the duck-and-cover cold-war paranoia in the early 1960s after my father had built part of the basement of our new house into a nuclear bomb shelter. The one-room shelter came complete with reinforced concrete and metal windows and a deep freeze packed with homemade TV dinners.
The sun burned so long and so brightly because there were in effect so many mushroom-cloud producing thermonuclear hydrogen-bomb explosions going off inside it and because there was so much hydrogen bomb-making material in the sun. The explosions were just like the hydrogen-bomb explosions that could scorch the earth and that could even incinerate the little bomb shelter if they went off close enough.
The logic of the explanation went well beyond explaining the strategic equilibrium of a nuclear Mexican standoff on a global scale. The good news that the sun would not burn out anytime soon came with the bad news that the sun would certainly burn out in a few billion years. But first it would engulf the molten earth in its red-giant phase.
The same explanation said further that in cosmic due course all the stars would burn out or blow up. There is no free lunch in the heat and light that results when simpler atoms fuse into slightly more complex atoms and when mass transforms into energy. There would not even be stars for long. The universe will go dark and get ever closer to absolute-zero cold. The result will be a faint white noise of sparse energy and matter. Even the black holes will over eons burn out or leak out into the near nothingness of an almost perfect faint white noise. That steady-state white noise will have effectively zero information content. It will be the last few steps in a staggeringly long sequence of irreversible nonlinear steps or processes that make up the evolution of the universe. So there will be no way to figure out the lives and worlds that preceded it even if something arose that could figure.
The explanation of why the sun still shines is deep as it gets. It explains doomsday.

Mathematician and Economist; Principal, Natron Group
Einstein's Revenge: The New Geometric Quantum
The modern theory of the quantum has only recently come to be understood to be even more exquisitely geometric than Einstein's General Relativity. How this realization unfolded over the last 40 years is a fascinating story that has, to the best of my knowledge, never been fully told as it is not particularly popular with some of the very people responsible for this stunning achievement.
To set the stage, recall that fundamental physics can be divided into two sectors with separate but maddeningly incompatible advantages. The gravitational force has, since Einstein's theory of general relativity, been admired for its four dimensional geometric elegance. The quantum, on the other hand encompasses the remaining phenomena, and is lauded instead for its unparalleled precision, and infinite dimensional analytic depth.
The story of the geometric quantum begins at some point around 1973-1974, when our consensus picture of fundamental particle theory stopped advancing. This stasis, known as the 'Standard Model', seemed initially like little more than a temporary resting spot on the relentless path towards progress in fundamental physics, and theorists of the era wasted little time proposing new theories in the expectation that they would be quickly confirmed by experimentalists looking for novel phenomena. But that expected entry into the promised land of new physics turned into a 40-year period of half-mad tribal wandering in an arid desert, all but devoid of new phenomena.
Yet just as particle theory was failing to advance in the mid 1970s, something amazing was quietly happening over lunch at the State University of New York at Stony Brook. There, Nobel physics laureate CN Yang and geometer (and soon to billionaire) Jim Simons had started an informal seminar to understand what, if anything, modern geometry had to do with quantum field theory. The shocking discovery that emerged from these talks was that both geometers and quantum theorists had independently gotten hold of different collections of insights into a common structure that each group had independently discovered for themselves. A Rosetta stone of sorts called the Wu-Yang dictionary was quickly assembled by the physicists, and Isadore Singer of MIT took these results from Stony Brook to his collaborator Michael Atiyah in Oxford where their research with Nigel Hitchin began a geometric renaissance in physics inspired geometry that continues to this day.
While the Stony Brook history may be less discussed by some of today's younger mathematicians and physicists, it is not a point of contention between the various members of the community. The more controversial part of this story, however, is that a hoped for golden era of theoretical physics did not emerge in the aftermath to produce a new consensus theory of elementary particles. Instead the interaction highlighted the strange idea that, just possibly, Quantum theory was actually a natural and elegant self-assembling body of pure geometry that had fallen into an abysmal state of pedagogy putting it beyond mathematical recognition. By this reasoning, the mathematical basket case of quantum field theory was able to cling to life and survive numerous near death experiences in its confrontations with mathematical rigor only because it was being underpinned by a natural infinite dimensional geometry, which is to this day still only partially understood.
In short, most physicists were trying and failing to quantize Einstein's geometric theory of gravity because they were first meant to go in the opposite and less glamorous direction of geometrizing the quantum instead. Unfortunately for Physics, mathematicians had somewhat dropped the ball by not sufficiently developing the geometry of infinite dimensional systems (such as the Standard Model), which would have been analogous to the 4-dimensional Riemannian geometry appropriated from mathematics by Einstein.
This reversal could well be thought of as Einstein's revenge upon the excesses of quantum triumphalism, served ice cold decades after his death: the more researchers dreamed of becoming the Nobel winning physicists to quantize gravity, the more they were rewarded only as mathematicians for what some saw as the relatively remedial task of geometrizing the quantum. The more they claimed that the 'power and glory' of string theory (a failed piece of 1970s sub-atomic physics which has mysteriously lingered into the 21st century) was the 'only game in town', the more it suggested that it was the string theory-based unification claims that, in the absence of testable predictions, were themselves sinking with a glug to the bottom of the sea.
What we learned from this episode was profound. Increasingly, the structure of Quantum Field Theory appears to be a purely mathematical input-output machine where our physical world is but one of many natural inputs that the machine is able to unpack from initial data. In much the way that a simple one-celled human embryo self-assembles into a trillion celled infant of inconceivable elegance, the humble act of putting a function (called an 'action' by physicists) on a space of geometric waves appears to trigger a self-assembling mathematical Rube-Goldberg process which recovers the seemingly intricate features of the formidable quantum as it inexorably unfolds. It also appears that the more geometric the input given to the machine, the more the unpacking process conspires to steer clear of the pathologies which famously afflict less grounded quantum theories. It is even conceivable that sufficiently natural geometric input could ultimately reveal the recent emphasis on 'quantizing gravity' as an extravagant mathematical misadventure distracting from Einstein's dream of a unified physical field. Like genius itself, with the right natural physical input, the new geometric quantum now appears to many mathematicians and physicists to be the proverbial fire that lights itself.
Yet, if the physicists of this era failed to advance the standard model, it was only in their own terms that they went down to defeat. Just as in an earlier era in which physicists retooled to become the first generation of molecular biologists, their viewpoints came to dominate much of modern geometry in the last four decades, scoring numerous mathematical successes that will stand the tests of time. Likewise their quest to quantize gravity may well have backfired, but only in the most romantic and elegant way possible by instead geometrizing the venerable quantum as a positive externality.
But the most important lesson is that, at a minimum, Einstein's minor dream of a world of pure geometry has largely been realized as the result of a large group effort. All known physical phenomena can now be recognized as fashioned from the pure, if still heterogeneous, marble of geometry through the efforts of a new pantheon of giants. Their achievements, while still incomplete, explain in advance of unification that the source code of the universe is overwhelmingly likely to determine a purely geometric operating system written in a uniform programming language. While that leaves Einstein's greater quest for the unifying physics unfinished, and the marble something of a disappointing patchwork of motley colors, it suggests that the leaders during the years of the Standard Model stasis have put this period to good use for the benefit of those who hope to follow.

Managing Director, Digital Science, Macmillan Publishers Ltd.; Former Publisher, Nature.com; Co-Organizer, Sci Foo
Feynman's Lifeguard
I would like to propose not only a particular explanation, but also a particular exposition and exponent: Richard Feynman's lectures on quantum electrodynamics (QED) delivered at the University of Auckland in 1979. These are surely among the very best ever delivered in the history of science.
For a start, the theory is genuinely profound, having to do with the behaviour and interactions of those (apparently) most fundamental of particles, photons and electrons. And yet it explains a huge range of phenomena, from the reflection, refraction and diffraction of light to the structure and behaviour of electrons in atoms and their resultant chemistry. Feynman may have been exaggerating when he claimed that QED explains all of the phenomena in the world "except for radioactivity and gravity", but only slightly.
Let me give a brief example. Everyone knows that light travels in straight lines—except when it doesn't, such as when it hits glass or water at anything other than a right angle. Why? Feynman explains that light always takes the path of least time from point to point and uses the analogy of a lifeguard racing along a beach to save a drowning swimmer. (This being Feynman, the latter is, of course, a beautiful girl.) The lifeguard could run straight to the water's edge and then swim diagonally along the coast and out to sea, but this would result in a long time spent swimming, which is slower than running on the beach. Alternatively, he could run to the water's edge at the point nearest to the swimmer, and dive in there. But this makes the total distance covered longer than it needs to be. The optimum, if his aim is to reach the girl as quickly as possible, is somewhere in between these two extremes. Light, too, takes such a path of least time from point to point, which is why it bends when passing between different materials.
He goes on to reveal that this is actually an incomplete view. Using the so-called 'path integral formulation' (though he avoids that ugly term), Feynman explains that light actually takes every conceivable path from one point to another, but most of these cancel each other out, and the net result is that it appears to follow only the single path of least time. This also happens to explain why uninterrupted light (along with everything else) travels in straight lines—so fundamental a phenomenon that surely very few people even consider it to be in need of an explanation. While at first sight such a theory may seem preposterously profligate, it achieves the welcome result of minimising that most scientifically unsatisfactory of all attributes: arbitrariness.
My amateurish attempts at compressing and conveying this explanation have perhaps made it sound arcane. But on the contrary, a second reason to marvel is that it is almost unbelievably simple and intuitive. Even I, an innumerate former biologist, came away not merely with a vague appreciation that some experts somewhere had found something novel, but that I was able to share directly in this new conception of reality. Such an experience is all too rare in science generally, but in the abstract, abstruse world of quantum physics is all but unknown. The main reason for this perspicacity was the adoption of a visual grammar (those famous 'Feynman diagrams') and an almost complete eschewal of hardcore mathematics (the fact that the spinning vectors that are central to the theory actually represent complex numbers seems almost incidental). Though the world it introduces is as unfamiliar as can be, it makes complete sense in its own bizarre terms.

Founder of field of Evolutionary Psychology; Co-director, Center for Evolutionary Psychology, Professor of Anthropology, UC Santa Barbara
Falling Into Place: Entropy, Galileo's Frames of Reference, and the Desperate Ingenuity Of Life
The hardest choice I had to make in my early scientific life was whether to give up the beautiful puzzles of quantum mechanics, nonlocality, and cosmology for something equally arresting: To work instead on reverse engineering the code that natural selection had built into the programs that made up our species' circuit architecture. In 1970, the surrounding cultural frenzy and geopolitics made first steps toward a nonideological and computational understanding of our evolved design, "human nature", seem urgent; the recent rise of computer science and cybernetics made it seem possible; the almost complete avoidance of and hostility to evolutionary biology by behavioral and social scientists had nearly neutered those fields, and so made it seem necessary.
What finally pulled me over was that the theory of natural selection was itself such an extraordinarily beautiful and elegant inference engine. Wearing its theoretical lenses was a permanent revelation, populating the mind with chains of deductions that raced like crystal lattices through supersaturated solutions. Even better, it starts from first principles (such as set theory and physics), so much of it is nonoptional.
But still, from the vantage point of physics, beneath natural selection there remained a deep problem in search of an explanation: The world given to us by physics is unrelievedly bleak. It blasts us when it is not burning us or invisibly grinding our cells and macromolecules until we are dead. It wipes out planets, habitats, labors, those we love, ourselves. Gamma ray bursts wipe out entire galactic regions; supernovae, asteroid impacts, supervolcanos, and ice ages devastate ecosystems and end species. Epidemics, strokes, blunt force trauma, oxidative damage, protein cross-linking, thermal noise-scrambled DNA—all are random movements away from the narrowly organized set of states that we value, into increasing disorder or greater entropy. The second law of thermodynamics is the recognition that physical systems tend to move toward more probable states, and in so doing, they tend to move away from less probable states (organization) on their blind toboggan ride toward maximum disorder.
Entropy, then, poses the problem: How are living things at all compatible with a physical world governed by entropy, and, given entropy, how can natural selection lead over the long run to the increasing accumulation of functional organization in living things? Living things stand out as an extraordinary departure from the physically normal (e.g., the earth's metal core, lunar craters, or the solar wind). What sets all organisms—from blackthorn and alder to egrets and otters—apart from everything else in the universe is that woven though their designs are staggeringly unlikely arrays of highly tuned interrelationships—a high order that is highly functional. Yet as highly ordered physical systems, organisms should tend to slide rapidly back toward a state of maximum disorder or maximum probability. As the physicist Erwin Schrödinger put it, "It is by avoiding the rapid decay into the inert state that an organism appears so enigmatic."
The quick answer normally palmed off on creationists is true as far as it goes, but it is far from complete: The earth is not a closed system; organisms are not closed systems, so entropy still increases globally (consistent with the second law of thermodynamics) while (sometimes) decreasing locally in organisms. This permits but does not explain the high levels of organization found in life. Natural selection, however, can (correctly) be invoked to explain order in organisms, including the entropy-delaying adaptations that keep us from oxidizing immediately into a puff of ash.
Natural selection is the only known counterweight to the tendency of physical systems to lose rather than grow functional organization—the only natural physical process that pushes populations of organisms uphill (sometimes) into higher degrees of functional order. But how could this work, exactly?
It is here that, along with entropy and natural selection, the third of our trio of truly elegant scientific ideas can be adapted to the problem: Galileo's brilliant concept of frames of reference, which he used to clarify the physics of motion.
The concept of entropy was originally developed for the study of heat and energy, and if the only kind of real entropy (order/disorder) was the thermodynamic entropy of energy dispersal then we (life) wouldn't be possible. But with Galileo's contribution one can consider multiple kinds of order (improbable physical arrangements), each being defined with respect to a distinct frame of reference.
There can be as many kinds of entropy (order/disorder) as there are meaningful frames of reference. Organisms are defined as self-replicating physical systems. This creates a frame of reference that defines its kind of order in terms of causal interrelationships that promote the replication of the system (replicative rather than thermodynamic order). Indeed, organisms must be physically designed to capture undispersed energy, and like hydroelectric dams using waterfalls to drive turbines, they use this thermodynamic entropic flow to fuel their replication, spreading multiple copies of themselves across the landscape.
Entropy sometimes introduces copying errors into replication, but injected disorder in replicative systems is self-correcting. By definition the less well-organized are worse at replicating themselves, and so are removed from the population. In contrast, copying errors that increase functional order (replicative ability) become more common. This inevitable ratchet effect in replicators is natural selection.
Organisms exploit the trick of deploying different entropic frames of reference in many diverse and subtle ways, but the underlying point is that what is naturally increasing disorder (moving toward maximally probable states) for one frame of reference inside one physical domain can be harnessed to decrease disorder with respect to another frame of reference. Natural selection picks out and links different entropic domains (e.g., cells, organs, membranes) that each impose their own proprietary entropic frames of reference locally.
When the right ones are associated with each other, they do replicative work through harnessing various types of increasing entropy to decrease other kinds of entropy in ways that are useful for the organism. For example: oxygen diffusion from the lungs to the blood stream to the cells is the entropy of chemical mixing—falling toward more probable high entropy states, but increasing order from the perspective of replication-promotion.
Entropy makes things fall, but life ingeniously rigs the game so that when they do they often fall into place.

Physicist, MIT; Researcher, Precision Cosmology; Scientific Director, Foundational Questions Institute
Our Universe Grew Like A Baby
What caused our Big Bang? My favorite deep explanation is that our baby universe grew like a baby human—literally. Right after your conception, each of your cells doubled roughly daily, causing your total number of cells to increase day by day as 1, 2, 4, 8, 16, etc. Repeated doubling is a powerful process, so your Mom would have been in trouble if you'd kept doubling your weight every day until you were born: after nine months (about 274 doublings), you would have weighed more than all the matter in our observable universe combined.
Crazy as it sounds, this is exactly what our baby universe did according to the inflation theory pioneered by Alan Guth and others: starting out with a speck much smaller and lighter than an atom, it repeatedly doubled its size until it was more massive than our entire observable universe, expanding at dizzying speed. And it doubled not daily but almost instantly. In other words, inflation created our mighty Big Bang out of almost nothing, in a tiny fraction of a second. By the time you reached about 10 centimeters in size, your expansion had transitioned from accelerating to decelerating. In the simplest inflation models, our baby universe did the same when it was about 10 centimeters in size, its exponential growth spurt slowing to a more leisurely expansion where hot plasma diluted and cooled and its constituent particles gradually coalesced into nuclei, atoms, molecules, stars and galaxies.
Inflation is like a great magic show—my gut reaction is: "This can't possibly obey the laws of physics!'' 
Yet under close enough scrutiny, it does. For example, how can one gram of inflating matter turn into two grams when it expands? Surely, mass can't just be created from nothing? Interestingly, Einstein offered us a loophole through his special relativity theory, which says that energy E and mass m are related according to the famous formula E=mc², where c is the speed of light.
This means that you can increase the mass of something by adding energy to it. For example, you can make a rubber band slightly heavier by stretching it: you need to apply energy to stretch it, and this energy goes into the rubber band and increases its mass. A rubber band has negative pressure because you need to do work to expand it. Similarly, the inflating substance has to have negative pressure in order to obey the laws of physics, and this negative pressure has to be so huge that the energy required to expand it to twice its volume is exactly enough to double its mass. Remarkably, Einstein's theory of General Relativity says that this negative pressure causes a negative gravitational force. This in turn causes the repeated doubling, ultimately creating everything we can observe from almost nothing.
To me, the hallmark of a deep explanation is that it answers more than you ask. And inflation has proven to be the gift that keeps on giving, churning out answer after answer. It explained why space is so flat, which we've measured to about 1% accuracy. It explained why on average, our distant universe looks the same in all directions, with only 0.002% fluctuations from place to place. It explained the origins of these 0.002% fluctuations as quantum fluctuations stretched by inflation from microscopic to macroscopic scales, then amplified by gravity into today's galaxies and cosmic large scale structure. It even explained the cosmic acceleration that nabbed the 2011 physics Nobel Prize as inflation restarting, in slow motion, doubling the size of our universe not every split second but every 8 billion years, transforming the debate from whether inflation happened or not to whether it happened once or twice.
It's now becoming clear that inflation is an explanation that doesn't stop—inflating or explaining.
Just as cell division didn't make merely one baby and stop, but a huge and diverse population of humans, it looks like inflation didn't make merely one universe and stop, but a huge and diverse population of parallel universes, perhaps realizing all possible options for what we used to think of as physical constants. Which would explain yet another mystery: the fact that many constants in our own universe are so fine-tuned for life that if they changed by small amounts, life as we know it would be impossible—there would be no galaxies or no atoms, say. Even though most of the parallel universes created by inflation are stillborn, there will be some where conditions are just right for life, and it's not surprising that this is where we find ourselves.
Inflation has given us an embarrassment of riches—and embarrassing it is... Because this infinity of universes has brought about the so-called measure problem, which I view as the greatest crisis facing modern physics. Physics is all about predicting the future from the past, but inflation seems to sabotage this. Our physical world is clearly teeming with patterns and regularities, yet when we try quantifying them to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity.
The problem is that whatever experiment you make, inflation predicts that there will be infinite copies of you obtaining each physically possible outcome in an infinite number of parallel universes, and despite years of tooth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So strictly speaking, we physicists are no longer able to predict anything at all! Our baby universe has grown into an unpredictable teenager.
This is so bad that I think a radical new idea is needed. Perhaps we need to somehow get rid of the infinite. Perhaps, like a rubber band, space can't be expanded ad infinitum without undergoing a big snap? Perhaps those infinite parallel universes get destroyed by some yet undiscovered process, or perchance they're for some reason mere mirages? The very deepest explanations don't just provide answers, but also questions. I think inflation still has some explaining left to do!

Professor of Philosophy at Birkbeck College, University of London, and a Supernumerary Fellow of St Anne's College, Oxford; Author, The Good Book: A Humanist Bible
Russell's Theory of Descriptions
My favourite example of an elegant and inspirational theory in philosophy is Russell's Theory of Descriptions. It did not prove definitive, but it prompted richly insightful trains of enquiry into the structure of language and thought.
In essence Russell's theory turns on the idea that there is logical structure beneath the surface forms of language, which analysis brings to light; and when this structure is revealed we see what we are actually saying, what beliefs we are committing ourselves to, and what conditions have to be satisfied for the truth or falsity of what is thus said and believed.
One example Russell used to illustrate the idea is the assertion 'the present King of France is bald,' said when there is no King of France. Is this assertion true or false? One response might be to say that it is neither, since there is no King of France at present. But Russell wished to find an explanation for the falsity of the assertion which did not dispense with bivalence in logic, that is, the exclusive alternative of truth and falsity as the only two truth-values.
He postulated that the underlying form of the assertion consists in the conjunction of three logically more basic assertions: (a) there is something that has the property of being King of France, (b) there is only one such thing (this takes care of the implication of the definite article 'the') (c) and that thing has the further property of being bald. In the symbolism of first-order predicate calculus, which Russell took to be the properly unambiguous rendering of the assertion's logical form (I omit strictly correct bracketing so as not to clutter):
(Ex)Kx & [(y)Ky— >y=x] & Bx
which is pronounced 'there is an x such that x is K; and for anything y, if y is K then y and x are identical (this deals logically with 'the' which implies uniqueness); and x is B,' where K stands for 'has the property of being King of France' and B stands for 'has the property of being bald.' 'E' is the existential quantifier 'there is...' or 'there is at least one...' and '(y)' stands for the universal quantifier 'for all' or 'any.'
One can now see that there are two ways in which the assertion can be false; one is if there is no x such that x is K, and the other is if there is an x but x is not bald. By preserving bivalence and stripping the assertion to its logical bones Russell has provided what Frank Ramsey wonderfully called 'a paradigm of philosophy.'
To the irredeemable sceptic about philosophy all this doubtless looks like 'drowning in two inches of water' as the Lebanese say; but in fact it is in itself an exemplary instance of philosophical analysis, and it has been very fruitful as the ancestor of work in a wide range of fields, ranging from the contributions of Wittgenstein and W. V. Quine to research in philosophy of language, linguistics, psychology, cognitive science, computing and artificial intelligence.

Theoretical Physicist; University of the Mediterraneum, Marseille; Author, The First Scientist: Anaximander and His Legacy
How Apparent Finality Can Emerge
Darwin, no doubt. The beauty and the simplicity of his explanation is astonishing. I am sure that others have pointed out Darwin as their favorite deep, elegant, beautiful explanation, but I still want to emphasize the general reach of Darwin's central intuition, which goes well beyond the already monumental result of having clarified that we share the same ancestors with all living beings on Earth, and is directly relevant to the very core of the entire scientific enterprise.
Shortly after the ancient greek "physicists" started to develop naturalistic explanations of Nature, a general objection came forward. The objection is well articulated in Plato, for instance in the Phaedon, and especially in Aristotle discussion of the theory of the "causes". Naturalistic explanations rely on what Aristotle called the "the efficient cause", namely past phenomena producing effects. But the world appears to be dominated by phenomena that can be understood in terms of "final causes", namely an "aim" or a "purpose". These are evident in the kingdom of life. We have the mouth "so we can" eat. The importance of this objection cannot be underestimated. It is this objection that brought down ancient naturalism and in the minds of many it is still today the principal source of psychological resistance against a naturalistic understanding of the world.
Darwin has discovered the spectacularly simple mechanism where efficient causes can produce phenomena that appear to be governed by final causes: anytime we have phenomena that can reproduce, the actual phenomena that we observe are those that keep reproducing, and therefore are necessarily those better at reproducing, and we can thus read them in terms of final causes. In other words, a final cause can be effective to understanding the world because it is a shortcut for accounting the past history of a continuing phenomenon.
To be sure, the idea has appeared before. Empedocles discusses the idea that the apparent finality in the living kingdom could be the result of selected randomness, and Aristotle himself in his "Physics" mentions a version of this idea for species ("seeds"). But the times where not yet ripe, and the suggestion was lost in the following religious ages. I think that the resistance against Darwin is not just the difficulty of seeing the power of a spectacularly beautiful explanation: it is the fear of realizing the extraordinary power that such an explanation has in shattering rests of old world views.

Neuroscientist; Chairman, Board of Directors Human Science Center; Department of Medical Psychology, Munich University; Author, Mindworks
Trusting Trust
After many years
A little gift to Edge
From the first culture.
Using the Haiku
Five seven five syllables
To express a thought.
Searching for beauty
To explain the unexplained
Why should I do this?
What is my problem?
I don't need explanations!
I'm happy without!
A new morning comes
I wake up leaving my dreams
And I don't know why.
I don't understand
Why I can trust my body
In day and in night.
Looking at the moon
Always showing the same face
But I don't know why!
Must I explain this?
Some people certainly can.
Beyond my power!
I look at a tree.
But is there in fact a tree?
I trust in my eyes.
 But why do I trust?
Not understanding my brain
Being too complex.
Looking for answers
Searching for explanations
But living without.
Trust in my percepts
And trust in my memories
Trust in my feelings.
Where does it come from
This absolute certainty
This trust in the world?
Trusting in the future
Making plans for tomorrow,
Why do I believe?
I have no answer!
Knowledge is not sufficient.
Only questions count.
What is a question?
That is the real challenge!
Finding a new path.
But trust is required
Believing the new answers
Hiding in a shadow.
Deep explanations
Rest in the trust of answers
Which is unexplained.
Is there a way out?
Evading the paradox?
This answer is no!
The greatest challenge:
Accepting the present,
Giving no answers!

Professor of Geography, UCLA; Author, The World in 2050
For me, the answer to this year's Edge question is clear: The Continuity Equations.
These are already familiar to you, at least in anecdotal form. Most everyone has heard of the law of "Conservation of Mass" (sometimes using the word "matter" instead of mass) and probably its partner "Conservation of Energy" too. These laws tell us that for practical, real-world (i.e. non-quantum, non-general relativity) phenomena, matter and energy can never be created or destroyed, only shuffled around. That concept has origins tracing at least as far back as the ancient Greeks, was formally articulated in the 18th century (a major advance for modern chemistry), and today underpins virtually every aspect of the physical, life, and natural sciences. Conservation of Mass (matter) is what finally quashed the alchemists' quest to transform lead to gold; Conservation of Energy is what consigns the awesome power of a wizard's staff to the imaginations of legions of Lord of the Rings fans.
The Continuity Equations take these laws an important step further, by providing explicit mathematical formulations that track the storage and/or transfers of mass (Mass Continuity) and energy (Energy Continuity) from one compartment or state to another. As such, they are not really a single pair of equations but instead written into a variety of forms, ranging from the very simple to the very complex, in order to best represent the physical/life science/natural world phenomenon they are supposed to describe. The most elegant forms, adored by mathematicians and physicists, have exquisite detail and are therefore the most complex. A classic example is the set of Navier-Stokes equations (sometimes called the Saint-Venant equations) used to understand the movements and accelerations of fluids. The beauty of Navier-Stokes lies in their explicit partitioning and tracking of mass, energy and momentum through space and time. However, in practice such detail also makes them difficult to solve, requiring either hefty computing power or simplifying assumptions to be made to the equations themselves.
But the power of the Continuity Equations is not limited to complex forms comprehensible solely to mathematicians and physicists. A forest manager, for example, might use a simple, so-called "mass balance" form of a mass continuity equation to study her forest, by adding up the number, size, and density of trees, the rate at which seedlings establish, and subtracting the trees' mortality rate and number of truckloads of timber removed to learn if its total wood content (biomass) is increasing, decreasing, or stable. Automotive engineers routinely apply simple "energy balance" equations when, for example, designing a hybrid electric car to recapture kinetic energy from its braking system. None of the energy is truly created or destroyed just recaptured (e.g. from a combustion engine, which got it from breaking apart ancient chemical bonds, which got it from photosynthetic reactions, which got it from the Sun). Any remaining energy not recaptured from the brakes is not really "lost", of course, but instead transferred to the atmosphere as low-grade heat.
The cardinal assumption behind these laws and equations is that mass and energy are conserved (constant) within a closed system. In principle, the hybrid electric car only satisfies energy continuity if its consumption is tracked from start (the Sun) to finish (dissipation of heat into the atmosphere). This a bit cumbersome so it is usually treated as an open system. The metals used in the car's manufacture satisfy mass continuity only if tracked from their source (ores) to landfill. This is more feasible, and such "cradle-to-grave" resource accounting—a high priority for many environmentalists—is thus more compatible with natural laws than our current economic model, which tends to externalize (i.e., assume an open system) such resource flows.
Like the car, our planet, from a practical standpoint, is an open system with respect to energy and a closed system with respect to mass (while it's true that Earth is still being bombarded by meteorites, that input is now small enough to be neglected). The former is what makes life possible: Without the Sun's steady infusion of fresh, external energy, life as we know it would quickly end. An external source is required because although energy cannot be destroyed, it is constantly degraded into weaker, less useful forms in accordance with the 2nd law of thermodynamics (consider again the hybrid-electric car's brake pads—their dissipated heat is of not much use to anyone). The openness of this system is two-way, because Earth also streams thermal infrared energy back out to space.  Its radiation is invisible to us, but to satellites with "vision" in this range of the electromagnetic spectrum the Earth is a brightly glowing orb, much like the Sun.
Interestingly, this closed/open dichotomy is yet another reason why the physics of climate change are unassailable. By burning fossil fuels, we shuffle carbon (mass) out of the subsurface—where it has virtually no interaction with the planet's energy balance—to the atmosphere, where it does. It is well understood that carbon in the atmosphere alters the planet's energy balance (the physics of this have been known since 1893) and without carbon-based and other greenhouse gases our planet would be a moribund, ice-covered rock. Greenhouse gases prevent this by selectively altering the Earth's energy balance in the troposphere (the lowest few miles of the atmosphere, where the vast majority of its gases reside), thus raising the amount of thermal infrared radiation that it emits. Because some of this energy streams back down to Earth (as well as out to space) the lower troposphere warms, to achieve energy balance. Continuity of Energy commands this.
Our planet's carbon atoms, however, are stuck here with us forever—Continuity of Mass commands that too. The real question is what choices will make about how much, and how fast, to shuffle them out the ground. The physics of natural resource stocks, climate change and other problems can often be reduced to simple, elegant, equations—if only we had such masterful tools to dictate their solution.

Director, Cambridge Embodied Cognition and Emotion Laboratory; University Lecturer, Department of Social and Developmental Psychology Cambridge
Embodied Metaphors Unify Perception, Cognition and Action
Philosophers and psychologists grappled with a fundamental question for quite some time: How does the brain derive meaning? If thoughts consist of the manipulation of abstract symbols, just like computers are processing 0s and 1s, then how are such abstract symbols translated into meaningful cognitive representations? This so-called "symbol grounding problem" has now been largely overcome because many findings from cognitive science suggest that the brain does not really translate incoming information into abstract symbols in the first place. Instead, sensory and perceptual inputs from every-day experience are taken in their modality-specific form, and they provide the building blocks of thoughts.
British empiricists such as Locke and Berkeley long ago recognized that cognition is inherently perceptual. But following the cognitive revolution in the 1950ies psychology treated the computer as the most appropriate model to study the mind. Now we know that a brain does not work like a computer. Its job is not to store or process information; instead, its job is to drive and control the actions of the brain's large appendage, the body. A new revolution is taking shape, considered by some to bring an end to cognitivism, and giving way to a transformed kind of cognitive science, namely an embodied cognitive science.
The basic claim is thatthe mind thinks in embodied metaphors. Early proponents of this idea were linguists such as George Lakoff, and in recent years social psychologists have been conducting the relevant experiments, providing compelling evidence. But it does not stop here; there is also a reverse pathway: Because thinking is for doing, many bodily processes feed back into the mind to drive action.
Consider the following recent findings that relate to the very basic spatial concept of verticality. Because moving around in space is a common physical experience, concepts such as "up" or "down" are immediately meaningful relative to one's own body. The concrete experience of verticality serves as a perfect scaffold for comprehending abstract concepts, such as morality: Virtue is up, whereas depravity is down: Good people are "high minded" and "upstanding" citizens, whereas bad people are "underhanded" and the "low life" of society. Recent research by Brian Meier, Martin Sellbom and Dustin Wygant illustrated that research participants are faster to categorize moral words when they are presented in an up location, and immoral words when they are presented in a down location. Thus, people intuitively relate the moral domain to verticality; however, Meier and colleagues also found that peoplewho do not recognize moral norms, namely psychopaths, fail to do so, and do not show this effect.
People not only think of all things good and moral as up, but they also think of God as up, and the Devil as down. Further, those in power are conceptualized as being high up relative to those down below over whom they hover and exert control, as shown by Thomas Schubert.All the empirical evidence suggests that there is indeed a conceptual dimension that leads up, both literally and metaphorically. This vertical dimension that pulls the mind up to considering what higher power there might be is deeply rooted in the very basic physical experience of verticality.
However, verticality not only influences people's representation of what is good, moral and divine, but movement through space along the vertical dimension can even change their moral actions. Larry Sanna, Edward Chang, Paul Miceli and Kristjen Lundberg recently demonstrated that manipulating people's location along the vertical dimension can actually turn them into more "high minded" and "upstanding" citizens. They found that people in a shopping mall who had just moved up an escalator were more likely to contribute to a charity donation box than people who had moved down on the escalator. Similarly, research participants who had watched a film depicting a view from high above, namely flying over clouds seen from an airplane window subsequently showed more cooperative behaviour than participants who had watched a more ordinary, and less "elevating" view from a car window. Thus, being physically elevated induced people to act on "higher" moral values.
The growing recognition that embodied metaphors provide one common language of the mind has lead to fundamentally different ways of studying how people think. For example, under the assumption that the mind functions like a computer psychologists hoped to figure out how people think by observing how they play chess, or memorize lists of random words. From an embodied perspective it is evident that such scientific attempts were hopelessly doomed to fail. Instead, it is increasingly clear that cognitive operations of any creature, including humans, have to solve certain adaptive challenges of the physical environment. In the process, embodied metaphors are the building blocks of perception, cognition, and action. It doesn't get much more simple and elegant than that.

Professor and Chairman of Computer Science, Brandeis University
The Destructive Wrath of the General Purpose Computer
The core elegant explanation at the heart of Computer Science is known as the Church-Turing hypothesis, which is that all models of computing are equivalent to each other in that they are able to run all the same programs. The lemmas are that a fixed piece of hardware can change its personality with a different code, and that there really is no fundamental difference between a Mac and a PC, despite the actors who portray them on TV.
One thing we didn't warn you about was that, in the limit, the general purpose computer is God, whose destructive wrath, following Sodom, Gomorrah, and Katrina, is finally dawning upon us.
The computer is the destroyer of occupations. Every job has become equivalent: sitting in front of a monitor and keyboard, entering or editing information. Doctor, Dentist, CEO, Banker, Broker, Teller, Lawyer, Engineer: Today, they are all sitting in front of their console, with ever more decisions becoming automated.
The computer has destroyed the rewards of art, digitizing all copyrighted work into underground networks of anonymous file-sharing.
The computer has destroyed all gadgets. I remember owning and loving my calculators, radios, walkie-talkies, voice recorders, phones, text pagers, calendars, cameras, walkmen, gameboys, remote controls, and GPS systems. I bought the first pocket computer in Japan in 1984 with a 12 character screen and 4k of memory. Today's pocket computers, misnamed as smartphones, are so powerful that they have destroyed the consumer electronics business by absorbing every unique product as just another app.
The computer is on a path to destroy money. What started as gold and coin has evolved beyond paper and plastic into pure bits. The only essential difference in wealth between the 1% and the 99% is what is recorded in institutional databases, which unfortunately can be easily manipulated by insiders.
Finally—and those in AI have held this thought for a long time—that which makes us uniquely human is also just computable. While the advent of true AI is still far off, as general purpose computers continue to shrink, and the biological interface is perfected, we will become one with our new god. Choose your new religion wisely—Transhumanist, Singulartarian, or the new file-sharing cult recognized in Sweden, Kopimism.

Contributing Editor, Foreign Policy; Syndicated Columnist; Author, The Net Delusion
The Collingridge Dilemma
In 1980 David Collingridge, an obscure academic at the University of Aston in the UK, published an important book called The Social Control of Technology, which set the tone of many subsequent debates about technology assessment.
In it, he articulated what has become known as "The Collingridge dilemma"—the idea that there is always a trade-off between knowing the impact of a given technology and the ease of influencing its social, political, and innovation trajectories.
Collingridge's basic insight was that we can successfully regulate a given technology when it's still young and unpopular and thus probably still hiding its unanticipated and undesireable consequences—or we can wait and see what those consequences are but then risk losing control over its regulation.
Or as Collingridge himself so eloquently put it: "When change is easy, the need for it cannot be foreseen; when the need for change is apparent, change has become expensive, difficult and time consuming."
It's called a "dilemma" for good reasons—Collingridge didn't like this state of affairs and wanted to solve it (mostly by urging us to exert more control over the social life of a given technology).
Still, even unsolved, the Collingridge dilemma is one of the most elegant ways to explain many of the complex ethical and technological quandaries—think drones or automated facial recognition—that plague our globalized world today.

Senior Astrophysicist, Observational Cosmology Laboratory, NASA's Goddard
Cosmic Complexity
What explains the extraordinary complexity of the observed universe, on all scales from quarks to the accelerating universe? My favorite explanation (which I certainly did not invent) is that the fundamental laws of physics produce natural instability, energy flows, and chaos. Some call the result the Life Force, some note that the Earth is a living system itself (Gaia, a "tough bitch" according to Margulis), and some conclude that the observed complexity requires a supernatural explanation (of which we have many). But my dad was a statistician (of dairy cows) and he told me about cells and genes and evolution and chance when I was very small. So a scientist must look for the explanation of how nature's laws and statistics brought us into conscious existence. And how is that seemingly improbable events are actually happening all the time?
Well, the physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity. One of the most common to see is that cooling water vapor below the freezing point produces snowflakes, no two alike, and all complex and beautiful. We see it often so we are not amazed. But physicists have observed so many kinds of these changes from one structure to another (we call them phase transitions) that the Nobel Prize in 1992 could be awarded for understanding the mathematics of their common features.
Now for a few examples of how the laws of nature produce the instabilities that lead to our own existence. First, the Big Bang (what an insufficient name!) apparently came from an instability, in which the "false vacuum" eventually decayed into the ordinary vacuum we have today, plus the most fundamental particles we know, the quarks and leptons. So the universe as a whole started with an instability. Then, a great expansion and cooling happened, and the loose quarks, finding themselves unstable too, bound themselves together into today's less elementary particles like protons and neutrons, liberating a little energy and creating complexity. Then, the expanding universe cooled some more, and neutrons and protons, no longer kept apart by immense temperatures, found themselves unstable and formed helium nuclei. Then, a little more cooling, and atomic nuclei and electrons were no longer kept apart, and the universe became transparent. Then a little more cooling, and the next instability began: gravitation pulled matter together across cosmic distances to form stars and galaxies. This instability is described as a "negative heat capacity" in which extracting energy from a gravitating system makes it hotter—clearly the 2nd law of thermodynamics does not apply here! (This is the physicist's part of the answer to e e cummings' question: what is the wonder that's keeping the stars apart?) Then, the next instability is that hydrogen and helium nuclei can fuse together to release energy and make stars burn for billions of years. And then at the end of the fuel source, stars become unstable and explode and liberate the chemical elements back into space. And because of that, on planets like Earth, sustained energy flows support the development of additional instabilities and all kinds of complex patterns. Gravitational instability pulls the densest materials into the core of the Earth, leaving a thin skin of water and air, and makes the interior churn incessantly as heat flows outwards. And the heat from the Sun, received mostly near the equator and flowing towards the poles, supports the complex atmospheric and oceanic circulations.
And because of that, the physical Earth is full of natural chemical laboratories, concentrating elements here, mixing them there, raising and lowering temperatures, ceaselessly experimenting with uncountable events where new instabilities can arise. At least one of them was the new experiment called Life. Now that we know that there are at least as many planets as there are stars, it is hard to imagine that nature's ceaseless experimentation would not be able to produce Life elsewhere—but we don't know for sure.
And Life went on to cause new instabilities, constantly evolving, with living things in an extraordinary range of environments, changing the global environment, with boom-and-bust cycles, with predators for every kind of prey, with criminals for every possible crime, with governments to prevent them, and instabilities of the governments themselves.
One of the instabilities is that humans demand new weapons and new products of all sort, leading to serious investments in science and technology. So the natural/human world of competition and combat is structured to lead to advanced weaponry and cell phones. So here we are in 2012, with people writing essays and wondering whether their descendents will be artificial life forms travelling back into space. And, pondering what are the origins of those forces of nature that give rise to everything. Verlinde has argued that gravitation, the one force that has so far resisted our efforts at a quantum description, is not even a fundamental force, but is itself a statistical force, like osmosis.
What an amazing turn of events! But after all I've just said, I should not be surprised a bit.

Technology Forecaster; Consulting Associate Professor, Stanford University
Plate Tectonics Elegantly Validates Continental Drift
Plate Tectonics is a breathtakingly elegant explanation of a beautiful theory, continental drift. Both puzzle and answer were hiding in plain sight right under our feet. Generations of globe-twirling school children have noticed that South America's bulge seems to fit in the gulf of Africa, and that Baja California looks like it was cut out of the Mexican mainland. These and other more subtle clues led Alfred Wegner to propose to the German Geological Society in 1912 that the continents had once formed a single landmass. His beautiful theory was greeted with catcalls and scientific brickbats.
The problem was that Wegner's beautiful theory lacked a mechanism. Critics sneeringly pronounced that the lightweight continents could not possibly plow through a dense and unyielding oceanic crust. No one, including Wegner could imagine a force that could cause the continents to move. It didn't help that Wegner was an astronomer poaching in geophysical territory. He would die on an arctic expedition in 1931, his theory out of favor and all but forgotten.
Meanwhile, hints of a mechanism were everywhere, but at once too small and too vast to see with biased eyes. Like ants crawling on a globe, puny humans missed the obvious. It would take the slow arrival of powerful new scientific tools to reveal the hidden forensics of continental drift. Sonar traced mysterious linear ridges running zipper-like along ocean floors. Magnetometers towed over the seabed painted symmetrical zebra-striped patterns of magnetic reversals. Earthquakes betrayed plate boundaries to listening seismographs. And radiometric dating laid out a scale reaching into deep time.
Three decades after Wegner's death, the mechanism of plate tectonics emerged with breathtaking clarity. The continents weren't plowing through anything—they were rafting atop the crust like marshmallows stuck in a sheet of cooling chocolate. And the oceanic crust was moving like a conveyor, with new crust created in mid-ocean spreading centers and old crust subducted, destroyed or crumpled upwards into vast mountain ranges at the boundaries where plates met.
Elegant explanations are the Kuhnian solvent that leaches the glue from old paradigms, making space for new theories to take hold. Plate tectonics became established beyond a doubt in the mid-1960s. Contradictions suddenly made sense, and ends so loose no one thought they were remotely connected came together. Continents were seen for the wanderers they were, the Himalaya were recognized as the result of a pushy Indian plate smashing into its Eurasian neighbor, and it became obvious that an ocean was being born in Africa's Great Rift Valley. Mysteries fell like dominoes before the predictive power of a beautiful theory and its elegant explanation. The skeptics were silenced and Wegner was posthumously vindicated.

Neuroscientist, Stanford University; Author, Monkeyluv
The Simpleton Ant and the Intelligent Ants
The obvious answer should be the double helix. With the incomparably laconic "It has not escaped our notice….," it explained the very mechanism of inheritance. But the double helix doesn't do it for me. By the time I got around to high school biology, the double helix was ancient history, like pepper moths evolving or mitochondria as the power houses of the cell. Watson and Crick—as comforting but as taken for granted as Baskin and Robbins.
Then there's the work of Hubel and Wiesel, which showed that the cortex processes sensations with a hierarchy of feature extraction. In the visual cortex, for example, neurons in the initial layer each receive inputs from a single photoreceptor in the retina. Thus, when one photoreceptor is stimulated, so is "its" neuron in the primary visual cortex. Stimulate the adjacent photoreceptor, and the adjacent neuron activates. Basically, each of these neurons "knows" one thing, namely how to recognize a particular dot of light. Groups of I-know-a-dot neurons then project onto single neurons in the second cortical layer. Stimulate a particular array of adjacent neurons in that first cortical layer and a single second layer neuron activates. Thus, a second layer neuron knows one thing, which is how to recognize, say, a 45 degree angle line of light oriented. Then groups of I-know-a-line neurons send projections on to the next layer.
Beautiful, explains everything—just keep going, cortical layer upon layer of feature extraction, dot to line to curve to collection of curves to…….until there'd be the top layer where a neuron would know one complex, specialized thing only, like how to recognize your grandmother.  And it would be the same in the auditory cortex—first layer neurons knowing particular single notes, second layer knowing pairs of notes….some neuron at the top that would recognize the sound of your grandmother singing along with Lawrence Welk.
It turned out, though, that things didn't quite work this way. There are few "Grandmother neurons" in the cortex (although a 2005 Nature paper reported someone with a Jennifer Aniston neuron). The cortex can't rely too much on grandmother neurons, because that requires a gazillion more neurons to accommodate such inefficiency and overspecialization. Moreover, a world of nothing but grandmother neurons on top precludes making multi-modal associations (e.g., where seeing a particular Monet reminds you of croissants and Debussy's music and the disastrous date you had at an Impressionism show at the Met. Instead, we've entered the world of neural networks.
Switching to a more mundane level of beauty, consider the gastrointestinal tract. In addition to teaching neuroscience, I've been asked to be a good departmental citizen and fill in some teaching holes in our core survey course. Choices: photosynthesis, renal filtration or the gastrointestinal tract. I picked the GI tract, despite knowing nothing about it, since the first two subjects terrified me. Gut physiology turns out to be beautiful and elegant amid a huge number of multi-syllabic hormones and enzymes. As the Gentle Reader knows, the GI tract is essentially a tube starting at the mouth and ending at the anus. When a glop of food distends the tube, the distended area secretes some chemical messenger that causes that part of the tube to start doing something (e.g., contracting rhythmically to pulverize food). But the messenger also causes the part of the tract just behind to stop doing its now-completed task and causes area just ahead to prepare for its job. Like shuttling ships through the Panama Canal's locks, all the way to the bathroom.
Beautiful. But even bowelophiles wouldn't argue that this is deep on a fundamental, universe-explaining level. Which brings me to my selection, which is emergence and complexity, as represented by "swarm intelligence."
Observe a single ant, and it doesn't make much sense, walking in one direction, suddenly careening in another for no obvious reason, doubling back on itself. Thoroughly unpredictable.
The same happens with two ants, a handful of ants. But a colony of ants makes fantastic sense. Specialized jobs, efficient means of exploiting new food sources, complex underground nests with temperature regulated within a few degrees. And critically, there's no blueprint or central source of command—each individual ants has algorithms for their behaviors. But this is not wisdom of the crowd, where a bunch of reasonably informed individuals outperform a single expert. The ants aren't reasonably informed about the big picture. Instead, the behavior algorithms of each ant consist of a few simple rules for interacting with the local environment and local ants. And out of this emerges a highly efficient colony.
Ant colonies excel at generating trails that connect locations in the shortest possible way, accomplished with simple rules about when to lay down a pheromone trail and what to do when encountering someone else's trail—approximations of optimal solutions to the Traveling Salesman problem. This has useful applications. In "ant-based routing," simulations using virtual ants with similar rules can generate optimal ways of connecting the nodes in a network, something of great interest to telecommunications companies. It applies to the developing brain, which must wire up vast numbers of neurons with vaster numbers of connections without constructing millions of miles of connecting axons. And migrating fetal neurons generate an efficient solution with a different version of ant-based routine.
A wonderful example is how local rules about attraction and repulsion (i.e., positive and negative charges) allow simple molecules in an organic soup to occasionally form more complex ones. Life may have originated this way without the requirement of bolts of lightening to catalyze the formation of complex molecules.
And why is self-organization so beautiful to my atheistic self? Because if complex, adaptive systems don't require a blue print, they don't require a blue print maker. If they don't require lightening bolts, they don't require Someone hurtling lightening bolts.

Professor of Physics and Astronomy, UC-Irvine; Novelist, Anomalies
Beautiful, Unreasonable Mathematics
I find most beautiful not a particular equation or explanation, but the astounding fact that we have beauty and precision in science at all. That exactness comes from using mathematics to measure, check and even predict events. The deepest question is, why does this splendor work?
Beauty is everywhere in science. Physics abounds in symmetries and lovely curves, like the parabola we see in the path of a thrown ball. Equations like e+ 1 =0 show that there is exquisite order in mathematics, too.
Why does such beauty exist? That, too, has a beautiful explanation. This may be the most beautiful fact in science.
In 1960, Eugene Wigner published a classic article on the philosophy of physics and mathematics, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Wigner asked, why does mathematics work so well in describing our world? He was unsure.
We use Hilbert spaces in quantum mechanics, differential geometry in general relativity, and in biology difference equations and complex statistics. The role mathematics plays in these theories is also varied. Math both helps with empirical predictions and gives us elegant, economical statements of theories. I can't imagine how we could ever invent quantum mechanics or general relativity without it.
But why is this true? For beautiful reasons? I think so.
Darwin stated his theory of natural selection without mathematics at all, but it can explain why math works for us. It has always seemed to me that evolutionary mechanisms should select for living forms that respond to nature's underlying simplicities. Of course, it is difficult to know in general just what simple patterns the universe has. In a sense they may be like Plato's perfect forms, the geometric constructions such as the circle and polygons. Supposedly we see their abstract perfection with our mind's eye, but the actual world only approximately realizes them. Thinking further in like fashion, we can sense simple, elegant ways to viewing dynamical systems. Here's why that matters.
Imagine a primate ancestor who saw the flight of a stone, thrown after fleeing prey, as a complicated matter, hard to predict. It could try a hunting strategy using stones or even spears, but with limited success, because complicated curves are hard to understand. A cousin who saw in the stone's flight a simple and graceful parabola would have a better chance of predicting where it would fall. The cousin would eat more often and presumably reproduce more as well. Neural wiring could reinforce this behavior by instilling a sense of genuine pleasure at the sight of an artful parabola.
There's a further selection at work, too. To hit running prey, it's no good to ponder the problem for long. Speed drove selection: that primate had to see the beauty fast. This drove cognitive capacities all the harder. Plus, the pleasure of a full belly.
We descend from that appreciative cousin. Baseball outfielders learn to sense a ball's deviations from its parabolic descent, due to air friction and wind, because they are building on mental processing machinery finely tuned to the parabola problem. Other appreciations of natural geometric ordering could emerge from hunting maneuvers on flat plains, from the clever design of simple tools, and the like. We all share an appreciation for the beauty of simplicity, a sense emerging from our origins. Simplicity is evolution's way of saying, this works.
Evolution has primed humans to think mathematicallybecause they struggled to make sense of their world for selective advantage. Those who didn't aren't in our genome.
Many things in nature, inanimate and living, show bilateral, radial, concentric and other mathematically based symmetries. Our rectangular houses, football fields and books spring from engineering constraints, their beauty arising from necessity. We appreciate the curve of a suspension bridge, intuitively sensing the urgencies of gravity and tension.
Our cultures show this. Radial symmetry appears in the mandala patterns of almost every society, from Gothic stoneworks to Chinese rugs. Maybe they echo the sun's glare flattened into two dimensions. In all cultures, small flaws in strict symmetries express artful creativity. So do symmetry breaking particle theories.
Philosophers have three views of the issue: mathematics is objective and real; it arises from our preconceptions; or it is social.
Physicist Max Tegmark argues the first view, that math so well describes the physical world because reality really is completely mathematical. This radical Platonism says that reality is isomorphic to a mathematical structure. We're just uncovering this bit by bit. I hold the second view: we evolved mathematics because it describes the world and promotes survival. I differ from Tegmark because I don't think mathematics somehow generated reality; as Hawking says, what gives fire to the equations, and makes them construct reality?
Social determinists, the third view, think math emerges by consensus. This is true in that we're social animals, but this view also seems to ignore biology, which brought about humans themselves through evolution. Biology generates society, after all.
But how general were our adaptations to our world?
R. Lemarchand and Jon Lomberg have argued in detail that symmetries and other aesthetic principles should be truly universal, because they arise from fundamental physical properties. Aliens orbiting distant stars will still spring from evolutionary forces that reward a deep, automatic understanding of the laws of mechanics. The universe itself began with a Big Bang that can be envisioned as a four-dimensional symmetric expansion; yet without some flaws, so-called anisotropies, in the symmetry of the Big Bang, galaxies and stars would never happen.
Strategies for the Search for Extra-Terrestrial Intelligence, SETI, have assumed this since their beginnings in the early 1960s. Many supposed that interesting properties such as the prime numbers, which do not appear in nature, would figure in schemes to send messages by radio. Primes come from thinking about our mathematical constructions of the world, not directly from that world. So they're evidence for a high culture based on studying mathematics.     
A case for the universality of mathematics is in turn an argument for the universality of aesthetic principles: evolution should shape all of us to the general contours of physical reality. The specifics will differ enormously, of course, as a glance at the odd creatures in our fossil record shows.
Einstein once remarked, "How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?" But it isn't independent—and that's beautiful.

Professor of Quantum Mechanical Engineering, MIT; Author, Programming the Universe
The True Rotational Symmetry of Space
The following deep, elegant, and beautiful explanation of the true rotational symmetry of space comes from the late Sidney Coleman, as presented to his graduate physics class at Harvard. This explanation takes the form of a physical act that you will perform yourself. Although elegant, this explanation is verbally awkward to explain, and physically awkward to perform. It may need to be practised a few times. So limber up and get ready: you are about to experience in a deep and personal way the true rotational symmetry of space!
At bottom, the laws of physics are based on symmetries, and the rotational symmetry of space is one of the most profound of these symmetries. The most rotationally symmetric object is a sphere. So take a sphere such as a soccer—or basket-ball that has a mark, logo, or unique lettering at some spot on the sphere. Rotate the sphere about any axis: the rotational symmetry of space implies that the shape of the sphere is invariant under rotation. In addition, if there is a mark on the sphere, then when you rotate the sphere by three hundred and sixty degrees, the mark returns to its initial position. Go ahead. Try it. Hold the ball in both hands and rotate it by three hundred and sixty degrees until the mark returns.
That's not so awkward, you may say. But that's because you have not yet demonstrated the true rotational symmetry of space. To demonstrate this symmetry requires fancier moves. Now hold the ball cupped in one hand, palm facing up. Your goal is to rotate the sphere while always keeping your palm facing up. This is trickier, but if Michael Jordan can do it, so can you.
The steps are as follows:
Keeping your palm facing up, rotate the ball inward towards your body. At ninety degrees—one quarter of a full rotation—the ball is comfortably tucked under your arm.
Keep on rotating in the same direction, palm facing up. At one hundred and eighty degrees—half a rotation—your arm sticks out in back of your body to keep the ball cupped in your palm.
As you keep rotating to two hundred and seventy degrees—three quarters of a rotation—in order to maintain your palm facing up, your arm sticks awkwardly out to the side, ball precariously perched on top.
At this point, you may feel that it is impossible to rotate the last ninety degrees to complete one full rotation. If you try, however, you will find that you can continue rotating the ball keeping your palm up by raising your upper arm and bending your elbow so that your forearm sticks straight forward. The ball has now rotated by three hundred and sixty degrees—one full rotation. If you've done everything right, however, your arm should be crooked in a maximally painful and awkward position.
To relieve the pain, continue rotating by an additional ninety degrees to one and a quarter turns, palm up all the time. The ball should now be hovering over your head, and the painful tension in your shoulder should be somewhat lessened.
Finally, like a waiter presenting a tray containing the pi'ece de resistance, continue the motion for the final three quarters of a turn, ending with the ball and your arm—what a relief—back in its original position.
If you have managed to perform these steps correctly and without personal damage, you will find that the trajectory of the ball has traced out a kind of twisty figure eight or infinity sign in space, and has rotated around not once but twice. The true symmetry of space is not rotation by three hundred and sixty degrees, but by seven hundred and twenty degrees!
Although this excercise might seem no more than some fancy and painful basketball move, the fact that the true symmetry of space is rotation not once but twice has profound consequences for the nature of the physical world at its most microscopic level. It implies that 'balls' such as electrons, attached to a distant point by a flexible and deformable 'strings,' such as magnetic field lines, must be rotated around twice to return to their original configuration. Digging deeper, the two-fold rotational nature of spherical symmetry implies that two electrons, both spinning in the same direction, cannot be placed in the same place at the same time. This exclusion principle in turn underlies the stability of matter. If the true symmetry of space were rotating around only once, then all the atoms of your body would collapse into nothingness in a tiny fraction of a second. Fortunately, however, the true symmetry of space consists of rotating around twice, and your atoms are stable, a fact that should console you as you ice your shoulder.

Physicist, Harvard University; Author, Warped Passages; Knocking On Heaven's Door
The Higgs Mechanism
The beauty of science—in the long run—is its lack of subjectivity. So answering the question "what is your favorite deep, beautiful, or elegant explanation" can be a little disturbing to a scientist, since the only objective words in the question are "what", "is", "or", and (in an ideal scientific world) "explanation." Beauty and elegance do play a part in science but are not the arbiters of truth. But I will admit that simplicity, which is often confused with elegance, can be a useful guide to maximizing explanatory power.
As for the question, I'll stick to an explanation that I think is extremely nice, relatively simple (though subtle), and which might even be verified within the year. That is the Higgs mechanism, named after the physicist Peter Higgs who developed it. The Higgs mechanism is probably responsible for the masses of elementary particles like the electron. If the electron had zero mass (like the photon), it wouldn't be bound into atoms. If that were the case, none of the structure of our Universe (or of life) would be present. That's not the correct description of our world.
 In any case, experiments have measured the masses of elementary particles and they don't vanish. We know they exist. The problem is that these masses violate the underlying symmetry structure we know to be present in the physical description of these particles. More concretely, if elementary particles had mass from the get-go, the theory would make ridiculous predictions about very energetic particles. For example, it would predict interaction probabilities greater than one.
So there is a significant puzzle. How can particles have masses that have physical consequences and can be measured at low energies but act as if they don't have masses at high energies, when predictions would become nonsensical? That is what the Higgs mechanism tells us. We don't yet know for certain that it is indeed responsible for the origin of elementary particle masses but no one has found an alternative satisfactory explanation.
One way to understand the Higgs mechanism is in terms of what is known as "spontaneous symmetry breaking," which I'd say is itself a beautiful idea. A spontaneously broken symmetry is broken by the actual state of nature but not by the physical laws. For example, if you sit at a dinner table and use your glass on the right, so will everyone else. The dinner table is symmetrical—you have a glass on your right and also to your left. Yet everyone chooses the glass on the right and thereby spontaneously breaks the left-right symmetry that would otherwise be present.
Nature does something similar. The physical laws describing an object called a Higgs field respects the symmetry of nature. Yet the actual state of the Higgs field breaks the symmetry. At low energy, it takes a particular value. This nonvanishing Higgs field is somewhat akin to a charge is spread throughout the vacuum (the state of the universe with no actual particles). Particles acquire their masses by interacting with these "charges." Because this value appears only at low energies, particles effectively have masses only at these energies and the apparent bottleneck to elementary particle masses is apparently resolved.
Keep in mind that the Standard Model has worked extremely well, even without yet knowing for sure if the Higgs mechanism is correct. We don't need to know about the Higgs mechanism to know particles have masses and to make many successful predictions with the so-called Standard Model of particle physics. But the Higgs mechanism is essential to explaining how those masses can arise in a sensible theory. So it is rather significant.
The Standard Model's success nonetheless illustrates another beautiful idea essential to all of physics, which is the concept of an "effective theory." The idea is simply that you can focus on measurable quantities when making predictions and leave understanding the source of those quantities to later research when you have better precision.
Fortunately that time has now come for the Higgs mechanism, or at least the simplest implementation which involves a particle called the Higgs boson. The Large Hadron Collider at CERN near Geneva should have a definitive result on whether this particle exists within this coming year. The Higgs boson is one possible (and many think the most likely) consequence of the Higgs mechanism. Evidence last December pointed to a possible discovery, though more data is needed to know for sure. If confirmed, it will demonstrate that the Higgs mechanism is correct and furthermore tell us what is the underlying structure responsible for spontaneous symmetry breaking and spreading "charge" throughout the vacuum. The Higgs boson would furthermore be a new type of particle (a fundamental boson for those versed in physics terminology) and would be in some sense a new type of force. Admittedly, this is all pretty subtle and esoteric. Yet I (and much of the theoretical physics community) find it beautiful, deep, and elegant.
Symmetry is great. But so is symmetry breaking. Over the years many aspects of particle physics were first considered ugly and then considered elegant. Subjectivity in science goes beyond communities to individual scientists. And even those scientists change their minds over time. That's why experiments are critical. As difficult as they are, results are much easier to pin down than the nature of beauty. A discovery of the Higgs boson will tell us how that is done when particles acquire their masses.

Professor of Mathematical Physics, Tulane University; Coauthor, The Anthropic Cosmological Principle; Author, The Physics of Christianity
Parallel Universes
The most revolutionary, beautiful, elegant, and important idea to be advanced in the past two centuries is the idea that reality is made up of more than one universe. By an infinity of parallel universes, in fact. By "parallel universe" I mean universes exactly like ours, containing individuals exactly like each and every one of us. There are an infinity of Frank Tiplers, individuals exactly like me, each of whom has written an essay entitled "Parallel Universes" each of which is word-for-word identical to the essay you are now reading, and each of these essays is now being read by individuals who are exactly identical to you, the reader. And more: there are other universes which are almost identical to ours, but differ in minor ways: for example, universes in which you the reader (and I the writer!) really did marry that high school sweetheart—and universes in which you didn't if you did in this universe.
A truly mind-boggling idea, because were it to be true, it would infinitely expand reality. It would expand reality infinity more than the Copernican Revolution ever did, because at most, all that Copernicus did was increase the size of this single universe to infinity. The parallel universes concept proposes to multiply that single infinite Copernican universe an infinite number of times. Actually, an uncountable infinity of times.
Several physicists in the early to mid twentieth century independently came up with the parallel universes idea—for instances, the Nobel-Prize-winning physicists Erwin Schrödinger and Murray Gell-Mann—but only a Princeton graduate student named Hugh Everett had the guts to publish, in 1957, the mathematical fact that parallel universes were an automatic consequence of quantum mechanics. That is, if you accept quantum mechanics—and more than a century of experimental evidence says you have to—then you have to accept the existence of the parallel universes.
Like the Copernican Revolution, the Everettian Revolution will take decades before it is accepted by all educated people, and it will take even longer for the full implications of the existence of an infinite number of parallel universes to be worked out. The quantum computer, invented by the Everettian physicist David Deutsch, is one of the first results of parallel universe thinking. The idea of the quantum computer is simple: since the analogues of ourselves in the parallel universes are interested in computing the same thing at the same time, why not share the computation between the universes? Let one of us do part of the calculation, another do another part, and so on with the final result being shared between us all.
Quantum mechanics is only mysterious if one ignores the other universes. For example, the Heisenberg Uncertainly Relations, which in the old days were claimed to be an expression of a breakdown in determinism, are nothing of the kind. The inability to predict the future state of our particular universe is not due to a lack of determinism in Nature, but rather due to the interaction of the other parallel universes with our own universe. The mathematics of Everett shows that if one attempts to measure a particle's position, the interaction of the particle with its analogues in the other universes will make its momentum vary enormously. (This shows, by the way, that the parallel universes are real and detectable: they interact with our own universe.) If one leaves out most of reality when trying to predict the future, then of course one's predictions are going to be incorrect.
In fact, quantum mechanics is actually more deterministic than classical mechanics! It is possible to derive quantum mechanics mathematically from classical mechanics by requiring that classical mechanics be always deterministic—and also be composed of parallel universes. So adding the parallel universes ensures the validity of Albert Einstein's dictum: "God does not play dice with the universe."
Remarkably, the other great scientist of the past two hundred years, Charles Darwin, took the opposite point of view. God, Darwin insisted, does play dice with the universe. In the last chapter of his Variation of Animals and Plants Under Domestication, Darwin correctly pointed out that anyone who truly believes in determinism will not accept his theory of evolution by natural selection acting on "random" mutations. Obviously, because there are no "random" events of any sort. All events—and mutations—are determined. In particular, if it was determined in the beginning of time that I would be here 15 billion years later writing these words, then all previous evolutionary events leading to me, like the evolution of Homo sapiens, necessarily had to occur when they did occur.
So the Everettian Revolution means that we will have to choose between Einstein and Darwin.
Many leading evolutionary biologists have recognized that there is a problem with standard Darwinian theory. For example, Lynn Margulis and Dorian Sagan, in their book Acquiring Genomes, discuss these difficulties, but their own proposed replacement does not quite eliminate the difficulties (as the great evolutionist Ernst Mayr points out in the book's Forward), because they still accept the idea that there is randomness at the microlevel. If one gives up randomness and accepts determinism, there is no reason why speciation must be gradual. It could occur in a single generation. A Homo erectus mother could give birth to a Homo sapiens male-female pair of twins. In his early work on punctuated equilibrium, the famous Harvard evolutionist Stephen J. Gould was attracted to the idea of speciation in a single generation, but he could not imagine a mechanism that would make it work. The determinism that is an implication of the Everettian Revolution provides such a mechanism, and more, shows that this mechanism necessarily is in operation.
The existence of the parallel universes means that we shall have to rethink everything. Which is why I have called this idea the Everettian Revolution.

Founding Editor, 3QuarksDaily.com
Evolutionarily Stable Strategies
My example of a deep, elegant, and beautiful explanation in science is John Maynard Smith's concept of an evolutionarily stable strategy (ESS). Not only does this wonderfully straightforward idea explain a whole host of biological phenomena, it also provides a very useful heuristic tool to test the plausibility of various types of claims in evolutionary biology, allowing us, for example, to quickly dismiss group-selectionist misconceptions such as the idea that altruistic acts by individuals can be explained by the benefits that accrue to the species as a whole from these acts. Indeed, the idea is so powerful that it explains things which I didn't even realize needed explaining until I was given the explanation! I will now present one such explanation below to illustrate the power of ESS. I should note that while Smith developed ESS using the mathematics of game theory (along with collaborators G. R. Price and G. A. Parker), I will attempt to explain the main idea using almost no math.
So, here is a question: think of common animal species like cats, or dogs, or humans, or golden eagles; why do all of them have (nearly) equal numbers of males and females? Why are there not sometimes 30% males in a species and 70% females? Or the other way? Or some other ratio altogether? Why are sex ratios almost exactly 50/50? I, at least, never even considered the question until I read the incredibly elegant explanation.
Let us consider walruses: they exist in the normal 50/50 sex ratio but most walrus males will die virgins. (But almost all females will mate.) Only a few dominant walrus males monopolize most of the females (in mating terms). So what's the point of having all those extra males around, then? They take up food and resources, but in the only thing that matters to evolution, they are useless, because they do not reproduce. From a species point-of-view, it would be better and more efficient if only a small proportion of walruses were males, and the rest were females, in the sense that such a species of walrus would make much more efficient use of its resources and would, according to the logic of group-selectionists, soon wipe out the actual existing species of walrus with the inefficient 50/50 ratio of males to females. So why don't they?
Here's why: because a population of walruses (of course, you can substitute any of the other animals I have mentioned, including humans, for the walruses in this example) with, say, 10% males and 90% females (or any other non-50/50 ratio) would not be stable over a large number of generations. Why not? Remember that, given the 10% males and 90% females of this example, each male is producing about 9 times as many children as any female (by successfully mating with, on average, close to 9 females). Imagine such a population. If you were a male in this kind of population, it would be to your evolutionary advantage to produce more sons than daughters because each son could be expected to produce roughly 9 times as many offspring as any of your daughters. Let me run through some numbers to make it more clear: suppose that the average male walrus fathers 90 children (only 9 of which will be males and 81 females, on average), and the average female walrus mothers 10 baby walruses (only 1 of which will be a male and 9 will be females). Okay?
Here's the crux of the matter: suppose a mutation arose in one of the male walruses (as it well might over a large number of generations) that made it such that this particular male walrus had more Y (male-producing) sperm than X (female-producing) sperm. In other words, the walrus produced sperm that would result in more male offspring than female ones, this gene would spread like wildfire through the described population. Within a few generations, more and more male walruses would have the gene that makes them have more male offspring than female ones, and soon you would get to the 50/50 ratio that we see in the real world.
The same argument applies for females: any mutation in a female that caused her to produce more male offspring in the population of our example (though sex is determined by the sperm, not the egg, there are other mechanisms the female might employ to affect the sex ratio) than female ones, would spread quickly in this population, changing the ratio from 10/90 closer to 50/50 with each subsequent generation until it actually reaches the 50/50 mark. In fact, any significant deviation from the 50/50 ratio will not be evolutionarily stable for this reason, and will through random mutation soon revert to the 50/50 sex ratio.
One can, of course, use a mirror image of this argument to show that a population of 90% males and 10% females would also soon revert to the 50/50 ratio. So having children with any sex ratio other than 50/50 is not an evolutionarily stable strategy for either males or females. And this is just one example of the explanatory power of ESS.

Professor of Psychiatry, Member of the Duke Institute of Brain Sciences
My Favorite Explanation: Why Curry, Wine And Coffee Cure Most Ails
What makes an explanation beautiful? Many elegant explanations in science are those that have been vetted fully but there are just as many beautiful wildly popular explanations where the beauty is just skin deep. I want to give two examples from the field of brain health.
When preliminary mice studies showed that an ingredient in dietary curry spice may have anti-Alzheimer effects, I suspect every vindaloo lover thought that was a beautiful explanation for why India had a low rate of Alzheimer's. But does India really have a low Alzheimer's rate after adjusting for life span and genetic differences? No one really knows.
Likewise when an observational study in the 1990s reported wine drinkers in Bordeaux had lower rates of Alzheimer's, there was a collective "I knew it" from oenophiles.
The latest observational findings now link coffee drinking with lower risk for Alzheimer's, much to the delight of the millions of caffeine addicts.
In reality, neither coffee nor wine nor curry spice have been proven in controlled trials to have any benefits against Alzheimer's. Regardless, the cognitive resonance these "remedies" find with the reader far exceeds the available evidence. One can find similar examples in virtually every field of medicine and science.
I would like to suggest two conditions that might render an explanation unusually beautiful: 1) a ring of truth, 2) confirmation biases. We all favor explanations and test them in a manner that confirms our own beliefs (confirmation bias). A small amount of factual data can be magnified into a beautiful fully proven explanation in one's mind if the right circumstance exist—thus, beauty is in the eye of the beholder. This may occur less often in one's own specialized fields, but we are all vulnerable in fields in which we are less expert in.
Given how often leading scientific explanations are proven wrong in subsequent years, one would do well to bear in mind Santayana's quote that "almost every wise saying has an opposite one, no less wise, to balance it". As for me, I love my curry, coffee and wine but am not yet counting on them to stop Alzheimer's.

Visiting Professor, Center for Maritime System; Author, The Power of the Sea: Tsunamis, Storm Surges, and Our Quest to Predict Disasters
"It Just Is?"
The concept of an indivisible component of matter, something that cannot be divided further, has been around for at least two and half millennia, first proposed by early Greek and Indian philosophers. Democritus called the smallest indivisible particle of matter "átomos" meaning "uncuttable". Atoms were also simple, eternal, and unalterable. But in Greek thinking (and generally for about 2,000 years after) atoms lost out to the four basic elements of Empedocles—fire, air, water, earth—which were also simple, eternal, and unalterable, but not made up of little particles, Aristotle believing those four elements to be infinitely continuous.
Further progress in our understanding of the world based on the concept of atoms had to wait till the 18th century. By that time the four elements of Aristotle had been replaced by 33 elements of Lavoisier based on chemical analysis. Dalton then used the concept of atoms to explain why elements always react in ratios of whole numbers, proposing that each element is made up of atoms of a single type, and that these atoms can combine to form chemical compounds. Of course, by the early 20th century (through the work of Thompson, Rutherford, Bohr and many others) it was realized that atoms were not indivisible and they were thus not the basic units of matter. All atoms were made up of protons, neutrons, and electrons, which took over the title of being the indivisible components (basic building blocks) of matter.
Perhaps because the Rutherford-Bohr model of the atom is now considered transitional to more elaborate models based on quantum mechanics, or perhaps because it evolved over time from the work of many people (and wasn't a single beautiful proposed law), we have forgotten how much about the world can be explained by the concept of protons, neutrons, and electrons—probably more than any other theory ever proposed. With only three basic particles one could explain the properties of 118 atoms/elements and the properties of thousands upon thousands of compounds chemically combined from those elements. A rather amazing feat, and certainly making the Rutherford-Bohr model worthy of being considered a favorite deep, elegant, and beautiful explanation.
Since that great simplification, further developments in our understanding of the physical universe have gotten more complicated, not less. To explain the properties of our three basic particles of matter, we went looking for even-more-basic particles. We ended up needing 12 fermions (6 quarks, 6 leptons) to "explain" the properties of the 3 previously thought-to-be basic particles (as well as the properties of some other particles that were not known to us until we built high energy colliders). And we added 4 other particles, force-carrier particles, to "explain" the 4 basic force fields (electromagnetism, gravitation, strong interaction, and weak interaction) that affect those 3 previously thought-to-be basic particles. Of these 16 now thought-to-be basic particles most are not independently observable (at least at low energies).      
Even if the present Standard Model of particle physics turns out to be true, the question can be asked: "What next?" Every particle (whatever it's level in the hierarchy of particles) will have certain properties or characteristics. When asked "why" quarks have a particular electric charge, color charge, spin, or mass, do we simply say "they just do"? Or do we try to find even-more-basic particles which seem to explain the properties of quarks, and of leptons and bosons? And if so, does this continue on to still-even-more-basic particles? Could that go on forever? Or at some point, when asked the question "why does this particle have these properties", would we simply say "it just does"? At some point would we have to say that there is no "why" to the universe? "It just is."
At what level of our hierarchy of understanding would we resort to saying, "it just is"? The highest (and least understanding) level is religious—the gods of Mount Olympus each responsible for some worldly phenomenon, or the all-knowing monotheistic god creating the world and making everything work by means truly unknowable to humans. In their theories about how the world worked Aristotle and other Greek philosophers incorporated the gods of Mount Olympus (earth, water, fire, and air were all assigned to particular gods), but Democritus and other philosophers were deterministic and materialistic, and they looked for predictable patterns and simple building blocks that might create the complex world they saw around them. Throughout the growth and evolution of scientific thinking there have been various "it just is" moments, where an explanation/theory seems to hit a wall where one might say "it just is", only to have some one else come along and say "maybe not" and goes on to further advance our understanding. But as we get to the most basic questions about our universe (and our existence) the "it just is" answer becomes more likely. One very basic scientific question is whether there will ever be found truly indivisible particles of nature. The accompanying philosophical question is whether there can be truly indivisible particles of nature.
At some level the next group of mathematically derived "particles" may so obviously appear not to be observable/"real", that we will describe them instead as simply entities in a mathematical model that appears to accurately describe the properties of the observable particles in the level above. At which point the answer to the question of why these particles act as described by this mathematical model would be "they just do". How far down we go with such models will probably depend on how much a new level in the model allows us to explain previously unexplainable observed phenomena or to correctly predict new phenomena. (Or perhaps we might be stopped by the model becoming too complex.)
For determinists still unsettled by the probabilities inherent in quantum mechanics or the philosophical question about what would have come before a Big Bang, it is just one more step toward recognizing the true unsolvable mystery of our universe—recognizing it, but maybe still not accepting it; a new much better model could still come along.

Philosopher, Novelist; Author, Betraying Spinoza; 36 Arguments for the Existence of God: A Work of Fiction
An Unresolved (And, Therefore, Unbeautiful) Reaction To The Edge Question
This year's Edge question sits uneasily on a deeper question: Where do we get the idea—a fantastic idea if you stop and think about it—that the beauty of an explanation has anything to do with the likelihood of its being true? What do beauty and truth have to do with each other? Is there any good explanation of why the central notion of aesthetics (fluffy) should be inserted into the central notion of science (rigorous)?
You might think that, rather than being a criterion for assessing explanations, the sense of beauty is a phenomenon to be explained away. Take, for example, our impression that symmetrical faces and bodies are beautiful. Symmetry, it turns out, is a good indicator of health and, consequently, of mate-worthiness. It's a significant challenge for an organism to coordinate the production of its billions of cells so that its two sides proceed to develop as perfect matches, warding off disease and escaping injury, mutation and malnutrition. Symmetrical female breasts, for example, are a good predictor of fertility. As our own lustful genes know, the achievement of symmetry is a sign of genetic robustness, and we find lopsidedness a turnoff. So, too, in regard to other components of human beauty—radiant skin, shining eyes, neotony (at least in women). The upshot is that we don't want to mate with people because they're beautiful, but rather they're beautiful because we want to mate with them, and we want to mate with them because our genes are betting on them as replicators.
So, too, you might think that beauty of every sort is to be similarly explained away, an attention-grabbing epiphenomenon with no substance of its own.  Which brings me to the Edge question concerning beautiful explanations. Is there anything to this notion of explanatory beauty, a guide to choosing between explanatory alternatives, or it just that any explanation that's satisfactory will, for that very reason and no other, strike us as beautiful, beautifully explanatory, so that the reference to beauty is once again without any substance? That would be an explanation for the mysterious injection of aesthetics into science. The upshot would be that explanations aren't satisfying because they're beautiful, but rather they're beautiful because they're satisfying: they strip the phenomenon bare of all mystery, and maybe, as a bonus, pull in further phenomena which can be rendered non-mysterious using the same sort of explanation. Can explanatory beauty be explained away, summarily dismissed by way of an eliminative explanation? (Eliminative explanations are beautiful.)
I'd like to stop here, with a beautiful explanation for explaining away explanatory beauty, but somebody is whispering in my ear. It's that damned Plato. Plato is going on about how there is more in the idea of explanatory beauty than is acknowledged in the eliminative explanation. In particular, he's insisting, as he does in his Timaeus, that the beauty of symmetry, especially as it's expressed in the mathematics of physical laws, cannot be explained away with the legerdemain of the preceding paragraph. He's reproaching the eliminative explanation of explanatory beauty with ignoring the many examples in history when the insistence on the beauty of symmetry led to substantive scientific progress. What was it that led James Clerk Maxwell to his four equations of electromagnetism but his trying to impose mathematical symmetry on the domains of electricity and magnetism? What was it that led Einstein to his equations of gravity but an insistence on beautiful mathematics?
Eliminative explanations are beautiful, but only when they truly and thoroughly explain. So instead of offering an answer to this year's Edge question I offer instead an unresolved (and, therefore, unbeautiful) reaction to the deep question on which it rests.  

Computer Scientist, UC Berkeley, School of Information; Author, Search User Interfaces
Why Programs Have Bugs
From the earliest days of computer programming up through the present, we are faced with the unfortunate reality that the field does not know how to design error-free programs.
Why can't we tame the writing of computer programs to emulate the successes of other areas of engineering? Perhaps the most lyrical thinker to address this question is Fred Brooks, author most famously of the "The Mythical Man-Month."(If one bears in mind that this unfortunately titled book was first published in 1975, it is a bit easier to ignore the sexist language that litters this otherwise fine work; the points Brooks made more than 35 years ago are almost all accurate today except the assumption that all programmers are "he".)
When espousing the joys of programming, Brooks writes:
"The programmer, like the poet, works only slightly removed from pure thought-stuff. He builds his castles in the air, from air, creating by exertion of the imagination. Few media of creation are so flexible, so easy to polish and rework, so readily capable of realizing grand conceptual structures. ... Yet the program construct, unlike the poet's words, is real in the sense that it moves and works, producing visible outputs separate from the construct itself. It prints results, draws pictures, produces sounds, moves arms. The magic of myth and legend has come true in our time."
But this magic comes with the bite of its flip side:
"In many creative activities the medium of execution is intractable. Lumber splits; paints smear; electrical circuits ring. These physical limitations of the medium constrain the ideas that may be expressed, and they also create unexpected difficulties in the implementation.
... Computer programming, however, creates with an exceedingly tractable medium. The programmer builds from pure thought-stuff: concepts and very flexible representations thereof. Because the medium is tractable, we expect few difficulties in implementation; hence our pervasive optimism. Because our ideas are faulty, we have bugs; henour optimism is unjustified."
Just as there is an arbitrarily large number of ways to arrange the words in an essay, a staggering variety of different programs can be written to perform the same function. The universe of possibility is too wide open, too unconstrained, to permit elimination of errors.
There are additional compelling causes of programming errors, most importantly the complexiting of autonomously interacting independent systems with unpredictable inputs, often driven by even more unpredictable human actions interconnected on a world wide network. But in my view the beautfiul explanation is the one about unfettered thought-stuff.

Founder, TED Conference; eg Conference; TEDMED Conferences; Architect, Cartographer; Author, Information Architects
Understanding Is Power
Learning is remembering what you're interested in.
the informed quest
results in understanding
understanding is power

Philosophisches Seminar, Johannes Gutenberg-Universität Mainz; Author, The Ego Tunnel
Simplicity itself
Elegance is more than an aesthetic quality, or some ephemeral sort of uplifting feeling we experience in deeper forms of intuitive understanding. Elegance is formal beauty. And formal beauty as a philosophical principle is one of the most dangerous, subversive ideas humanity has discovered: it is the virtue of theoretical simplicity. Its destructive force is greater than Darwin's algorithm or that of any other single scientific explanation, because it shows us what the depth of an explanation is.
Elegance as theoretical simplicity comes in many different forms. Everybody knows Occam's razor, the ontological principle of parsimony: Entities are not to be multiplied beyond necessity. William of Occam gave us a metaphysical principle for choosing between competing theories: All other things being equal, it is rational to always prefer the theory that makes fewer ontological assumptions about the kinds of entities that really exist (souls, life forces, abstract objects, or an absolute frame of reference like electromagnetic ether). We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances—Isaac Newton formulated this as the First Rule of Reasoning in Philosophy, in his Principia Mathematica. Throw out everything that is explanatorily idle, and then shift the burden of proof to the proponent of a less simple theory. In Albert Einstein's words: The grand aim of all science … is to cover the greatest possible number of empirical facts by logical deductions from the smallest possible number of hypotheses or axioms.
Of course, in today's technical debates new questions have emerged: Why do metaphysics at all? Isn't it simply the number of free, adjustable parameters in competing hypotheses what we should measure? Is it not syntactic simplicity that captures elegance best, say, the number fundamental abstractions and guiding principles a theory makes use of? Or will the true criterion for elegance ultimately be found in statistics, in selecting the best model for a set of data points while optimally balancing parsimony with the "goodness of fit" of a suitable curve? And, of course, for Occam-style ontological simplicity the BIG question always remains: Why should a parsimonious theory more likely be true? Ultimately, isn't all of this rooted in a deeply hidden belief that God must have created a beautiful universe?
I find it fascinating to see how the original insight has kept its force over the centuries. The very idea of simplicity itself, applied as a metatheoretical principle, has demonstrated great power—the subversive power of reason and reductive explanation. The formal beauty of theoretical simplicity is deadly and creative at the same time. It destroys superfluous assumptions whose falsity we just cannot bring ourselves to believe, whereas truly elegant explanations always give birth to an entirely new way of looking at the world. What I would really like to know is this: Can the fundamental insight—the destructive, creative virtue of simplicity—be transposed from the realm of scientific explanation into culture or onto the level of conscious experience? What kind of formal simplicity would make our culture a deeper, more beautiful culture? And what is an elegant mind?

Professor of Computer Science, Cornell University
The Pigeonhole Principle
Certain facts in mathematics feel as though they contain a kind of compressed power—they look innocuous and mild-mannered when you first meet them, but they're dazzling when you see them in action. One of the most compelling examples of such a fact is the Pigeonhole Principle.
Here's what the Pigeonhole Principle says. Suppose a flock of pigeons lands in a group of trees, and there are more pigeons than trees. Then after all the pigeons have landed, at least one of the trees contains more than one pigeon.
This fact sounds obvious, and it is: there are simply too many pigeons, and so they can't each get their own tree. Indeed, if this were the end of the story, it wouldn't be clear why this is a fact that even deserves to be named or noted down. But to really appreciate the Pigeonhole Principle, you have to see some of the things you can do with it.
So let's move on to a fact that doesn't look nearly as straightforward. The statement itself is intriguing, but what's more intriguing is the effortless way it will turn out to follow from the Pigeonhole Principle. Here's the fact: Sometime in the past 4000 years, there have been two people in your family tree—call them A and B—with the property that A was an ancestor of B's mother and also an ancestor of B's father. Your family tree has a "loop", where two branches growing upward from B come back together at A—in other words, there's a set of parents in your ancestry who are blood relatives of each other, thanks to this relatively recent shared ancestor A.
It's worth mentioning a couple of things here. First, the "you" in the previous paragraph is genuinely you, the reader. Indeed, one of the intriguing features of this fact is that I can blithely make such assertions about you and your ancestors, despite the fact that I don't even know who you are. Second, the statement doesn't rely on any assumptions about the evolution of the human race, or the geographic sweep of human history. Here, in particular, are the only assumptions I'll need. (1) Everyone has two biological parents. (2) No one has children after the age of 100. (3) The human race is at least 4000 years old. (4) At most a trillion human beings have lived in the past 4000 years. (Scientists' actual best estimate for (4) is that roughly a hundred billion human beings have ever lived in all of human history; I'm bumping this up to a trillion just to be safe.) All four assumptions are designed to be as uncontroversial as possible; and even then, a few exceptions to the first two assumptions and an even larger estimate in the fourth would only necessitate some minor tweaking to the argument.
Now back to you and your ancestors. Let's start by building your family tree going back 40 generations: you, your parents, their parents, and so on, 40 steps back. Since each generation lasts at most 100 years, the last 40 generations of your family tree all take place within the past 4000 years. (In fact, they almost surely take place within just the past 1000 or 1200 years, but remember that we're trying to be uncontroversial.)
We can view a drawing of your family tree as a kind of "org chart", listing a set of jobs or roles that need to be filled by people. That is, someone needs to be your mother, someone needs to be your father, someone needs to be your mother's father, and so forth, going back up the tree. We'll call each of these an "ancestor role"—it's a job that exists in your ancestry, and we can talk about this job regardless of who actually filled it. The first generation back in your family tree contains two ancestor roles, for your two parents. The second contains four ancestor roles, for your grandparents; the third contains eight roles, for your great-grandparents. Each level you go back doubles the number of ancestor roles that need to be filled, so if you work out the arithmetic, you find that 40 generations in the past, you have more than a trillion ancestor roles that need to be filled.
At this point it's time for the Pigeonhole Principle to make its appearance. The most recent 40 generations of your family tree all took place within the past 4000 years, and we decided that at most a trillion people ever lived during this time. So there are more ancestor roles (over a trillion) than there are people to fill these roles (at most a trillion). This brings us to the crucial point: at least two roles in your ancestry must have been filled by the same person. Let's call this person A.
Now that we've identified A, we're basically done. Starting from two different roles that A filled in your ancestry, let's walk back down the family tree toward you. These two walks downward from A have to first meet each other at some ancestor role lower down in the tree, filled by a person B. Since the two walks are meeting for the first time at B, one walk arrived via B's mother, and the other arrived via B's father. In other words, A is an ancestor of B's mother, and also an ancestor of B's father, just as we wanted to conclude.
Once you step back and absorb how the argument works, you can appreciate a few things. First, in a way, it's more a fact about simple mathematical structures than it is about people. We're taking a giant family tree—yours—and trying to stuff it into the past 4000 years of human history. It's too big to fit, and so certain people have to occupy more than one position in it.
Second, the argument has what mathematicians like to call a "non-constructive" aspect. It never really gave you a recipe for finding A and B in your family tree; it convinced you that they must be there, but very little more.
And finally, I like to think of it as a typical episode in the lives of the Pigeonhole Principle and all the other quietly powerful statements that dot the mathematical landscape—a band of understated little facts that seem to frequently show up at just the right time and, without any visible effort, clean up an otherwise messy situation.

Theoretical Physicist, Dartmouth College; Author, A Tear a the Edge of Creation
Atomism: Reconciling Change with No-Change
In contributing to this volume, I decided to go back to the basics, literally to the beginnings of Western scientific thought. For already in Ancient Greece we find the striving for ideas with beauty and elegance that remains so important to our culture. As we will see, their influence is more than merely historical.
So, back to the late pre-Socratic philosophers we go, to around 450 BCE. (Thus, not quite "pre" Socrates, as he was born c. 469 BCE.) At the time, there were two warring views of reality, which had been developed and refined for some 200 years. On the one hand, the Ionians—Thales of Miletus being the first—claimed that what was essential in Nature was change: nothing was permanent, everything was in flux. "You cannot step in the same river twice," proclaimed Heraclitus of Ephesus (although not in so direct a manner). Later on, Aristotle commented on this view of perpetual change in his Physics: "some say…that all things are in motion all the time, but that this escapes our attention." This Ionian philosophy is known as a philosophy of "becoming," focusing on transformation and the transient nature of natural phenomena.
On the other hand, the Eleatics—Parmenides of Elea being the first—claimed the exact opposite: what is essential is that which doesn't change. So, to find the true nature of things we look for what is permanent. Among the Eleatics we find Zeno, whose famous paradoxes aimed at proving that motion was an illusion. This was a philosophy of "being," focusing on the unchangeable.
If you were an ambitious young philosopher starting out around 450 BCE, what were you to do? Two schools (let's leave the Pythagoreans out), two opposite views of reality. It is here that Leucippus came in, a man who, like Thales, was probably also from Miletus. He and his prolific pupil Democritus came up with a beautifully simple solution to the change vs. no-change dilemma. What if, they reasoned, everything was made from tiny bits of matter, like pieces of a Lego set? The bits are indestructible and indivisible—the eternal atoms, and thus give material existence to the Eleatic notion of "being". On the other hand, the bits can combine in myriad ways, giving rise to the changing shapes and forms of all objects in Nature. So, objects of being combine to forge the changing nature of reality: being and becoming are unified!
Fast forward to the present. Atoms are now very different entities: not indivisible, but made of yet smaller bits. Not uncountable, but with a total number of 94 naturally-occurring and a few others made artificially in labs. Notwithstanding the differences between ancient and modern atoms, the core notions that all objects are made of smaller bits and that the properties of composite objects can be understood studying the properties of these bits—the essence of reductionism— has served science extremely well.
Yet, as science marched on to describe the properties of the elementary bits of matter, the elementary particles, a new notion came to substitute that of small bits, the concept of "field". Nowadays, particles are seen as excitations of underlying fields: electrons are excitations of the electron field, quarks of the quark field, and so on. The fields are fundamental, not the particles. Furthermore, many scientists today express their discontent with reductionism, stating that a more holistic approach to science may open new avenues of understanding. There is much truth to this, since it's impracticable to think that we can understand the behavior of, say, a DNA molecule—a huge entity with hundreds of billions of atoms—by integrating the behavior of each one of its atoms. Matter organizes in different ways at different levels of complexity, and new laws are needed to describe each of these different levels.
Are we then done with Atomism's intellectual inheritance? Not if we look at its essence, as an attempt to reconcile change and no-change, which necessarily coexist. Our modern view of physical reality remains a construction built upon these twin concepts: on the one hand, the material world, made of changing fields, their excitations, and their interactions. On the other, we know that these interactions are ruled by certain laws which, by their very nature, are unchangeable: the laws of nature. Thus, we still understand the world based on the twin pillars of being and becoming, as pre-Socratic philosophers did some two and a half millennia ago. The tools have changed, the rules have changed, but the beauty and elegant simplicity of the idea that change and no-change coexist remains as vivid today as it was then.

Associate Professor of Biology in Harvard's Department of Organismic and Evolutionary Biology; author, Genomic Imprinting and Kinship
The Double Helix
The Double Helix is a strong candidate.

Software Pioneer; Philosopher; Author, "The History of the Future", "Frax—the first Realtime Fractals", "Chron—A Timeline of Literature"
"So Much From So Little? Now That Explains A Lot!"
There is a deep fascination I have been carrying with me for decades now, ever since earliest childhood: the interplay between simplicity and complexity.
Unable to express it verbally at the time, in hindsight it seems clear: they are all about that penultimate question: what is life and how did this world come into existence?
In many stages and phases I discovered a multitude of ideas that are exactly what is called for here: deep, elegant and beautiful explanations of the principles of nature.
Simplicity is embodied in a reductionist form in the YinYang symbol: being black or white.
In other familiar words: To be or not to be.
Those basic elements combined: that is the process spawning diversity, in myriads of forms.
As a youngster I was totally immersed in 'Lego' blocks. There are a handful of basic shapes (never liked the 'special' ones and clamored instead for a bigger box of basics) and you could put them together in arrangements that become houses, ships, bridges...entire towns I had growing up the sides of my little room to the tops of wardrobes. And I sensed it then: there is something deep about this.
A bit later I got into a mechanical typewriter (what a relief to be able to type clearly, my handwriting had always been horrid—the hand not being able to keep up with the thinking... and relished the ability to put together words, sentences, paragraphs. Freezing a thought in a material fashion, putting it on paper to recall later. What's more—to let someone else follow your thinking! I sensed: this is a thing of beauty.
Then I took up playing the piano. The embryonic roots of the software designer of later decades probably shuddered at the interface: 88 unlabeled keys! Irregular intervals of black ones interspersed... and almost the exact opposite of todays "we need to learn this in one minute and no, we never ever look at manuals" attitude. It took months to make any sense of it, but despite the frustrations, it was deeply fascinating. String together a few notes with mysterious un-definable skill and out comes... deeply moving emotion?
So the plot thickens: a few Lego blocks, a bunch of lettershapes or a dozen musical notes... and you take that simplicity of utterly lame elements, put them together...and out pops complexity, meaning, beauty.
Later in the early 70s I delved into the very first generation of large synthesizers and dealt specifically with complex natural sounds being generated from simple unnatural ingredients and processes. By 1977—now in California—it was computer graphics that became the new frontier—and again: seemingly innocent little pixels combine to make ... any image—as in: anything one can imagine. Deep.
In those days I also began playing chess, and carom billiards—simple rules, a few pieces, 3 balls...but no game is ever the same. Not even close. The most extreme example of this became another real fascination: the game of GO. Just single moves of black and white stones, on a plain grid of lines with barely a handful of rules—but a huge variety of patterns emerges. Elegant.
The earliest computing, in the first computer store in the world, Dick Heyser in Santa Monica, had me try something that I had read in SciAm by Martin Gardner: Conway's 'Game of Life'. The literal incarnation of the initial premise: Simplicity reduced to that YinYang: a cell is On or Off, black or white. But there is one more thing added here now: iteration. With just four rules each cell is said to live or die and in each cycle the pattern changes, iteratively. From dead dots on paper, and static pixels on phospor, it sprang to—life! Not only patterns, but blinkers, gliders, even glider guns, heck glider gun canons! Indeed, it is now seen as a true Turing-complete machine. Artificial Life. Needless to say: very deep.
Another example in that vein are of course fractals. Half an inch of a formula, when iterated, is yielding worlds of unimaginably intricate shapes and patterns. It was a great circle closing after 20 years for me to re-examine this field, now flying through them as "frax" on a little iPhone, in realtime and in real awe.
The entire concept of the computer embodies the principles of simple on/off binary codes, much like YinYang, being put together to form still simplistic gates and then flip-flops, counters, all the way to RAM and complex CPU/GPUs and beyond. And now we have a huge matrix computer with billions of elements networked together (namely 'us', including this charming little side corridor called 'Edge'), just a little over
70 years after Zuse's Z3 we reached untold complexity—with no sign of slowing down.
Surely the ultimate example of 'simplexity' is the genetic code—four core elements being combined by simple rules to extreme complex effect—the DNA to build archaea, felis or homo somewhat sapiens.
Someone once wrote on Edge "A great analogy is like...a diagonal frog" which embodies the un-definable art of what constitutes a deep, beautiful or elegant explanation: Finding the perfect example! The lifelong encounters with "trivial ingredients turning to true beauty" recited here are in themselves neither terse mathematical proofs nor eloquently worded elucidations (such as one could quote easily from almost any Nobel laureate's prize-worthy insights).
Instead of the grandeur of 'the big formulas' I felt that the potpourri of AHA!  moments over six decades may be just as close to that holy grail of scientific thinking: to put all the puzzle pieces together in such away that a logical conclusion converges further on... the truth. And I guess one of the pillars of that truth, in my eyes, is the charmingly disarmingly miniscule insight:
 "So much from so little. Now that explains a lot!"

Professor of Ethology, Cambridge University; Co-author, Design for a Life
Subverting Biology
Two years ago I reviewed the evidence on inbreeding in pedigree dogs. Inbreeding can result in reduced fertility both in litter size and sperm viability, devel­opmental disruption, lower birth rate, higher infant mortality, shorter life span, increased expression of inherited disorders and reduction of immune sys­tem function. The immune system is closely linked to the removal of cancer cells from a healthy body and, indeed, reduction of immune system function increased the risk of full-blown tumours. These well-documented cases in domestic dogs confirm what is known from many wild populations of other species. It comes as no surprise, therefore, that a variety of mechanisms render inbreeding less likely in the natural world. One such is the choice of unfamiliar individuals as sexual partners.
Despite all the evidence, the story is more complicated than at first appears and this is where the explanation for what happens has a certain beauty. While inbreeding is generally seen as being undesirable, the debate has become much more nu­anced in recent years. Purging of the genes with seriously damaging ef­fects can carry obvious benefits. This can happen when a population is inbred.Outcrossing, which is usually perceived as advantageous, does carry the possibility that the benefits of purging are un­done by introducing new harmful genes into the population. Furthermore a population adapted to one environment may not do well if crossed with a population adapted to another environment. So a balance is often struck between inbreeding and outbreeding
When the life history of the species demands careful nurturing of the offspring, the parents may go to a lot of trouble to mate with the best partner possible. A mate should be not too similar to oneself but not too dissimilar either. Thirty years I found that Japanese quail of both sexes preferred partners that were first cousins. Subsequent animal studies have suggested that an optimal degree of relatedness is most beneficial to the organism in terms of reproductive success. A study of a human Icelandic population also pointed to the same conclusion. Couples who were third or fourth cousins had a larger number of grandchildren than more closely related or more distantly related partners. Much evidence from humans and non-human animals suggests that the choice of a mate is dependent on experience in early life, with individuals tending to choose partners who are a bit different but not too different from familiar individuals, who are usually but not always close kin.
The role of early experience in determining sexual and social preferences bears on a well-known finding that humans are extremely loyal to members of their own group. They are even prepared to give up their own lives in defence of those with whom they identify. In sharp contrast, they can behave with lethal aggressiveness towards those who are unfamiliar to them. This suggests then a hopeful resolution to the racism and intolerance that bedevils many societies. As people from different countries and ethnic backgrounds become better acquainted with each other, they will be more likely to treat them well, particularly if the familiarity starts at an earlier age. If familiarity leads to marriage the couples may have fewer grandchildren, but that may be a blessing on an over-populated planet. This optimistic principle, generated by knowledge of how a balance has been struck between inbreeding and outbreeding, subverts biology, but it does hold for me considerable beauty.

Senior Scientist, MacroCognition LLC; Author, Sources of Power
Watson and Crick Explain How DNA Carries Genetic Information
In 1953, when James Watson pushed around some two-dimensional cut-outs and was startled to find that an adenine-thymine pair had an isomorphic shape to the guanine-cytosine pair, he solved eight mysteries simultaneously. In that instant he knew the structure of DNA: a helix. He knew how many strands: two. It was a double helix. He knew what carried the information: the nucleic acids in the gene, not the protein. He knew what maintained the attraction: hydrogen bonds. He knew the arrangement: The sugar-phosphate backbone was on the outside and the nucleic acids were in the inside. He knew how the strands match: through the base pairs. He knew the arrangement: the two identical chains ran in opposite directions. And he knew how genes replicated: through a zipper-like process.
The discovery that Watson and Crick made is truly impressive, but I am also interested in what we can learn from the process by which they arrived at their discovery. On the surface, the Watson-Crick story fits in with five popular claims about innovation, as presented below. However, the actual story of their collaboration is more nuanced than these popular claims suggest.
It is important to have clear research goals. Watson and Crick had a clear goal, to describe the structure of DNA, and they succeeded.
But only the first two of their eight discoveries had to do with this goal. The others, arguably the most significant, were unexpected byproducts.
Experience can get in the way of discoveries. Watson and Crick were newcomers to the field and yet they scooped all the established researchers, demonstrating the value of fresh eyes.
However, Watson and Crick as a team actually had more comprehensive expertise than the other research groups. The leading geneticists didn't care about biochemistry; they were just studying the characteristics of genes. The organic chemists who were studying DNA weren't interested in genetics. In contrast Crick had a background in physics, x-ray techniques, protein and gene function. Watson brought to the table biology, phages, and bacterial genetics. Crick was the only crystallographer interested in genes. Watson was the only one coming out of the U.S.-based phage group interested in DNA.
Fixation on theories blinds you to the data. Many of the researchers at the time had been gripped by a flawed belief that proteins carried the genetic information, because DNA seemed too simple with only four bases. That was the handicap that the experienced researchers carried, not their expertise. Watson and Crick, being new to the field, weren't fixated by the protein hypothesis and were excited by new data suggesting that DNA played a central role in genetic information.
On the other hand, excessive reliance on data also carries a penalty because the data can be flawed. Rosalind Franklin was handicapped in her research by earlier results that had mixed dry and wet forms of DNA. She pursued the dry form of DNA, whereas she needed to be studying the wet form. She didn't have the over-arching theory of Watson and Crick that DNA must be a helix, which would have helped her make sense of her own data. She ignored an important photograph for 10 months whereas Watson was struck by its significance as soon as he saw it. As modelers, Watson and Crick benefited from a top-down perspective that helped them judge which kinds of data were important.
Also, Watson and Crick were gripped by a flawed theory of their own. They believed that DNA would be a triple helix, a belief that sent them off in some wrong directions but also provided them with concrete ideas they could test. They were in a "speculate and test" mode rather than trying to keep an open mind.
Pressure for results gets in the way of creativity. No granting agency was sponsoring their research. They didn't have to demonstrate progress in order to get funding renewal.
Actually, the two of them felt enormous pressure to unravel the mystery of DNA, particularly when Linus Pauling showed interest. Unlike Pauling or any of the other research groups, Watson and Crick perceived themselves to be in a frantic race for the prize.
Scientists need to safeguard their reputation for accuracy. Scientific reputations are important. You won't be taken seriously as a scientist if you are seen as doing sloppy research or jumping to unfounded conclusions. For example, Oswald Avery had shown in 1944 that bacterial genes were carried by DNA. But the scientific community thought that Avery's work lacked the necessary controls. He wasn't seen as a careful researcher and his findings weren't given as much credence as they deserved.
However, Watson and Crick weren't highly regarded either. Rosalind Franklin was put off by their eagerness to speculate about questions that would eventually be resolved by carefully gathering data. When Watson and Crick enthusiastically unveiled their triple helix model to her in Cambridge she had little difficulty shooting it down.
I think this last issue is the most important. Too many scientists are very careful not to make errors, not to make claims that later have to be retracted. For many, the ideal is to only announce results that can withstand all criticisms, results that can't possibly be wrong. Unfortunately, the safer the claim, the lower the information value. Watson and Crick embody an opposite tendency, to make the strongest claim that they can defend.

Systems-Level Thinker; Futurist; Applied Genomics Expert; Principal, MS Futures Group; Founder, DIYgenomics
Next Node Foment
Kepler's planetary motion ellipses, Bohr's electron shells, and Watson and Crick's double helix are good examples of bringing a bolt of clarity and explanation to a specific scientific problem. Another level of explanatory power is ideas that are applicable on more of a universal basis to many phenomena thereby making sense of things at a higher order. Some examples of these ideas include: Occam's Razor, the invisible hand, survival of the fittest, the incompleteness theorem, and cellular reprogramming.
Therefore some of the best explanations may have the parameters of being intuitively beautiful and elegant, offering an explanation for the diverse and complicated phenomena found in the natural universe and human-created world, being universally applicable or at least portable to other contexts, and making sense of things at a higher order. Fields like cosmology, philosophy, and complexity theory have already delivered in this exercise: they encompass many other science fields in their scope and explain a variety of micro and macro scale phenomena.
Next node foment is an idea inspired by complexity theory. As large complex adaptive systems move across time and landscape, they periodically cycle between order and chaos, in a dynamic progression of symmetry-attaining and symmetry-breaking. These nodes of symmetry are ephemeral. A moment of symmetry in a dynamic system is unstable because system forces drive progression away from the stuck state of Buridan's ass and back into the search space of chaos towards the next node of symmetry. This is the process of life, of intelligence, of the natural world, and of complex man-made systems. Pressure builds to force innovation in the dynamic process or the system gains entropy and stagnates into a fixed state or death.
A classic example of next node foment can be found in the history of computing paradigms, cycling in and out of symmetry and moving to the next nodes through a process of capacity exhaust, frustration, competition, and innovation. These paradigms have evolved from the electro-mechanical punch card to the relay to the vacuum tube to the transistor to the integrated circuit to whatever is coming next. The threatened end of Moore's law is not a disaster but an invitation for innovation. Creative foment towards the next node is already underway in the areas of block copolymers, DNA nanoelectronics, the biomolecular integration of organic and inorganic materials, 3D circuits, quantum computing, and optical computing.
Another area is energy, as any resource starts to run out (e.g.; wood, whale oil, coal, petroleum), innovators develop new ideas to push the transition. For example, the shifts in the automotive industry in the last few years have been significant, driven by both resource depletion (the 'end of oil') and a political emphasis on energy independence. Some of the entrants competing for the next node paradigm are synthetic biofuels, electric cars, hybrids, and hydrogen fuel-cell cars.
Other classic examples of next node foment and symmetry-breaking behavior can be found in the fields of complexity theory and chaos theory. These include the phases of cosmic expansion, the occurrence of neutrinos, and the chiral structure of proteins and lipids. For example, one benefit of non-equilibrium systems is that they transform energy from the environment into an ordered behavior of a new typethat ischaracterized by symmetry breaking.
Information compression eras is another area of next node foment: the progression from analog to digital and the developing friction for the next era. Analog and digital are modes of modulating information onto the electromagnetic spectrum with increasing efficacy. The next era could be characterized by the even greater effectiveness of electromagnetic spectrum control, particularly moving to multidimensional attribute modulation. Already DNA is a potential alternative encoding system with four and maybe eight combinations instead of the 1s and 0s of the digital era. Terahertz networking and data provenance are early guides in the progress to the next node of information compression.
Part of the beauty of next node foment is that it extends beyond science and technology to a wide range of areas such as philosophy. For example, one of the lesser-known definitions of irony is when individuals experience a sense of dissimulation from a group. This feeling of being dissimulated is that of experiencing an anxious uncanniness about what it means to be a doctor, a Christian, a New Yorker, etc., because the norms of the group no longer hold for the individual. However, it is only by cultivating this anxious uncanniness that the progression to next node can be realized: redefining oneself or the group norms, or starting a new group. As the end of Moore's law is an invitation for innovation, so too is anxious uncanniness an invitation for intellectual growth and cultural evolution.
Next node foment can also be seen in areas of current conflict in scientific theories, where two elegant high-order paradigms with explanative power are themselves in competition, uncomfortable coexistence, or broken symmetry fomenting towards a larger explanatory paradigm. Some examples include a grand unified theory to unify the general theory of relativity with electromagnetism, mathematical theories that include both power laws and randomness, and a behavioral theory of beyond-human level intelligence that includes both computronium and aesthetics (e.g.; does AI do art, solely compute, or is there no distinction at that level of cosmic navel-gazing?).
Next node foment is a novel and effective explanation for many diverse and complicated phenomena found in the natural universe and human-created world. It has intuitive simplicity, beauty, and elegance, wide and perhaps universal applicability, and the ability to make sense of things at a higher order. Next node foment explains natural world phenomena in cosmology, physics, and biology, and human-derived phenomena in the progression of technology innovation, energy eras, information compression eras, and the evolution of culture.

Psychiatrist; Clinical Associate Professor of Psychiatry, NYU School of Medicine
The Dark Matter Of The Mind
There are people who want a stable marriage, yet continue to cheat on their wives.
There are people who want a successful career, yet continue to undermine themselves at work.
Aristotle defined Man as a rational animal. Contradictions like these show that we are not.
All people live with the conflicts between what they want and how they live.
For most of human history we had no way to explain this paradox until Freud's discovery of the unconscious resolved it. Before Freud, we were restricted to our conscious awareness when looking for answers regarding what we knew and felt. All we had to explain incompatible thoughts, feelings and motivations was limited to what we could access in consciousness. We knew what we knew and we felt what we felt. Freud's elegant explanation postulated a conceptual space that is not manifest to us but where irrationality rules. This aspect of the mind is not subject to the constraints of rationality such as logical inference, cause and effect, and linear time. The unconscious explains why presumably rational people live irrational lives.
Critics may take exception as to what Freud believed resides in the unconscious—drives, both sexual and aggressive, defenses, conflicts, fantasies, affects and beliefs—but no one would deny its existence; the unconscious is now a commonplace. How else to explain our stumbling through life, unsure of our motivations, inscrutable to ourselves? I wonder what a behaviorist believes is at play while in the midst of divorcing his third astigmatic redhead.
The universe consists primarily of dark matter. We can't see it, but it has an enormous gravitational force. The conscious mind—much like the visible aspect of the universe—is only a small fraction of the mental world. The dark matter of the mind, the unconscious, has the greatest psychic gravity. Disregard the dark matter of the universe and anomalies appear. Ignore the dark matter of the mind and our irrationality is inexplicable.

Sherrell J. Aston Professor of Psychology at the University of Virginia; Co-author, Social Psychology; Author, Strangers to Ourselves; Redirect
We Are What We Do
My favorite is the idea that people become what they do. This explanation of how people acquire attitudes and traits dates back to the philosopher Gilbert Ryle, but was formalized by the social psychologist Daryl Bem in his self-perception theory. People draw inferences about who they are, Bem suggested, by observing their own behavior.
Self-perception theory turns common wisdom on its head. People act the way they do because of their personality traits and attitudes, right? They return a lost wallet because they are honest, recycle their trash because they care about the environment, and pay $5 for a caramel brulée latte because they like expensive coffee drinks. While it is true that behavior emanates from people's inner dispositions, Bem's insight was to suggest that the reverse also holds. If we return a lost wallet, there is an upward tick on our honesty meter. After we drag the recycling bin to the curb, we infer that we really care about the environment. And after purchasing the latte, we assume that we are coffee connoisseurs.
Hundreds of experiments have confirmed the theory and shown when this self-inference process is most likely to operate (e.g., when people believe they freely chose to behave the way they did, and when they weren't sure at the outset how they felt).
Self-perception theory is an elegant in its simplicity. But it is also quite deep, with important implications for the nature of the human mind. Two other powerful ideas follow from it. The first is that we are strangers to ourselves. After all, if we knew our own minds, why would we need to guess what our preferences are from our behavior? If our minds were an open book, we would know exactly how honest we are and how much we like lattes. Instead, we often need to look to our behavior to figure out who we are. Self-perception theory thus anticipated the revolution in psychology in the study of human consciousness, a revolution that revealed the limits of introspection.
But it turns out that we don't just use our behavior to reveal our dispositions—we infer dispositions that weren't there before. Often, our behavior is shaped by subtle pressures around us, but we fail to recognize those pressures. As a result, we mistakenly believe that our behavior emanated from some inner disposition. Perhaps we aren't particularly trustworthy and instead returned the wallet in order to impress the people around us. But, failing to realize that, we infer that we are squeaky clean honest. Maybe we recycle because the city has made it easy to do so (by giving us a bin and picking it up every Tuesday) and our spouse and neighbors would disapprove if we didn't. Instead of recognizing those reasons, though, we assume that we should be nominated for the Green Neighbor of the Month Award. Countless studies have shown that people are quite susceptible to social influence, but rarely recognize the full extent of it, thereby misattributing their compliance to their true wishes and desires--the well-known fundamental attribution error.
Like all good psychological explanations, self-perception theory has practical uses. It is implicit in several versions of psychotherapy, in which clients are encouraged to change their behavior first, with the assumption that changes in their inner dispositions will follow. It has been used to prevent teenage pregnancies, by getting teens to do community service. The volunteer work triggers a change in their self-image, making them feel more a part of their community and less inclined to engage in risky behaviors. In short, we should all heed Kurt Vonnegut's advice: "We are what we pretend to be, so we must be careful about what we pretend to be."

Social Psychologist, University of British Columbia
Why We Feel Pressed for Time
Recently, I found myself on the side of the road, picking gravel out of my knee and wondering how I’d ended up there. I had been biking from work to meet a friend at the gym, pedalling frantically to make up for being a few minutes behind schedule. I knew I was going too fast, and when I hit a patch of loose gravel while careening through a turn, my bike slid out from under me. How had I gotten myself in this position? Why was I in such a rush?
I thought I knew the answer. The pace of life is increasing; people are working more and relaxing less than they did 50 years ago. At least that’s the impression I got from the popular media. But as a social psychologist, I wanted to see the data. As it turns out, there is very little evidence that people are now working more and relaxing less than they did in earlier decades. In fact, some of the best studies suggest just the opposite. So, why do people report feeling so pressed for time?
A beautiful explanation for this puzzling phenomenon was recently offered by Sanford DeVoe, at the University of Toronto and Jeffrey Pfeffer, at Stanford. They argue that as time becomes worth more money, time is seen as scarcer. Scarcity and value are perceived as conjoined twins; when a resource—from diamonds to drinking water—is scarce, it is more valuable, and vice versa. So, when our time becomes more valuable, we feel like we have less of it. Indeed, surveys from around the world have shown that people with higher incomes report feeling more pressed for time. But there are lots of plausible reasons for this, including the fact that more affluent people often work longer hours, leaving them with objectively less free time.
DeVoe and Pfeffer proposed, however, that simply perceiving oneself as affluent might be sufficient to generate feelings of time pressure. Going beyond past correlational analyses, they used controlled experiments to put this causal explanation to the test. In one experiment, DeVoe and Pfeffer asked 128 undergraduates to report the total amount of money they had in the bank. All the students answered the question using an 11-point scale, but for half the students, the scale was divided into $50 increments, ranging from $0-$50 (1) to over $500 (11), whereas for the others, the scale was divided into much larger increments, ranging from $0-$500 (1) to over $400,000 (11). When the scale was divided into $50 increments, most undergraduates circled a number near the top of the scale, leaving them with the sense that they were relatively well-off. And this seemingly trivial manipulation led participants to feel that they were rushed, pressed for time, and stressed out. In other words, just feeling affluent led students to experience the same sense of time pressure reported by genuinely affluent individuals. Other studies confirmed that increasing the perceived economic value of time increases its perceived scarcity.
If feelings of time scarcity stem in part from the sense that time is incredibly valuable, then ironically, one of the best things we can do to reduce this sense of pressure may be to give our time away. Indeed, new research suggests that giving time away to help others can actually alleviate feelings of time pressure. Companies like Home Depot provide their employees with opportunities to volunteer their time to help others, potentially reducing feelings of time stress and burnout. And Google encourages employees to use 20% of their time on their own pet project, which may or may not payoff. Although some of these projects have resulted in economically valuable products like Gmail, the greatest value of this program might lie in reducing employees’ sense that their time is scarce.
As well as pointing to innovative solutions to feelings of time pressure, DeVoe and Pfeffer’s work can help to account for important cultural trends. Over the past 50 years, feelings of time pressure have risen dramatically in North America, despite the fact that weekly hours of work have stayed fairly level and weekly hours of leisure have climbed. This apparent paradox may be explained, in no small part, by the fact that incomes have increased substantially during the same period. This causal effect may also help to explain why people walk faster in wealthy cities like Tokyo and Toronto than in cities like Nairobi and Jakarta. And at the level of the individual, this explanation suggests that as incomes grow over the life course, time seems increasingly scarce. Which means that, as my career develops, I might have to force myself to take those turns a little slower.

Computational Neuroscientist; Francis Crick Professor, the Salk Institute; Coauthor, The Computational Brain
Nature is More Clever Than We Are
We have the clear impression that our deliberative mind makes the most important decisions in our life: What work we do, where we live, who we marry. But contrary to this belief the biological evidence points toward a decision process in an ancient brain system called the basal ganglia, brain circuits that consciousness cannot access. Nonetheless, the mind dutifully makes up plausible explanations for the decisions.
The scientific trail that led to this conclusion began with honeybees. Worker bees forage the spring fields for nectar, which they identify with the color, fragrance and shape of a flower. The learning circuit in the bee brain converges on VUMmx1, a single neuron that receives the sensory input and, a bit later, the value of the nectar, and learns to predict the nectar value of that flower the next time the bee encounters it. The delay is important because the key is prediction, rather than a simple association. This is also the central core of temporal-difference (TD) learning, which can learn a sequence of decisions leading to a goal and is particularly effective in uncertain environments like the world we live in.
Buried deep in your midbrain there is a small collection of neurons, found in our earliest vertebrate ancestors, that project throughout the cortical mantle and basal ganglia that are important for decision making. These neurons release a neurotransmitter called dopamine, which has a powerful influence on our behavior. Dopamine has been called a "reward" molecule, but more important than reward itself is the ability of these neurons to predict reward: If I had that job, how happy would I be? Dopamine neurons, which are central to motivation, implement TD learning, just like VUMmx1.
TD learning solves the problem of finding the shortest path to a goal. It is an "online" algorithm because it learns by exploring and discovers the value of intermediate decisions in reaching the goal. It does this by creating an internal value function, which can be used to predict the consequences of actions. Dopamine neurons evaluate the current state of the entire cortex and inform the brain about the best course of action from the current state. In many cases the best course of action is a guess, but because guesses can be improved, over time TD learning creates a value function of oracular powers. Dopamine may be the source of the "gut feeling" you sometime experience, the stuff that intuition is made from.
When you consider various options, prospective brain circuits evaluate each scenario and the transient level of dopamine registers the predicted value of each decision. The level of dopamine is also related to your level of motivation, so not only will a high level of dopamine indicate a high expected reward, but you will also have a higher level of motivation to pursue it. This is quite literally the case in the motor system, where a higher tonic dopamine level produces faster movements. The addictive power of cocaine and amphetamines is a consequence of increased dopamine activity, hijacking the brain's internal motivation system. Reduced levels of dopamine lead to anhedonia, an inability to experience pleasure, and the loss of dopamine neurons results in Parkinson's Disease, an inability to initiate actions and thoughts.
TD learning is powerful because it combines information about value along many different dimensions, in effect comparing apples and oranges in achieving distant goals. This is important because rational decision-making is very difficult when there many variables and unknowns, so having an internal system that quickly delivers good guesses is a great advantage, and may make the difference between life and death when a quick decision is needed. TD learning depends on the sum of your life experiences. It extracts what is essential from these experiences long after the details of the individual experiences are no longer remembered.
TD learning also explains many of the experiments that were performed by psychologists who trained rats and pigeons on simple tasks. Reinforcement learning algorithms have traditionally been considered too weak to explain more complex behaviors because the feedback from the environment is sparse and minimal. Nonetheless reinforcement learning is universal among nearly all species and is responsible for some of the most complex forms of sensorimotor coordination, such as piano playing and speech. Reinforcement learning has been honed by hundreds of millions of years of evolution. It has served countless species well, in particular our own.
How complex a problem can TD learning solve? TD gammon is a computer program that learned how to play backgammon by playing itself. The difficulty with this approach is that the reward comes only at the end of the game, so it is not clear which were the good moves that led to the win. TD gammon started out with no knowledge of the game, except for the rules. By playing itself many times and applying TD learning to create a value function to evaluation game positions, TD gammon climbed from beginner to expert level, along the way picking up subtle strategies similar to ones that humans use. After playing itself a million times it reached championship level and was discovering new positional play that astonished human experts. Similar approaches to the game of Go have achieved impressive levels of performance and are on track to reach professional levels.
When there is a combinatorial explosion of possible outcomes, selective pruning is helpful. Attention and working memory allow us to focus on most the important parts of a problem. Reinforcement learning is also supercharged by our declarative memory system, which tracks unique objects and events. When large brains evolved in primates, the increased memory capacity greatly enhanced the ability to make more complex decisions, leading to longer sequences of actions to achieve goals. We are the only species to create an educational system and to consign ourselves to years of instruction and tests. Delayed gratification can extend into the distant future, in some cases extending into an imagined afterlife, a tribute to the power of dopamine to control behavior.
At the beginning of the cognitive revolution in the 1960s the brightest minds could not imagine that reinforcement learning could underlie intelligent behavior. Minds are not reliable. Nature is more clever than we are.

Psychologist, MIT; Internet Culture Researcher; Author, Alone Together
Transitional Objects
I was a student in psychology in the mid-1970s at Harvard University. The grand experiment that had been "Social Relations" at Harvard had just crumbled. Its ambition had been to bring together the social sciences in one department, indeed, most in one building, William James Hall. Clinical psychology, experimental psychology, physical and cultural anthropology, and sociology, all of these would be in close quarters and intense conversation.
But now, everyone was back in their own department, on their own floor. From my point of view, what was most difficult was that the people who studied thinking were on one floor and the people who studied feeling were on another.
In this Balkanized world, I took a course with George Goethals in which we learned about the passion in thought and the logical structure behind passion. Goethals, a psychologist who specialized in adolescence, was teaching a graduate seminar in psychoanalysis. Goethals focus was on a particular school of analytic thought: British object relations theory. This psychoanalytic tradition kept its eye on a deceptively simple question: How do we bring people and what they meant to us "inside" us? How do these internalizations cause us to grow and change? The "objects" of its name were, in fact, people.
Several classes were devoted to the work of David Winnicott and his notion of the transitional object. Winnicott called transitional the objects of childhood—the stuffed animals, the bits of silk from a baby blanket, the favorite pillows—that the child experiences as both part of the self and of external reality. Winnicott writes that such objects mediate between the child's sense of connection to the body of the mother and a growing recognition that he or she is a separate being. The transitional objects of the nursery—all of these are destined to be abandoned. Yet, says Winnicott, they leave traces that will mark the rest of life. Specifically, they influence how easily an individual develops a capacity for joy, aesthetic experience, and creative playfulness. Transitional objects, with their joint allegiance to self and other, demonstrate to the child that objects in the external world can be loved.
Winnicott believes that during all stages of life we continue to search for objects we experience as both within and outside the self. We give up the baby blanket, but we continue to search for the feeling of oneness it provided. We find them in moments of feeling "at one" with the world, what Freud called the "oceanic feeling." We find these moments when we are at one with a piece of art, a vista in nature, a sexual experience.
As a scientific proposition, the theory of the transitional object has its limitations. But as a way of thinking about connection, it provides a powerful tool for thought. Most specifically, it offered me a way to begin to understand the new relationships that people were beginning to form with computers, something I began to study in the late 1970s and early 1980s. From the very beginning, as I began to study the nascent digital culture culture, I could see that computers were not "just tools." They were intimate machines. People experienced them as part of the self, separate but connected to the self.
A novelist using a word processing program referred to "my ESP with the machine. The words float out. I share the screen with my words." An architect who used the computer to design goes went even further: "I don't see the building in my mind until I start to play with shapes and forms on the machine. It comes to life in the space between my eyes and the screen."
After studying programming, a thirteen year old girl said, that when working with the computer, "there's a little piece of your mind and now it's a little piece of the computer's mind and you come to see yourself differently." A programmer talked about his "Vulcan mind meld" with the computer.
When in the late 1970s, I began to study the computer's special evocative power, my time with George Goethals and the small circle of Harvard graduate students immersed in Winnicott came back to me. Computers served as transitional objects. They bring us back to the feelings of being "at one" with the world. Musicians often hear the music in their minds before they play it, experiencing the music from within and without. The computer similarly can be experienced as an object on the border between self and not-self. Just as musical instruments can be extensions of the mind's construction of sound, computers can be extensions of the mind's construction of thought.
This way of thinking about the computer as an evocative objects puts us on the inside of a new inside joke. For when psychoanalysts talked about object relations, they had always been talking about people. From the beginning, people saw computers as "almost-alive" or "sort of alive." With the computer, object relations psychoanalysis can be applied to, well, objects. People feel at one with video games, with lines of computer code, with the avatars they play in virtual worlds, with their smartphones. Classical transitional objects are meant to be abandoned, their power recovered in moments of heightened experience. When our current digital devices—our smartphones and cellphones—take on the power of transitional objects, a new psychology comes into play. These digital objects are never meant to be abandoned. We are meant to become cyborg.

Artist; Co-Founder, Edge.org; President, Brockman, Inc.; Author: Short Lives
Occam's Razor

Professor of Psychology, Hope College; author Psychology, 10th Edition
Group Polarization
Forty-five years ago, some social psychological experiments posed story problems that assessed people's willingness to take risks (for example, what odds of success should a budding writer have in order to forego her sure income and attempt writing a significant novel?). To everyone's amazement, group discussions in various countries led people to advise more risk, setting off a wave of speculation about group risk taking by juries, business boards, and the military.
Alas, some other story problems surfaced for which group deliberation increased caution (should a young married parent with two children gamble his savings on a hot stock tip?).
Out of this befuddlement—does group interaction increase risk, or caution?—there emerged a deeper principle of simple elegance: group interaction tends to amplify people's initial inclinations (as when advising risk to the novelist, and caution in the investing).
This "group polarization" phenomenon was then repeatedly confirmed. In one study, relatively prejudiced and unprejudiced students were grouped separately and asked to respond—before and after discussion—to racial dilemmas, such as a conflict over property rights versus open housing. Discussion with like-minded peers increased the attitude gap between the high- and low-prejudiced groups.
Fast forward to today. Self-segregation with kindred spirits is now rife. With increased mobility, conservative communities attract conservatives and progressive communities attract progressives. As Bill Bishop has documented, the percentage of landslide counties—those voting 60 percent or more for one presidential candidate—nearly doubled between 1976 and 2008. And when neighborhoods become political echo chambers, the consequence is increased polarization, as David Schkade and colleagues demonstrated by assembling small groups of Coloradoans in liberal Boulder and conservative Colorado Springs. The community discussions of climate change, affirmative action, and same-sex unions further diverged Boulder folks leftward and Colorado Springs folks rightward.
Terrorism is group polarization writ large. Virtually never does it erupt suddenly as a solo personal act. Rather, terrorist impulses arise among people whose shared grievances bring them together. In isolation from moderating influences, group interaction becomes a social amplifier.
The Internet accelerates opportunities for like-minded peacemakers and neo-Nazis, geeks and goths, conspiracy schemers and cancer survivors, to find and influence one another. When socially networked, birds of a feather find their shared interests, attitudes, and suspicions magnified.
Ergo, one elegant and socially significant explanation of diverse observations is simply this: opinion segregation + conversation → polarization.

Independent Investigator and Theoretician; Author, The Nurture Assumption; No Two Alike: Human Nature and Human Individuality
True or False: Beauty Is Truth
"Beauty is truth, truth beauty," said John Keats. But what did he know? Keats was a poet, not a scientist.
In the world that scientists inhabit, truth is not always beautiful or elegant, though it may be deep. In fact, it's my impression that the deeper an explanation goes, the less likely it is to be beautiful or elegant.
Some years ago, the psychologist B. F. Skinner proposed an elegant explanation of "the behavior of organisms," based on the idea that rewarding a response—he called it reinforcement—increases the probability that the same response will occur again in the future. The theory failed, not because it was false (reinforcement generally does increase the probability of a response) but because it was too simple. It ignored innate components of behavior. It couldn't even handle all learned behavior. Much behavior is acquired or shaped through experience, but not necessarily by means of reinforcement. Organisms learn different things in different ways.
The theory of the modular mind is another way of explaining behavior—in particular, human behavior. The idea is that the human mind is made up of a number of specialized components, often called modules, working more or less independently. These modules collect different kinds of information from the environment and process it in different ways. They issue different commands—occasionally, conflicting commands. It's not an elegant theory; on the contrary, it's the sort of thing that would make Occam whip out his razor. But we shouldn’t judge theories by asking them to compete in a beauty pageant. We should ask whether they can explain more, or explain better, than previous theories were able to do.
The modular theory can explain, for example, the curious effects of brain injuries. Some abilities may be lost while others are spared, with the pattern differing from one patient to another.
More to the point, the modular theory can explain some of the puzzles of everyday life. Consider intergroup conflict. The Montagues and the Capulets hated each other; yet Romeo (a Montague) fell in love with Juliet (a Capulet). How can you love a member of a group, yet go on hating that group? The answer is that two separate mental modules are involved. One deals with groupness (identification with one's group and hostility toward other groups), the other specializes in personal relationships. Both modules collect information about people, but they do different things with the data. The groupness module draws category lines and computes averages within categories; the result is called a stereotype. The relationship module collects and stores detailed information about specific individuals. It takes pleasure in collecting this information, which is why we love to gossip, read novels and biographies, and watch political candidates unravel on our TV screens. No one has to give us food or money to get us to do these things, or even administer a pat on the back, because collecting the data is its own reward.
The theory of the modular mind is not beautiful or elegant. But not being a poet, I prize truth above beauty.

Professor of Genomics, The Scripps Research Institute; Author, The Creative Destruction of Medicine
Seeing Is Believing: From Placebos To Movies In Our Brain
Our brain of one hundred billion neurons and a quadrillion of synapses, give or take a few billion here or there, has to be considered one of the most complex entities to demystify. And that may be a good thing, since we don't necessarily want others to be able to read our minds, which would not only be regarded as terribly invasive, but also taking the recent megatrend of transparency much too far.
But the ability to use functional magnetic resonance (fMRI) and positron emission tomography (PET) to image the brain and construct sophisticated activation maps is fulfilling the "seeing is believing" aphorism for any skeptics. One of the longest controversies in medicine has been whether the placebo effect, a notoriously complex, mind-body end product, has a genuine biological mechanism. That now seems to be resolved with the recognition that the opiod drug pathway — the one that is induced by drugs like morphine and oxycontin—shares the same brain activation pattern as seen with the administration of placebo for pain relief. And just like we have seen neuroimaging evidence of dopamine "squirts" from our Web-based networking and social media engagement, dopamine release from specific regions of the brain has been directly visualized after administering a placebo to patients with Parkinson's disease. Indeed, the upgrading of the placebo effect to having discrete, distinguishable psychobiological mechanisms has now even evoked the notion of deliberately administering placebo medications as therapeutics and Harvard recently set up a dedicated institute called "The Program in Placebo Studies and the Therapeutic Encounter."
The decoding of the placebo effect seems to be just a nascent step along the way to the more ambitious quest of mind reading. This past summer a group at UC Berkeley was able to show, via reconstructing brain imaging activation maps, a reasonable facsimile of short YouTube movies that were shown to individuals. In fact, it is pretty awe-inspiring and downright scary to see the resemblance of the frame-by-frame comparison of the movie shown and what was reconstructed from the brain imaging.
Coupled with the new initiative of developing miniature, eminently portable MRIs, are we on the way to watching our dreams in the morning on our iPad? Or, even more worrisome, potentially having others see the movies in our brain. I wonder what placebo effect that might have.

Roboticist; Panasonic Professor of Robotics (emeritus) , MIT; Founder, Chairman & CTO, Heartland Robotics, Inc.; Author, Flesh and Machines
Moore's Law
Moore's Law originated in a four page 1965 magazine article written by Gordon Moore, then at Fairchild Semiconductor and later one of the founders of Intel. In it he predicted that the number of components on a single integrated circuit would rise from the then current number of roughly two to the sixth power, to roughly two to the sixteenth power in the following ten years, i.e., the number of components would double every year. He based this on four empirical data points and one null data point, fitting a straight line on a graph plotting the log of the number of components on a single chip against a linear scale of calendar years. Intel later amended Moore's Law to say that the "number of transistors on a chip roughly doubles every two years".
Moore's law is rightly seen as the fundamental driver of the information technology revolution in our world over the last fifty years as doubling the number of transistors every so often has made our computers twice as powerful for the same price, doubled the amount of data they can store or display, made them twice as fast, made them smaller, made them cheaper and in general improved them in every possible way by a factor of two on a clockwork schedule.
But why does it happen? Automobiles have not obeyed Moore's Law, neither have batteries, nor clothing, nor food production, nor the level of political discourse. All but the last have demonstrably improved due to the influence of Moore's Law, but none have had the same relentless exponential improvements.
The most elegant explanation for what makes Moore's Law possible is that digital logic is all about an abstraction, and in fact a one-bit abstraction, a yes/no answer to a question, and that abstraction is independent of physical bulk.
In a world that consists entirely of piles of red sand and piles of green sand, the size of the piles is irrelevant. A pile is either red or green, and you can take away half the pile, and it is still either a pile of red sand or a pile of green sand. And you can take away another half, and another half, and so on, and still the abstraction is maintained. And repeated halving at a constant rate makes an exponential.
That is why Moore's Law works on digital technology, and doesn't work on technologies that require physical strength, or physical bulk, or must deliver certain amounts of energy. Digital technology uses physics to maintain an abstraction and nothing more.
Some caveats do apply:
1. In his short paper Moore expressed some doubt as to whether his prediction would hold for linear, rather than digital, integrated circuits as he pointed out that by their nature, "such elements require the storage of energy in a volume" and that the volume would necessarily be large.
2. It does matter when you get down to piles of sand with just one grain, and then technology has to shift and you need to use some new physical property to define the abstraction—such technology shifts have happened again and again, in the maintenance of Moore's Law over almost fifty years.
3. It does not explain the sociology of how Moore's Law is implemented and what determines the time constant of a doubling, but it does explain why exponentials are possible in this domain. 

Recipient, Nobel Prize in Physiology or Medicine, 2002; Professor of Biochemistry and Molecular Biophysics, Columbia University; Author, The Age of Insight; In Search of Memory
How Psychotherapy Can Be Placed On A Scientific Basis: 5 Easy Lessons
How did psychoanalysis, once a major mode for treating non-psychotic mental disorders fall so badly in the estimation of the medical community in the United States and in the estimation of the public at large. How could it be reversed? Let me try to address this question putting it in a bit of historical perspective.
While an undergraduate at Harvard College I was drawn to Psychiatry—and specifically to Psychoanalysis. During my training from 1960-1965, psychotherapy was the major mode of treating mental illness and this therapy was derived from psychoanalysis and was based on the belief that one needed to understand mental symptoms in terms of their historical roots in childhood. These therapies tended to take years and neither the outcome nor the mechanisms were studied systematically because this was thought to be very difficult. Psychotherapy and in the limit psychoanalysis when successful allowed people to work a bit better and to love a bit and these were dimensions that were thought to be difficult to measure.
In the 1960s Aaron Beck changed all that by introducing five major obvious, but nevertheless elegant and beautiful innovations:
First, he introduced instruments for measuring mental illness. Up until the time of Beck's work, psychiatric research was hampered by a dearth of techniques for operationalizing the various disorders and measuring their severity. Beck developed a number of instruments, beginning with a Depression Inventory, a Hopelessness Scale, and a Suicide Intent Scale. These scales helped to objectify research in psychopathology and facilitated the establishment of better clinical outcome trials.
Second, Beck introduced a new short-term, evidence-based therapy he called Cognitive Behavioral Therapy.
Third, Beck manualized the treatments. He wrote a cookbook so method could be reliably taught to others. You and I could in principle learn to do Cognitive Behavioral Therapy.
Fourth, he carried out with the help of several colleagues, progressively better controlled studies which documented that Cognitive Behavioral Therapy worked more effectively than placebo and as effectively as antidepressants in mild and moderate depression. In severe depression it did not act as effectively as an anti-depressant but acted synergistically with them to enhance recovery.
Fifth and finally, Beck's work was picked up by Helen Mayberg, another one of my heroes in psychiatry. She carried out FMRI studies of depressed patients and discovered that Brodmann area 25 was a focus of abnormal activity in depression. She went on to find that if—and only if—a patient responded to cognitive behavior therapy or to antidepressants SSRI's (selective serotonin reuptake inhibitors) this abnormality reverted to normal.
What I find so interesting in this recital is the Edge question: What elegant, deep explanation did Aaron Beck bring to his work that differentiated him from the rest of my generation of psychotherapists and allowed him to be so original?
Aaron Beck trained as a psychoanalyst in Philadelphia, but soon became impressed with the radical idea that the central issue in many psychiatric disorders is not unconscious conflict but distorted patterns of thinking. Beck conceived of this novel idea from listening with a critical—and open—mind to his patients with depression. In his early work on depression Aaron set out to test a specific psychoanalytic idea: that depression was due to "introjected anger." Patients with depression, it was argued, experienced deep hostility and anger toward someone they loved. They could not deal with having hostile feelings toward someone they valued and so they would repress their anger and direct it inward toward themselves. Beck tested this idea by comparing the dreams—the royal road to the unconscious—of depressed patients with those of non-depressed patients and found that in their dreams depressed patients showed—if anything—less hostility than non-depressed patients. Instead Beck found that in their dreams as in their waking lives depressed patients have a systematic negative bias in their cognitive style, in the way they thought about themselves and their future. They saw themselves as "losers."
Aaron saw these distorted patterns of thinking not simply as a symptom—a reflection of a conflict lying deep within the psyche—but as a key etiological agent in maintaining the disorders.
This led Beck to develop a systematic psychological treatment for depression that focused on distorted thinking. He found that by increasing the patients' objectivity regarding their misinterpretation of situations or their cognitive distortions and their negative expectancies, the patients experienced substantial shifts in their thinking and subsequently improvements in their affect and behavior.
In the course of his work on depression Beck focused on suicide and provided for the first time a rational basis for the classification and assessment of suicidal behaviors that made it possible to identify high-risk individuals. His prospective study of 9,000 patients led to the formulation of an algorithm for predicting future suicide that has proven to have high predictive power. Of particular importance was his identification of clinical and psychological variables such as hopelessness and helplessness to predict future suicides. These proved to be better predictors of suicide than clinical depression per se. Beck's work on suicide, and that of others such as John Mann at Columbia, demonstrated that a short-term cognitive intervention can significantly reduce subsequent suicide attempts when compared to a control group.
In the 1970s, Beck carried out the randomized controlled trials I referred to earlier. Later, the NIMH did similar trials and together these established cognitive therapy as the first ever-psychological treatment that could objectively be shown to be effective in clinical depression.
As soon as cognitive therapy had been found to be effective in the treatment of depression, Beck turned to other disorders. In a number of controlled clinical trials he demonstrated that cognitive therapy is effective in panic disorder, posttraumatic stress disorder, and obsessive-compulsive disorder. In fact even earlier than Helen Mayberg's work on depression—Lewis Baxter at UCLA had imaged patients with obsessive-compulsive disorder and found they had an abnormality in the caudate nucleus that was reversed when patients improved with cognitive behavioral therapy.
Aaron Beck has recently turned his attention to patients with schizophrenia—and has found that cognitive therapy helps improve their cognitive and negative symptoms, particularly their motivational deficits. Another amazing advance.
So—the answer to the decline of psychoanalysis may not simply lie in the limitation of Freud's thought—but perhaps much more so in the lack of a deep, critical scientific attitude of many of the subsequent generation of therapists. I have little doubt that insight therapy is extremely useful as a therapy. And there are studies that support that contention. But an elegant, deep and beautiful proof requires putting a set of highly validated approaches together to make the point in a convincing manner and perhaps even an idea of how the therapeutic result is achieved.

theoretical physicist; Professor, Department of Physics, University of California, Santa Barbara
Gravity Is Curvature Of Spacetime … Or Is It?
My favorite elegant explanation is probably wrong—but is deeply powerful nonetheless. It is: gravity is curvature of spacetime.
This central idea has shaped our ideas of modern cosmology, given us the image of the expanding universe, and has led to remarkable understandings—such as the apparent presence of a black hole four million times the mass of the sun at the center of our galaxy. It even offers a possible explanation of the origin of our Universe—as quantum tunneling from "nothing."
This idea lies at the heart of Einstein's General Theory of Relativity, which is still our best understanding of gravity, after nearly 100 years. Its essence is embodied in Wheeler's famous words: "matter tells spacetime how to curve, and curved spacetime tells matter how to move" The equations expressing this are even simpler, once one has understood the background math. The theory exudes simple, essential beauty.
But when brought together with quantum mechanics, an epic conflict between the two theories results. Apparently, they both cannot be right. And, the lessons of black holes—and Hawking's discovery that they ultimately explode—seem to teach us that quantum mechanics must win, and classical spacetime is doomed.
We do not yet know the full shape of the quantum theory providing a complete accounting for gravity. We do have many clues, from studying the early quantum phase of cosmology, and ultrahigh energy collisions that produce black holes and their subsequent disintegrations into more elementary particles. We have hints that the theory draws on powerful principles of quantum information theory. And, we expect that in the end it has a simple beauty, mirroring the explanation of gravity-as-curvature, from an even more profound depth.

Journalist; Editor, Nova 24, of Il Sole 24 Ore
The Importance Of Context
In a thriller novel, the explanation comes at the end. In a newspaper article, it usually comes at the beginning. In an executive summary meant to be read by the top management, the explanation, comes at the beginning of the memo. And for a scientific paper, a summary, with findings and hypothesis is presented at the beginning. There is not a single aesthetics of explanations. True: their beauty, deepness, elegance, always rely on the beauty, deepness and elegance of the question to which they answer: but the way the answer is introduced depends on conventional wisdom in different disciplines.
What changes the structure of the questioning-answering conventions?
The major difference is probably in the importance of context.
In entertainment, in a novel or in a movie, the context is the world of meanings that is created by storytellers. Questions appear as surprising twists in the context description. And, mastering the whole thing, the storyteller lets the reader enjoy an entertaining experience by explaining everything at the end. In science, in the news, in a company, the context is in a world of meanings that is already present to the mind of the reader, the storyteller doesn't master the whole thing, everybody feels to be part of the story, and the correct approach is to explain everything as soon as possible, and then to share all the specific findings to help everybody evaluate the quality of the explanation.
But what happens when a really great scientific or economic breakthrough needs to be proposed and shared? What happens when an important new notion that will change the paradigm of its discipline is to be explained? And what happens when something even changes the world of meanings in which the discipline is accustomed to develop?
When Nicolaus Copernicus wrote his masterpiece, De revolutionibus orbium coelestium, he had to make a choice. After having dedicated his work to Pope Paul III, he started the first book introducing a vision of the universe, based on his heliocentric idea. He continued writing three books about mathematics, descriptions of stars, movements of the Sun and the Moon. Only at the end did he explained his new system and how to calculate the movements of all astronomical objects in a heliocentric model.
That was a deep, elegant and beautiful explanation of an historic change. It was an explanation that had to create a new vision of everything, of a new paradigm.

Professor of Neurobiology and Psychiatry, UCSF; Author, Making Sense of People
Personality Differences: The Importance of Chance
In the golden age of Greek philosophy Theophrastus, Aristotle's successor, posed a question for which he is still remembered: "Why has it come about that, albeit the whole of Greece lies in the same clime, and all Greeks have a like upbringing, we have not the same constitution of character [personality]?" The question is especially noteworthy because it bears on our sense of who each of us is, and we now know enough to offer an answer: each personality reflects the activities of brain circuits that gradually develop under the combined direction of the person's unique set of genes and experiences. What makes the implications of this answer so profound is that they lead to the inescapable conclusion that personality differences are greatly influenced by chance events.
Two types of chance events influence the genetic contribution to personality. The first, and most obvious, is the events that brought together the person's mom and dad. Each of them has a particular collection of gene variants—a personal sample of the variants that have accumulated in the collective human genome—and the two parental genetic repertoires set limits on the possible variants that can be transmitted to their offspring. The second chance event is the hit-or-miss union of the particular egg and sperm that make the offspring, each of which contains a random selection of half of the gene variants of each parent. It is the interactions of the resultant unique mixture of maternal and paternal gene variants that plays a major part in the 25-year-long developmental process that builds the person's brain and personality. So two accidents of birth—the parents who conceive us, and the egg–sperm combinations that make us—have decisive influences on the kinds of people we become.
But genes don't act alone. Although there are innate programs of gene expression that continue to unfold through early adulthood to direct the construction of rough drafts of brain circuits, these programs are specifically designed to incorporate information from the person's physical and social world. Some of this adaptation to the person's particular circumstances must come at specific developmental periods, called critical periods. For example, the brain circuits that control the characteristic intonations of a person's native language are only open for environmental input during a limited window of development.
And just as chance influences the particular set of genes we are born with, so does it influence the particular environment we are born into. Just as our genes incline us to be more or less friendly, or confident, or reliable, the worlds we grow up in incline us to adopt particular goals, opportunities and rules of conduct. The most obvious aspects of these worlds are cultural, religious, social, and economic, each transmitted by critical agents: parents, siblings, teachers, and peers. And the specific content of these important influences—the specific era, place, culture etc. we happen to have been born into—is as much a toss of the dice as the specific content of the egg and sperm that formed us.
Of course, chance is not fate. Recognizing that chance events contribute to individual personality differences doesn't mean each life is predetermined or that there is no free will. The personality that arises through biological and socio-cultural accidents of birth can be deliberately modified in many ways, even in maturity. Nevertheless, the chance events that direct brain development in our first few decades leave enduring residues.
When thinking about a particular personality it is, therefore, helpful to be aware of the powerful role that chance played in its construction. Recognizing the importance of chance in our individual differences doesn't just remove some of their mystery. It can also have moral consequences by promoting understanding and compassion for the wide range of people with whom we share our lives.

Physicist, Perimeter Institute; Author, Time Reborn
The Principle of Inertia
My favorite explanation in science is the principle of inertia. It explains why the earth moves in spite of the fact that we don't feel any motion, which was perhaps the most counterintuitive revolutionary step taken in all of science. It was first proposed by Galileo and Descartes and has been the core of all the successful explanations in physics in the centuries since.
The principle of inertia is the answer to a very simple question: how would an object that is free, in the sense that no eternal influences or forces affect its motion, move?
This is a seemingly simple question, but notice that to answer it we have to have in mind a definition of motion. What does it mean for something to move?
The modern conception is that motion has to be described relative to an observer.
Consider an object that is sitting at rest relative to you, say a cat sleeping on your lap, and imagine how it appears to move as seen by other observers. Depending on how the observer is moving the cat can appear to have any motion at all. If the observer spins relative to you, the cat will appear to them to spin.
So to make sense of the question of how free objects move we have to refer to a special class of observers. The answer to the question is the following:
There is a special class of observers, relative to whom all free objects appear to either be at rest or to move in straight lines with constant speeds.
I have just stated the principle of inertia.
The power of this principle is that it is completely general. Once a special observer sees one free object move in a straight line with constant speed, she will observe all other free objects to so move.
Furthermore suppose you are a special observer. Any observer who moves in a straight line at a constant speed with respect to you will also see the free objects move at a constant speed in a straight line, with respect to them.
So these special observers form a big class, all of which are moving with respect to each other. These special observers are called inertial observers.
An immediate and momentous consequence is that there is no absolute meaning in not moving. An object may be at rest with respect to one inertial observer, but other inertial observers will see it moving-always in a straight line at constant speed. This can be formulated as a principle:
There is no way, by observing objects in motion, to distinguish observers at rest from other inertial observers.
Thus, any inertial observer has equal rights to say they are at rest and it is the others that are moving.
This is called Galileo's principle of relativity. It explains why the Earth may be moving without us observing gross effects.
To appreciate how revolutionary this was notice that physicists of the 16th Century could disprove Copernicus's claim that the Earth moves by a simple observation. Just drop a ball from the top of a tower. Were the Earth rotating around its axis and revolving around the Sun at the speeds Copernicus required, the ball would land far from the base of the tower. QED. The Earth is at rest.
But this proof assumes that motion is absolute, defined with respect to a special observer at rest, with respect to whom objects with no forces on them come to rest. By altering the definition of motion, Galileo could argue that the very same experiment that previously proved that the Earth is at rest now demonstrates that the Earth could be moving.
The principle of inertia was not just the core of the scientific revolutions of the 17th Century. It contained the seeds of revolutions to come. To see why, notice the qualifier in the statement of the principle of relativity: "by observing objects in motion." For many years it was thought that there would be other kinds of observations that could be used to tell which inertial observers are really moving and which are really at rest. Einstein constructed his theory of special relativity simply by removing this qualifier. Einstein's principle of relativity states:
There is no way to distinguish observers at rest from other inertial observers.
And there was more. A decade after special relativity, the principle of inertia was the seed also for the next revolution—the discovery of general relativity. The principle was generalized by replacing "moving in a straight line with constant speed" to "moving along a geodesic in spacetime." A geodesic is the generalization of a straight line in a curved geometry—it is the shortest distance between two points. So now the principle of inertia reads:
There is a special class of observers, relative to whom all free objects appear to either be at rest or to move along geodesics in spacetime. These are observers who are in free fall in a gravitational field.
And there is consequent generalization of the principle of relativity.
There is no way to distinguish observers in free fall from each other.
This becomes Einstein's equivalence principle that is the core of his general theory of relativity.
But is the principle of inertia really true? So far it has been tested in circumstances where the energy of motion of a particle is as much as eleven orders of magnitude greater than its mass. This is pretty impressive, but there is still a lot of room for the principle of inertia and its twin, the principle of relativity, to fail. Only experiment can tell us if these principles or their failures will be the core of revolutions in science to come.
But whatever happens, no other explanation in science besides the principle of inertia has survived unscathed for so long, nor proved valid over such a range of scales, nor has any other been the seed of several scientific revolutions separated by centuries.

Professor Emeritus of Psychology at Stanford University; Author, The Lucifer Effect: Understanding How Good People Turn Evil
Time Perspective Theory
I am here to tell you that the most powerful influence on our every decision that can lead to significant action outcomes is something that most of us are both totally unaware of and at the same time is the most obvious psychological concept imaginable.
I am talking about our sense of psychological time, more specifically, the way our decisions are framed by the time zones that you have learned to prefer and tend to overuse. We all live in multiple time zones, learned from childhood, shaped by education, culture, social class, and experiences with economic and family stability-instability. For most of us, we develop a biased temporal orientation that favors one time frame over others, becoming excessively oriented to past, present, or the future.
Thus, at decision time for major or minor judgments, some of us are totally influenced by factors in the immediate situation: The stimulus qualities, what others are doing, saying, urging, and one’s biological urges. Others facing the same decision matrix ignore all those present qualities by focusing instead on the past, the similarities between current and prior settings, remembering what was done and its effects. Finally, a third set of decision makers ignores the present and the past by focusing primarily on the future consequences of current actions, calculating costs vs. gains.
To complicate matters, there are sub domains of each of these primary time zones. Some past-oriented people tend to focus on negatives in their earlier experiences, regret, failure, abuse, trauma, while others are primarily past positive, focusing instead on the good old days, nostalgia, gratitude, and successes. There are two ways to be present-oriented, to live in present- hedonistic domain of seeking pleasure and novelty, and sensation seeking versus being present- fatalistic, living in a default present by believing nothing one does can make any changes in one’s future life. Future-oriented people are goal setters, plan strategies, tend to be successful, but another future focus is on the transcendental future—life begins after the death of the mortal body.
My interest in Time Perspective Theory inspired me to create an inventory to make it possible to determine exactly the extent to which we fit into each of these six time zones. The Zimbardo Time Perspective Inventory, or ZTPI correlates scores on these time dimensions with a host of other psychological traits and behaviors. We have demonstrated that Time Perspective has a major impact across a vast domain of human nature. In fact, some of the relationships uncovered reveal correlation coefficients much greater than ever seen in traditional personality assessment. For example, Future orientation correlates .70 with the trait of conscientiousness, which in turn predicts to longevity. Present Hedonism correlates .70 with sensation seeking and novelty seeking. Those high on Past Negative are most likely to be high on measures of anxiety, depression and anger, with correlations as robust as .75. Similarly substantial correlations are uncovered between Present Fatalism and these measures of personal distress. I should add that this confirmatory factor analysis was conducted on a sample of functioning college students, thus such effects should be cause for alarm by counselors. Beyond mere correlations of scale measures, the ZTPI scales predict to a wide range of behaviors: Course grades, risk taking, alcohol, drug use and abuse, environmental conservation, medical checkups, creativity, problem solving, and much more.
Finally, one of the most surprising discoveries is the application of Time Perspective theory to time therapy in “curing” PTSD in Veterans, as well as in sexually abused women or civilians suffering from motor vehicle fatality experiences. Dr. Richard Sword and Rosemary Sword have been treating with remarkably positive outcomes a number of veterans from all US recent wars and also civilian clients. The core of the treatment replaces the Past Negative and Present Fatalistic biased time zones common to those suffering from PTSD with a balanced time perspective that highlights the critical role of the hope-filled future, adds in some selected present hedonism, and introduces memories of a Past Positive nature. In a sample of 30 PTSD vets of varying ages and ethnicities, treated with Time Perspective Therapy for a relatively few sessions (compared to traditional cognitive behavioral therapies), dramatic positive changes have been found for all PTSD standard assessments, as well as in life-changing social and professional relationships.  It is so rewarding to see many of our honored veterans who have continued to suffer for decades from their combat-related severe traumas to discover a new life rich with opportunities, friends, family, fun and work by being exposed to this simple, elegant reframing of their mental orientation toward the life of their time.

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