From: Mike Dougherty (msd001@gmail.com)
Date: Fri Feb 24 2006 - 13:21:06 MST
http://www.cut-the-knot.org/Curriculum/Algebra/MandelbrotIterations.shtml
while exploring this demo of iterative functions, I considered how much the
Mandelbrot looks like a bug, and that the graph resulting from Julia set
iterations at various points inside the Mandelbrot set reminds me of a an
MRI for the bug's nervous system.
For starting points that settle into cycles, it could be conceived that
there is sufficient coherence to build for the "thought" to be consistent
and deemed "True." Those starting points that do not cycle, yet remain
bounded within a region may be considered "Likely" within the bounding
region. This may be analogous to thoughts which continue to yield insights
after having been classified by a specific category. Points outside the
Mandelbrot may appear to be asymptotically close to the Mandelbrot boundary,
but iterate quickly away towards infinity. Those iterative processes that
run away to infinity might be considered divergent, inherently unTrue or
nonsensical.
Starting points in the first bulb to the left of the main body have values
ranging into the central region of the body, which struck me as an
interesting means of providing a non-locality of awareness. ex: suppose
navigating three iterations from starting point A yields a point responsible
for a particular subsystem. If that subsystem were "rooted" at point B,
then beginning a new iteration starting at B yields a new graph/set.
Consider that an iterative function starting from A yields a cycle of 12
values, each of which may be used as initial values for the iterative
function to yield a new graph (which may be bound by an attractor, thereby
capable of generating an infinite set) The point A would be effectively
"encoding" a conceptual framework of many idea-points using far less
information to compute than would be required to list. (I believe this
relates to the description of the potential information encoded in a zygote)
Does it seem to anyone else like there would be value in further exploring
this concept?
This reminds me of
Orphanogenesis<http://gregegan.customer.netspace.net.au/DIASPORA/01/Orphanogenesis.html>.
Also, the idea of consistency of cyclic iterations being an evaluation of
Truth reminds me of the Autoverse-native gnat swarm intelligence from
another Egan work, Permutation
City<http://en.wikipedia.org/wiki/Permutation_City>
.
On 2/24/06, Keith Henson <hkhenson@rogers.com> wrote:
>
>
> This may have been stated here before, but the brain of a newborn
> obviously
> would require many orders of magnitude more information to describe it to
> even the cell level than was present in the zygote.
>
> This is not unlike the Mandelbrot set--which can be inscribed on a postage
>
> stamp and expands to infinite complexity.
>
> Real life truncates after a small number of iterations. It might be worth
> noting that one of the differences between chimps and humans is that human
> precursor brain cells double two more times than chimps in the brain
> development process. (IIRC, can't find the reference, but makes sense.)
>
> I don't know this has relevance to seed AI problems, but it might.
>
> Keith Henson
>
>
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