Hi Günther,

Le 25-mars-08, à 13:35, Günther Greindl a écrit :

>
> Dear Bruno,
>
> I have used the Easter holidays to read again through your SANE 2004
> paper, and I have a question regarding step 7.
>
> (I am fine with step 1-6, step 8 seems OK but I will withhold judgment
> until I understand step 7 ;-)


Nice. Step eight is the more difficult, but for some people---those who  
have never start to believe in a *primary* physical universal--- it can  
be considered as redundant.


>
> The things I am unclear about are:
> 1) maximally complete computational histories going through a state ->
> what are these?


We assume comp ok? So for example, my current relative mind state can  
be associated with a computational state. By Church thesis, this state  
is accessed an infinity of times by the Universal Dovetailer through an  
infinity of infinite computations. OK? A complete computational history  
is just such an infinite computation. Sometimes I use the word  
"history" to refer to the internal view of some machine whose current  
state has been accessed by the UD. In that case some similarity  
equivalence class is in play. To get the math of those similarity  
classes I proceed in interviewing such machines.



>
> 2) Why do they correspond to _consistent_ extensions, and how do you
> define these consistent extensions (in a normal logical way -> no
> contradiction; or differently?)-

Just "no contradiction". Now a computation is not per se a theory, so  
the notion of contradiction is not directly applicable. That is why I  
identify a computation with a proof of a Sigma_1 sentence of  
(elementary, Robinsonian) arithmetic. Of course this leads to the white  
rabbit issue, a lot of statement are relatively consistent and false at  
the same time, like the "self-inconsistency statement" (by Godel's  
second theorem the proposition "I am inconsistent" is consistent (when  
asserted by a Robinsonian machine or a Lobian machine).
I recall that a Robinsonian machine is a machine having Turing  
Universal abilities, but without the introspective power to acknowledge  
that. On the contrary Lobian machine are universal and know that they  
are universal.

>
> 3) And how do you treat the Boltmann brain issue which crops up in
> modern cosmology but also in a UD generating _all_ computational  
> histories?

Thanks for the references out of line. I will read those papers once I  
have the time. At first sight it looks like the cosmologists begin to  
be aware of a (third person) white rabbit problem. It will still take  
time before they realize the first person white rabbit problem. The  
reason is that they have no formation on the "mind-body" problem I  
think.

I hope this can help you a bit.

I take the liberty to put online the references you gave me because I  
think it is of general interest:

http://arxiv.org/abs/hep-th/0611043 (Andrei Linde)
or
http://arxiv.org/abs/hep-th/0610079 (Don Page)

The New York Times had a piece about this stuff in January:
http://www.nytimes.com/2008/01/15/science/15brain.html? 
_r=1&pagewanted=all&oref=slogin


Bruno



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


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