Re: [redecentralize] Zooko's triangle vs. Gödel incompleteness the
- From:
- Jörg F. Wittenberger
- Date:
- 2014-08-25 @ 08:58
Am 21.08.2014 14:20, schrieb Ximin Luo:
> On 21/08/14 11:22, Jörg F. Wittenberger wrote:
>> Hi all,
>>
>> I've got a problem for someone better at math than me. Though the result
>> should be tremendous interesting to many people and projects on this list.
>>
>> The challenge: Show how precisely the challenge seen in Zooko's triangle
>> is different from precondition of Gödel's incompleteness theorem.
>>
>> Alternative: Show that there is no difference and thus prove Zooko's
>> conjecture true.
>>
>> http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
>> http://en.wikipedia.org/wiki/Zooko%27s_triangle
>>
>> Personally I'd bet at latter. About 20yrs. ago – after reading "Gödel,
>> Escher, Bach" – I stopped trying at such self-proofing and universal
>> naming systems precisely for _believing_ in this equivalence. Since I'm
>> treating such schemes as either "probably broken" or outright evil.
>>
>> But it could be just me; after all: I don't have a formal proof. Can you
>> prove it being either way?
>>
>> Best
>>
>> /Jörg
>>
> Why do you think there is any relationship whatsoever between those two things?
I don't have a formalization of Zooko's triangle either. Hence my
challenge to do so.
For me I'm seeing Zooko's triangle as the intention to collect proofs
for name-value pairs into some system.
Maybe I'm already wrong here? If I'm right, then name-value pairs would
be "sentences in a language" (for the Gödel side). The collecting system
would essentially perform the Gödel-enumeration (in some refined form
like mapping to another human meaningful expression than natural numbers
– but that's at worst a recursive incarnation of the same problem).
What am I missing?
> We don't even know if Zooko's triangle is actually true or not. It has
not even been formalised into precise mathematical language.
That's the actual problem. I'm seeing three alternatives: a) some
genius formalizing it, this should then lead to a proof b) betting for
not being true and try to come up with a solution, a proof by counter
example c) betting for being true and develop concepts to deal with it.
(Actually a 4th one: ignore the problem and wait.)
> There are lots of unsolved problems in mathematics, including problems
that don't have good formal descriptions. Why not try to find a link
between Zooko's triangle and the Riemman Hypothesis, or P vs NP?
Yes, why not try? So far I'm just suggesting Gödel, because that's
looking to me as all too similar. Plus: this argument made me *not* try
alternative (b).
> What about the problem of consciousness, or strong AI?
"problem of consciousness" – any good reference? (There have been all
too many people writing about that topic.)
But how should consciousness be related at all?
/Jörg