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Jörg F. Wittenberger [LibreList] Zooko's triangle vs. Gödel incompleteness the 2014-08-21 12:22:09 (6 years 21 days 19:29:00 ago)
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

Ximin Luo [LibreList] Re: [redecentralize] Zooko's triangle vs. Gödel incompleteness the 2014-08-21 13:20:19 (6 years 21 days 18:31:00 ago)
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?

We don't even know if Zooko's triangle is actually true or not. It has not even been formalised into precise mathematical language.

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? What about the problem of consciousness, or strong AI?

X

-- 
GPG: 4096R/1318EFAC5FBBDBCE
git://github.com/infinity0/pubkeys.git
Jörg F. Wittenberger [LibreList] Re: [redecentralize] Zooko's triangle vs. Gödel incompleteness the 2014-08-25 10:58:38 (6 years 17 days 20:53:00 ago)
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

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