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From: obnoxio@BRAHMS.BERKELEY.EDU.UUCP
Newsgroups: sci.philosophy.tech
Subject: Re: Complexity Philosophy
Message-ID: <8706041841.AA14805@brahms.Berkeley.EDU>
Date: Thu, 4-Jun-87 14:41:48 EDT
Article-I.D.: brahms.8706041841.AA14805
Posted: Thu Jun  4 14:41:48 1987
Date-Received: Sat, 6-Jun-87 08:45:53 EDT
Sender: daemon@ucbvax.BERKELEY.EDU
Reply-To: obnoxio@brahms.berkeley.edu (Obnoxious Math Grad Student)
Organization: Brahms Gang Posting Central
Lines: 36

In article <19233@ucbvax.BERKELEY.EDU>, tedrick@ernie (Tom Tedrick) writes
about "Zero Knowledge Interactive Proof Systems", ie, methods of convincing
anyone that you do indeed know a proof to something without giving out clues:

>					  It seems to me that we
>have had basically one notion of mathematical proof since Euclid,
>and now after 2000+ years all of a sudden a new notion of proof appears.

Hardly new.  Renaissance mathematicians used to pose problems to each
other and not reveal their solution techniques.  Thus, at the time they
all knew that Tartaglio (or was it his buddy Cardano?) had proven that
cubic equations were solvable, and similarly they knew that Pell's equa-
tion was solvable by Fermat, but they did not infer much about what the
actual proofs were.

But seriously, Tom, this isn't a new notion of proof, but of mathematical
epistemology.

This reminds me of the Y/Yb "scandal" in that first paper about the new
high-temperature superconductors, as reported in _Science_.  There were
very strong requests that Physical Review not leak any details out before
publication, yet rumors of the ytterbium-based material ran around.  Of
course, those particular "Yb"s were a misprint for "Y", which coincident-
ally never was spelled out.  The proofs were corrected on the last poss-
ible day.

What happens to science when one knows that other people know stuff, but
not much more?  Does it fall apart?  I doubt it, considering how frag-
mented scientific knowledge is already without any malicious intentions.
Even the Einsteins and Goedels are not irreplaceable for the advances in
our knowledge that they discovered.

ucbvax!brahms!weemba	Matthew P Wiener/Brahms Gang/Berkeley CA 94720
Some billion years ago, an anonymous speck of protoplasm protruded the
first primitive pseudopodium into the primeval slime, and perhaps the
first state of uncertainty occurred.		--I J Good