I consult in image and signal processing and parallel computing. I have extensive experience in object orient programming and project management. Click for a conventional resume.
Following is an unconventional resume.
In high school I became convinced that no infinite or continuous structures exist. Limits and structures that can be defined by passing to the limit are not built out of distinct points. They are higher levels abstraction not unrelated to the neural circuits that fire when one sees straight lines.
The quantization of energy in physics was further evidence to me of the discrete discontinuous nature of reality. In my first course in quantum mechanics I came to suspect that a discretized finite difference approximation to the wave equation was a good candidate for explaining quantum mechanical effects. The wave equation is both the relativistic Schrödinger for a single zero rest mass particle and the equation for electromagnetic waves. Discretizing it introduces nonlinearity and immense complexity not present in the differential equation.
I was struck by how all of mathematics and computer science was pure structure. Zermelo Frankel set theory plus the axiom of choice (ZFC) includes virtually all of contemporary mathematics. The only fundamental undefined entity in ZFC is the empty set or nothing at all. Everything else is built from the empty set. For example the number 1 is the set containing the empty set.
Computers were a comparative novelty in the late 60's and I was able to work with one of these extraordinary machines. I could program it to do complex tasks using simple instructions. The computer itself was constructed from simple operations. In mathematics everything is structure with empty set at the root of the structure. In computer science the basic logic elements were trivial. Any algorithm could be constructed out of the simplest of logical elements.
This train of thought led me as an undergraduate to ask what is structured in physical reality. The one "essence" that I knew exists is my own conscious experience. This led me to conclude the essence and totality of the existence of physical structure is immediate conscious experience in some form.
For a time I tried to develop my ideas about physics for a Ph.D. thesis. I could not make progress fast enough and von Neumann's false proof that no more complete theory was possible was still widely accepted. Bell's refutation of this proof was published around this time but I was not aware of it. I became an Acting Assistant Professor at UCLA before completing my thesis and eventually completed a conventional thesis in computer science, but academia held little interest for me. I was powerfully drawn to pursue my more radical ideas even though there was no external support for this.
With my inability to make progress on my ideas about physics I pursed another avenue. I investigated the mathematical implications of rejecting completed infinite totalities. I came to understand that most of the mathematics that is dependent on such structures could be reinterpreted as the mathematics of creativity in a potentially infinite universe. I discussed these ideas at the time with some leading logicians but since there was no new mathematics involved nothing came of these discussions.
About this time I became interested in the work of Carl Jung. I eventually read his collected works. Two aspects of his thinking were had a powerful impact on me. Psychological Types helped me to put my life path in perspective. I am an introverted thinking type but my greatest strength is my intuition. Thus helped me understand why I often saw things in unconventional ways.
The other aspect of Jungian theory that had a big impact on me was his focus on the creative nature of the psyche. The contradictory instincts and archetypes that drive us are the engine of human creativity. I started to relate the ideas of Jung to my understanding of the foundations of mathematics and especially the creative nature of mathematics that I think follows from Godel's Incompleteness Theorem. Jung had an intuition that number was the archetypal mediator between the physical world and the higher world but was never able to develop this. Part of the reason was no doubt his ignorance of mathematics. I believe I have been able to do so in part through my idea that the essence of the existence of physical structure is conscious experience in some form.
This work is available as the partial draft of a book, What is and what will be.
As a complement to all this head tripping I have become addicted to Dance Jam.
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