Wednesday, March 08, 2006
Generative Methodology Glass Bead Games
On the limits of the OWL standard à [184]
Reading material [1]
Reading material [2]
Reading material [3]
Summary of the discussion up to this point à [186]
On ontological modeling of expression
The metaphor between gene, cell and social
expression à [217]
On Formal verses Natural systems à [206]
Dear Paul,
This has been a very intellectually productive year for me as I continue to probe the issues related to syntactic versus semantic models. I have enjoyed reading the discussion by Sowa, Ballard and J. Rosen on related issues--though I must confess that attack on the problem comes from a different (though related) direction.
The issue of 'time' is certainly an issue to be discussed with some care. Prigogine and I spent two days discussing this issue when he visited my lab on at Radford. I have spent much time working on the issue of biomaps (DNA, RNA, amino acid, metabolic maps, genotype à phenotype mapping, phenotype à genotype mapping, and why these are not inverses), there is no current theory in the bio literature about the nature of these mapping (other than conventional engineering control maps).
There are many new finding over the past 15 years due to the role of microarrays. I am also back working on the core problems of the Hamiltonian (linear, nonlinear) as a special class of bride between the configuration and tangent spaces, this is especially important with respect to the issue of time.
There are related issues associated with the bridge maps between the Hamiltonian and Lagrangian; this bridge is also related to the issue of relationship holonomic versus non-holonomic constraints.
As a side note: I think you and Pribram use holonomic constraints is a special sense that is quite difference from the standard usage. The holonomic constraint is a material constraint that occupies physical degrees of freedom in the universe, it is always locally defined.
A computer is the essence of a holonomic machine--the internet as a set of symbols (with no observer) is also a system composed only of holonomic constraints--here I mean internet as a set of constraints that exist independent of the user. This assumption of independence (from user and associated semantic content) is what allows the axioms of a formal system to be introduced as a modeling tool.
In this isolated form the set of symbols involves only holonomic constraints. Sowa is very clear on the domain of focus for his tools, Ballard is less clear as his hubris tends to enthusiastically slide him out of the holonomic domain. J. Rosen has to be careful that she doesn't find herself looking for relational constraints in a purely holonomic domain; this domain has some special properties of reducibility that do not easily generalize to the domain of ‘field constraints’, where the real issue of relational content and nonlocality is manifest.
pnk
Cape Cod