Category theory- warning, tome ahead

Lance Sherman lancesherman at insightBB.com
Wed May 4 10:10:43 EST 2005


my thanks to those who did not reply to the below message by pointing out
that i should be sure and take my meds every day

i will try not to repeat such uncivilized behavior
  "Lance Sherman" <lancesherman at insightBB.com> wrote in message news:oIPde.44807$NU4.12906 at attbi_s22...
  i offer comments that bear slightly on what category theory is.

  common decency requires the following disclaimer/apology 

  1. i am not a mathematician
  2. i am not smart enuf to be offering theories of the overall organization of mentality
  3. i have great reservations about the limits and utility of cognitive science.
  4. as the first responder, i shamelessly segued from the original poster's clearly indicated focus.
  5. my windiness is unbounded.
  6. my laziness is unboun

  explaining or defining a major branch of math, category theory (CT), is similar to defining topology or calculus. a long way from the applications to the definintions.  the formal definition may bring very little light to the non-nuser. calculus, the limits of difference quotients of domains/co-domains.
  topology, the continuous transformations of one space into another (one definition).

  so let me ramble into what CT is to me.

  my work is of the same scope as Grossberg or Edelman (!) but not on purpose.
  that would be utterly presumptuous and laughable - see disclaimer #2
  my "ai" interests began humbly, in the area of natural language processing, and i thought i just might make some increment of addition to a field that would probably make slow progress toward better and better, not really smarter and smarter, machines to ease human mental labors. i certainly did not expect, in 1970, to even dimly understand how brains work and how we might make an artificial one.

   if anyone had even a clue (where the data is and how it's processed), it was not apparent to me, but i, like many, unfettered by religous beliefs or philisophical naievite thought it possible, inevitable. i dismissed Dreyfuss and Searle, etc.

  during this daunting and exciting period, i studied Newell and Simon, Wiener,  Winograd, Sjejnowski, Albus, speech recognition, visual recognition, blah, blah. 

  i serendipitously found myself thinking of a very simple, well-defined little problem. while watching disco dancing, i thought a robot could do this. 

  first, i thought a lo-res FFT could extract the fundamental rhythm, the beat, which is the main input for that very free form, disco dancing. my apple II (a pc) could do this with plenty of processing power left over for memory and motor control. but more lifelike dancing requires the recognition of additional rhythmic structure - cadence,  accent and stuff i cannot name. (additional disclaimer - i am not a musician or a dancer)

  it seemed that a process i called heirarchical demodulation - merely taking the output of the beat detector as the input to another, even lower-res FFT - could extract cadence and higher order rhythmic info. the whole problem seemed a lot more solvable and fun and it occupied me more and more. 

  i was never so naive as to ignore neurobiology and the similarity of neural tissue to a directed graph; i saw an elegant  solution for the dancing robot: a directed graph in which the edge lengths corresponded to time delay and the nodes worked in the biologically plausible manner of a leaky integrator with variable threshhold.

  perhaps you can already see that the dancing robot's control system (the DR) selects appropriate paths (those whose delay to the next involved node is the beat interval or an integral multple). and that the focus here is on the simplest connection between perception and action. and that this is an active system, even absent input, that requires a continuous, stochastic, intrinsic activity.

  further, i was struck by the fact that a single channel lensed *visual* input would produce a sufficiently similar data stream that could be identically processed. same for a tactile input. a deaf dancer or a deaf and blind dancer was possible.

  a control system that resembled neural tissue, and that processed input from different sensory modalities without an executive. an amateur like me escapes from the ubiquitous homunculus and the binding problems. ok!

  so i blundered alone along this line of thought for years.  in my little mind, it seemed that the problems of attention, leading and following, free will - all could be dealt with in these dynamic terms.

  DR led me into the areas of association, sequencing, chunking, timing. I believed many of these problems were solved together tho I hardly claimed to even "see", much less have actually worked out on paper a refined, explainable idea, a theory.

  i  found Emelyanov-Yaroslavsky but understood little. Still, more my way of thinking than anyone else i had found. Donald MacKay's beautiful  Organization of Perception and Action  seemed to subsume E-Y and DR but is admittedly incomplete.

  readers who are still awake may notice by now that i had increasingly moved toward something tightly coupled to its environment, like an organism.

  so i started the arduous reading of Robert Rosen - Life Itself, and Essays on Life Itself, eventually, Anticipatory Systems. i was skeptical of his claim, a machine can never be an organism. machines are simple. complexity is a property of organisms, living things.  he does hint, maybe in Essays, that it is possible to make a complex control system. 

  SKIMMER ALERT- finally getting to CT

  Rosen (a theoretical biologist)  uses CT to show the problems physics and its stupid sister, biology, suffer from in causation. this was my motivation to put a toe in the water of CT, and i read a couple intros, understanding an iota or two. i have some competence in groups and topology, which are related to CT.

  CT can be a powerful tool for analyzing the modeling process and most of us with competence in programming and math use the modeling process with ease, unaware of our assumptions about causation.  then we stuggle with problems of will and consciousness.

  SKIMMER ALERT - may not be much CT in the following

  so i began digesting E-Y (links found earlier in this thread and easily Googled) and soon concluded (with mixed feelings) that he had carried out the entire program that i only glimpsed thru a glass, darkly. what he labeled in questionable translation, the neuroenergetic concept of intelligence.

  he makes no mention of CT in my reading, and makes no claim for what i see as the  man made anticipatory system par excellence.

  i continue searching for others who see E-Y as the creator of the most complete, accurate and implementable theory of how living control systems work, that permits the creation of an artificial control system with those elusive properties.

  returning to the original poster: in the Healy articles mentioned in my first reply, CT is the basis for some theories that attack more specific, dare i say, smaller problems in biologically plausible control systems. and i should add i only read a little of those papers and understood less. like a lot of cognitive science, not clearly relevant to my thinking. behaviorists, take heart.

  and to poster I3- imho, CT is not quackery
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