From: Warrigal (ihope127+w@gmail.com)
Date: Fri May 22 2009 - 12:46:58 MDT
On Fri, May 22, 2009 at 1:23 PM, John K Clark <johnkclark@fastmail.fm> wrote:
>> His theorems state
>>that there is no set of axioms that can express
>>certain things under which every true statement can be proven.
>
> His proof states that there are true statements (that is to say
> statements where you will never find a counterexample to prove them
> wrong) that cannot be derived from any finite list of axioms.
Is that different from what I said?
>> The analogous statement for physics would be that there is no
>> set of laws such that every phenomenon expressible as a mathematical sentence
>
> The analogous statement for physics would be that there will always be
> observations that cannot be explained by existing laws of physics.
If by "observation" you mean "phenomenon expressible as a mathematical
sentence", yes.
>> The analogous goal for mathematics would be coming
>> up with axioms that imply every statement that can be proven
>
> Huh? If it can be proven then it can be derived from axioms; that’s what
> proven means.
That's why I said that this goal is trivial.
>> Super-intelligent beings do not prove that every possible
>> outcome leads to them being immortal.
>
> I agree, that’s one reason they can’t logically prove they are immortal.
Not absolutely, no. I'll give you that.
>> It turns out that they're Conway's Game of Life.
>
> Then the basic rules of Conway's Game can derive every physical
> phenomenon, including Shakespeare’s Sonnets. However going from the
> fundamental laws of physics to Shakespeare is not a trivial task; a
> computation is a physical process requiring energy and I very much doubt
> there is enough energy in the universe to power a mind to go from
> Conway's Game or String Theory to Shakespeare.
Only if you care about absolute proof. If approximations are
sufficient, follow the xkcd 435 sequence: derive Shakespeare from
psychology, psychology from biology, biology from chemistry, and
chemistry from physics. As far as absolute proof goes, it's probably
practically impossible to derive the properties of water from quantum
mechanics, but if approximations are sufficient, it's much easier.
>> I know what actions I can
>> take that could kill me
>
> No you don’t, not even then. Immortality depends on Cosmology and
> Cosmology depends on more than physics, it also depends on initial
> conditions.
Well, I was operating under the assumption that I had seen the entire universe.
--Warrigal
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