**From:** John K Clark (*johnkclark@fastmail.fm*)

**Date:** Fri May 22 2009 - 11:23:51 MDT

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On Thu, 21 May 2009 "Warrigal" <ihope127+w@gmail.com> Wrote:

*> Goedel's theorems do not apply at all here.
*

No at all?! Not even a little?

*> His theorems state
*

It’s not a theorem, it’s a proof.

*>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.

*> 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.

*> 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. And you don’t want axioms that can prove every statement,

only the true ones. It would be nice if it could also prove all true

statements, but Gödel proved that could not be dome.

It would also be helpful if we could identify all statements (Goldbach's

conjecture perhaps) that are either false or true but unprovable so we

could stop wasting time trying to prove them, but Turing proved we can’t

do that either. If Goldbach is one of these (and if it isn’t there are

an infinite number of similar statements that are) then a billion years

from now our decedents will still be looking, unsuccessfully for a proof

(a derivation from axioms) to prove it correct and still be crunching

huge numbers looking, unsuccessfully, for a counterexample to prove it

wrong.

*> 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.

*> Suppose that I am a super-intelligent being,
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*> and I've figured out the laws of physics.
*

OK, I’m feeling extraordinarily generous so 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.

*> 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. Even if you know the rules of Conway's Life you can’t know

what the next iteration of the game will be unless you know the previous

one. Likewise the past can be foggy too even if you know the laws of

physics and the present state of the game; you can’t know the previous

iteration because there is more than one way the game could have gotten

into its present condition.

John K Clark

-- John K Clark johnkclark@fastmail.fm -- http://www.fastmail.fm - Choose from over 50 domains or use your own

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