Hi Jason,

Le 03-déc.-08, à 17:20, Jason Resch a écrit :

> On Wed, Dec 3, 2008 at 9:53 AM, Bruno Marchal <[EMAIL PROTECTED]> 
> wrote:
>>> and that by virtue of this imposed order, defines relations between 
>>> particles.  Computation depends on relations, be it electrons in 
>>> silicon, Chinese with radios or a system of beer cans and ping-pong 
>>> balls;
>> Here you are talking about instantiations of computations relatively 
>> to our most probable computations, which have a physical "look". But 
>> strictly speaking computations are only relation between numbers.
> Bruno,
> Thanks for your reply, I am curious what exactly you mean by the most 
> probable computations going through our state if these computations 
> cannot be part of a larger (shared universe) computation.  

Hmmm... It means you have still a little problem with step seven. I 
wish we share a computable environment, but we cannot decide this at 
will.  I agree we have empirical evidence that here is such (partially) 
computable environment, and I am willing to say I trust nature for 
this. Yet, the fact is that to predict my next first person experience 
I have to take into account ALL computations which exist in the 
arithmetical "platonia" or in the universal dovetailing.

> Where does the data provided to the senses come from if not from a 
> computation which also includes that of the environment as well?  

You don't know that. The data and their statistics come from all 
computational histories going through my state. The game is to take 
completely seriously the comp hyp, and if it contradicts facts, we will 
abandon it. But that day has not yet come .... Until then we have to 
derive the partial computability of our observable enviroment from a 
statistic on all computations made by the UD.

> Also, why does the computation have to be between numbers specifically,

They don't. Sometimes I use the combinators. They have to be finite 
objects, and this comes from the *digital* aspect of the comp. hyp.

> could a program in the deployment that calculates the evolution of a 
> universe

This is something you have to define. If you do it I bet you will find 
a program equivalent to a universal dovetailer, a bit like Everett 
universal quantum wave.

> perform the necessary computations to generate an observer?  

Sure. The problem is that there will be an infinity of program 
generating the same observer, in the same state, and the observer 
cannot know in which computations it belongs. Never? Measurement 
particularizes, but never get singular.

> If they can, then it stands other mathematical objects besides pure 
> turing machines and besides the UD could implement computations 
> capable of generating observers.

Not really. Those objects are internam construction made by programs 
relatively to trheir most probable history.

>  I noticed in a previous post of yours you mentioned 'Kleene 
> predicates' as a way of deriving computations from true statements, do 
> you know of any good sources where I could learn more about Kleene 
> predicates?

A very good introduction is the book by N.J. Cutland. See the reference 
in my thesis. There are other books. I will think to make a list with 
some comments. Actually I really love Kleene's original "Introduction 
to Metamathematics", but the notations used  are a bit old fashioned.

Hope I am not too short. I am a bit busy today,




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