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Hi People, good morning from Santa Barbara CA. I just landed here in Azimuth, and thought I'd say hello. The way the world looks to me these days, I'd say the general ambitions of this place are critically important ("scientists and mathematicians and engineers collaborate to save the planet") -- but I can also sense how hard this is to do. I'm a ColdFusion/SQL database programmer -- and not a professional scientist or academic -- but I'm highly interested in this general objective, and have been working on collaborative projects for a long time.
Earlier in my life, I made a rather all-out effort to analyze the semantic/categorical structure of what might be called "conceptual space", and did come up with a very ambitious theory I called "synthetic dimensionality", which attempts to model "absolutely all" conceptual structure in terms of a universal algebraic primitive I called a "synthetic dimension". There's a pretty strong bibliography behind this project, and a lot of holistic intuition.
If I were to summarize what I would want to bring to the Azimuth project, it might revolve around my notion that what the world needs today -- and is increasingly ready for, maybe in some very dramatic and exciting ways -- is what amounts to the emergence of "a revolutionary new theory" in semantic ontology. This is a hard thing to prove, and I keep dabbling with it in occasional if scattered bursts of creative enthusiasm -- but I think the world -- and "the scientific community" -- are highly crippled by what popular author Gillian Tett calls "The Silo Effect" in her recent book (published Sept 1). The world's demographic and cultural and scientific communities have evolved within the presumptive constraints of inherent category systems, which become perceptual lenses through which members of those communities view the world. This effect can be blinding or disabling. I think this is a problem that needs solving, in a highly motivated way.
This fact of cultural evolution is highly related to problems in incommensurate database systems. System 1 does not map into system 2. Yet all over the world, there is a powerful dawning recognition that we must be "silo busting" and interconnecting systems to support cross-sector collaboration. As I see it, we need some new "holistic and integral" foundation for mathematics and conceptual structure that helps us see the world as a smooth continuum -- probably embodying no inherent distinctions whatsoever -- that is then "parsed" by the analytic/symbolic human mind into endlessly complex alternative frameworks that are represented as models in abstract symbolic space.
My sense is -- this process can be generalized. There is strong push in semantic ontology all over the world (maybe not so much here in Azimuth, where a search for "ontology" returns almost nothing) -- but for a community of motivated first-class mathematicians, this might become an intriguing issue.
This morning, maybe just as an intellectual exercise -- but also because I find the basic dimensions of this discussion very germane -- I am looking at a thread from John Baez on a curious property of word-pairs ("opposites"), as those pairs are re-ordered and form a Moebius Strip. Does this miscellaneous observation carry some deeper clue? I don't know, but I want to see if I can really understand it. This discussion not only shows a fascinating "loop" process I want to understand -- but it also gets into the dimensionality of similarity, which is the core idea of synthetic dimensionality. Thanks!
"A Moebius Strip in the Space of Concepts" https://plus.google.com/117663015413546257905/posts/jkqH5e48w6L