X-Message-Number: 22397
From: 
Date: Thu, 21 Aug 2003 09:27:57 EDT
Subject: more responses

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Mike Perry writes in part:

>Consider the following proposition: "One computer (generally) has many 
features lacking in another one, and conversely. Thus a simulation of one 
computer by another cannot be fully isomorphic." Yet we know it can (or can 
be "sufficiently isomorphic" at any rate), that is, one general-purpose 
machine can emulate another one.<

Yes, one Turing computer is sufficiently isomorphic to another so they can do 
the same computations and are interchangeable in that respect. But we already 
know that a computer (ideally) will model a brain accurately enough to be "as 
good as" or "the same as" the brain in those particular ways and to the 

accuracy allowable. The question is whether that is sufficient, and I know of no
good reason to be confident that it is.

And:

>f a theory of everything can be developed, it would seem to indicate that 
reality as a whole can be regarded as a formal system<

I don't follow that. A formal system differs from reality in several 

ways--most importantly, the formal system uses symbols that have no meaning 
except in 
the context of a metalanguage. (Conceivably, a sufficiently large language 
might allow of only one interpretation, but that has not been proven.) 

Also, in most formal systems of interest there are formally undecidable 
propositions, which hardly seems allowable for reality.

Also, the undefined terms in the formal system may have unclear meaning even 
in the metalanguage. This is a formidable philosophical problem, including the 
basics of ontology. Nobody has a clear idea of what a "thing" or "object" is.

Finally:

>On the other hand, 
we may ask, really, what is meant by "formal system." Does it imply 
"predictable"? If that is true, then all we need is to equip our computer 
with a quantum random number generator, and it ceases to be a formal system.<

The full ramifications of this would be lengthy, but among other things it 
underscores the point that a general purpose digital computer is a classical 
system. It can calculate quantum quantities--as you could with pencil and 

paper--but it itself is classical. The present mathematical formulations of 
quantum 

physics allow only calculations of probabilities, and in particular of the most
probable successor state of a simulated system. And again, for ultimate 
integrity you need the quantum state of the universe, which may not even be 

meaningful, since the wave equation reflects probabilities, which referred to 
the 
whole universe has no clear interpretation.

Robert Ettinger


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