typodupeerror
\end{proof}
• This was news 20 years ago... (Score:2, Interesting)

on Wednesday April 06, 2005 @01:55PM (#12156573)
...but it's old hat now. Seriously, we're actually coming up on the 30th anniversary of the Haken-Appel proof of the four-color theorem, the FSG classification has been around for quite a while now, and from my perspective most of the people fretting about the nature of proof these days are philosophers, not mathematicians. Most of the serious (and many of the amateur) mathematicians I know consider the computer an essential part of their toolbox; Mathematica never accidentally flips a sign while it's going through two pages of calculations for you. There are even journals devoted to computer-aided mathematical exploration: Experimental Mathematics [expmath.org] is more than a decade old now.
• Re:Science by AI (Score:3, Interesting)

on Wednesday April 06, 2005 @02:57PM (#12157283) Homepage
No, this is basically bullshit. Penrose allows his irrational belief to determine his science, which is a big no-no for a scientist. He postulated that human mind is not a computer and grasps every straw to show how it might potentiall be so. Since he is a renowned and respected mathematician, his views are given a modicum of respect, just sufficient to guarantee he will not shut up for about 20-30 more years (by then we will probably have self-conscious strong AI that passes the Turing test and more).

This particular argument is patently stupid, but again, since Penrose has a big name, he gets away with it. The argument is as follows. Take two tiles that can fill the plane in a unique aperiodic way (one of Penrose's achievements was coming up with such things). Give an infinite amount of such tiles to a human and a "computer". Ask them to start tiling the plane and then ask whether the tiles can in fact tile the whole plane. Since the mosaic is aperiodical, according to Penrose the computer will not see a pattern, but a human will (the pattern being that you could always add a tile (as far as you tried), so the plane must be tileable). Penrose explains this by saying that humans have some magical "human consciousness" that allows them to have some "insight" about the world, to "understand" it, while computer doesn't have it. He then proceeds to explain this with some crackpot theories about quantum effects in microtubules in the human neurons, which is total bullshit, but again, his big name allows him to get away with spouting such garbage.

His argument is, of course, wrong. Humans can easily see patterns, because we were programmed to see them. This, of course, doesn't mean that we are always correct, when we believe there is a pattern. For example, consider the following sequence of numbers: 1, 3, 5, 7... Is there a pattern? If you think I listed odd numbers, you are wrong. It could have been a year, it could have been some random digits, it could have been a part of a different sequence, etc.

If monkeys could understand what an Euclidean plane is, they could reach the same conclusions as humans just as quickly. 1) You place a tile, it fits. 2) You place another, it fits. Repeat 10 times. Wow, it must be a magical pattern! This is just a heuristic that we humans have. The conclusions it helps us come to are not necessarily correct. We are not better than computers in solving the halting problem. It's just that too often we are willing to shout the answer, before we can be reasonably sure. Of course, sometimes we are lucky and the answer is correct. But we can program a computer to do just the same - it will gain the magical ability to "understand" and "see" the answer, at the price of often being completely wrong.

Penrose is just a persistent moron, don't listen to him.

Related LinksTop of the: day, week, month.

Make sure your code does nothing gracefully.

Working...