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[David C. Ullrich]

On Mon, 4 Jun 2001 00:46:49 -0400, "Tim Peters" <tim.one at home.com>
wrote:

>[David C. Ullrich, on http://www.cs.umaine.edu/~chaitin/cmu.html]
>
>> ...
>> Very interesting stuff, without a doubt. He wants to say that
>> his point of view makes incompleteness seems inevitable he
>> may well be right. But when he gets into statements like
>>
>> "there is no reason that individual bits [of Omega] are 0 or 1!"
>>
>> it's just too... well I better omit the adjective and just say
>> that "there is no reason that individual bits are 0 or 1" is not
>> a mathematical statement amenable to proof.
>
>It *sounds* powerful, though <wink>.  I don't really object, because it
>conveys *something* of the story in a way that would otherwise be over his
>audience's head.

Yes. When he says "for no reason" it's clear that that's not _exactly_
what he means. But people who don't realize that taking "no reason"
literally makes no sense are going to read it literally. This leads
to problems with storage space on usenet servers.

>For example, over the last few weeks we've had several examples on c.l.py of
>printing the exact decimal value of a machine binary floating-point value
>with a non-zero fractional part.  I don't know whether anyone noticed, but
>every such example ended, in decimal, with the digit 5.  The natural
>inclination of anyone with even a slight bent toward mathematical thought is
>to ask "Hmm!  Was that just luck, or is there 'a reason' that's so?".  With
>a little thought, and even in the absence of a formal notion of axioms or
>proof, I expect many people could get close to proving that 5 is no
>accident -- it must be a 5, "it makes sense", "there's a reason for it".
>And, indeed, that's the only kind of problem most people get exposed to in
>school:  "prove or disprove".
>
>It's at least a minor revelation then that some questions can't be answered
>that way (by appeal to principle or proof -- "a reason"), that brute force
>can be the only answer there is.  But *phrasing* it as "no reason" is too
>close to "senseless" for my tastes, so I'm sure it misleads people too.
>
>> Preciate the reference - I definitely learned one thing, at least:
>>
>> "Now what is the reaction of the world to this work?! Well, I think
>> it's fair to say that the only people who like what I'm doing are
>> physicists!"
>>
>> Not having studied his stuff or people's reactions to it I thought
>> it was just me (seriously). (Um: It's _not_ true that mathematicians
>> don't like his work, I know of plenty of mathematicians who find it
>> fascinating. What people don't like is his [adjective] claims
>> about what his work _means_...)
>
>I agree:  it's the popular presentation, not the work, that people object
>to.  I read that Gödel delayed presenting his incompleteness theorem (surely
>a much greater shock at the time!) because he feared nobody would believe
>him, so worried over every little detail of the arithmetic coding to make
>the proof unassailable first.  But by all accounts I've read, the ideas
>behind the proof were compelling the instant logicians heard about them, and
>despite that it wasn't what they were hoping to hear, and most skipped over
>the laborious coding details as curious drudgery.  Mathematicians are quite
>calm in the face of crisis <wink>.

Or perhaps they're quite good at recognizing the trivial bits.

>OTOH, Gödel kept what he thought his result "meant" to himself.  Take
>someone who learned it from the philosophy dept and another from the math
>dept, lock them in the same room, and see whether they have *anything* in
>common <wink>.  But Rudy Rucker reported that in private conversation,
>Gödel's beliefs were actually closer to the former, that the result had
>profound implications beyond just pointing out a limitation of formal proof
>systems.  I wish he would have written more about that; at least I won't
>have the same regret with Chaitin.

I certainly believe all that. My "preferences" would be different...

>> The (or in any case _a_) point being things like
>>
>> "I think there may be political reasons, but I think there are also
>> legitimate conceptual reasons, because these are ideas that
>> are so foreign, the idea of randomness or of things that are true by
>> accident is so foreign to a mathematician or a logician,
>> that it's a nightmare! This is their worst nightmare come true! I
>> think they would prefer not to think about it."
>>
>> He insists that the world of mathematics is all upset over his
>> well-defined but unknowable Omega.  If that irritates people what
>> irritates them is not the well-defined but unknowable character
>> of those bits, it's the idea that the idea of something being
>> well-defined but unknowable started with him.  It's no big deal,
>> people have been dealing with "unknowables" for a long time.
>
>Wholly agreed.  Some people were driven to despair and even suicide by
>Gödel's results at the time. 

Suicide? Anyone I've heard of?

> Everything since (and there's been a lot) has
>been greeted with "Wow -- here's yet *another* thing we can't know.  Cool!".
>
>the-first-time-was-a-major-surprise-but-that-was-70-years-
>    ago-ly y'rs  - tim
>
>



David C. Ullrich
*********************
"Sometimes you can have access violations all the 
time and the program still works." (Michael Caracena, 
comp.lang.pascal.delphi.misc 5/1/01)