STEVE GIDDINGS
Theoretical Physicist, University of California, Santa Barbara

I believe that black holes do not destroy information, as Hawking argued long ago, and the reason is that strong gravitational effects undermine the statement that degrees of freedom inside and outside the black hole are independent.

On the first point, I am far from alone; many string theorists and others now believe that black holes don't destroy information, and thus don't violate quantum mechanics. Hawking himself recently announced that he believes this, and has conceded a famous bet, but has not yet published the work giving a sharp statement where his original logic went wrong.

The second point I believe, but cannot yet prove to the point of convincing many of my colleagues. While many believe that Hawking was wrong, there is a lot of dissent over where exactly his calculation fails, and none of the arguments previously presented have sharply identified this point of failure. If black holes emit information instead of destroying it, this probably comes from a breakdown of locality. Lowe, Polchinski, Susskind, Thorlacius, and Uglum have argued that the mechanism for locality violation involves formation of long strings. Horowitz and Maldacena have argued that the singularity at the center of a black hole must be a unique state, in effect squeezing information out in a ghostly way. And others have made other suggestions.

But I believe, and my former student Lippert and I have published arguments, that the breakdown of locality that invalidates Hawking's work involves strong gravitational physics that makes it inconsistent to think of separate and independent degrees of freedom inside and outside the black hole. The assumption that these degrees of freedom are separate is fundamental to Hawking's argument. Our argument for where it fails has a satisfying generality that mirrors the generality of Hawking's original work—neither depends on the specifics of what kind of matter exists in the theory.

We base our argument on a principle we call the locality bound. This is a criterion for when physical degrees of freedom can be independent (in technical language, described by vanishing of commutators of corresponding operators). Roughly, a degree of freedom corresponding to a particle at position x with momentum p and another at y with momentum q will be independent only if the separation x-y is large enough that they are outside of a black hole that would form from their mutual energy. I believe this is the beginning of a general criterion (which will ultimately more precisely formulated) for when locality breaks down in physics. This could be the beginning of a deeper understanding of holography. And, it should be relevant to black hole physics because of the large relative energies of the Hawking radiation and degrees of freedom falling into a black hole. But this is not fully proven. Yet.

HOWARD RHEINGOLD
Communications Expert; Author, Smart Mobs

I believe that we humans, who know so much about cosmology and immunology, lack a framework for thinking about why and how humans cooperate. I believe that part of the reason for this is an old story we tell ourselves about the world:  Businesses and nations succeed by competing well. Biology is a war, where only the fit survive. Politics is about winning. Markets grow solely from self-interest. Rooted in the zeitgeist of Adam Smith's and Charles Darwin's eras, the scientific, social, economic, political stories of the 19th and 20th centuries overwhelmingly emphasized the role of competition as a driver of evolution, progress, commerce, society.

I believe that the outlines of a new narrative are becoming visible—a story in which cooperative arrangements, interdependencies, and collective action play a more prominent role and the essential (but not all-powerful) story of competition and survival of the fittest shrinks just a bit.

Although new knowledge in biology about the evolution of altruistic behavior and the role of symbiotic relationships, new understandings of economic behavior derived from experiments in game theory, neuroeconomic research, sociological investigations of institutions for collective action, computation-enabled technologies such as grid computing, mesh networks, and online markets all provide important clues, I don't believe anyone is likely to formulate an algorithm or recipe for human cooperation. I suspect that the complex interdependencies of human thought, behavior and culture entails an equivalent to the limits Heisenberg found to physics and Gödel established for mathematics.

I believe that more knowledge than what we have now, together with a conceptual framework that is neither reductionistic nor theological, could lead to better-designed economic and political policies and institutions. Institutional and conceptual barriers to mounting such an effort are as formidable as the methodological barriers. I am reminded of Doug Engelbart's problem in the 1950s. He couldn't convince computer engineers, librarians, public policy analysts that computing machinery could be used to augment human thinking, as well as performing scientific calculation and business data processing. Nobody and no institution had ever thought about computing machinery that way, and older ways of thinking about what machines could be designed to do were inadequate. Engelbart had to create "A Framework for Augmenting Human Intellect" before the various hardware, software, and human interface designers could create the first personal computers and networks.

By necessity, useful new understandings of how humans cooperate and fail to cooperate is an interdisciplinary task. I don't believe that the obvious importance of such an effort guarantees that it will be successfully accomplished. All our institutions for gathering and validating knowledge—universities, corporate research laboratories, and foundations—reward and support specialization.

LEO CHALUPA
Ophthalmologist and Neurobiologist, University of California, Davis

Here are three of my unproven beliefs:

(i) The human brain is the most complex entity in the known universe;

(ii) With this marvelous product of evolution we will be successful in eventually discovering all that there is to discover about the physical world, provided of course, that some catastrophic event doesn't terminate our species; and

(iii) Science provides the best means to attain this ultimate goal.

When the scientific endeavor is considered in relation to the obvious limitations of the human brain, the knowledge we have gained in all fields to date is astonishing. Consider the well-documented variability in the functional properties of neurons. When recordings are made from a single cell—for instance in the visual cortex to a flashing spot of light—one can't help but be amazed by the trial-to-trial variations in the resulting responses.

On one trial this simple stimulus might elicit a high frequency burst of discharges, while on the next trial there could be just a hint of a response. The same thing is apparent when EEG recordings are made from the human brain. Brain waves change in frequency and amplitude in seemingly random fashion even when the subject is lying in a prone position without any variations in behavior or the environment.
And such variability is also evident when one does brain imaging; the pretty pictures seen in publications are averages of many trials that have been "massaged" by various computer programs.

So how does the brain do it? How can it function as effectively as it does given the "noise" inherent in the system? I don't have a good answer, and neither does anyone else, in spite of the papers that have been published on this problem. But in line with the second of the three beliefs I have listed above, I am certain that someday this question will be answered in a definitive manner.

CARLO ROVELLI
Physicist; Institut Universitaire de France & University of the Mediterraneum; Author, Quantum Gravity

I am convinced, but cannot prove, that time does not exist. I mean that I am convinced that there is a consistent way of thinking about nature, that makes no use of the notions of space and time at the fundamental level. And that this way of thinking will turn out to be the useful and convincing one.

I think that the notions of space and time will turn out to be useful only within some approximation. They are similar to a notion like "the surface of the water" which looses meaning when we describe the dynamics of the individual atoms forming water and air: if we look at very small scale, there isn't really any actual surface down there. I am convinced space and time are like the surface of the water: convenient macroscopic approximations, flimsy but illusory and insufficient screens that our mind uses to organize reality.

In particular, I am convinced that time is an artifact of the approximation in which we disregard the large majority of the degrees of freedom of reality. Thus "time" is just the reflection of our ignorance.

I am also convinced, but cannot prove, that there are no objects, but only relations. By this I mean that I am convinced that there is a consistent way of thinking about nature, that refers only to interactions between systems and not to states or changes of individual systems. I am convinced that this way of thinking nature will end up to be the useful and natural one in physics.

Beliefs that one cannot prove are often wrong, as proven by the fact that this Edge list contains contradictory beliefs. But they are essential in science and often healthy. Here is a good example from 25 centuries ago: Socrates, in Plato's Phaedon says:

"... seems to me very hard to prove, and I think I wouldn't be able to prove it ... but I am convinced ... that the Earth is spherical."

Finally, I am also convinced, but cannot prove, that we humans have an instinct to collaborate, and that we have rational reasons for collaborating. I am convinced that ultimately this rationality and this instinct of collaboration will prevail over the shortsighted egoistic and aggressive instinct that produces exploitation and war. Rationality and instinct of collaboration have already given us large regions and long periods of peace and prosperity. Ultimately, they will lead us to a planet without countries, without wars, without patriotism, without religions, without poverty, where we will be able to share the world. Actually, maybe I am not sure I truly believe that I believe this; but I do want to believe that I believe this.

JOHN McCARTHY
Computer Scientist; Artificial Intelligence Pioneer, Stanford University

I think, as did Gödel, that the continuum hypothesis is false. No-one will ever prove it false from the presently accepted axioms of set theory. Chris Freiling's proposed new (1986) axioms prove it false, but they are not regarded as intuitive.

I think human-level artificial intelligence will be achieved.

JAMES O'DONNELL
Classicist; Cultural Historian; Provost, Georgetown University; Author, Avatars of the Word

What do I believe is true even though I cannot prove it? This question has a double edge and needs two answers.

First, and most simply: "everything". On a strict Popperian reading, all the things I "know" are only propositions that I have not yet falsified. They are best estimates, hypotheses that, so far, make sense of all the data that I possess. I cannot prove that my parents were married on a certain day in a certain year, but I claim to "know" that date quite confidently. Sure, there are documents, but in fact in their case there are different documents that present two different dates, and I recall the story my mother told to explain that and I believe it, but I cannot "prove" that I am right. I also know Newton's Laws and indeed believe them, but I also now know their limitations and imprecisions and suspect that more surprises may lurk in the future.

But that's a generic answer and not much in the forward-looking and optimistic spirit that characterizes Edge. So let me propose this challenge to practitioners of my own historical craft. I believe that there are in principle better descriptions and explanations for the development and sequence of human affairs than human historians are capable of providing. We draw our data mainly from witnesses who share our scale of being, our mortality, and for that matter our viewpoint. And so we explain history in terms of human choices and the behavior of organized social units. The rise of Christianity or the Norman Conquest seem to us to be events we can explain and we explain them in human-scale terms. But it cannot be excluded or disproved that events can be better explained on a much larger time scale or a much smaller scale of behavior. An outright materialist could argue that all my acts, from the day of my birth, have been a determined result of genetics and environment. It was fashionable a generation ago to argue a Freudian grounding for Luther's revolt, but in principle it could as easily be true and, if we could know it, more persuasive to demonstrate that his acts were determined a the molecular and submolecular level.

The problem with such a notion is, of course, that we are very far from being able to outline such a theory, much less make it persuasive, much less make it something that another human being could comprehend. Understanding even one other person's life at such microscopic detail would take much more than one lifetime.

So what is to be done? Of course historians will constantly struggle to improve their techniques and tools. The advance of dendrochronology (dating wood by the tree rings, and consequently dating buildings and other artifacts far more accurately than ever before) can stand as one example of the way in which technological advance can tell us things we never knew before. But we will also continue to write and to read stories in the old style, because stories are the way human beings most naturally make sense of their world. An awareness of the powerful possibility of whole other orders of possible description and explanation, however, should at least teach us some humility and give us some thoughtful pause when we are tempted to insist too strongly on one version of history—the one we happen to be persuaded is true. Even a Popperian can see that this kind of intuition can have beneficial effect.

PAMELA McCORDUCK
Writer; Author, Machines Who Think

Although I can't prove it, I believe that thanks to new kinds of social modeling, that take into account individual motives as well as group goals, we will soon grasp in a deep way how collective human behavior works, whether it's action by small groups or by nations. Any predictive power this understanding has will be useful, especially with regard to unexpected outcomes and even unintended consequences. But it will not be infallible, because the complexity of such behavior makes exact prediction impossible.

MARTIN REES
Cosmologist, Cambridge University; UK Astronomer Royal; Author, Our Final Hour

I believe that intelligent life may presently be unique to our Earth, but that, even so, it has the potential to spread through the galaxy and beyond—indeed, the emergence of complexity could still be near its beginning. If SETI searches fail, that would not render life a cosmic sideshow Indeed, it would be a boost to our cosmic self-esteem: terrestrial life, and its fate, would become a matter of cosmic significance. Even if intelligence is now unique to Earth, there's enough time lying ahead for it to spread through the entire Galaxy, evolving into a teeming complexity far beyond what we can even conceive.

There's an unthinking tendency to imagine that humans will be around in 6 billion years, watching the Sun flare up and die. But the forms of life and intelligence that have by then emerged would surely be as different from us as we are from a bacterium. That conclusion would follow even if future evolution proceeded at the rate at which new species have emerged over the 3 or 4 billion years of the geological past. But post-human evolution (whether of organic species or of artefacts) will proceed far faster than the changes that led to emergence, because it will be intelligently directed rather than being—like pre-human evolution—the gradual outcome of Darwinian natural selection. Changes will drastically accelerate in the present century—through intentional genetic modifications, targeted drugs, perhaps even silicon implants in to the brain. Humanity may not persist as a single species for more than a few centuries—especially if communities have by then become established away from the earth.

But a few centuries is still just a millionth of the Sun's future lifetime—and the entire universe probably has a longer future still. The remote future is squarely in the realm of science fiction. Advanced intelligences billions of years hence might even create new universes. Perhaps they'll be able to choose what physical laws prevail in their creations. Perhaps these beings could achieve the computational capability to simulate a universe as complex as the one we perceive ourselves to be in.

My belief may remain unprovable for billions of years. It could be falsified sooner—for instance, we (or our immediate post-human descendents) may develop theories that reveal inherent limits to complexity. But it's a substitute for religious belief, and I hope it's true.

CAROLYN PORCO
Planetary Scientist; Leader, Cassini Imaging Team; Director, CICLOPS, Space Science Institute, Boulder

This is a treacherous question to ask, and a trivial one to answer. Treacherous because the shoals between the written lines can be navigated by some to the conclusion that truth and religious belief develop by the same means and are therefore equivalent. To those unfamiliar with the process by which scientific hunches and hypotheses are advanced to the level of verifiable fact, and the exacting standards applied in that process, the impression may be left that the work of the scientist is no different than that of the prophet or the priest.

Of course, nothing could be further from reality.

The whole scientific method relies on the deliberate, high magnification scrutiny and criticism by other scientists of any mechanisms proposed by any individual to explain the natural world. No matter how fervently a scientist may "believe'"something to be true, and unlike religious dogma, his or her belief is not accepted as a true description or even approximation of reality until it passes every test conceivable, executable and reproducible. Nature is the final arbiter, and great minds are great only in so far as they can intuit the way nature works and are shown by subsequent examination and proof to be right.

With that preamble out of the way, I can say that for me personally, this is a trivial question to answer. Though no one has yet shown that life of any kind, other than Earthly life, exists in the cosmos, I firmly believe that it does. My justification for this belief is a commonly used one, with no strenuous exertion of the intellect or suspension of disbelief required.

Our reconstruction of early solar system history, and the chronology of events that led to the origin of the Earth and moon and the subsequent development of life on our planet, informs us that self-replicating organisms originated from inanimate materials in a very narrow window of time. The tail end of the accretion of the planets—a period known as "the heavy bombardment"—ended about 3.8 billion years ago, approximately 800 million years after the Earth formed. This is the time of formation and solidification of the big flooded impact basins we readily see on the surface of the Moon, and the time when the last large catastrophe-producing impacts also occurred on the Earth. In other words, the terrestrial surface environment didn't settle down and become conducive to the development of fragile living organisms until nearly a billion years had gone by.

However, the first appearance of life forms on the Earth, the oldest fossils we have discovered so far, occurred shortly after that: around 3.5 billion years ago or even earlier. The interval in between—only 300 millions years and less than the time represented by the rock layers in the walls of the Grand Canyon—is the proverbial blink of the cosmic eye. Despite the enormous complexity of even the simplest biological forms and processes, and the undoubtedly lengthy and complicated chain of chemical events that must have occurred to evolve animated molecular structures from inanimate atoms, it seems an inevitable conclusion that Earthly life developed very quickly and as soon as the coast was clear long enough to do so.

Evidence is gathering that the events that created the solar system and the Earth, driven predominantly by gravity, are common and pervasive in our galaxy and, by inductive reasoning, in galaxies throughout the cosmos. The cosmos is very, very big. Consider the overwhelming numbers of galaxies in the visible cosmos alone and all the Sun-like stars in those galaxies and the number of habitable planets likely to be orbiting those stars and the ease with which life developed on our own habitable planet, and it becomes increasingly unavoidable that life is itself a fundamental feature of our universe ... along with dark matter, supernovae, and black holes.

I believe we are not alone. But it doesn't matter what I think because I can't prove it. It is so beguiling a question, though, that humankind is presently and actively seeking the answer. The search for life and so-called "habitable zones" is becoming increasingly the focus of our planetary explorations, and it may in fact transpire one day that we discover life forms under the ice on some moon orbiting Jupiter or Saturn, or decode the intelligible signals of an advanced, unreachably distant, alien organism. That will be a singular day indeed. I only hope I'm still around when it happens.

CHARLES SIMONYI
Computer Scientist, Intentional Software Corporation; formerly Chief Architect, Microsoft Corporation

I believe that we are writing software the wrong way. There are sound evolutionary reasons for why we are doing what we are doing—that we can call the "programming the problem in a computer language" paradigm, but the incredible success of Moore's law blinded us to being stuck in what is probably an evolutionary backwater. There are many warning signs. Computers are demonstrably ten thousand times better than not so long ago. Yet we are not seeing their services improving at the same rate (with some exceptions—for example games and internet searches.) On an absolute scale, a business or administration problem that would take maybe one hundred pages to describe precisely, will take millions of dollars to program for a computer and often the program will not work. Recently a smaller airline came to a standstill due to a problem in crew scheduling software—raising the ire of Congress, not to mention their customers. My laptop could store 200 pages of text (1/2 megabytes) for each and every crew member at this airline just in its fast memory and hundred times more (a veritable encyclopedia of 20,000 pages) for each person on its hard disk. Of course for a schedule we would need maybe one or two—or at most ten pages per person. Even with all the rules—the laws, the union contracts, the local, state, federal taxes, the duty time limitations, the FAA regulations on crew certification; is there anyone who believes that the problem is not simple in terms of computing? We need to store and process at the maximum 10 pages per person where we have capacity for two thousand times more in one cheap laptop! Of course the problem is complex in terms of the problem domain—but not shockingly so. I would estimate that all the rules possibly relevant to aircraft crew scheduling are expressible in less than a thousand pages—or 1/2 of one percent of the fast memory.
Software is surely the bottleneck on the high-tech horn of plenty. The scheduling program for the airline takes many thousand times more memory than what I believe it should be. Hence the software represents complexity that is many thousand times greater than what I believe the problem is—no wonder that some planes are assigned three pilots by the software while the others can't fly because the copilot is not scheduled. Note that the cost of the memory is not the issue—we could afford that waste. But the use of so much memory for software is an indication of some complexity inflation that occurs during programming that is the real bottleneck.

What is going on? I like to use cryptography as the metaphor. As we know, in cryptography we take a message and we combine it with a key using a difficult-to-invert function to get the code. Programmers using today's paradigm start from a problem statement, for example that a Boeing 767 requires a pilot, a copilot, and seven cabin crew with various certification requirements for each—and combine this with their knowledge of computer science and software engineering—that is how this rule can be encoded in computer language and turned into an algorithm. This act of combining is the programming process, the result of which is called the source code. Now, programming is well known to be a difficult-to-invert function, perhaps not to cryptography's standards, but one can joke about the possibility of the airline being able to keep their proprietary scheduling rules secret by publishing the source code for the implementation since no one could figure out what the rules were—or really whether the code had to do with scheduling or spare parts inventory—by studying the source code, it can be that obscure.

The amazing thing is that today it is the source code—that is the encrypted problem—which is the artifact all of software engineering is focusing on. To add insult to the injury, the "encryption", that is programming, is done manually which means high costs, low throughput and high error rates. In contrast with software maintenance, when the General realizes that he is about to send a wrong encrypted message, no one would think of editing the code after the encryption or "fixing the code"; instead the clear text would be first edited and then this improved message would be re-encrypted at computer speeds and computer accuracy. In other words the message may be wrong, but it won't be wrong because of the encryption and it is easily fixed.

We see that the complexity inflation comes from encoding. The problem statement above is obviously oversimplified, but remember that we used just two lines from our realistic budget of a thousand pages and we haven't even used the aviation jargon which can make these statements even more compact and more precise. But once these statements are viewed through the funhouse mirror of software coding, it becomes all but unrecognizable: thousand times fatter, disjointed, foreign. And as any manual product, it will have many flaws—beyond the errors in the rules themselves.

What can be done? Follow the metaphor. First, refocus on recording the problem statement—the "cleartext" in our metaphor. This is not a program in any sense of the word—it is just a straightforward recording of the subject matter experts' contributions using their own terms-of-art, their jargon, their own notations. Next, empower the programmers to program not the problem itself, but to express their software engineering expertise and decisions as a computer code for the encoder that takes the recorded problem statement and generates the code from it. This is called generative programming and I believe it is the future of software.

CHRIS W. ANDERSON
Editor-In-Chief, Wired

The Intelligent Design movement has opened my eyes. I realize that although I believe that evolution explains why the living world is the way it is, I can't actually prove it. At least not to the satisfaction of the ID folk, who seem to require that every example of extraordinary complexity and clever plumbing in nature be fully traced back (not just traceable back) along an evolutionary tree to prove that it wasn't directed by an invisible hand. If the scientific community won't do that, then the arguments goes that they must accept a large red "theory" stamp placed on the evolution textbooks and that alternative theories, such as "guided" evolution and creationism, be taught alongside.

So, by this standard, virtually everything I believe in must now fall under the shadow of unproveability. Most importantly, this includes the belief that democracy, capitalism and other market-driven systems (including evolution!) are better than their alternatives. Indeed, I suppose I should now refer to them as the "theory of democracy" and the "theory of capitalism", to join the theory of evolution, and accept the teaching of living Marxism and fascism as alternatives in high schools.

VERENA HUBER-DYSON
Mathematician, Emeritus Professor, Dept of Philosophy, University of Calgary; Author, Gödel's Theorems

Most of what I believe I cannot prove, simply for lack of time and energy; truths that I'd claim to know because they have been proved by others. That is how inextricably our beliefs are tied up with labors accomplished by fellow beings. And then there are mathematical truths that we now know are not provable. These phenomena have become favorites with the media but can only be made sense of by a serious scrutiny of the idea of mathematical truth and a specific articulation of a proof-concept,

But running across Esther's contribution I came up with a catchy response:

I believe in the creative power of boredom.

Or, to put it into the form suggested by the Edge question:

I believe that, no matter how relentlessly we overfeed our young with prepackaged interactive entertainments, before long they will break out and invent their own amusements. I know from experience; boredom drove me into mathematics during my preteens. But I cannot prove it, till it actually happens. Probably in less than a generation kids will be amusing themselves and each other in ways that we never dreamt of.

Such is my belief in human nature, in the resilience of its good sense.

Here is an observation from mathematical practice. By now the concept of an algorithm, well- defined, is widely hailed as the way to solve problems, more precisely sequences of problems labeled by a numerical parameter. The implementation of a specific algorithm may be boring, a task best left to a machine, while the construction of the algorithm together with a rigorous proof that it works is a creative and often laborious enterprise.

For illustration consider group theory. A group is defined as a structure consisting of a non-empty set and a binary operation obeying certain laws. The theory of groups consists of all sentences true of all groups; its restriction to the formal "first order" language L determined by the group structure is called the elementary theory TG of groups. Here we have a formal proof procedure, proven complete by Gödel in his PHD thesis the year before his incompleteness proof was published. The elementary theory of groups is axiomatizable: it consists of exactly those sentences that are derivable from the axioms by means of the rules of first order logic. Thus TG is an effectively (recursively) enumerable subset of L; a machine, unlimited in power and time, could eventually come up with a proof of every elementary theorem of group theory. However, a human group theorist would still be needed to select the interesting theorems out of the bulk of the merely true. The development of TG is no mean task, although its language is severely restricted.

The axiomatizability of a theory always raises the question how to recognize the non-theorems. The set FF of those L-sentences that fail in some finite group is recursively enumerable by an enumeration of all finite groups, a simple matter, in principle. But, as all the excitement over the construction of finite simple monsters has amply demonstrated, that again is in reality no simple task.

Neither the theory of finite groups nor the theory of all groups is decidable. The most satisfying proof of this fact shows how to construct to every pair (A, B) of disjoint recursively enumerable sets of L-sentences, where A contains all of TG and B contains FF, a sentence S that belongs neither to A nor to B. This is the deep and sophisticated theorem of effective non-separability proved in the early sixties independently by Mal'cev in the SSSR and Tarski's pupil Cobham.

It follows that constructing infinite counter-examples in group theory is a truly creative enterprise, while the theory of finite groups is not axiomatizable and so, to recognize a truth about finite groups requires deep insight and a creative jump. The concept of finiteness in group theory is not elementary and yet we have a clear idea of what is meant by talking about all finite groups, a marvelously intriguing situation.

To wind up with a specific answer to the 2005 Question:

I do believe that every sentence expressible in the formal language of elementary group theory is either true of all finite groups or else fails for at least one of them.

This statement may at first sight look like a logical triviality. But when you try to prove it honestly you find that you would need a decision procedure, which would, given any sentence of L, yield either a proof that S holds in all finite groups or else a finite group in which S fails. By the inseparability theorem mentioned above, there is no such procedure.

If asked whether I hold the equivalent belief for the theory of all groups I would hesitate because the concept of an infinite counterexample is not as concrete to my mind as that of the totality of all finite groups. These are the areas where personal intuition starts to come into play.

REBECCA GOLDSTEIN
Philosopher and Novelist, Trinity College; Author, Incompleteness

I believe that scientific theories are a means of going—somewhat mysteriously—beyond what we are able to observe of the physical world, penetrating into the structure of nature. The "theoretical" parts of scientific theories—the parts that speak in seemingly non-observational terms—aren't, I believe, ultimately translatable into observations or aren't just algorithmic black boxes into which we feed our observations and churn out our predictions. I believe the theoretical parts have descriptive content and are true (or false) in the same prosaic way that the observational parts of theories are true (or false). They're true if and only if they correspond to reality.

I also believe that my belief about scientific theories isn't itself scientific. Science itself doesn't decide how it is to be interpreted, whether realistically or not.

That the penetration into unobservable nature is accomplished by way of abstract mathematics is a large part of what makes it mystifying—mystifying enough to be coherently if unpersuasively (at least to me) denied by scientific anti-realists. It's difficult to explain exactly how science manages to do what it is that I believe it does—notoriously difficult when trying to explain how quantum mechanics, in particular, describes unobserved reality. The unobservable aspects of nature that yield themselves to our knowledge must be both mathematically expressible and connected to our observations in requisite ways. The seventeenth-century titans, men like Galileo and Newton, figured out how to do this, how to wed mathematics to empiricism. It wasn't a priori obvious that it was going to work. It wasn't a priori obvious that it was going to get us so much farther into nature's secrets than the Aristotelian teleological methodology it was supplanting. A lot of assumptions about the mathematical nature of the world and its fundamental correspondence to our cognitive modes (a correspondence they saw as reflective of God's friendly intentions toward us) were made by them in order to justify their methodology.

I also believe that since not all of the properties of nature are mathematically expressible—why should they be? it takes a very special sort of property to be so expressible—that there are aspects of nature that we will never get to by way of our science. I believe that our scientific theories—just like our formalized mathematical systems (as proved by Gödel)—must be forever incomplete. The very fact of consciousness itself (an aspect of the material world we happen to know about, but not because it was revealed to us by way of science) demonstrates, I believe, the necessary incompleteness of scientific theories.

JONATHAN HAIDT
Psychologist, University of Virginia

I believe, but cannot prove, that religious experience and practice is generated and structured largely by a few emotions that evolved for other reasons, particularly awe, moral elevation, disgust, and attachment-related emotions. That's not a prediction likely to raise any eyebrows in this forum.

But I further believe (and cannot prove) that hostility toward religion is an obstacle to progress in psychology. Most human beings live in a world full of magic, miracles, saints, and constant commerce with divinity. Psychology at present has little to say about these parts of life; we focus instead on a small set of topics that are fashionable, or that are particularly tractable with our favorite methods. If psychologists took religious experience seriously and tried to understand it from the inside, as anthropologists do with other cultures, I believe it would enrich our science. I have found religious texts and testimonials about purity and pollution essential for understanding the emotion of disgust.

DONALD I. WILLIAMSON
Biologist, University of Liverpool; Author, The Origins of Larvae

I believe I can explain the Cambrian explosion.

The Cambrian explosion refers to the first appearance in a relatively short space of geological time of a very wide assortment of animals more than 500 million years ago. I believe it came about through hybridization.

Many well preserved Cambrian fossils occur in the Burgess shale, in the Canadian Rockies. These fossils include small and soft-bodied animals, several of which were planktonic but none were larvae. Compared with modern animals, some of them seem to have the front end of one animal and rear end of another. Modern larvae present a comparable set-up: larvae seem to be derived from animals in different groups from their corresponding adults. I have amassed a bookful of evidence that the basic forms of larvae did indeed originate as animals in other groups and that such forms were transferred by hybridization. Animals with larvae are "sequential chimeras", in which one body-form—the larva—is followed by another, distantly related form—the adult. I believe there were no Cambrian larvae, and Cambrian hybridizations produced "concurrent chimeras", in which two distantly related body-forms appeared together.

About 700 million years ago, shortly before the Cambrian, animals with tissues (metazoans) made their first appearance. I agree with Darwin that there were several different forms (Darwin suggested four or five), and I believe they resulted from hybridizations between different colonial protists. Protists are mostly single-celled, but colonial forms consist of many similar cells. All Cambrian animals were marine, and, like most modern marine animals, they shed their eggs and sperm into the water, where fertilization took place. Eggs of one species frequently encountered sperm of another, and there were only poorly developed mechanisms to prevent hybridization. Early animals had small genomes, leaving plenty of spare gene capacity. These factors led to many fruitful hybridizations, which resulted in concurrent chimeras. Not only did the original metazoans hybridize but the new animals resulting from these hybidizations also hybridized, and this produced the explosion in animal form.

The acquisition of larvae by hybridization came much later, when there was little spare genome capacity in recipes for single animals, and it is still going on. In the echinoderms (the group that includes sea-urchins and starfish) there is evidence that there were no larvae in either the Cambrian or the Ordovician (the following period), and this might well apply to other major groups. Acquiring parts, rather than larvae, by hybridization continued, I believe, throughout the Cambrian and Ordovician and probably later, but, as genomes became larger and filled most of the available space, later hybridizations led to smaller changes in adult form or to acquisitions of larvae. The gradual evolution of better mechanisms to prevent eggs being fertilized by foreign sperm resulted in fewer fruitful hybridizations, but occasional hybridizations still take place.

Hybridogenesis, the generation of new organisms by hybridization, and symbiogenesis, the generation of new organisms by symbiosis, both involve fusion of lineages, whereas Darwinian "descent with modification" is entirely within separate lineages. These forms of evolution function in parallel, and "natural selection" works on the results.

I cannot prove that Cambrian animals had poorly developed specificity and spare gene capacity, but it makes sense.

SETH LLOYD
Quantum Mechanical Engineer, Massachusetts Institute of Technology

I believe in science. Unlike mathematical theorems, scientific results can't be proved.They can only be tested again and again, until only a fool would not believe them.

I cannot prove that electrons exist, but I believe fervently in their existence. And if you don't believe in them, I have a high voltage cattle prod I'm willing to apply as an argument on their behalf. Electrons speak for themselves.

MARTIN NOWAK
Biological Mathematician, Harvard University; Director, Center for Evolutionary Dynamics

I believe the following aspects of evolution to be true without knowing how to turn them into (respectable) research topics.

Important steps in evolution are robust. Multi-cellularity evolved at least ten times. There are several independent origins of eusociality. There were a number of lineages leading from primates to humans. If our ancestors would not have evolved language, somebody else would have.

Cooperation and language define humanity. Every special trait of humans is derivative of language.

Mathematics is a language and therefore a product of evolution.

W. DANIEL HILLIS
Physicist, Computer Scientist; Chairman, Applied Minds, Inc.; Author, The Pattern on the Stone

I know that it sounds corny, but I believe that people are getting better. In other words, I believe in moral progress. It is not a steady progress, but there is a long-term trend in the right direction—a two steps forward, one step back kind of progress.

I believe, but cannot prove, that our species is passing through a transitional stage, from being animals to being true humans. I do not pretend to understand what true humans will be like, and I expect that I would not even understand it if I met them. Yet, I believe that our own universal sense of right and wrong is pointing us in the right direction, and that it is the direction of our future.

I believe that ten thousand years from now, people (or whatever we are by then) will be more empathetic and more altruistic than we are. They will trust each other more, and for good reason. They will take better care of each other. They be more thoughtful about the broader consequences of their actions. They will take better care of their future than we do of ours.

ROBERT R. PROVINE
Psychologist and Neuroscientist, University of Maryland; Author, Laughter

Human Behavior is Unconsciously Controlled.

Until proven otherwise, why not assume that consciousness does not play a role in human behavior? Although it may seem radical on first hearing, this is actually the conservative position that makes the fewest assumptions. The null position is an antidote to philosopher's disease, the inappropriate attribution of rational, conscious control over processes that may be irrational and unconscious. The argument here is not that we lack consciousness, but that we over-estimate the conscious control of behavior. I believe this statement to be true. But proving it is a challenge because it's difficult to think about consciousness. We are misled by an inner voice that generates a reasonable but often fallacious narrative and explanation of our actions. That the beam of conscious awareness that illuminates our actions is on only part of the time further complicates the task. Since we are not conscious of our state of unconsciousness, we vastly overestimate the amount of time that we are aware of our own actions, whatever their cause.

My thinking about unconscious control was shaped by my field studies of the primitive play vocalization of laughter. When I asked people to explain why they laughed in a particular situation, they would concoct some reasonable fiction about the cause of their behavior—"someone did something funny," "it was something she said," "I wanted to put her at ease." Observations of social context showed that such explanations were usually wrong. In clinical settings, such post hoc misattributions would be termed "confabulations," honest but flawed attempts to explain one's actions.

Subjects also incorrectly presumed that laughing is a choice and under conscious control, a reason for their confident, if bogus, explanations of their behavior. But laughing is not a matter speaking "ha-ha," as we would choose a word in speech. When challenged to laugh on command, most subjects could not do so. In certain, usually playful, social contexts, laughter simply happens. However, this lack of voluntary control does not preclude a lawful pattern of behavior. Laughter appears at those places where punctuation would appear in a transcription of a conversation—laughter seldom interrupts the phrase structure of speech. We may say, "I have to go now—ha-ha," but rarely, "I have to—ha-ha—go now." This punctuation effect is highly reliable and requires the coordination of laughing with the linguistic structure of speech, yet it is performed without conscious awareness of the speaker. Other airway maneuvers such as breathing and coughing punctuate speech and are performed without speaker awareness.

The discovery of lawful but unconsciously controlled laughter produced by people who could not accurately explain their actions led me to consider the generality of this situation to other kinds of behavior. Do we go through life listening to an inner voice that provides similar confabulations about the causes of our action? Are essential details of the neurological process governing human behavior inaccessible to introspection? Can the question of animal consciousness be stood on its head and treated in a more parsimonious manner? Instead of considering whether other animals are conscious, or have a different, or lesser consciousness than our own, should we question if our behavior is under no more conscious control than theirs? The complex social order of bees, ants, and termites documents what can be achieved with little, if any, conscious control as we think of it. Is machine consciousness possible or even desirable? Is intelligent behavior a sign of conscious control? What kinds of tasks require consciousness? Answering these questions requires an often counterintuitive approach to the role, evolution and development of consciousness.

PAUL BLOOM
Psychologist, Yale University; Author, Descartes' Baby

John MacNamara once proposed that children come to learn about right and wrong, good and evil, in much the same way that they learn about geometry and mathematics. Moral development is not merely cultural learning, and it does not arise from innate principles that have evolved through natural selection. It is not like the development of language or sexual preference or taste in food.

Instead, moral development involves the construction of a intricate formal system that makes contact with the external world in a significant way. This cannot be entirely right. We know that gut-feelings, such as reactions of empathy or disgust, have a major influence on how children and adults reason about morality. And no serious theory of moral development can ignore the role of natural selection in shaping our moral intuitions. But what I like about Macnamara's proposal is that it allows for moral realism. It allows for the existence of moral truths that people come to discover, just as we come to discover truths of mathematics. We can reject the nihilistic position (help by many researchers) that our moral intuitions are nothing more than accidents of biology or culture.

And so I believe (though I cannot prove it) that the development of moral reasoning is the same sort of process as the development of mathematical reasoning.

The "group mind" that developed among these soldiers was created by a set of known social psychological conditions, some of which are nicely featured in Golding's Lord of the Flies. The same processes that I witnessed in my Stanford Prison Experiment were clearly operating in that remote place: Deindividuation, dehumanization, boredom, groupthink, role-playing, rule control, and more. Beyond the relatively benign conditions in my study, in that Iraqi prison, the guards experienced extreme fatigue and exhaustion from working 12-hour shifts, 7 days a week, for over a month at a time with no breaks.

There was fear of being killed from mortar and grenade attacks and from prisoners rioting. There was revenge for buddies killed, and prejudice against these foreigners for their strange religion and cultural traditions. There was encouragement by staff "to soften up" the detainees for interrogation because Tier 1A was the Interrogation-Soft Torture center of that prison. Already in place when these young men and women arrived there for their tour of duty were abusive practices that had been "authorized" from the top of the chain of command: Use of nakedness as a humiliation tactic, sensory and sleep deprivation, stress positions, dog attacks, and more.

In addition to the situational variables and processes operating in that behavioral setting were a serious of systemic processes that created the barrel into which these good soldiers were forced to live and work. Most of the reports of independent investigation committees cite a failure of leadership, lack of leadership, or irresponsible leadership as factors that contributed to these abuses. Then there was lack of mission-specific training of the guards, no oversight, no accountability to senior officers, poor resources, overcrowded facilities, confusing commands from civilian interrogators at odds with the CIA, military intelligence and other agencies and agents all working in Tier 1A without clear communication channels and much confusion.

I was recently an expert witness for the defense of Sgt. Ivan "Chip" Frederick in his Baghdad trial. Before the trial, I spent a day with him, giving him an in-depth interview, checking all background information, and arranging for him to be psychologically assessed by the military. He is one of the alleged "bad apples" who these investigations have labeled as "morally corrupt." What did he bring into that situation and what did that situation bring into him?

He seemed very much to be a normal young American. His psych assessments revealed no sign of any pathology, no sadistic tendencies, and all his psych assessment scores are in the normal range, as is his intelligence. He had been a prison guard at a small minimal security prison where he performed for many years without incident. So there is nothing in his background, temperament, or disposition that could have been a facilitating factor for the abuses he committed at the Abu Ghraib Prison.

After a four-day long trial, part of which included my testimony elaborating on the points noted here, the Judge took barely one hour to find him guilty of all eight counts and to sentence Sgt. Frederick to 8 years in prison, starting in solitary confinement in Kuwait, dishonorable discharge, broken in rank from Sgt. to Pvt., loss of his 20 years retirement income and his salary. This military judge held Frederick personally responsible for the abuses, because he had acted out of free will to intentionally harm these detainees since he was not forced into these acts, was not mentally incompetent, or acting in self-defense. All of the situational and systemic determinants of his behavior and that of his buddies were disregarded and given a zero weighting coefficient in assessing causal factors.

The real reason for the heavy sentence was the photographic documentation of the undeniable abuses along with the smiling abusers in their "trophy photos." It was the first time in history that such images were publicly available of what goes on in many prisons around the world, and especially in military prisons. They humiliated the military, and the entire chain of command all the way up the ladder to the White House. Following this exposure, investigations of all American military prisons in that area of the world uncovered similar abuses and worse, many murders of prisoners. Recent evidence has revealed that similar abuses started taking place again in Abu Ghraib prison barely one month after these disclosures became public—when the "Evil Eight Culprits" were in other prisons—as prisoners.

Based on more than 30 years of research on "The Lucifer Effect"—the transformation of good people into perpetrators of evil—I believe that there are powerful situational and systemic forces operating on individuals in certain situations that can undercut a lifetime of morality and rationality. The Dionysian aspect of human nature can triumph over the Apollonian, not only during Mardi Gras, but in dynamic group settings like gang rapes, fraternity hazing, mob riots, and in that Abu Ghraib prison. I believe in that truth in general and especially in the case of Sgt. Frederick, but I was not able to prove it in a military court of law.

ALUN ANDERSON
Editor-in-Chief, New Scientist

Strangely, I believe that cockroaches are conscious. That is probably an unappealing thought to anyone who switches on a kitchen light in the middle of the night and finds a family of roaches running for cover. But it's really shorthand for saying that I believe that many quite simple animals are conscious, including more attractive beasts like bees and butterflies.

I can't prove that they are, but I think in principle it will be provable one day and there's a lot to be gained about thinking about the worlds of these relatively simple creatures, both intellectually—and even poetically. I don't mean that they are conscious in even remotely the same way as humans are; if that we were true the world would be a boring place. Rather the world is full of many overlapping alien consciousnesses.

Why do I think they might be multiple forms of conscious out there? Before becoming a journalist I spent 10 years and a couple of post-doctoral fellowships getting inside the sensory worlds of a variety of insects, including bees and cockroaches. I was inspired by A Picture Book of Invisible Worlds, a slim out-of-print volume by Jakob von Uexkull (1864-1944).

The same book had also inspired Niko Tinbergen and Konrad Lorenz, the Nobel Prize winners who founded the field of ethology (animal behaviour). Von Uexkull studied the phenomenal world of animals, what he called their "umwelt", the worlds around animals as they themselves perceive them. Everything that an animals senses means something to it, for it has evolved to fit and create its world. Study of animals and their sensory worlds have now morphed into the field of sensory ecology, or on a wilder path, the newer science of biosemiotics.

I studied time studying how honey bees could find their way around my laboratory room (they had learnt to fly in through a small opening in the window) and find a hidden source of sugar. Bees could learn all about the pattern of key features in the room and would show they were confused if objects were moved around when they were out of the room. They were also easily distracted by certain kinds of patterns, particularly ones with lots of points and lines that had very abstract similarities to the patterns on flowers, as well as by floral scents, and by sudden movements that signalled danger. In contrast, when they were busy gorging on the sugar almost nothing could distract them, making it possible for myself to paint a little number on their backs so I distinguish individual bees.

To make sense of this ever changing behaviour, with its shifting focus of attention, I always found it simplest to figure out what was happening by imagining the sensory world of the bee, with its eye extraordinarily sensitive to flicker and colours we can't see, as a "visual screen" in the same way I can sit back and "see" my own visual screen of everything happening around me, with sights and sounds coming in and out of prominence. The objects in the bees world have significances or "meaning" quite different from our own, which is why its attention is drawn to things we would barely perceive.

That's what I mean by consciousness—the feeling of "seeing" the world and its associations. For the bee, it is the feeling of being a bee. I don't mean that a bee is self-conscious or spends time thinking about itself. But of course the problem of why the bee has its own "feeling" is the same incomprehensible "hard problem" of why the activity of our nervous system gives rise to our own "feelings".

But at least the bee's world is very visual and capable of being imagined. Some creatures live in sensory worlds that are much harder to access. Spiders that hunt at night live in a world dominated by the detection of faint vibration and of the tiniest flows of air that allow them to see fly passing by in pitch darkness. Sensory hairs that cover their body give them a sensitivity to touch far more finely grained than we can possibly feel through our own skin.

To think this way about simple creatures is not to fall into the anthropomorphic fallacy. Bees and spiders live in their own world in which I don't see human-like motives. Rather it is a kind of panpsychism, which I am quite happy to sign up to, at least until we know a lot more about the origin of consciousness. That may take me out of the company of quite a few scientists who would prefer to believe that a bee with a brain of only a million neurones must surely be a collection of instinctive reactions with some simple switching mechanism between then, rather have some central representation of what is going on that might be called consciousness. But it leaves me in the company of poets who wonder at the world of even lowly creatures.

"In this falling rain,
where are you off to
snail?"

wrote the haiku poet Issa.

And as for the cockroaches, they are a little more human than the spiders. Like the owners of the New York apartments who detest them, they suffer from stress and can die from it, even without injury. They are also hierarchical and know their little territories well. When they are running for it, think twice before crushing out another world.

MARGARET WERTHEIM
Science writer and Commentator; Author, Pythagoras' Trousers

We all believe in something and science itself is premised on a whole set of beliefs. Above all, science is founded on the belief that things are comprehensible and that by the ingenuity of our minds and the probing of ever more subtle instruments we will ultimately come to know It All. But is the All inherently knowable? I believe, though I cannot prove it, that there will always be things we do not know—large things, small things, interesting things and important things.

If theoretical physics is any guide we might suppose that science is a march towards a finite goal. For the past few decades theoretical physicists have been searching for a so-called "Theory of Everything," what Nobel laureate Stephen Weinberg has also called a "Final Theory." This "ultimate" set of equations that would tie together all the fundamental forces which physicists recognize today—the four essential powers of gravity, electromagnetism, and the nuclear forces inside the cores of atoms. But such theory—if we are lucky enough to extract it from the current mass of competing contenders—would not tell us anything about how proteins form or how DNA came into being. Less still would it illuminate the machinations of a living cell, or the workings of the human mind. Frankly, a "theory of everything" would not even help us to understand how snowflakes form.

In an age when we have discovered the origin of the universe and observed the warping of space and time it is shocking to hear that scientists do not understand something as "paltry" as the formation of ice crystals. But that is indeed the case.

Kenneth Libbrecht, chairman of the Cal tech physics department is a world expert on ice crystal formation, a hobby project he took on more than twenty years ago precisely because as he puts it "there are six billion people on this planet, and I thought that at least one of us should understand how snow crystals form." After two decades of meticulous experimentation inside specially constructed pressurized chambers Libbrecht believes he has made some headway in understanding how ice crystallizes at the edge of the quasi-liquid layer which surrounds all ice structures. He calls his theory "structure dependent attachment kinetics," but he is quick to point out that this is far from the ultimate answer. The transition from water to ice is a mysteriously complex process that has engaged minds as brilliant as Johannes Kepler and Michael Faraday. Libbrecht hopes he can add the small next step in our knowledge of this wondrous substance that is so central to life itself.

Studying ice crystals is Libbrecht's hobby—in his "day job" he is one of the hundreds of physicists who are working on the LIGO detector which is designed to detect gravitational waves that are believed to emanate from black holes and other massive cosmological entities. Gravity waves have been predicted by the general theory of relativity, and hence physicists believe they must exist. Here the matter of belief has literally bought into being a an extremely expensive machine. Any successful theory of everything will have to account for gravity, the most mysterious of all the forces and the one physicists least understand. Like the other three forces, physicists believe gravity must ultimately manifest itself in both wave and particle forms. LIGO is designed to detect such waves, if indeed they do exist.

Some years ago the science writer John Horgan wrote a marvelously provocative book in which he suggested that science was coming to an end, all the major theoretical edifices now supposedly being in place. Horgan was right in one sense, for high-energy physics may be on the verge of achieving its final unification. But in so many other areas, science is just beginning. Only now are we acquiring the scientific tools and techniques to begin to investigate how our atmosphere works, how ecological systems function, how genes create proteins, how cells evolve, and how brains work. The very success of "fundamental science" has opened doors undreamed of by earlier generations and in many ways it seems there is more than ever that we do not know. At a time when journals tout theories about how to create entire universes it is easy to imagine that science has grasped the whole of reality. In truth our ignorance is vast—and personally I believe it will always be so.

Rather than pretend we will soon know it all, I suggest we might adopt instead the attitude of the great fifteenth century champion of science, Cardinal Nicholas of Cusa. Cusa titled his major work On Learned Ignorance. A complex and poetic fusion of mathematics, scientific speculation and Catholic theology, Cusa puts forward in this book the view that we can never —even in principle—know everything. Only God can do that. We mortals, confined within the world itself can never see it whole, from the outside as it were. But while we cannot know it All, Cusa insists we can know a great deal and that science and mathematics will take our knowledge forward. Our ignorance then can be ever more learned. Not omniscience then, but an ever more subtle and insightful unknowing is the goal that Cusa advocated. In the humble snowflakes Ken Libbrecht studies we have the perfect metaphor for such a view—though they melt on your tongue, each tiny crystal of ice encapsulates a universe whose basic rules we have barely begun to unravel.

KENNETH FORD
Physicist; Retired director, American Institute of Physics; Author, The Quantum World

I believe that microbial life exists elsewhere in our galaxy.

I am not even saying "elsewhere in the universe." If the proposition I believe to be true is to be proved true within a generation or two, I had better limit it to our own galaxy. I will bet on its truth there.

I believe in the existence of life elsewhere because chemistry seems to be so life-striving and because life, once created, propagates itself in every possible direction. Earth's history suggests that chemicals get busy and create life given any old mix of substances that includes a bit of water, and given practically any old source of energy; further, that life, once created, spreads into every nook and cranny over a wide range of temperature, acidity, pressure, light level, and so on.

Believing in the existence of intelligent life elsewhere in the galaxy is another matter. Good luck to the SETI people and applause for their efforts, but consider that microbes have inhabited Earth for at least 75 percent of its history, whereas intelligent life has been around for but the blink of an eye, perhaps 0.02 percent of Earth's history (and for nearly all of that time without the ability to communicate into space). Perhaps intelligent life will have staying power. We don't know. But we do know that microbial life has staying power.

Now to a supposition: that Mars will be found to have harbored life and harbors life no more. If this proves to be the case, it will be an extraordinarily sobering discovery for humankind, even more so than the view of our fragile blue ball from the Moon, even more so than our removal from the center of the universe by Copernicus, Galileo, and Newton—perhaps even more so than the discovery of life elsewhere in the galaxy.

DONALD HOFFMAN
Cognitive Scientist, UC, Irvine; Author, Visual Intelligence

I believe that consciousness and its contents are all that exists. Spacetime, matter and fields never were the fundamental denizens of the universe but have always been, from their beginning, among the humbler contents of consciousness, dependent on it for their very being.

The world of our daily experience—the world of tables, chairs, stars and people, with their attendant shapes, smells, feels and sounds—is a species-specific user interface to a realm far more complex, a realm whose essential character is conscious. It is unlikely that the contents of our interface in any way resemble that realm. Indeed the usefulness of an interface requires, in general, that they do not. For the point of an interface, such as the windows interface on a computer, is simplification and ease of use. We click icons because this is quicker and less prone to error than editing megabytes of software or toggling voltages in circuits. Evolutionary pressures dictate that our species-specific interface, this world of our daily experience, should itself be a radical simplification, selected not for the exhaustive depiction of truth but for the mutable pragmatics of survival.

If this is right, if consciousness is fundamental, then we should not be surprised that, despite centuries of effort by the most brilliant of minds, there is as yet no physicalist theory of consciousness, no theory that explains how mindless matter or energy or fields could be, or cause, conscious experience. There are, of course, many proposals for where to find such a theory—perhaps in information, complexity, neurobiology, neural darwinism, discriminative mechanisms, quantum effects, or functional organization. But no proposal remotely approaches the minimal standards for a scientific theory: quantitative precision and novel prediction. If matter is but one of the humbler products of consciousness, then we should expect that consciousness itself cannot be theoretically derived from matter. The mind-body problem will be to physicalist ontology what black-body radiation was to classical mechanics: first a goad to its heroic defense, later the provenance of its final supersession.

The heroic defense will, I suspect, not soon be abandoned. For the defenders doubt that a replacement grounded in consciousness could attain the mathematical precision or impressive scope of physicalist science. It remains to be seen, of course, to what extent and how effectively mathematics can model consciousness. But there are fascinating hints: According to some of its interpretations, the mathematics of quantum theory is itself, already, a major advance in this project. And perhaps much of the mathematical progress in the perceptual and cognitive sciences can also be so interpreted. We shall see.

The mind-body problem may not fall within the scope of physicalist science, since this problem has, as yet, no bona fide physicalist theory. Its defenders can surely argue that this penury shows only that we have not been clever enough or that, until the right mutation chances by, we cannot be clever enough, to devise a physicalist theory. They may be right. But if we assume that consciousness is fundamental then the mind-body problem transforms from an attempt to bootstrap consciousness from matter into an attempt to bootstrap matter from consciousness. The latter bootstrap is, in principle, elementary: Matter, spacetime and physical objects are among the contents of consciousness.

The rules by which, for instance, human vision constructs colors, shapes, depths, motions, textures and objects, rules now emerging from psychophysical and computational studies in the cognitive sciences, can be read as a description, partial but mathematically precise, of this bootstrap. What we lose in this process are physical objects that exist independent of any observer. There is no sun or moon unless a conscious mind perceives them, for both are constructs of consciousness, icons in a species-specific user interface. To some this seems a patent absurdity, a reductio of the position, readily contradicted by experience and our best science. But our best science, our theory of the quantum, gives no such assurance. And experience once led us to believe the earth flat and the stars near. Perhaps, in due time, mind-independent objects will go the way of flat earth.

This view obviates no method or result of science, but integrates and reinterprets them in its framework. Consider, for instance, the quest for neural correlates of consciousness (NCC). This holy grail of physicalism can, and should, proceed unabated if consciousness is fundamental, for it constitutes a central investigation of our user interface. To the physicalist, an NCC is, potentially, a causal source of consciousness. If, however, consciousness is fundamental, then an NCC is a feature of our interface correlated with, but never causally responsible for, alterations of consciousness. Damage the brain, destroy the NCC, and consciousness is, no doubt, impaired. Yet neither the brain nor the NCC causes consciousness. Instead consciousness constructs the brain and the NCC. This is no mystery. Drag a file's icon to the trash and the file is, no doubt, destroyed. Yet neither the icon nor the trash, each a mere pattern of pixels on a screen, causes its destruction. The icon is a simplification, a graphical correlate of the file's contents (GCC), intended to hide, not to instantiate, the complex web of causal relations.

DENIS DUTTON
Philosopher of Art, University of Canterbury, New Zealand; Editor, Arts & Letters Daily

In a 1757 essay, philosopher David Hume argued that because "the general principles of taste are uniform in human nature" the value of some works of art might be essentially eternal. He observed that the "same Homer who pleased at Athens and Rome two thousand years ago, is still admired at Paris and London." The works that manage to endure over millennia, Hume thought, do so precisely because they appeal to deep, unchanging features of human nature.

Some unique works of art, for example, Beethoven's Pastoral Symphony, possess this rare but demonstrable capacity to excite the human mind across cultural boundaries and through historic time. I cannot prove it, but I think a small body of such works—by Homer, Bach, Shakespeare, Murasaki Shikibu, Vermeer, Michelangelo, Wagner, Jane Austen, Sophocles, Hokusai—will be sought after and enjoyed for centuries or millennia into the future. As much as fashions and philosophies are bound to change, these works will remain objects of permanent value to human beings.

These epochal survivors of art are more than just popular. The majority of works of popular art today are not inevitably shallow or worthless, but they tend to be easily replaceable. In the modern mass art system, artistic forms endure, while individual works drop away. Spy thrillers, romance novels, pop songs, and soap operas are daily replaced by more thrillers, romance novels, pop songs, and soap operas. In fact, the ephemeral nature of mass art seems more pronounced than ever: most popular works are incapable of surviving even a year, let alone a couple of generations. It's different with art's classic survivors: even if they began, as Sophocles' and Shakespeare's did, as works of popular art, they set themselves apart in their durable appeal: nothing kills them. Audiences keep coming back to experience these original works themselves.

Against the idea of permanent aesthetic values is cultural relativism, which is taught as the default orthodoxy in many university departments. Aesthetic values have been widely construed by academics as merely contingent reflections of local social and economic conditions. Beauty, if not in the eye of the beholder, has been misconstrued as merely in the eyes of society, a conditioning that determines values of cultural seeing. Such veins of explanation often include no small amount of cynicism: why do people go to the opera? Oh, to show off their furs. Why are they thrilled by famous paintings? Because they're worth millions. Beneath such explanations is a denial of intrinsic aesthetic merit.

Such aesthetic relativism is decisively refuted, as Hume understood, by the cross-cultural appeal of a small class of art objects over centuries: Mozart packs Japanese concerts halls, as Hiroshige does Paris galleries, while new productions of Shakespeare in every major language of the world are endless. And finally, it is beginning to look as though empirical psychology is equipped to address the universality of art. For example, evolutionary psychology is being used by literary scholars to explain the persistent themes and plot devices in fiction. The rendering of faces, bodies, and landscape preferences in art is amenable to psychological investigation. The structure of musical perception is now open to experimental analysis as never before. Poetic experience can be elucidated by the insights of contemporary linguistics. None of this research promises a recipe for creating great art, but it can throw light on what we already know about aesthetic pleasure.

What's going on most days in the Metropolitan Museum and most nights at Lincoln Center involves aesthetic experiences that will be continuously revived and relived by our descendents into an indefinite future. In a way, this makes the creations of the greatest artists as much permanent achievements as the discoveries of greatest scientists. That much I think I know. The question we should now ask is, What makes this possible? What is it about the highest works of art that gives them eternal appeal?

DAVID MYERS
Psychologist, Hope College; Author, Intuition

As a Christian monotheist, I start with two unproven axioms:

1. There is a God.

2. It's not me (and it's also not you).

Together, these axioms imply my surest conviction: that some of my beliefs (and yours) contain error. We are, from dust to dust, finite and fallible. We have dignity but not deity.

And that is why I further believe that we should

a) hold all our unproven beliefs with a certain tentativeness (except for this one!),

b) assess others' ideas with open-minded skepticism, and

c) freely pursue truth aided by observation and experiment.

This mix of faith-based humility and skepticism helped fuel the beginnings of modern science, and it has informed my own research and science writing. The whole truth cannot be found merely by searching our own minds, for there is not enough there. So we also put our ideas to the test. If they survive, so much the better for them; if not, so much the worse.

Within psychology, this "ever-reforming" process has many times changed my mind, leading me now to believe, for example, that newborns are not so dumb, that electro convulsive therapy often alleviates intractable depression, that America's economic growth has not improved our morale, that the automatic unconscious mind dwarfs the conscious mind, that traumatic experiences rarely get repressed, that most folks don't suffer low self-esteem, and that sexual orientation is not a choice.

ESTHER DYSON
Editor of Release 1.0; Trustee, Long Now Foundation; Author, Release 2.0

We're living longer, and thinking shorter.

[Disclaimer: Since I'm not a scientist, I'm not even going to attempt to take on something scientific. Rather, I want to talk about something that can't easily be measured, let alone proved.

And second, though what I'm saying may sound gloomy, I love the times we live in. There has never been a time more interesting, more full of things to explain, interesting people to meet, worthy causes to support, challenging problems to solve.]

It's all about time.

I think modern life has fundamentally and paradoxically changed our sense of time. Even as we live longer, we seem to think shorter. Is it because we cram more into each hour? Or because the next person over seems to cram more into each hour?

For a variety of reasons, everything is happening much faster and more things are happening. Change is a constant.

It used to be that machines automated work, giving us more time to do other things. But now machines automate the production of attention-consuming information, which takes our time. For example, if one person sends the same e-mail message to 10 people, then 10 people have to respond.

The physical friction of everyday life—the time it took Isaac Newton to travel by coach from London to Cambridge, the dead spots of walking to work (no iPod), the darkness that kept us from reading—has disappeared, making every minute not used productively into an opportunity cost.

And finally, we can measure more, over smaller chunks of time. From airline miles to calories (and carbs and fat grams), from friends on Friendster to steps on a pedometer, from realtime stock prices to millions of burgers consumed, we count things by the minute and the second.

Unfortunately, this carries over into how we think and plan: Businesses focus on short-term results; politicians focus on elections; school systems focus on test results; most of us focus on the weather rather than the climate. Everyone knows about the big problems, but their behavior focuses on the here and now.

I first noticed this phenomenon in a big way in the US right after 9/11, when it became impossible to schedule an appointment or get anyone to make a commitment. To me, it felt like Russia (where I had been spending time since 1989), where people avoided long-term plans because there was little discernible relationship between effort and result. Suddenly, even in the US, people were behaving like the Russians of those days, reluctant to plan for anything more than a few days out.

Of course, that immediate crisis has passed, but there's still the same sense of unpredictability dogging our thinking in the US (in particular). Best to concentrate on the current quarter, because who knows what job I'll have next year. Best to pass that test, because what I actually learn won't be worth much ten years from now anyway.

How can we reverse this?

It's a social problem, but I think it may also herald a mental one—which I describe as mental diabetes.

Whatever's happening to adults, most of us grew up reading books (at least occasionally) and playing with "uninteractive" toys that required us to make up our own stories, dialogue and behavior for them. Today's children are living in an information-rich, time-compressed environment that often seems to replace a child's imagination rather than stimulate it. I posit that being fed so much processed information—video, audio, images, flashing screens, talking toys, simulated action games—is akin to being fed too much processed, sugar-rich food. It may seriously mess up children's information metabolism and their ability to process information for themselves. In other words, will they be able to discern cause and effect, to put together a coherent story line, to think scientifically?

I don't know the answers, but these questions are worth thinking about, for the long term.

DAVID BUSS
Psychologist, University of Texas, Austin; Author, The Evolution of Desire

True love.

I've spent two decades of my professional life studying human mating. In that time, I've documented phenomena ranging from what men and women desire in a mate to the most diabolical forms of sexual treachery. I've discovered the astonishingly creative ways in which men and women deceive and manipulate each other. I've studied mate poachers, obsessed stalkers, sexual predators, and spouse murderers. But throughout this exploration of the dark dimensions of human mating, I've remained unwavering in my belief in true love.

While love is common, true love is rare, and I believe that few people are fortunate enough to experience it. The roads of regular love are well traveled and their markers are well understood by many—the mesmerizing attraction, the ideational obsession, the sexual afterglow, profound self-sacrifice, and the desire to combine DNA. But true love takes its own course through uncharted territory. It knows no fences, has no barriers or boundaries. It's difficult to define, eludes modern measurement, and seems scientifically wooly. But I know true love exists. I just can't prove it.

MARIA SPIROPULU
Physicist, currently at CERN

I believe nothing to be true (clearly real) if it cannot be proved.

I'll take the question and make a pseudo-invariant transformation that makes it more apt to my brain. When Bohr was asked what is the complementary variable of "truth" (Wirklichkeit) he replied with no hesitation "clarity" (Klarheit). Contrary to Bohr, and since neither truth nor clarity are quantum mechanical variables, real truth and comprehensive clarity should be simultaneously achievable given rigorous experimental evidence. [In particular since "Wirklichkeit" means reality, and "Klarheit" is clarity in the sense of good understanding.]

In fact I will use clarity (as in "clear reality"), in the place of truth.

I will also invent equivalents for proof and for belief. Proof will be interchangeable with "experimental scientific evidence". Belief is more tricky given that it has to do with complex carbonic life. It can be interchangeable with "theoretical assessment" or "assessment by common sense" (depending on the scale and the available technology). In this process (no doubt in a path full of traps and pitfalls) I have cannibalized the original question to the following:

What do you (commonsensical/theoretically) assess to be clearly real even though you have no experimental scientific evidence for it?

Now this is hard: there are many theoretical assessments for the explanation of the natural phenomena at the extreme energy scales (from the subnuclear to the supercosmic), that possess a degree of clarity. But all of them are inspired by the vast collection of conciliatory data that scale by scale speak of Nature's works. This is so even for string theory. 

So the answer is still...nothing.

Following Bohr's complementarity I would spot that belief and proof are in some way complementary: if you believe you don't need proof, and (arguably) if you have proof you don't need to believe.(I would assign the hard-core string theorists who do not really care about experimental scientific evidence in the first category).

But Edge wants us to identify the equivalent(s) of the general theory of relativity in today's scientific thinking(s). Or a prediction of what are the big things in science that come at us unexpectedly. In my field, even frameworks that explain the world using extra dimensions of space (in extreme versions) are not unexpected. As a matter of fact we are preparing to discover or exclude them using the data. My hunch (and wish) is that in the laboratory we will be able to segment spacetime so finely that gravity will be studied and understood in a controlled environment, and that gravitational particle physics will be a new field.

J. CRAIG VENTER
Genomics Researcher; Founder & President, J. Craig Venter Science Foundation

Life is ubiquitous throughout the universe. Life on our planet earth most likely is the result of a panspermic event (a notion popularized by the late Francis Crick).

DNA, RNA and carbon based life will be found wherever we find water and look with the right tools. Whether we can prove life happens, depends on our ability to improve remote sensing and to visit faraway systems. This will also depend on whether we survive as a species for a sufficient period of time. As we have seen recently in the shotgun sequencing of the Sargasso Sea, when we look for life here on Earth with new tools of DNA sequencing we find life in abundance in the microbial world. In sequencing the genetic code of organisms that survive in the extremes of zero degrees C to well over boiling water temperatures we begin to understand the breadth of life, including life that can thrive in extremes of caustic conditions of strong acids to basic pH's that would rapidly dissolve human skin. Possible indicators of panspermia are the organisms such as Deinococcus radiodurans, which can survive millions of RADs of ionizing radiation and complete desiccation for years or perhaps millennia. These microbes can repair any DNA damage within hours of being reintroduced into an aqueous environment.

Our human centric view of life is clearly unwarranted. From the millions of genes that we have just discovered in environmental organisms over the past months we learn that a finite number of themes are used over and over again and could have easily evolved from a few microbes arriving on a meteor or on intergalactic dust. Panspermia is how life is spreads throughout the universe and we are contributing to it from earth by launching billions of microbes into space.

STEPHEN PETRANEK
Editor-in-Chief, Discover Magazine

I believe that life is common throughout the universe and that we will find another Earth-like planet within a decade.

The mathematics alone ought to be proof to most people (billions of galaxies with billions of stars in each galaxy and around most of those stars are planets). The numbers suggest that for life not to exist elsewhere in the universe is the unlikely scenario. But there is more to this idea than a good chance. We've now found more than 130 planets just looking at nearby stars in our tiny little corner of the Milky Way. The results suggest there are uncountable numbers of planets in our galaxy alone. Some of them are likely to be earthlike, or at least earth-sized, although the vast majority that we've found so far are huge gas giants like Jupiter and Saturn which are unlikely to harbor life. Furthermore, there were four news events this year that made the discovery of life elsewhere extraordinarily more likely.

First, the NASA Mars Rover called Opportunity found incontrovertible evidence that a briny--salty-sea once covered the area where it landed, called Meridiani Planum. The only question about life on Mars now is whether that sea—which was there twice in Martian history—existed long enough for life to form. The Phoenix mission in 2008 may answer that question.

Second, a team of astrophysicists reported in July that radio emissions from Sagittarius B2, a nebula near the center of the Milky Way, indicate the presence of aldehyde molecules, the prebiotic stuff of life. Aldehydes help form amino acids, the fundamental components of proteins. The same scientists previously reported clouds of other organic molecules in space, including glycolaldehyde, a simple sugar. Outer space is thus full of complex molecules—not just atoms—necessary for life. Comets in other solar systems could easily deposit such molecules on planets, as they may have done in our solar system with earth.

Third, astronomers in 2004 found much smaller planets around other stars for the first time. Barbara McArthur at the University of Texas at Austin found a planet 18 times the mass of Earth around 55 Cancri, a star with three other known planets. A team in Portugal announced finding a 14-mass planet. These smaller planets are likely to be rock, not gas. McArthur says, "We're on our way to finding an extrasolar earth."

Fourth, astronomers are not only getting good at finding new planets around other stars, they're getting the resolution of the newest telescopes so good that they can see the dim light from some newly found planets. Meanwhile, even better telescopes are being built, like the large binocular scope on Mt. Graham in Arizona that will see more planets. With light we can analyze the spectrum a new planet reflects and determine what's on that planet—like water. Water, we also discovered recently is abundant in space in large clouds between and near stars.

So everything life needs is out there. For it not to come together somewhere else as it did on earth is remarkably unlikely. In fact, although there are Goldilocks zones in galaxies where life as we know it is most likely to survive (there's too much radiation towards the center of the Milky Way, for example), there are almost countless galaxies out there where conditions could be ripe for life to evolve. This is a golden age of astrophysics and we're going to find life elsewhere.

SIMON BARON-COHEN
Psychologist, Autism Research Centre, Cambridge University; Author, The Essential Difference

I am not interested in ideas that cannot in principle be proven or disproven. I am as capable as the next guy in believing in an idea that is not yet proven so long as it could in principle be proven or disproven.

In my chosen field of autism, I believe that the cause will turn out to be assortative mating of two hyper-systemizers. I believe this because we already have 3 pieces of the jig-saw: (1) that fathers of children with autism are more likely to work in the field of engineering (compared to fathers of children without autism); (2) that grandfathers of children with autism—on both sides of the family—were also more likely to work in the field of engineering (compared to grandfathers of children without autism); and (3) that both mothers and fathers of children with autism are super-fast at the embedded figures test, a task requiring analysis of patterns and rules. (Note that engineering is a chosen example because it involves strong systemizing. But other related scientific and technical fields [such as math or physics] would have been equally good examples to study).

We have had these three pieces of the jigsaw since 1997, published in the scientific literature. They do not yet prove the assortative mating theory. They simply point to it being highly likely. Direct tests of the theory are still needed. I will be the first to give up this idea if it is proven wrong, since I'm not in the business of holding onto wrong ideas. But I won't give up the idea simply because it will be unpopular to certain groups (such as those who want to believe that the cause of autism is purely environmental). I will hold onto the idea until it has been properly tested. Popperian science is about being able to let go of an idea when the evidence goes against it, but it is also about being able to hold onto an idea until the evidence has been collected, if you have enough reasons to believe it might be true.

The causes of autism are likely to be complex, including at the very least multiple genes interacting with environmental factors, but the assortative mating theory may describe some contributing factors.

TOM STANDAGE
Technology Editor, The Economist

I believe that the radiation emitted by mobile phones is harmless.

My argument is not based so much on the scientific evidence—because there isn't very much of it, and what little there is has either found no effect or is statistically dubious. Instead, it is based on a historical analogy with previous scares about overhead power lines and cathode-ray computer monitors (VDUs). Both were also thought to be dangerous, yet years of research—decades in the case of power lines—failed to find conclusive evidence of harm.

Mobile phones seem to me to be the latest example of what has become a familiar pattern: anecdotal evidence suggests that a technology might be harmful, and however many studies fail to find evidence of harm, there are always calls for more research.

The underlying problem, of course, is the impossibility of proving a negative. During the fuss over genetically modified crops in Europe, there were repeated calls for proof that GM technology was safe. Similarly, in the aftermath of the BSE scare in Britain, scientists were repeatedly asked for proof that beef was safe to eat. But you cannot prove that something has no effect: absence of evidence is not evidence of absence. All you can do is look for evidence of harm. If you don't find it, you can look again. If you still fail to find it, the question is still open: "lack of evidence of harm" means both "safe as far as we can tell" and "we still don't know if it's safe or not". Scientists are often unfairly accused of logic-chopping when they point this out.

Looking back even further, I expect mobile phones will turn out to be merely the latest in a long line of technologies that raised health concerns that subsequently turned out to be unwarranted. In the 19th century, long before the power-line and VDU scares, telegraph wires were accused of affecting the weather, and railway travel was believed to cause nervous disorders.

The irony is that since my belief that mobile phones are safe is based on a historical analysis, I am on no firmer ground scientifically than those who believe mobile phones are harmful. Still, I believe they are safe, though I can't prove it.

MICHAEL SHERMER
Publisher, Skeptic magazine; Columnist, Scientific American; Author Science Friction

I believe, but cannot prove...that reality exists over and above human and social constructions of that reality. Science as a method, and naturalism as a philosophy, together form the best tool we have for understanding that reality. Because science is cumulative—that is, it builds on itself in a progressive fashion—we can strive to achieve an ever-greater understanding of reality. Our knowledge of nature remains provisional because we can never know if we have final Truth. Because science is a human activity and nature is complex and dynamic, fuzzy logic and fractional probabilities best describe both nature and the estimations of our approximation toward understanding that nature.

There is no such thing as the paranormal and the supernatural; there is only the normal and the natural and mysteries we have yet to explain.

What separates science from all other human activities is its belief in the provisional nature of all conclusions. In science, knowledge is fluid and certainty fleeting. That is the heart of its limitation. It is also its greatest strength. There are, from this ultimate unprovable assertion, three additional insoluble derivatives.

1. There is no God, intelligent designer, or anything resembling the divinity as proffered by the world's religions (although an extra-terrestrial being of significantly greater intelligence and power than us would be indistinguishable from God).

After thousands of years of the world's greatest minds attempting to prove or disprove the divinity's existence or nonexistence, with little agreement or consensus amongst scholars as to the divinity's ultimate state of being, a reasonable conclusion is that the God question can never be solved and that one's belief, disbelief, or skepticism ultimately rests on a non-rational basis.

2. The universe is ultimately determined, but we have free will.

As with the God question, scholars of considerable intellectual power for many millennia have failed to resolve the paradox of feeling free in a determined universe. One provisional solution is to think of the universe as so complex that the number of causes and the complexity of their interactions make the predetermination of human action pragmatically impossible