Are thoughts REALLY Random?

[Scott.Fahlman@B.GP.CS.CMU.EDU]

** I guess this shouldn't be forwarded either, since Jordan doesn't want **
** the initial message to be.                                            **

    However, since programs of the same size, when executed, can yield
    structures with vastly different APPARENT randomness and bit-counts,
    some useful measure of the "Platonic density" seems to be missing
    from the complexity menu.  I find it difficult to believe that the
    Mandelbrot set is only as complex as the program to "access" it!
    
    Can somebody please help me make sense out of this? 
    
As a medium in which useful information is to be "mined" from an apparently
random heap of bits, do you see any fundamental difference between the
Mandelbrot set and the proverbial infinite number of monkeys with
typewriters?  Offhand, I don't see any fundamental difference, as long as
we are sure that the Mandelbrot set does not sytematically exclude any
particular set of bit patterns as it folds itself into a pattern of
infinite variability.  Both are very low-density forms of "information
ore", and probably not worth mining for that reason.  Sure, anything you
might want is "in there" in some useless sense, but at these low densities
the work of rejecting the nonsense is certainly greater than the work of
creating the patterns you want in some more direct way.  (-: Some have
claimed the same thing for the typical collection of papers currently being
written in this field. :-)

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.  If M >= N on the average, then the structure is
not of any particular use as a generator.  You're better off storing the
N-bit patterns directly than storing the M-bit adrress along with a
Madelbrot chip.  And if you want to systematically search a space, to make
sure that you visit all possibilities eventually, you're better off
searching the N-bit space of bit-patterns directly than wandering through
the Mandelbroth.  Even if you exhaustively search an M-bit subspace of the
Mandelbrot set, you have no guarantee that your pattern is in there.

Any reason to believe that M < N for Mandelbrot sets or monkey type?  I've
seen no compelling arguments that this should be so.  If M >= N for all
these sets, then worrying about which has greater or less density seems
foolish -- they're all useless.

-- Scott