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From: minsky@media.mit.edu (Marvin Minsky)
Subject: Re: Dennett versus Searle
Message-ID: <1995Mar15.033421.18223@news.media.mit.edu>
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Cc: minsky
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References: <3k2agh$i87@mp.cs.niu.edu>> <OZ.95Mar14152024@nexus.yorku.ca> <3k57hg$da@mp.cs.niu.edu>
Date: Wed, 15 Mar 1995 03:34:21 GMT
Lines: 54

In article <3k57hg$da@mp.cs.niu.edu> rickert@cs.niu.edu (Neil Rickert) writes:
>In <OZ.95Mar14152024@nexus.yorku.ca> oz@nexus.yorku.ca (ozan s. yigit) writes:
>
>>Neil Rickert:
>
>>   The Turing machine formalism is inadequate for describing realtime
>>   computations.
>
>>i have no idea what this means.
>
>The TM formalism assumes that all of the input data is present before
>the computation begins, and the output is not considered until the
>computation has concluded.  Realtime computation allows continuous
>input and output.  Moreover, part of the input may depend on some of
>the earlier output in ways not defined by the TM, such as when a
>computer user interactively corrects some text during editing.
>

Rickert is technically right about this:--at least I've seen proofs of
it.  I think Carl Hewitt has a good paper about it.  Nevertheless, I
don't think it has any important implications for us.  Clearly, if a
Turing machine has as input a non-computable sequence then, clearly,
its output can be non-computable too, simply by printing out the input
tape.  On the other hand, if the "world" a Turing machine is in is
another Turing machine, and the two are synchronous, then the
comnbination's effect is computable.  If the two are non-synchronous,
in the sense that there is a variable delay with a non-computable
description, then the result is accordingly noncomputable.

In other words, it seems to me, that if the *system* is created with a
noncomputable parameter in its "world" then, yes, the result may be
noncomputable.  But this amounts to saying, garbage-in, garbage-out
or, if you will, transcendental-infinite-vision-in, tiv-out. In
neither case do we get any new insight, for there's no way to decide
if the world we're in is or is not an enormous cellular-array type
computable automaton.  I don't see modern quantum theory affecting
this, either from a wave-function of Feynman-path point of view,
because these, too appear to be realizable in a suitable-dimensional
CA machine.  At least, it is according to Fredkin, and I more than
once heard Feynman agree that this seemed to be right.

On a dimly related topic, there is a great theorem of Moore, Shannon,
DeLeeuw and Shapiro (published in Automata Studies, around 1956) which
shows that if we introduce a binary (coin-tossing) probabilistic
variable into a Turing Machine's input then the resulting computation
is, in a strong asymptotic sense, computable--if the coin's
probability itself is a computable real number.  [It would take too
long to explain precisely in what sense, but the paper explains it
clearly.]

Again, though, there's no way to know if a coin is "computable" so
Rickert would be right about this one, too--but again I don't see much
philosophical significance here.

