Dear colleagues,
While reading the book "On Intelligence" (J. Hawkins, 2004--the creator of
the "palm" computer), with the proposal of a unitary algorithm for the
neocortex, capable of transforming successions within successions of
sensory information into simultaneous hierarchies and heterarchies of
categorizations, I was strongly reminded about Karl's works on the logics
of the sequential versus the concurrent (see his recent message last week
on addition). Although I have disagreed with him in this list on how to
"count" the number of multidimensional partitions (and then the subsequent
relationship sequential/concurrent), and how to apply it to biological
stuff --- I find quite fascinating that theme, and by far deserving a
serious research program to analyze the subject in depth (with many eyes!).
The strict limitation on the categorizations you can pile up upon the
elements of a set is --to my knowledge-- a work to be done yet.
I wonder whether Jerry's proto-numbers might be represented by the above
apparatus of multidimensional partitions --chemical bonds included? At the
time being one has to be skeptical that any formal treatment may capture
the variety of chemical bonds and derived dynamics present, eg, in water.
No consistent model exists of this "simple" substance yet , the source of
life's amazing connectivity, structure, dynamics,...
Briefly returning to my recent disgressions on a top-down vision of
biomolecular networks, let me cite the work Kevin A. Janes et al. (Science,
310, 9 December 2005, p. 1646-1653) about a systems biology approach to
signaling in apoptosis. It is a vast analysis of the intracellular events
following activation of different signaling system pathways... "suggesting
that cell survival is determined by signaling through a canonical set of
fundamental dimensions (molecular 'basis axes')..." The paper contains
excellent statistical work on a highly sophisticate measurement set of Ab
microarrays, kinase assays, western blot, etc., etc.
But a curious point on signaling and apoptosis could be stated as follows:
if you have a molecular information processing system with many "inputs",
and correspondingly quite many "outputs", but with your outputs what you
imply is the very disappearance of your system --apoptosis, cellular
suicide-- something strange has happened. A computational "annihilation
state" makes no immediate sense, a categorial leap has occured. The paradox
("self-explosion of one's computer ") makes even less sense in terms of
Turing Machines: rather than the "halting problem" one finds the "survival
problem"... in "ecosystems" of cooperative/predatory sequences for Turing
Machines?--of course, nonsense. Is this an irrelavant meta-problem? I do
not think so. At least, the difference between the "processing" and the
"processual" (embodiment) in terms of dynamics becomes clearer and perhaps
more amenable to conceptualization...
best regards
Pedro
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Received on Fri Jan 20 15:25:36 2006
