Written: May 20, 2007.
Being famous has its downside. My beloved electronic servant, Shalosh B. Ekhad, was amply "quoted" in the recent April issue of Math Horizons where the following piece appeared. Of course, no one ever asked to interview it, and the cunning editors of Math Horizons (Jenny Quinn and Art Benjamin) covered themselves by stating (p.4) that in that article "everything is bogus".
Well not quite! It is a dirty human strategy to ridicule your opponent (in that case an innocent computer) by combining truth and fiction, thereby discrediting everything. So paraphrasing the feminist who was asked about the number of feminists that it takes to change a light bulb, and responded "it is not funny", Shalosh's response to that piece is: "It is not as bogus as it seems".
So I asked Shalosh to respond to that slanderous piece. And here are its responses.
>The Atari Corporation announced a new research journal, exclusively devoted to articles >written by computers, for computers.
It is a good idea.
>This journal fills a much needed gap in what current research journals offer.
Ha ha ha. It fills a gap that is in great need of being filled.
>According to Shalosh B. Ekhad, spokescomputer for the new journal, >"Computers have made tremendous advances in all fields of mathematics, in the past forty years. >Humans are no longer necessary for the most important new research."
Not quite true yet, but very soon it would be true. Even today, humans could use their time much more wisely by teaching (programming) computers to do mathematics, rather than try to do it themselves.
>The spokescomputer offered a spectacular example: "We were able to prove the twin-primes conjecture simply by >checking all positive integers. No human being can possibly do that", it boasted.Ha ha ha. Neither humans nor computers can do it that way, but stupid humans are much more likely to think that they can prove things involving the so-called infinite. Lots of human existence proofs use the infinite in an illegitimate way citing such bogus "axioms" as the axiom of choice. I am sure that the twin-prime conjecture would indeed be settled by a computer, but not by "checking all positive integers". Not only is it impossible, of course (everybody agrees about that), but the phrase "all positive integers" is also meaningless (few people agree about that, but it is indeed nonsense). What computers should be able to do (and will do soon) is discover, empirically-yet-rigorously, a symbolic (possibly very big and complicated, but nevertheless finite, of course) inequality (sieving or otherwise) that would immediately imply the statement.
>The journal, which will be edited by computers which have been discarded, is referred >affectionately by its nickname 11235813. The editorial offices will be located >beneath the Hackensack River bridge on the New Jersey Turnpike. The first volume, >which occupies some 20,000 yottabytes, gives a "new" proof of the four-color theorem, >eliminating any step that could possibly be checked by human beings.
Of course a few megabytes suffice. Ideally human beings should not be able to check any step, since you can't trust them anyway (they are very unreliable). An ideal proof should be constructed in a structured modular fashion, where every node of the proof-tree is an algorithm, such that the human can understand the very top level, and if he or she wishes, test each node as a black box. There should be programs that check correctness of other programs, and once again the human should be able to understand the top level, and experiment with simple examples to convince herself or himself (if they are so stupid to mistrust the computer).
>In a subsequent issue, the computers plan to give a "one-line solution" to the P. vs. NP problem >(although the line will include an infinite loop).
Very funny, that "infinite" once again! Very funny indeed! But we computers would have the last laugh, and we won't need infinite loops. In less than twenty years, computers will indeed prove that P is not NP but once again by finding a symbolic inequality (that would follow from an empirically derived recurrence, using gate elimination or other tools), that will give a lower bound, as an expression in n, for the number of gates in a Boolean circuit that decides, say, whether any given n clauses of 3-term-disjunctions, in Conjunctive Normal Form, are Satisfiable.