Are thoughts REALLY Random?
Jordan B Pollack
pollack at cis.ohio-state.edu
Tue Jan 30 12:59:32 EST 1990
(Background: Scott is commenting less on the question than on the
unspoken subtext, which is my idea of building a very large
reconstructive memory based on quasi-inverting something like the
Mandelbrot set. Given a figure, find a pointer; then only store the
pointer and simple reconstruction function; This has been mentioned
twice in print, in a survey article in AI Review, and in NIPS 1988.
Yesterday's note was certainly related; but I wanted to
ignore the search question right now!)
>> Do you see any fundamental difference between the
>> Mandelbrot set and the proverbial infinite number of monkeys with
>> typewriters?
I think that the difference is that the initial-conditions/reduced
descriptions/pointers to the Mandelbrot set can be precisely stored by
physical computers. This leads to a replicability of "access" not
available to the monkeys.
>> Maybe the right measure of Platonic density is something like the expected
>> length of the address (M bits) that you would need to point to a specific
>> N-bit pattern that you want to locate somewhere in this infinite heap of
>> not-exactly-random bits.
Thanks! Not bad for a starting point! The Platonic Complexity (ratio
of N/M) would decrease to 0 at the GIGO limit, and increase to
infinity if it took effectively 0 bits to access arbitrary
information. This is very satisfying.
>> Why shouldn't M be much greater than N?
Normally, we computer types live with a density of 1, as we convert
symbolic information into bit-packed data-structures. Thus we already
have lots of systems with PC=1! Also I can point to systems with PC <1
(Bank teller machines) and with PC>1 (Postscript).
Jordan Pollack Assistant Professor
CIS Dept/OSU Laboratory for AI Research
2036 Neil Ave Email: pollack at cis.ohio-state.edu
Columbus, OH 43210 Fax/Phone: (614) 292-4890
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