Le 29-mars-06, à 21:58, Wei Dai a écrit :

>
> Is there a difference between physical existence and mathematical 
> existence?
> I suggest thinking about this problem from a different angle.
>
> Consider a mathematical substructure as a rational decision maker. It 
> seems
> to me that making a decision ideally would consist of the following 
> steps:
>
> 1. Identify the mathematical structure that corresponds to "me" (i.e., 
> my
> current observer-moment)


You can't. It is just absolutely impossible in term of first person OM 
(implicitly the OM notion of Bostrom), and you can, but only by guess 
and chance, for some third person description of the OM. But in that 
case ....



> 2. Identify the mathematical structures that contain me as 
> substructures.


... There will be an unameable infinity of such mathematical 
structures. I think P. Jones got that right.
To apply your trick we need to get the physial laws from comp first 
(but then i'm OK).



> 3. Decide which of those I care about.
> 4. For each option I have, and each mathematical structure (containing 
> me)
> that I care about, deduce the consequences on that structure of me 
> taking
> that option.
> 5. Find the set of consequences that I prefer overall, and take the 
> option
> that corresponds to it.
>
> Of course each of these steps may be dauntingly difficult, maybe even
> impossible for natural human beings, but does anyone disagree that 
> this is
> the ideal of rationality that an AI, or perhaps a computationally 
> augmented
> human being, should strive for?

OK then, but with the proviso above (and apparently you are aware of 
the difficulties).


>
> How would a difference between physical existence and mathematical
> existence, if there is one, affect this ideal of decision making?


By affecting the very structure of the physical laws. Of course that 
will not change the way you prepare coffee (nor will the choice between 
Loop Theory and String theory affects such things).



> It's a
> rhetorical question because I don't think that it would. One possible 
> answer
> may be that a rational decision maker in step 3 would decide to only 
> care
> about those structures that have physical existence.


But with the comp hyp, what would that mean?



> But among the
> structures that contain him as substructures, how would he know which 
> ones
> have physical existence, and which one only have mathematical 
> existence? And
> even if he could somehow find out, I don't see any reason why he must 
> not
> care about those structures that only have mathematical existence.


Because with comp, even if matter exists, it is devoid of any 
explanation power. Like the Napoleon's God is unnecessary in a 
Laplacian Universe. If you accept comp, what do you mean by Physical?  
It seems the UDA shows such a notion is untenable as primitive notion. 
The physical is really what emerges from the interference of many 
"mathematical histories" The "many" is due to person's inability to 
make distinction of the finer grained histories; finer relatively to 
its substitution level.

Bruno

http://iridia.ulb.ac.be/~marchal/


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