From: John K Clark (email@example.com)
Date: Fri May 22 2009 - 11:23:51 MDT
On Thu, 21 May 2009 "Warrigal" <firstname.lastname@example.org> Wrote:
> Goedel's theorems do not apply at all here.
No at all?! Not even a little?
> His theorems state
Itís not a theorem, itís 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; thatís what
proven means. And you donít want axioms that can prove every statement,
only the true ones. It would be nice if it could also prove all true
statements, but GŲdel 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 canít
do that either. If Goldbach is one of these (and if it isnít 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
> Super-intelligent beings do not prove that every possible
> outcome leads to them being immortal.
I agree, thatís one reason they canít logically prove they are immortal.
> Suppose that I am a super-intelligent being,
> and I've figured out the laws of physics.
OK, Iím feeling extraordinarily generous so Iíll 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 Shakespeareís 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 donít, 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 canít 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 canít know the previous
iteration because there is more than one way the game could have gotten
into its present condition.
John K Clark
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