Insights From Brilliant People

There’s an absolutely fascinating series of responses by leading scientists and intellectuals to the question, “WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?”

Like this funny dialog by Stanford prof Leonard Susskind.

Conversation With a Slow Student

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…

Or the somewhat more heady essay on the limited utility of formal proofs by Stanford mathemetician Keith Devlin

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.

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.

Or Seth Lloyd from MIT:

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.

And the apparently lone theist, David Myers:

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.

Anyway, interesting stuff.