[263]                           home                           [265]

 

Sunday, December 04, 2005

 

 The BCNGroup Beadgames

National Project à 

Challenge Problem  à

 Center of Excellence Proposal à

[bead thread on curriculum reform]

 

 

The Taos Institute

(on the possibilities)

 

 

John, Paul (Werbos) and Dick,

 

It is with great honor that I might participate in this discussion.  My own history should be developed as well as Dick Ballard develops his at [262].  A short version might suffice.

 

Serious university work started in around 1976, when I discovered that mathematics was able to avoid the philosophical issues that I saw as bringing confusion to the American intellectual scene.  So between 1976 – 78 I completed a BA in mathematics.  I was then able to enjoy the beauty of pure mathematics for two years at Southern Methodist University.  I had a scholarship and stipend.  The experience at SMU was all about esthetics, the foundations of mathematics – philosophy of mathematics – and topology and abstract algebra. 

 

In 1980, I meet my wife Pat and completed the MA in pure mathematics.

 

At this point there was a great naiveté in regards to the philosophical issues.  These issues were deeply informed before 1976, due to studies in esoteric schools, of which I will mention only the I-Ching (so as to minimize controversy).    

 

Pat and I moved to Denton and bought a small house.  I re-started a broad based study of science, philosophy and mathematics, and worked on PhD level numerical analysis, topology, and real analysis.  During this time three issues were always present.

 

1)       My interests in mathematical models of learning were inconsistent with the available graduate courses in Artificial Intelligence and the faculty attitudes in computer science.

2)       Mathematics as a discipline was advanced not so much through original work, but be joining one group or another group.  Without this joining behavior, there was no way that the PhD could be completed.

3)       The freshman mathematics classes, that graduate students taught, were characterized by a profound dislike and inability to learn simple curriculum, mostly college algebra and the simplest part of the calculus. 

 

In three years, I completed all coursework and examinations for the PhD, but had no thesis.  The thesis I wished to work on was on the mathematical models of immune system response as an approach towards describing why freshman students were not successful in the freshman mathematics classes.  In September 1985, I moved from the department of mathematics to the school of education, at University of North Texas with the intent of completing a thesis on why many students were unable to learn the freshman curriculum.  The program was supposed to take only one year, given that I was all but dissertation and in excellent standing in the mathematics department. 

 

At the end of the year (1985) it was apparent to me that the intellectual foundations of American educational philosophy (mostly from Dewey and Piaget) were not consistent with the types of advanced notions from modern quantum-neuroscience (Freeman, Pribram, Penrose, Edelman) the foundations of mathematics and applications of formal thought to biological processes involved in learning.

 

I was introduced to Dan Levine, one of Stephen Grossberg’s early PhD students, and he immediately saw the thesis I was developing, and suggested that I transfer to the University of Texas at Arlington.  I did this and started work in three directions:

 

1)       Neural models of selective attention and preservation of errors in mammals (following the work of Grossberg, Levine and Pribram)

2)       Discrete and continuous models of plant and mammalian immune response (following work by Stu Kauffman, and immunologists)

3)       The study of computer architecture, including the Macintosh architecture, and computational fractals.

 

The models of immune response allowed me to examine that notion of a switching network, and things similar to Sowa’s spreading activation as a means to interact between an external stimulus (values given to the computer program from the user or another program) and some large set of locally defined structural relationships and categories.  Here, as in Sowa’s current work, there is a relationship between the continuous (differential equation) and discrete networks acting with some specification of logic.  This line of work reached the point of publishing in the journal “Complex Systems” in 1987 on systems of continuously defined plainer rotators as models of neural cellular growth on silicon. 

 

I describe the surface of this work in my chapter one, in the unpublished (Internet published) book:  [Foundations of Knowledge Science]  The work was targeted at developing a real theory, grounded in biology and neuroscience, explaining why the students in the freshman class were exhibiting a type of learning disability.  The theory crystallized during my two years at UTA, mostly while sitting on the floor reading in the immunology section of the university library.  The experience crystallized two insights that had pre-cursors in past experiences.  The first was about the scientific knowledge of immune responses, very generally considered (Burnet, Jerne, Richter).  The second was that learning of a new discipline could occur if a belief that one could not possible learn “immunology”, in several weeks, was dismissed or suspended. 

 

Sitting on the floor, day after day for 8 days, I read hundreds of journals mostly starting at the back page and moving to the front, without being concerned about “knowing” what I was reading.  At one point, the localized associations of words and concepts “ignited”, in what I was later to see as the phenomenon that Stu Kauffman talked about as “auto-catalytic ignition”.  (This work is essential to understanding my theory of formative and differential ontology and why substrate ontology (Sowa and Ballard’s semantic primitive frameworks) has to separate form from meaning).  The semantics in anticipatory technology “ignites” in the mind of the human who makes an interpretation of patterns of co-occurrence (see next bead [265] ) 

 

The preliminary work on “Acquired Learning Disability” is given on my web site at: 

 

A Question of Access

 

This work leads to my current proposal to re-structure the mathematics and computer science curriculums based on a need to introduce novelty and relevance within the standard curriculum:

 

The Taos Discussion

 

The grounding of this work on educational renewal is developed in my PhD thesis (1988) and in over twenty publications made between 1987 and 1995 (when I gave up on attempts to be part of a university faculty).  The period 1995 to present has been largely focused on contractor work for government agencies.  See [RoadMap].

 

In the next BCNGroup Glass bead, I will make some comments regarding the discussion between Drs John Sowa, Richard Ballard and Paul Werbos… à  [265] .

 

Paul Prueitt

Taos, New Mexico