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More on Zero Information proofs:

In article <19257@ucbvax.BERKELEY.EDU>, tedrick@ernie (Tom Tedrick) writes:
>>>and now after 2000+ years all of a sudden a new notion of proof appears.
>
>>Hardly new.  Renaissance mathematicians used to [play games with each other]

>(1). Was the method completely general? [etc]

No.  No.  And no.  Of course not.  These were all meant as *examples* of
zero-information proofs, not the general theory.  They could, at times,
for certain problems, convince the mathematical community that they
indeed knew a proof of certain problems.

Just like:

>People tried to give demonstrations before formal logic, still formal
>logic was a blindingly brilliant discovery.

Right.  They could give proofs, without knowing what a "proof" in fact
was.

>>But seriously, Tom, this isn't a new notion of proof, but of mathematical
>>epistemology.
>
>Could you explain in more detail? I don't think I understand what
>you mean.

The zero information proofs still require that a proof in the classical
sense be written out somewhere, which proof is then transformed into a
clever graph-theoretic problem.

What's different here is how one *knows* that a given theorem is known.

>>Even the Einsteins and Goedels are not irreplaceable for the advances in
>>our knowledge that they discovered.
>
>I'm not so sure about that. I don't know the official name for my
>philosophical position (catastrophe theorist? :-) but I am inclined
>to the view that the acts of one individual can radically alter the
>course of human affairs.

Ah!  Remember though, the course of human affairs is one thing, the sum
total of human knowledge is another.  I've often wondered just how diff-
erent mathematics *could* be--unlike history, I think there would be no
non-cosmetic differences, give or take a few decades.  Look how often a
great idea is rediscovered, or found to have strong precursors, etc.

>By the way, have you talked to Solovay about these 0-knowledge creatures?

Be serious.  We rarely talk about anything *finite*!  How droll.

ucbvax!brahms!weemba	Matthew P Wiener/Brahms Gang/Berkeley CA 94720