tag:blogger.com,1999:blog-28755195.post3854776622746801510..comments2023-09-25T04:26:51.568-06:00Comments on The Barefoot Bum: Evidentiary and deductive reasoningLarry Hamelinhttp://www.blogger.com/profile/08788697573946266404noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-28755195.post-46551867646160589962010-02-14T03:18:39.551-07:002010-02-14T03:18:39.551-07:00[I]t might not be beyond the ability of a supercom...<i>[I]t might not be beyond the ability of a supercomputer to generate [Fermat's last theorem] from a number theory production system.</i><br /><br />Based on my understanding of combinatorial math and number theory, I'm not holding my breath. Even today, supercomputer implementations of AI topics depend on speed and brute force, not cleverness.<br /><br />"Billions and billions" is very misleading. Combinatorial numbers speed past orders of magnitude before they have their first cup of coffee, get past exponents and towers of exponents by lunch, and we have to invent <a href="http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation" rel="nofollow">new systems of notation</a> before they've finished their first day of work.Larry Hamelinhttps://www.blogger.com/profile/08788697573946266404noreply@blogger.comtag:blogger.com,1999:blog-28755195.post-6265471864919680362010-02-14T02:55:35.884-07:002010-02-14T02:55:35.884-07:00Interesting to speculate that if Fermat really did...Interesting to speculate that if Fermat really did fit a clever proof of his last theorem in the margin of his book (instead of the book-length proof that eventually solved it), it might not be beyond the ability of a supercomputer to generate it from a number theory production system. The trouble, of course, would be in recognizing the theorem for what it was amongst the billions and billions.Hunthttps://www.blogger.com/profile/03589253382301604435noreply@blogger.com