WHY PHYSICAL LAWS ?
-------------------

>Chris Maloney wrote:
><<< The answer is that the structure(s) we are in obey physical laws,
>not because they were cast by  fiat from some omnipotent being, but
>simply because the structures that do obey physical laws are more
>numerous than those that do  not, and hence we are likely to find
>ourselves in those.
>
>GSLevy wrote:
><<  We can find ourselves ONLY in those structures that obey physical
>laws because these are the ONLY structures that can support us as
>rational beings (SAS). The assumption that worlds with (rational)
>physical laws are  more more numerous than those without is therefore
>unwarranted.  In fact I would believe in the opposite. That the worlds
>without rational physical laws, (if these could be called worlds at
>all), are more numerous than those with rational physical laws.


I agree with GSLevy.
I agree with Chris Maloney.

What GSLevy says is a consequence (with comp) of Cantor diagonal argument.
What Chris Maloney says is a consequence (with comp) of the PE-omega 
thought experiment (see the archive of the list).

We can find ourselves ONLY in those structures which are relatively 
numerous, not to survive but to remain with others and a (relatively) 
stable environment.

[I would say *sharable histories* instead of *structures* but precise words here are 
probably premature]

Once you experience a *deep histories* with friends, what you can communicate, in some 
verifiable way, with those friends *are* the physical laws.
But this only works (with comp) if the physical laws are such that 
"*deep histories* with friends" have some kind of measure one with respect
to each "observer-moment" (or instant, I borrow the word of Hal, do I?) belonging to 
such deep history. (= relative strong SSA).

I agree with GSLevy when he says: the "worlds without rational physical laws" are more 
numerous than those with rational physical laws. But, at least with comp, we must 
explain why, from the point of view of a sufficiently rich (cognitively) observer, non 
aberrant worlds (histories)
are relatively more numerous than aberrant one (cf PE-omega).
I should say: non aberrant (sharable) continuations (in the computer 
science sense) are relatively more numerous than aberrant one.

With comp it means to extract physical laws from a "conditional" measure on the set of 
computationnal histories. 

(by observer I mean you, me or any universal machine (self referentially correct with 
respect to her more numerous continuations, in the ideal case).

There are neither worlds nor physical laws, but a web of dreams.
(where dreams are first person point of view on a computationnal history)
Those dream which are deep (in Bennett() sense) and sharable among population of 
(self-referentially correct) machines can be said *physical*.

To sum up: the computationnalist hypothesis forces us to accept kind of
Everett interpretation of arithmetic.
Time, space, space-time, energy... are internal modalities of arithmetical
truth.
Physical laws emerges from arithmetical truth.
Where does arithmetical truth comes from ? Well, there exist logical reason
why no machines can answer this question. 

Bruno

() Bennett C. H. (1988). Logical Depth and Physical Complexity. In Herken,
R., Editor, The Universal Turing Machine A Half-Century Survey, pages 227-
258. Oxford University Press.


 Bruno MARCHAL            Phone :  +32 (0)2 6502711         
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