> From [EMAIL PROTECTED]  Thu May 31 18:14:55 2001
> From: Karl Stiefvater <[EMAIL PROTECTED]>
>       O         
>      O             > Maybe you'd like to write down formally
> O    O             > what you mean.
>  O      O       
>  O      O       sure. i suspect we're talking past each other.
>    O O          
>      OO  O      let M be the set of universes. let A_i be a
> O O  O          sequence of finite subsets of M, such that A_i
>   O  O          is a strict subset of A_(i+1). define e(i) be
>  O  O O         the expected complexity of a uniformly chosen
>     OOO         member of A_i.
> O O  O          
>   O O  O        then lim i->inf e(i) = inf.

This will not give you a uniform distribution on infinitely many
things.  For simplicity, consider integers instead of universes. Assign 
something like probability P(n)=6/(n^2 pi) to integer n. This yields 
nonvanishing probability for infinitely many integers. But it's not 
uniform. Uniformness and nonzero limits are incompatible.


> O  OO   O          > Practical unpredictability due to
>    OO  OO          > deterministic chaos and Heisenberg
>  O OO O  O         > etc is very different from true
>  O  O O  O         > unpredictability. For instance, despite of
>   O O O OO         > chaos and uncertainty principle my computer
>   OOO O  O         > probably will not disappear within the
> O  OO  O O         > next hour. But in most possible futures it
> OO  O  O O         > won't even see the next instant - most are
>  OO O  O O         > maximally random and unpredictable.
> OO  O OO O      
> OOO  O O O      yes - i think i understand what you're saying
>  OO O  O O      here. a universe with high complexity is a very
> OOO O   OO      messy place indeed - computers disappear, etc.
> O OOO O OO      however, i think you'll agree, that our universe
> O OO  OOOO      (unless it *is* using a pseudo-random number
> OO O OOOO       generator) is quite messy.

Not at all. It seems extremely regular. Whatever appears messy 
may be due to lack of knowledge, not to lack of regularity.

>  OOOO  OOO      i'm wondering if perhaps a different force is
> OOOO OO OO      keeping the complexity low. an anthropic force
> OOOO OO OO      - if complexity is too high, then life doesn't
> OOO OOO OO      evolve - and we don't see it.

According to the weak anthropic principle, the conditional probability
of finding ourselves in a universe compatible with our existence equals
1. But most futures compatible with our existence are complex.  So why 
is ours so regular? Algorithmic TOEs explain this, and add predictive 
power to the weak anthropic principle.

http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/



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