ROBERT SAPOLSKY
Neuroscientist, Stanford University, Author, A Primate's Memoir

Well, of course, it is tempting to go for something like, "That the wheel, agriculture, and the Macarena were all actually invented by yetis." Or to do the sophomoric pseudo-ironic logic twist of, "That every truth can eventually be proven." Or to get up my hackles, draw up to my full height and intone, "Sir, we scientists believe in nothing that cannot be proven by the whetstone of science, verily our faith is our lack of faith," and then go off in a lab coat and a huff.

The first two aren't worth the words, and the third just isn't so. No matter how many times we read Arrowsmith, scientists are subjective humans operating in an ostensibly objective business, so there 's probably lots of things we take on faith.

So mine would be a fairly simple, straightforward case of an unjustifiable belief, namely that there is no god(s) or such a thing as a soul (whatever the religiously inclined of the right persuasion mean by that word). I'm very impressed, moved, by one approach of people on the other side of the fence. These are the believers who argue that it would be a disaster, would be the very work of Beelzebub, for it to be proven that god exists. What good would religiosity be if it came with a transparently clear contract, instead of requiring the leap of faith into an unknowable void?

So I'm taken with religious folks who argue that you not only can, but should believe without requiring proof. Mine is to not believe without requiring proof. Mind you, it would be perfectly fine with me if there were a proof that there is no god. Some might view this as a potential public health problem, given the number of people who would then run damagingly amok. But it's obvious that there's no shortage of folks running amok thanks to their belief. So that wouldn 't be a problem and, all things considered, such a proof would be a relief—many physicists, especially astrophysicists, seem weirdly willing to go on about their communing with god about the Big Bang, but in my world of biologists, the god concept gets mighty infuriating when you spend your time thinking about, say, untreatably aggressive childhood leukemia.

Finally, just to undo any semblance of logic here, I might even continue to believe there is no god, even if it was proven that there is one. A religious friend of mine once said to me that the concept of god is very useful, so that you can berate god during the bad times. But it is clear to me that I don't need to believe that there is a god in order to berate him.

FREEMAN DYSON
Physicist, Institute of Advanced Study, Author, Disturbing the Universe

Since I am a mathematician, I give a precise answer to this question. Thanks to Kurt Gödel, we know that there are true mathematical statements that cannot be proved. But I want a little more than this. I want a statement that is true, unprovable, and simple enough to be understood by people who are not mathematicians. Here it is.

Numbers that are exact powers of two are 2, 4, 8, 16, 32, 64, 128 and so on. Numbers that are exact powers of five are 5, 25, 125, 625 and so on. Given any number such as 131072 (which happens to be a power of two), the reverse of it is 270131, with the same digits taken in the opposite order. Now my statement is: it never happens that the reverse of a power of two is a power of five.

The digits in a big power of two seem to occur in a random way without any regular pattern. If it ever happened that the reverse of a power of two was a power of five, this would be an unlikely accident, and the chance of it happening grows rapidly smaller as the numbers grow bigger. If we assume that the digits occur at random, then the chance of the accident happening for any power of two greater than a billion is less than one in a billion. It is easy to check that it does not happen for powers of two smaller than a billion. So the chance that it ever happens at all is less than one in a billion. That is why I believe the statement is true.

But the assumption that digits in a big power of two occur at random also implies that the statement is unprovable. Any proof of the statement would have to be based on some non-random property of the digits. The assumption of randomness means that the statement is true just because the odds are in its favor. It cannot be proved because there is no deep mathematical reason why it has to be true. (Note for experts: this argument does not work if we use powers of three instead of powers of five. In that case the statement is easy to prove because the reverse of a number divisible by three is also divisible by three. Divisibility by three happens to be a non-random property of the digits).

It is easy to find other examples of statements that are likely to be true but unprovable. The essential trick is to find an infinite sequence of events, each of which might happen by accident, but with a small total probability for even one of them happening. Then the statement that none of the events ever happens is probably true but cannot be proved.

JOHN McWHORTER
Linguist, Senior Fellow, Manhattan Institute; Author, Doing Our Own Thing

This year, researching the languages of Indonesia for an upcoming book, I happened to find out about a few very obscure languages spoken on one island that are much simpler than one would expect.

Most languages are much, much more complicated than they need to be. They take on needless baggage over the millennia simply because they can. So, for instance, most languages of Indonesia have a good number of prefixes and/or suffixes. Their grammars often force the speaker to attend to nuances of difference between active and passive much more than a European languages does, etc.

But here were a few languages that had no prefixes or suffixes at all. Nor do they have any tones, like many languages in the world. For one thing, languages that have been around forever that have no prefixes, suffixes, or tones are very rare worldwide. But then, where we do find them, they are whole little subfamilies, related variations on one another. Here, though, is a handful of small languages that contrast bizarrely with hundreds of surrounding relatives.

One school of thought in how language changes says that this kind of thing just happens by chance. But my work has been showing me that contrasts like this are due to sociohistory. Saying that naked languages like this are spoken alongside ones as bedecked as Italian is rather like saying that kiwis are flightless just "because," rather than because their environment divested them of the need to fly.

But for months I scratched my head over these languages. Why just them? Why there?

So isn't it interesting that the island these languages is spoken on is none other than Flores, which has had its fifteen minutes of fame this year as the site where skeletons of the "little people" were found. Anthropologists have hypothesized that this was a different species of Homo. While the skeletons date back 13,000 years ago or more, local legend recalls "little people" living alongside modern humans, ones who had some kind of language of their own and could "repeat back" in modern humans' language.

The legends suggest that the little people only had primitive language abilities, but we can't be sure here: to the untutored layman who hasn't taken any twentieth-century anthropology or linguistics classes, it is easy to suppose that an incomprehensible language is merely babbling.

Now, I can only venture this highly tentatively now. But what I "know" but cannot prove this year is: the reason languages like Keo and Ngada are so strangely streamlined on Flores is that an earlier ancestor of these languages, just as complex as its family members tend to be, was used as second language by these other people and simplified. Just as our classroom French and Spanish avoids or streamlines a lot of the "hard stuff," people who learn a language as adults usually do not master it entirely.

Specifically, I would hypothesize that the little people were gradually incorporated into modern human society over time—perhaps subordinated in some way—such that modern human children were hearing the little people's rendition of the language as much as a native one.

This kind of process is why, for example, Afrikaans is a slightly simplified version of Dutch. Dutch colonists took on Bushmen as herders and nurses, and their children often heard second-language Dutch as much as their parents. Pretty soon, this new kind of Dutch was everyone's everyday language, and Afrikaans was born.

Much has been made over the parallels between the evolution of languages and the evolution of animals and plants. However, I believe that one important difference is that while animals and plants can evolve towards simplicity as well as complexity depending on conditions, languages do not evolve towards simplicity in any significant, overall sense—unless there is some sociohistorical factor that puts a spoke in the wheel.

So normally, languages are always drifting into being like Russian or Chinese or Navajo. They only become like Keo and Ngada—or Afrikaans, or creole languages like Papiamentu and Haitian, or even, I believe, English—because of the intervention of factors like forced labor and population relocation. Just maybe, we can now add interspecies contact to the list!

MARTIN E.P. SELIGMAN
Psychologist, University of Pennsylvania, Author, Authentic Happiness

The "rotten-to-the-core" assumption about human nature espoused so widely in the social sciences and the humanities is wrong. This premise has its origins in the religious dogma of original sin and was dragged into the secular twentieth century by Freud, reinforced by two world wars, the Great Depression, the cold war, and genocides too numerous to list. The premise holds that virtue, nobility, meaning, and positive human motivation generally are reducible to, parasitic upon, and compensations for what is really authentic about human nature: selfishness, greed, indifference, corruption and savagery. The only reason that I am sitting in front of this computer typing away rather than running out to rape and kill is that I am "compensated," zipped up, and successfully defending myself against these fundamental underlying impulses.

In spite of its widespread acceptance in the religious and academic world, there is not a shred of evidence, not an iota of data, which compels us to believe that nobility and virtue are somehow derived from negative motivation. On the contrary, I believe that evolution has favored both positive and negative traits, and many niches have selected for morality, co-operation, altruism, and goodness, just as many have also selected for murder, theft, self-seeking, and terrorism.

More plausible than the rotten-to-the-core theory of human nature is the dual aspect theory that the strengths and the virtues are just as basic to human nature as the negative traits: that negative motivation and emotion have been selected for by zero-sum-game survival struggles, while virtue and positive emotion have been selected for by positive sum game sexual selection. These two overarching systems sit side by side in our central nervous system ready to be activated by privation and thwarting, on the one hand, or by abundance and the prospect of success, on the other.

ALISON GOPNIK
Psychologist, UC-Berkeley; Coauthor, The Scientist In the Crib

I believe, but cannot prove, that babies and young children are actually more conscious, more vividly aware of their external world and internal life, than adults are. I believe this because there is strong evidence for a functional trade-off with development. Young children are much better than adults at learning new things and flexibly changing what they think about the world. On the other hand, they are much worse at using their knowledge to act in a swift, efficient and automatic way. They can learn three languages at once but they can't tie their shoelaces.

This trade-off makes sense from an evolutionary perspective. Our species relies more on learning than any other, and has a longer childhood than any other. Human childhood is a protected period in which we are free to learn without being forced to act. There is even some neurological evidence for this. Young children actually have substantially more neural connections than adults—more potential to put different kinds of information together. With experience, some connections are strengthened and many others disappear entirely. As the neuroscientists say, we gain conductive efficiency but lose plasticity.

What does this have to do with consciousness? Consider the experiences we adults associate with these two kinds of functions. When we know how to do something really well and efficiently, we typically lose, or at least, reduce, our conscious awareness of that action. We literally don't see the familiar houses and streets on the well-worn route home, although, of course, in some functional sense we must be visually taking them in. In contrast, as adults when we are faced with the unfamiliar, when we fall in love with someone new, or when we travel to a new place, our consciousness of what is around us and inside us suddenly becomes far more vivid and intense. In fact, we are willing to expend lots of money, and lots of emotional energy, for those few intensely alive days in Paris or Beijing that we will remember long after months of everyday life have vanished.

Similarly, as adults when we need to learn something new, say when we learn to skydive, or work out a new scientific idea, or even deal with a new computer, we become vividly, even painfully, conscious of what we are doing—we need, as we say, to pay attention. As we become expert we need less and less attention, and we experience the actual movements and thoughts and keystrokes less and less. We sometimes say that adults are better at paying attention than children, but really we mean just the opposite. Adults are better at not paying attention. They're better at screening out everything else and restricting their consciousness to a single focus. Again there is a certain amount of brain evidence for this. Some brain areas, like the dorsolateral prefrontal cortex, consistently light up for adults when they are deeply engaged in learning something new. But for more everyday tasks, these areas light up much less. For children, though the pattern is different—these areas light up even for mundane tasks.

I think that, for babies, every day is first love in Paris. Every wobbly step is skydiving, every game of hide and seek is Einstein in 1905.

The astute reader will note that this is just the opposite of what Dan Dennett believes but cannot prove. And this brings me to a second thing I believe but cannot prove. I believe that the problem of capital-C Consciousness will disappear in psychology just as the problem of Life disappeared in biology. Instead we'll develop much more complex, fine-grained and theoretically driven accounts of the connections between particular types of phenomenological experience and particular functional and neurological phenomena. The vividness and intensity of our attentive awareness, for example, may be completely divorced from our experience of a constant first-person I. Babies may be more conscious in one way and less in the other. The consciousness of pain may be entirely different from the consciousness of red which may be entirely different from the babbling stream of Joyce and Woolf.

STEVEN PINKER
Psychologist, Harvard University; Author, The Blank Slate

In 1974, Marvin Minsky wrote that "there is room in the anatomy and genetics of the brain for much more mechanism than anyone today is prepared to propose." Today, many advocates of evolutionary and domain-specific psychology are in fact willing to propose the richness of mechanism that Minsky called for thirty years ago. For example, I believe that the mind is organized into cognitive systems specialized for reasoning about object, space, numbers, living things, and other minds; that we are equipped with emotions triggered by other people (sympathy, guilt, anger, gratitude) and by the physical world (fear, disgust, awe); that we have different ways for thinking and feeling about people in different kinds of relationships to us (parents, siblings, other kin, friends, spouses, lovers, allies, rivals, enemies); and several peripheral drivers for communicating with others (language, gesture, facial expression).

When I say I believe this but cannot prove it, I don't mean that it's a matter of raw faith or even an idiosyncratic hunch. In each case I can provide reasons for my belief, both empirical and theoretical. But I certainly can't prove it, or even demonstrate it in the way that molecular biologists demonstrate their claims, namely in a form so persuasive that skeptics can't reasonably attack it, and a consensus is rapidly achieved. The idea of a richly endowed human nature is still unpersuasive to many reasonable people, who often point to certain aspects of neuroanatomy, genetics, and evolution that appear to speak against it. I believe, but cannot prove, that these objections will be met as the sciences progress.

At the level of neuroanatomy and neurophysiology, critics have pointed to the apparent homogeneity of the cerebral cortex and of the seeming interchangeability of cortical tissue in experiments in which patches of cortex are rewired or transplanted in animals. I believe that the homogeneity is an illusion, owing to the fact that the brain is a system for information processing. Just as all books look the same to someone who does not understand the language in which they are written (since they are all composed of different arrangements of the same alphanumeric characters), and the DVD's of all movies look the same under a microscope, the cortex may look homogeneous to the eye but nonetheless contain different patterns of connectivity and synaptic biases that allow it to compute very different functions. I believe this these differences will be revealed in different patterns of gene expression in the developing cortex. I also believe that the apparent interchangeability of cortex occurs only in early stages of sensory systems that happen to have similar computational demands, such as isolating sharp signal transitions in time and space.

At the level of genetics, critics have pointed to the small number of genes in the human genome (now thought to be less than 25,000) and to their similarity to those of other animals. I believe that geneticists will find that there is a large store of information in the noncoding regions of the genome (the so-called junk DNA), whose size, spacing, and composition could have large effects on how genes are expressed. That is, the genes themselves may code largely for the meat and juices of the organism, which are pretty much the same across species, whereas how they are sculpted into brain circuits may depend on a much larger body of genetic information. I also believe that many examples of what we call "the same genes" in different species may differ in tiny ways at the sequence level that have large consequences for how the organism is put together.

And at the level of evolution, critics have pointed to how difficult it is to establish the adaptive function of a psychological trait. I believe this will change as we come to understand the genetic basis of psychological traits in more detail. New techniques in genomic analysis, which look for statistical fingerprints of selection in the genome, will show that many genes involved in cognition and emotion were specifically selected for in the primate, and in many cases the human, lineage.

JANNA LEVIN
Physicist, Columbia University; Author, How The Universe Got Its Spots

I believe there is an external reality and you are not all figments of my imagination. My friend asks me through the steam he blows off the surface of his coffee, how I can trust the laws of physics back to the origins of the universe. I ask him how he can trust the laws of physics down to his cup of coffee. He shows every confidence that the scalding liquid will not spontaneously defy gravity and fly up in his eyes. He lives with this confidence born of his empirical experience of the world. His experiments with gravity, heat, and light began in childhood when he palpated the world to test its materials. Now he has a refined and well-developed theory of physics, whether expressed in equations or not.

I simultaneously believe more and less than he does. It is rational to believe what all of my empirical and logical tests of the world confirm—that there is a reality that exists independent of me. That the coffee will not fly upwards. But it is a belief nonetheless. Once I've gone that far, why stop at the perimeter of mundane experience? Just as we can test the temperature of a hot beverage with a tongue, or a thermometer, we can test the temperature of the primordial light left over from the big bang. One is no less real than the other simply because it is remarkable.

But how do I really know? If I measure the temperature of boiling water, all I really know is that mercury climbs a glass tube. Not even that, all I really know is that I see mercury climb a glass tube. But maybe the image in my mind's eye isn't real. Maybe nothing is real, not the mercury, not the glass, not the coffee, not my friend. They are all products of a florid imagination. There is no external reality, just me. Einstein? My creation. Picasso? My mind's forgery. But this solopsism is ugly and arrogant. How can I know that mathematics and the laws of physics can be reasoned down to the moment of creation of time, space, the entire universe? In the very same way that my friend believes in the reality of the second double cappuccino he orders. In formulating our beliefs, we are honest and critical and able to admit when we are wrong—and these are the cornerstones of truth.

When I leave the café, I believe the room of couches and tables is still on the block at 122nd Street, that it is still full of people, and that they haven't evaporated when my attention drifts away. But if I am wrong and there is no external reality, then not only is this essay my invention, but so is the web, edge.org, all of its participants and their ingenious ideas. And if you are reading this, I have created you too. But if I am wrong and there is no external reality, then maybe it is me who is a figment of your imagination and the cosmos outside your door is your magnificent creation.

HAIM HARARI
Physicist, former President, Weizmann Institute of Science

The electron has been with us for over a century, laying the foundations to the electronic revolution and all of information technology. It is believed to be a point-like, elementary and indivisible particle. Is it?

The neutrino, more than a million times lighter than the electron, was predicted in the 1920's and discovered in the 1950's. It plays a crucial role in the creation of the stars, the sun and the heavy elements. It is elusive, invisible and weakly interacting. It is also considered fundamental and indivisible. Is it?

Quarks do not exist as free objects, except at extremely tiny distances, deep within the confines of the particles which are constructed from them. Since the 1960's we believe that they are the most fundamental indivisible building blocks of protons, neutrons and nuclei. Are they?

Nature has created two additional, totally unexplained, replicas of the electron, the neutrino and the most abundant quarks, u and d, forming three "generations" of fundamental particles. Each "generation" of particles is identical to the other two in all properties, except that the particle masses are radically different. Since each "generation" includes four fundamental particles, we end up with 12 different particles, which are allegedly indivisible, point-like and elementary. Are they?

The Atom, the nucleus and the proton, each in its own time, were considered elementary and indivisible, only to be replaced later by smaller objects as the fundamental building blocks. How can we be so arrogant as to exclude the possibility that this will happen again? Why would nature arbitrarily produce 12 different objects, with a very orderly pattern of electric charges and "color forces", with simple charge ratios between seemingly unrelated particles (such as the electron and the quark) and with a pattern of masses, which appears to be taken from the results of a lottery? Doesn't this "smell" again of further sub-particle structure?

There is absolutely no experimental evidence for a further substructure within all of these particles. There is no completely satisfactory theory which might explain how such light and tiny particles can contain objects moving with enormous energies, a requirement of quantum mechanics. This is, presumably, why the accepted "party line" of particle physicists is to assume that we already have reached the most fundamental level of the structure of matter.

For over twenty years, the hope has been that the rich spectrum of so-called fundamental particles will be explained as various modes of string vibrations and excitations. The astonishingly tiny string or membrane, rather than the point-like object, is allegedly at the bottom of the ladder describing the structure of matter. However, in spite of absolutely brilliant and ingenious mathematical work, not one experimental number has been explained in more than twenty years, on the basis of the string hypothesis.

Based on common sense and on an observation of the pattern of the known particles, without any experimental evidence and without any comprehensive theory, I have believed for many years, and I continue to believe, that the electron, the neutrino and the quarks are divisible. They are presumably made of different combinations of the same small number (two?) of more fundamental sub-particles. The latter may or may not have the string structure, and may or may not be themselves composites.

Will we live to see the components of the electron?

PAUL DAVIES
Physicist, Macquarie University, Sydney; Author, How to Build a Time Machine

One of the biggest of the Big Questions of existence is, Are we alone in the universe? Science has provided no convincing evidence one way or the other. It is certainly possible that life began with a bizarre quirk of chemistry, an accident so improbable that it happened only once in the entire observable universe—and we are it. On the other hand, maybe life gets going wherever there are earthlike planets. We just don't know, because we have a sample of only one. However, no known scientific principle suggests an inbuilt drive from matter to life. No known law of physics or chemistry favors the emergence of the living state over other states. Physics and chemistry are, as far as we can tell, "life blind."

Yet I don't believe that life is a freak event. I think the universe is teeming with it. I can't prove it; indeed, it could be that mankind will never know the answer for sure. If we find life in our solar system, it most likely got there from Earth (or vice versa) in rocks kicked off planets by comet impacts. And to go beyond the solar system is the stuff of dreams. The best hope is that we develop instruments sensitive enough to detect life on extra-solar planets from Earth orbit. But, whilst not impossible, this is a formidable technical challenge.

So why do I think we are not alone, when we have no evidence for life beyond Earth? Not for the fallacious popular reason: "the universe is so big there must be life out there somewhere." Simple statistics shows this argument to be bogus. If life is in fact a freak chemical event, it would be so unlikely to occur that it wouldn't happen twice among a trillion trillion trillion planets. Rather, I believe we are not alone because life seems to be a fundamental, and not merely an incidental, property of nature. It is built into the great cosmic scheme at the deepest level, and therefore likely to be pervasive. I make this sweeping claim because life has produced mind, and through mind, beings who do not merely observe the universe, but have come to understand it through science, mathematics and reasoning. This is hardly an insignificant embellishment on the cosmic drama, but a stunning and unexpected bonus. Somehow life is able to link up with the basic workings of the cosmos, resonating with the hidden mathematical order that makes it tick. And that's a quirk too far for me.

KEVIN KELLY
Editor-At-Large, Wired; Author, New Rules for the New Economy

The orthodoxy in biology states that every cell in your body shares exactly the same DNA. It's your identity, your indelible fingerprint, and since all the cells in your body have been duplicated from your initial unique stem cell these zillion of offspring cells all maintain your singular DNA sequence. It follows then that when you submit a tissue sample for genetic analysis it doesn't matter where it comes from. Normally technicians grab some from the easily accessible pars of your mouth, but they could just as well take some from your big toe, or your liver, or eyelash and get the same results.

I believe, but cannot prove, that the DNA in your body (and all bodies) varies from part to part. I make this prediction based on what we know about biology, which is that natures abhors uniformity. No where else in nature do we see identity maintained to such exactness. No where else is there such fixity.

I do not expect intra-soma variation to diverge very much. Indeed the genetic variation among individual humans is already relatively mild, among the least of all animals, so the diversity within a human body is unlikely to be greater than among human bodies—although that may be possible. More likely, intra-soma variation will be less than racial diversity but greater than zero.

Biologists already know (even if the public doesn't) that the full sequence of DNA in your cells changes over time as your chromosomes are shorten each time they divide in growth. Because of a bug in the system, DNA is unable to duplicate itself when it gets to the very very tip of its chain, so at each division it winds up a few hundred bases short. This slight reduction after each of the cell's scores of divisions is currently seen as the chief culprit in cell death and thus your own death. But the variation I believe is happening is more fundamental. My guess is that DNA mutates in a population of the cells in your body much as it does in a population of bodies.

The consequences are more than just curious. At the trivial end, if my belief were true, it would matter where you selected to sample your DNA from. And it might also affect when you get it, as this variation could change over time. If true, this variation might have some effect on locating the correct seminal cells for growing replacement organs and tissues.

While I have no evidence for my belief right now, it is a provable assertion. It will be shown to be true or false as soon as we have ubiquitous cheap full-genome sequences at discount mall prices. That is, pretty soon. I believe that once we have a constant reading of our individual full DNA (many times over our lives) we will have no end of surprises. I would not be surprised to discover that pet owners accumulate some tiny fragments of their pet's DNA,which has somehow been laterally transferred via viruses to their own cellular DNA. Or that diary farmers amass noticeable fragments of bovine DNA. Or that the DNA in our limbs somehow drift genetically in a "limby" way, distinct from the variation in the cells in our nervous systems.

But I consider all this minor compared to a possible major breakthrough in understanding. We have a pretty good idea of how the "selection" in natural selection works: less fit organisms die. But when it comes to understanding how variation arises in Darwinian evolution all we can say is "random mutation" which is another way of saying "we don't know exactly." If there were intra-somatic variation and if we could easily observe it via massive constant full-genome sequencing then we might be able to figure out exactly how a mutation occurs, and whether there are patterns to those mutations, and to what extant such variation is induced or influenced by the body or the environment—all ideas which currently challenge the Darwinian wisdom that the body does not directly influence the genetic makeup of a cell. Monitoring genetic drift within a body may be a window into the origins of mutation itself.

Even if these larger ideas don't pan out, the simple fact that DNA in each cell of your body is not 100% identical would be worth investigating. Such a fact would be a surprise, except to me.