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From: ada612@csc.anu.oz.au
Newsgroups: comp.ai
Subject: simulating brains
Message-ID: <1990Sep21.113002.2876@csc.anu.oz.au>
Date: 21 Sep 90 01:30:00 GMT
Organization: Computer Services, Australian National University
Lines: 52

Here is a basic  question about digital simulations of analog computing
systems such as the human brain is currently taken to be.  Namely, is there
any theorem that shows that this is in general possible, assuming
that the precision of the arithmetic is fixed (or, equivalently,
I hope, if the device has a fixed upper bound on the time needed
to compute the state at t_{i+1} from that it at t_i).

More precisely, discussions of brain simulations (as in Hofstadter's
Book-of-Einstein's-Brain scenario) assume that one can can simulate
a brain by breaking the passage of time into small intervals, and
using the equations governing the evolution of the system to
compute the state at t_{i+1} from that at t_{i}, furthermore using
approximations to physical & mathematical constants such as e and pi.

For this procedure to be convincing, we need to know that as our
time-interval size decreases and arithmetic precision increases, the
predicted state of the system at t (given initial conditions for t_0)
converges to a limit.  This is obviously true for the kinds of well-
behaved systems that we look at in baby Calculus, but is it provable or
plausibly conjecturable for brains?

Reasons for suspecting that it isn't are:

I: A semi-ignorant reading of the semi-popular literature on chaos theory
suggests that it might be possible to set up systems that passed
through critical periods t_c with the property that tiny differences
in the state at t_c would magnify into big differences at a later
time t, such that the states calculated for t_c with different
approximation methods produced non-convergingly different answers
at t.

II: The conclusion that a fixed-precision simulation of a brain is possible
leads immediately to the conclusion that a finite-state machine can simulate
the brain, which leads to one of the following conclusions, which I find
implausible:

  A) a finite state machine can be a sentient being.

  B) a finite state machine can simulate the behavior of a sentient
       being without being sentient.

Note the importance of the proviso that the simulation be fixed-precision.
If we allow the precision of the simulation to grow as the calculation
proceeds, it ceases to be finite state, but also, the time needed to
calculate the next state function would increase as the simulation
proceeded, and we wouldn't really have a functional equivalent to
a brain.  Thus an algorithm might be able to provide a sort of
semi-simulation of a brain (with the time scale expanding as the
simulation proceeded) without leading us to conclude either (A) or
(B) for algorithms.

Avery Andrews   ada612@csc.anu.oz.au