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Churchland,Evolution & Brain models
Sheldon Klein (sklein@CS.WISC.EDU)
Thu, 21 Sep 1995 13:51:44 -0500
On 19 Sept. 1995 John McCreery wrote:
>In my last message, I was talking about Patricia Churchland's
>_Neurophilosophy_ ...
>
>She observes that the software imagined by cognitive
>psychologists and philosophers characteristically takes the form
>of sentential logic, i.e., a logic in which sentences are related
>sequentially by formal rules that govern valid sequences. The
>mind is thus conceived as operating like a program written to
>run on a single CPU that can process only one instruction at a
>time. The central difficulty of programs written in this way
>which attempt to mimic the operations of human thinking is
>combinatorial blowup. They require literally millions and billions
>of steps to calculate the contingencies involved in apparently
>simple acts, e.g., recognizing a familiar face. (More complex
>calculations would require more steps than the number of
>electrons in the visible universe!) But, as Churchland observes,
>and Helmholtz demonstrated, nerve impulses travel much slower
>than the speed of sound. If, while silicon switches operate at
>nanosecond speeds, neurons fire in milliseconds, so that even the
>simplest reflexes require between 100 and 200 milliseconds,
>how, then, can the brain outperform the computer? The answer
>must be some form of massively parallel processing with
>cascading operations whose form is not at all that of sequential,
>sentential logic.
I suspect that the combinatoric problems implied
are not removed by a resort to massively parallel processing.
There may be a trade-off between combinatorially increasing
processsing time (in the serial model, as the number of elements
in the system increases linearly),
and a combinatorially inceasing number of connections
(in the massively parallel model, as the number of elements
in the system increases linearly).
The following might make matters a bit clearer,
(apologies for the author's self-reference to
Klein, S. 1991, The invention of computationally plausible
knowledge systems in the Upper Paleolithic.
IN, The Origins of Human Behaviour, edited by R.A. Foley,
London: Unwin Hyman, p. 80 (note 1)):
"An assumption that the brain is a massively parallel computer does not
mitigate the problem. The addition of n parallel processors can reduce
the computation time by a factor of n, but the problem domain involves
a processing time than can increase combinatorially with the size of the
data base. If an additional computer processor is added for each new
item in the data base, the processing time may increase at rate of
n!/n = (n-1)! [interpolated translation: n factorial divided by n
equals (n-1) factorial]
A connectionist brain model presents an analogous difficulty:
the need for combinatorially increasing processing time is replaced by
a need for combinatorially increasing connectivity."
PS For anyone who manages to read the original paper
(World Archaeological Congress, Southampton, England, 1986),
and the revised version in the Rob Foley volume, the first
paragraph of the 1991 publication was written by Rob, but
left unsigned, and should be treated as his editorial comment,
not mine.
__________________________________________________________________
Prof. Sheldon Klein sklein@cs.wisc.edu
Computer Sciences Dept. Linguistics Dept.
University of Wisconsin 1163 Van Hise
1210 W. Dayton St. University of Wisconsin
Madison, Wisconsin 53706 Madison, Wisconsin 53706
USA
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