1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10


"What Do You Believe Is True Even Though You Cannot Prove It?"

Printer-friendly version


Alun Anderson

Chris W. Anderson

Philip W. Anderson

Scott Atran

Simon Baron-Cohen

John Barrow

Gregory Benford

Jesse Bering

Susan Blackmore

Ned Block

Paul Bloom

David Buss

William Calvin

Leo Chalupa

Mihaly Csikszentmihalyi

Paul Davies

Richard Dawkins

Stanislas Deheane

Daniel C. Dennett

Keith Devlin

Jared Diamond

Denis Dutton

Esther Dyson

Freeman Dyson

George Dyson

Jeffrey Epstein

Todd Feinberg

Christine Finn

Kenneth Ford

Howard Gardner

David Gelernter

Neil Gershenfeld

Steve Giddings

Daniel Gilbert

Rebecca Goldstein

Daniel Goleman

Brian Goodwin

Alison Gopnik

Jonathan Haidt

Haim Harari

Judith Rich Harris

Sam Harris

Marc D. Hauser

Marti Hearst

W. Daniel Hillis

Donald Hoffman

John Horgan

Verena Huber-Dyson

Nicholas Humphrey

Piet Hut

Stuart Kauffman

Alan Kay

Kevin Kelly

Stephen Kosslyn

Kai Krause

Lawrence Krauss

Ray Kurzweil

Jaron Lanier

Leon Lederman

Janna Levin

Joseph LeDoux

Seth Lloyd

Benoit Mandelbrot

Gary Marcus

Lynn Margulis

John McCarthy

Pamela McCorduck

Ian McEwan

John McWhorter

Thomas Metzinger

Oliver Morton

David Myers

Randolph Nesse

Tor Nørretranders

Martin Nowak

James O'Donnell

Alex Pentland

Irene Pepperberg

Stephen Petranek

Clifford Pickover

Steven Pinker

Jordan Pollack

Carolyn Porco

Robert R. Provine

Martin Rees

Howard Rheingold

Carlo Rovelli

Rudy Rucker

Douglas Rushkoff

Karl Sabbagh

Robert Sapolsky

Roger Schank

Jean Paul Schmetz

Stephen H. Schneider

Gino Segre

Martin E. P. Seligman

Terrence Sejnowski

Rupert Sheldrake

Michael Shermer

Charles Simonyi

John R. Skoyles

Lee Smolin

Elizabeth Spelke

Maria Spiropulu

Tom Standage

Paul Steinhardt

Bruce Sterling

Leonard Susskind

Nassim Taleb

Timothy Taylor

Arnold Trehub

Robert Trivers

J. Craig Venter

Alexander Vilenkin

Margaret Wertheim

Donald I. Williamson

Ian Wilmut

Ellen Winner

Anton Zeilinger


Psychologist, University of Massachusetts, Amherst; Author, The Cognitive Brain.

I have proposed a law of conscious content which asserts that for any experience, thought, question, or solution, there is a corresponding analog in the biophysical state of the brain. As a corollary to this principle, I have argued that conventional attempts to understand consciousness by simply searching for the neural correlates of consciousness (NCC) in theoretical and empirical investigations are too weak to ground a good understanding of conscious content. Instead, I have proposed that we go beyond NCC and explore brain events that have at least some similarity to our phenomenal experiences, namely, neuronal analogs of conscious content (NAC). In support of this approach, I have presented a theoretical model that goes beyond addressing the sheer correlation between mental states and neuronal events in the brain. It explains how neuronal analogs of phenomenal experience (NAC) can be generated, and it details how other essential human cognitive tasks can be accomplished by the particular structure and dynamics of putative neuronal mechanisms and systems in the brain.

A large body of experimental findings, clinical findings, and phenomenal reports can be explained within a coherent framework by the neuronal structure and dynamics of my theoretical model. In addition, the model accurately predicts many classical illusions and perceptual anomalies. So I believe that the neuronal mechanisms and systems that I have proposed provide a true explanation for many important aspects of human cognition and phenomenal experience. But I can't prove it. Of course, competing theories about the brain, cognition, and consciousness can't be proved either. But I can't prove it. Providing the evidence is the best we can do—I think.

Writer and Developmental Psychologist; Author, The Nurture Assumption

I believe, though I cannot prove it, that three—not two—selection processes were involved in human evolution.

The first two are familiar: natural selection, which selects for fitness, and sexual selection, which selects for sexiness.

The third process selects for beauty, but not sexual beauty—not adult beauty. The ones doing the selecting weren't potential mates: they were parents. Parental selection, I call it.

What gave me the idea was a passage from a book titled Nisa: The Life and Words of a !Kung Woman, by the anthropologist Marjorie Shostak. Nisa was about fifty years old when she recounted to Shostak, in remarkable detail, the story of her life as a member of a hunter-gatherer group.

One of the incidents described by Nisa occurred when she was a child. She had a brother named Kumsa, about four years younger than herself. When Kumsa was around three, and still nursing, their mother realized she was pregnant again. She explained to Nisa that she was planning to "kill"—that is, abandon at birth—the new baby, so that Kumsa could continue to nurse. But when the baby was born, Nisa's mother had a change of heart. "I don't want to kill her," she told Nisa. "This little girl is too beautiful. See how lovely and fair her skin is?"

Standards of beauty differ in some respects among human societies; the !Kung are lighter-skinned than most Africans and perhaps they pride themselves on this feature. But Nisa's story provides a insight into two practices that used to be widespread and that I believe played an important role in human evolution: the abandonment of newborns that arrived at inopportune times (this practice has been documented in many human societies by anthropologists), and the use of aesthetic criteria to tip the scales in doubtful cases.

Coupled with sexual selection, parental selection could have produced certain kinds of evolutionary changes very quickly, even if the heartbreaking decision of whether to rear or abandon a newborn was made in only a small percentage of births. The characteristics that could be affected by parental selection would have to be apparent even in a newborn baby. Two such characteristics are skin color and hairiness.

Parental selection can help to explain how the Europeans, who are descended from Africans, developed white skin over such a short period of time. In Africa, a cultural preference for light skin (such as Nisa's mother expressed) would have been counteracted by other factors that made light skin impractical. But in less sunny Europe, light skin may actually have increased fitness, which means that all three selection processes might have worked together to produce the rapid change in skin color.

Parental selection coupled with sexual selection can also account for our hairlessness. In this case, I very much doubt that fitness played a role; other mammals of similar size—leopards, lions, zebras, gazelle, baboons, chimpanzees, and gorillas—get along fine with fur in Africa, where the change to hairlessness presumably took place. I believe (though I cannot prove it) that the transition to hairlessness took place quickly, over a short evolutionary time period, and involved only Homo sapiens or its immediate precursor.

It was a cultural thing. Our ancestors thought of themselves as "people" and thought of fur-bearing creatures as "animals," just as we do. A baby born too hairy would have been distinctly less appealing to its parents.

If I am right that the transition to hairlessness occurred very late in the sequence of evolutionary changes that led to us, then this can explain two of the mysteries of paleoanthropology: the survival of the Neanderthals in Ice Age Europe, and their disappearance about 30,000 years ago.

I believe, though I cannot prove it, that Neanderthals were covered with a heavy coat of fur, and that Homo erectus, their ancestor, was as hairy as the modern chimpanzee. A naked Neanderthal could never have made it through the Ice Age. Sure, he had fire, but a blazing hearth couldn't keep him from freezing when he was out on a hunt. Nor could a deerskin slung over his shoulders, and there is no evidence that Neanderthals could sew. They lived mostly on game, so they had to go out to hunt often, no matter how rotten the weather. And the game didn't hang around conveniently close to the entrance to their cozy cave.

The Neanderthals disappeared when Homo sapiens, who by then had learned the art of sewing, took over Europe and Asia. This new species, descended from a southern branch of Homo erectus, was unique among primates in being hairless. In their view, anything with fur on it could be classified as "animal"—or, to put it more bluntly, game. Neanderthal disappeared in Europe for the same reason the woolly mammoth disappeared there: the ancestors of the modern Europeans ate them. In Africa today, hungry humans eat the meat of chimpanzees and gorillas.

At present, I admit, there is insufficient evidence either to confirm or disconfirm these suppositions. However, evidence to support my belief in the furriness of Neanderthals may someday be found. Everything we currently know about this species comes from hard stuff like rocks and bones. But softer things, such as fur, can be preserved in glaciers, and the glaciers are melting. Someday a hiker may come across the well-preserved corpse of a furry Neanderthal.

Novelist; Author, Globalhead

I can sum my intuition up in five words: we're in for climatic mayhem.

Computer Scientist; Personal Computer Visionary, Senior Fellow, HP Labs

Einstein said "You must learn to distinguish between what is true and what is real". An apt longer quote of his is: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality". I.e. it is "true" that the three angles of a triangle add up to 180 in Euclidean geometry of the plane, but it is not known how to show that this could hold in our physical universe (if there is any mass or energy in our universe then it doesn't seem to hold, and it is not actually known what our universe would be like without any mass or energy).

So, science is a relationship between what we can represent and are able to think about, and "what's out there": it's an extension of good map making, most often using various forms of mathematics as the mapping languages. When we guess in science we are guessing about approximations and mappings to languages, we are not guessing about "the truth" (and we are not in a good state of mind for doing science if we think we are guessing "the truth" or "finding the truth"). This is not at all well understood outside of science, and there are unfortunately a few people with degrees in science who don't seem to understand it either.

Sometimes in math one can guess a theorem that can be proved true. This is a useful process even if one's batting average is less than .500. Guessing in science is done all the time, and the difference between what is real and what is true is not a big factor in the guessing stage, but makes all the difference epistemologically later in the process.

One corner of computing is a kind of mathematics (other corners include design, engineering, etc.). But there are very few interesting actual proofs in computing. A good Don Knuth quote is: "Beware of bugs in the above code; I have only proved it correct, not tried it."

An analogy for why this is so is to the n-body problems (and other chaotic systems behaviors) in physics. An explosion of degrees of freedom (3 bodies and gravity is enough) make a perfectly deterministic model impossible to solve analytically for a future state. However, we can compute any future state by brute force simulation and see what happens. By analogy, we'd like to prove useful programs correct, but we either have intractable degrees of freedom, or as in the Knuth quote, it is very difficult to know if we've actually gathered all the cases when we do a "proof".

So a guess in computing is often architectural or a collection of "covering heuristics". An example of the latter is TCP/IP which has allowed "the world's largest and most scalable artifact—The Internet—to be successfully built. An example of the former is the guess I made in 1966 about objects—not that one could build everything from objects—that could be proved mathematically—but that using objects would be a much better way to represent most things. This is not very provable, but like the Internet, now has quite a body of evidence that suggests this was a good guess.

Another guess I made long ago—that does not yet have a body of evidence to support it—is that what is special about the computer is analogous to and an advance on what was special about writing and then printing. It's not about automating past forms that has the big impact, but as McLuhan pointed out, when you are able to change the nature of representation and argumentation, those who learn these new ways will wind up to be qualtitatively different and better thinkers, and this will (usually) help advance our limited conceptions of civilization.

This still seems like a good guess to me—but "truth" has nothing to do with it.

Psychologist & Computer Scientist; Author, Designing World-Class E-Learning

Irrational choices.

I do not believe that people are capable of rational thought when it comes to making decisions in their own lives. People believe that are behaving rationally and have thought things out, of course, but when major decisions are made—who to marry, where to live, what career to pursue, what college to attend, people's minds simply cannot cope with the complexity. When they try to rationally analyze potential options, their unconscious, emotional thoughts take over and make the choice for them.

As an example of what I mean consider a friend of mine who was told to select a boat as a wedding present by his father in law. He chose a very peculiar boat which caused a real rift between him and his bride. She had expected a luxury cruiser, which is what his father in law had intended. Instead he selected a very rough boat that he could fashion as he chose. As he was an engineer his primary concern was how it would handle open ocean and he made sure the engines were special ones that could be easily gotten at and that the boat rode very low in the water. When he was finished he created a very functional but very ugly and uncomfortable boat.

Now I have ridden with him on his boat many times. Always he tells me about its wonderful features that make it a rugged and very useful boat. But, the other day, as we were about to start a trip, he started talking about how pretty he thought his boat was, how he liked the wood, the general placement of things, and the way the rooms fit together. I asked him if he was describing a boat that he had been familiar with as a child and suggested that maybe this boat was really a copy of some boat he knew as a kid. He said, after some thought, that that was exactly the case, there had been a boat like in his childhood and he had liked it a great deal.

While he was arguing with his father in law, his wife, and nearly everyone he knew about his boat, defending his decision with all the logic he could muster, destroying the very conceptions of boats they had in mind, the simple truth was his unconscious mind was ruling the decision making process. It wanted what it knew and loved, too bad for the conscious which had to figure how to explain this to everybody else.

Of course, psychoanalysts have made a living on trying to figure out why people make the decisions they do. The problem with psychoanalysis is that it purports to be able to cure people. This possibility I doubt very much. Freud was a doctor so I guess he got paid to fix things and got carried away. But his view of the unconscious basis of decision making was essentially correct. We do not know how we decide things, and in a sense we don't really care. Decisions are made for us by our unconscious, the conscious is in charge of making up reasons for those decisions which sound rational. We can, on the other hand, think rationally about the choices that other people make. We can do this because we do not know and are not trying to satisfy unconscious needs and childhood fantasies. As for making good decisions in our lives, when we do it is mostly random. We are always operating with too little information consciously and way too much unconsciously.

Physicist, University of Pennsylvania; Author, A Matter of Degrees

The Big Bang, that giant explosion of more than 13 billion years ago, provides the accepted description of our Universe's beginning. We can trace with exquisite precision what happened during the expansion and cooling that followed that cataclysm, but the presence of neutrinos in that earliest phase continues to elude direct experimental confirmation.

Neutrinos, once in thermal equilibrium, were supposedly freed from their bonds to other particles about two seconds after the Big Bang. Since then they should have been roaming undisturbed through intergalactic space, some 200 of them in every cubic centimeter of our Universe, altogether a billion of them for every single atom. Their presence is noted indirectly in the Universe's expansion. However, though they are presumably by far the most numerous type of material particle in existence, not a single one of those primordial neutrinos has ever been detected. It is not for want of trying, but the necessary experiments are almost unimaginably difficult. And yet those neutrinos must be there. If they are not, our whole picture of the early Universe will have to be totally reconfigured.

Wolfgang Pauli's original 1930 proposal of the neutrino's existence was so daring he didn't publish it. Enrico Fermi's brilliant 1934 theory of how neutrinos are produced in nuclear events was rejected for publication by Nature magazine as being too speculative. In the 1950s neutrinos were detected in nuclear reactors and soon afterwards in particle accelerators. Starting in the 1960s, an experimental tour de force revealed their existence in the solar core. Finally, in1987 a ten second burst of neutrinos was observed radiating outward from a supernova collapse that had occurred almost 200,000 years ago. When they reached the Earth and were observed, one prominent physicist quipped that extra-solar neutrino astronomy "had gone in ten seconds from science fiction to science fact". These are some of the milestones of 20th century neutrino physics.

In the 21st century we eagerly await another one, the observation of neutrinos produced in the first seconds after the Big Bang. We have been able to identify them, infer their presence, but will we be able to actually see these minute and elusive particles? They must be everywhere around us, even though we still cannot prove it.

Astrophysicist, Institute of Advanced Study

Science, like most human activities, is based on a belief, namely the assumption that nature is understandable.

If we are faced with a puzzling experimental result, we first try harder to understand it with currently available theory, using more clever ways to apply that theory. If that really doesn't work, we try to improve or perhaps even replace the theory. We never conclude that a not-yet understood result is in principle un-understandable.

While some philosophers might draw a different conclusion—see the contribution by Nicholas Humphrey—as a scientist I strongly believe that Nature is understandable. And such a belief can neither be proved nor disproved.

Note: undoubtedly, the notion of what counts as "understandable" will continue to change. What physicists consider to be understandable now is very different from what had been regarded as such one hundred years ago. For example, quantum mechanics tells us that repeating the same experiment will give different results. The discovery of quantum mechanics led us to relax the rigid requirement of a deterministic objective reality to a statistical agreement with a not fully determinable reality. Although at first sight such a restriction might seem to limit our understanding, we in fact have gained a far deeper understanding of matter through the use of quantum mechanics than we could possibly have obtained using only classical mechanics.

Computer scientist, IBM's T. J. Watson Research Center; Author, Calculus and Pizza

If we believe that consciousness is the result of patterns of neurons in the brain, our thoughts, emotions, and memories could be replicated in moving assemblies of Tinkertoys. The Tinkertoy minds would have to be very big to represent the complexity of our minds, but it nevertheless could be done, in the same way people have made computers out of 10,000 Tinkertoys. In principle, our minds could be hypostatized in patterns of twigs, in the movements of leaves, or in the flocking of birds. The philosopher and mathematician Gottfried Leibniz liked to imagine a machine capable of conscious experiences and perceptions. He said that even if this machine were as big as a mill and we could explore inside, we would find "nothing but pieces which push one against the other and never anything to account for a perception."

If our thoughts and consciousness do not depend on the actual substances in our brains but rather on the structures, patterns, and relationships between parts, then Tinkertoy minds could think. If you could make a copy of your brain with the same structure but using different materials, the copy would think it was you. This seemingly materialistic approach to mind does not diminish the hope of an afterlife, of transcendence, of communion with entities from parallel universes, or even of God. Even Tinkertoy minds can dream, seek salvation and bliss—and pray.

Psychologist, Visiting Lecturer, University of the West of England, Bristol; Author The Meme Machine

It is possible to live happily and morally without believing in free will. As Samuel Johnson said "All theory is against the freedom of the will; all experience is for it." With recent developments in neuroscience and theories of consciousness, theory is even more against it than it was in his time, more than 200 years ago. So I long ago set about systematically changing the experience. I now have no feeling of acting with free will, although the feeling took many years to ebb away.

But what happens? People say I'm lying! They say it's impossible and so I must be deluding myself to preserve my theory. And what can I do or say to challenge them? I have no idea—other than to suggest that other people try the exercise, demanding as it is.

When the feeling is gone, decisions just happen with no sense of anyone making them, but then a new question arises—will the decisions be morally acceptable? Here I have made a great leap of faith (or the memes and genes and world have done so). It seems that when people throw out the illusion of an inner self who acts, as many mystics and Buddhist practitioners have done, they generally do behave in ways that we think of as moral or good. So perhaps giving up free will is not as dangerous as it sounds—but this too I cannot prove.

As for giving up the sense of an inner conscious self altogether—this is very much harder. I just keep on seeming to exist. But though I cannot prove it—I think it is true that I don't.

Mathematician, Stanford University; Author, The Millennium Problems

Before we can answer this question we need to agree what we mean by proof. (This is one of the reasons why its good to have mathematicians around. We like to begin by giving precise definitions of what we are going to talk about, a pedantic tendency that sometimes drives our physicist and engineering colleagues crazy.) For instance, following Descartes, I can prove to myself that I exist, but I can't prove it to anyone else. Even to those who know me well there is always the possibility, however remote, that I am merely a figment of their imagination. If it's rock solid certainty you want from a proof, there's almost nothing beyond our own existence (whatever that means and whatever we exist as) that we can prove to ourselves, and nothing at all we can prove to anyone else.

Mathematical proof is generally regarded as the most certain form of proof there is, and in the days when Euclid was writing his great geometry text Elements that was surely true in an ideal sense. But many of the proofs of geometric theorems Euclid gave were subsequently found out to be incorrect—David Hilbert corrected many of them in the late nineteenth century, after centuries of mathematicians had believed them and passed them on to their students—so even in the case of a ten line proof in geometry it can be hard to tell right from wrong.

When you look at some of the proofs that have been developed in the last fifty years or so, using incredibly complicated reasoning that can stretch into hundreds of pages or more, certainty is even harder to maintain. Most mathematicians (including me) believe that Andrew Wiles proved Fermat's Last Theorem in 1994, but did he really? (I believe it because the experts in that branch of mathematics tell me they do.)

In late 2002, the Russian mathematician Grigori Perelman posted on the Internet what he claimed was an outline for a proof of the Poincare Conjecture, a famous, century old problem of the branch of mathematics known as topology. After examining the argument for two years now, mathematicians are still unsure whether it is right or not. (They think it "probably is.")

Or consider Thomas Hales, who has been waiting for six years to hear if the mathematical community accepts his 1998 proof of astronomer Johannes Keplers 360-year-old conjecture that the most efficient way to pack equal sized spheres (such as cannonballs on a ship, which is how the question arose) is to stack them in the familiar pyramid-like fashion that greengrocers use to stack oranges on a counter. After examining Hales' argument (part of which was carried out by computer) for five years, in spring of 2003 a panel of world experts declared that, whereas they had not found any irreparable error in the proof, they were still not sure it was correct.

With the idea of proof so shaky—in practice—even in mathematics, answering this year's Edge question becomes a tricky business. The best we can do is come up with something that we believe but cannot prove to our own satisfaction. Others will accept or reject what we say depending on how much credence they give us as a scientist, philosopher, or whatever, generally basing that decision on our scientific reputation and record of previous work. At times it can be hard to avoid the whole thing degenerating into a slanging match. For instance, I happen to believe, firmly, that staples of popular-science-books and breathless TV-specials such as ESP and morphic resonance are complete nonsense, but I can't prove they are false. (Nor, despite their repeated claims to the contrary, have the proponents of those crackpot theories proved they are true, or even worth serious study, and if they want the scientific community to take them seriously then the onus if very much on them to make a strong case, which they have so far failed to do.)

Once you recognize that proof is, in practical terms, an unachievable ideal, even the old mathematicians standby of G¤del's Incompleteness Theorem (which on first blush would allow me to answer the Edge question with a statement of my belief that arithmetic is free of internal contradictions) is no longer available. G¤del's theorem showed that you cannot prove an axiomatically based theory like arithmetic is free of contradiction within that theory itself. But that doesn't mean you can't prove it in some larger, richer theory. In fact, in the standard axiomatic set theory, you can prove arithmetic is free of contradictions. And personally, I buy that proof. For me, as a living, human mathematician, the consistency of arithmetic has been proved—to my complete satisfaction.

So to answer the Edge question, you have to take a common sense approach to proof—in this case proof being, I suppose, an argument that would convince the intelligent, professionally skeptical, trained expert in the appropriate field. In that spirit, I could give any number of specific mathematical problems that I believe are true but cannot prove, starting with the famous Riemann Hypothesis. But I think I can be of more use by using my mathematician's perspective to point out the uncertainties in the idea of proof. Which I believe (but cannot prove) I have.

Physicist, Stanford University

Conversation With a Slow Student

Student: Hi Prof. I've got a problem. I decided to do a little probability experiment—you know, coin flipping—and check some of the stuff you taught us. But it didn't work.

Professor: Well I'm glad to hear that you're interested. What did you do?

Student: I flipped this coin 1,000 times. You remember, you taught us that the probability to flip heads is one half. I figured that meant that if I flip 1,000 times I ought to get 500 heads. But it didn't work. I got 513. What's wrong?

Professor: Yeah, but you forgot about the margin of error. If you flip a certain number of times then the margin of error is about the square root of the number of flips. For 1,000 flips the margin of error is about 30. So you were within the margin of error.

Student: Ah, now I get if. Every time I flip 1,000 times I will always get something between 970 and 1,030 heads. Every single time! Wow, now that's a fact I can count on.

Professor: No, no! What it means is that you will probably get between 970 and 1,030.

Student: You mean I could get 200 heads? Or 850 heads? Or even all heads?

Professor: Probably not.

Student: Maybe the problem is that I didn't make enough flips. Should I go home and try it 1,000,000 times? Will it work better?

Professor: Probably.

Student: Aw come on Prof. Tell me something I can trust. You keep telling me what probably means by giving me more probablies. Tell me what probability means without using the word probably.

Professor: Hmmm. Well how about this: It means I would be surprised if the answer were outside the margin of error.

Student: My god! You mean all that stuff you taught us about statistical mechanics and quantum mechanics and mathematical probability: all it means is that you'd personally be surprised if it didn't work?

Professor: Well, uh...

If I were to flip a coin a million times I'd be damn sure I wasn't going to get all heads. I'm not a betting man but I'd be so sure that I'd bet my life or my soul. I'd even go the whole way and bet a year's salary. I'm absolutely certain the laws of large numbers—probability theory—will work and protect me. All of science is based on it. But, I can't prove it and I don't really know why it works. That may be the reason why Einstein said, "God doesn't play dice." It probably is.

< previous

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10

next >