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From: cowan@marob.masa.com (John Cowan)
Newsgroups: comp.ai
Subject: Re: simulating brains
Message-ID: <270367E4.160B@marob.masa.com>
Date: 28 Sep 90 15:10:28 GMT
References: <1990Sep26.202658.2906@csc.anu.oz.au>
Organization: ESCC, New York City
Lines: 60

In article <1990Sep26.202658.2906@csc.anu.oz.au> ada612@csc.anu.oz.au writes:
>From <1292@fornax.UUCP> miron@fornax.UUCP (Miron Cuperman)
>
>>What is a sufficient condition for a simulation of a brain to be good enough?
>>The noise induced by the finite precision of the simulation must be on the
>>order of magnitude of normal noise we experience.  If that is so, the
>>simulation is adequate.
>
>Reflecting on my original question, this seems right:  since neural
>behavior is sloppy and imprecise, the roundoff errors of fixed precision
>digital simulations shouldn't make any difference to the quality of
>performance.

Turing actually makes this very point in "Can Machines Think?".  He points
out that while a digital computer cannot exactly simulate the behavior of an
(analog) differential analyzer (because the digital machine has only finite
precision), it can approximate the random error in the analyzer's behavior
to an arbitrarily close degree.

>>Conclusion:  Brains are finite state machines with noise.  Therefore there
>>is no a-priori reason why they cannot be simulated.
>
>But this seems wrong, because brains can also *grow* while they operate,
>which is not something that finite state machines can do.  Turing
>machines on the other hand can grow in the rather limited sense that
>they amount of tape they have written on can get larger, but brains
>can add new active computational agents, in the form of synapse connections.
>This is clearly a more radical form of extensibility (if you're interested
>in what can be done in real time).

I don't understand the sense of your final parenthesis.  Neglecting it for
a moment, the claim that brains are superior to Turing machines because they
can add "new active computational agents" seems clearly wrong.

The universal Turing machine has a fixed finite-state repertoire and a single
tape, like any Turing machine.  However, the tape may be thought of as
logically divided into two tapes.  The H-tape contains a symbolic representation
of the finite-state part of the TM being simulated by the UTM, and the S-tape
is the simulated tape of the simulated TM.

In the standard UTM, the H-tape contains both the unchanging representation of
the finite-state machine hardware, and the changing representation of the
current state.  The machine hardware representation (MHR) is not changed during
operation of the UTM.  However, there is no problem with constructing a variant
UTM which is allowed to change the MHR.  In particular, the amount of
MHR table space can grow without bound, since the H-tape is of infinite length.
(The easiest way to simulate an H-tape/S-tape pair is to use alternate cells
of the physical tape.)  Of course, such a modified UTM cannot simulate an
oracle (an infinite-state machine) because it would take infinite time to
"grow" the representation of such a machine on the H-tape.

OTOH, a brain cannot grow to infinite size (and processing power) in less than
infinite time either.  Turing machines are notoriously slow in "arbitrary time
units": they have to work confoundedly hard to overcome the limitations of
serial access.  But I don't see that "real time" has much to do with it.
If the modified UTM hardware is made fast enough, within quantum limits,
surely it could simulate an arbitrarily fast finite-state device?
-- 
cowan@marob.masa.com			(aka ...!hombre!marob!cowan)
			e'osai ko sarji la lojban