Tuesday, January 10, 2006
Additional reading:
Cory Casanave's paper on Data
Access
work on ontology for biological signal pathways
[126]
ß parallel discussion in generative
methodology bead thread
Discussion on informational invariance
[342], [343], [344], [345], [346]
Note from Dr Richard Ballard, Knowledge Foundations Inc
Paul & Friends:
A quick comment on "reversible mappings" versus "time reversibility". I do not want to see what I communicated over-stated.
Reversible mappings deal with the issue reversing the roles of independent and dependent variables, for example, in some functional transformation. The example I used was in the matrix transformation between the tri-diagonal matrix (isomorphic to any second order partial differential operator) and its inverse (integral) representation (isomorphic with any Green's function kernel). This reversible mapping connects two totally different views (point vs field) dual representations of the same reality. Since the reality is unchanged, but the point of view only is different, one should expect information conservation intuitively. Time is not changing. just view.
So the example cited is not the same as time reversal. The time evolution of a physical system, depends not simply on information conservation in matrix inversion, but with its properties given any physical theory proposed and the particular force laws assumed, e.g. the time dependent Schrodinger equation vs Dirac equations, Electromagnetic forces vs Yukawa potentials, relativity vs non-rel. The matrix transformations for describing these are "propagation or time-evolution operators" and these are always more stochastic in nature and most show the wave always spreading in time, going in any direction (i.e. time evolving Heisenburg uncertainty growth).
Be clear that physics understands that mathematics per se is not a fundamental representation of anything truth conditional but self-consistency. The rules of self-consistent logic have no special relationship to natural laws (Einstein quote), so the challenge to any new science of knowledge representation is not about predicting any particular content of natural laws, but rather the general sufficiency of its any proposed systems of representation to faithfully reproduce all possible predictions and forms of reasoning those laws might demand. Mathematics cannot do this as I suggested before because natural laws deal with finite resources and reasoning with them must recognize either accidental or deliberate competition between processes sharing the same resource.
Self-consistency without Occam’s razor ("no repetition beyond necessity" e.g. information bandwidths) is mathematics fatal deficiency. It can be partially rectified, but so far has not.
In the meantime the issue I address is, Can "theory-based semantics" offer all suitable alternative representations and reasoning systems needed to deal with all of QM's demands for reasoning with uncertainty. Offering "conservative mappings" for "view changes" ("dualities") is one, Heisenburg uncertainty increases for "time evolution" or "time reversals" are another, measures of information conservation or entropy (irreversible information loses) is yet another guaranteeing cost awareness.
Paul, these ideas were the promised missing part of that letter I sent you around Christmas time.
Dick