Are thoughts REALLY Random?

[Jordan B Pollack]

(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