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 Paul Werbos,
Dr. Ballard and colleagues
Richard Ballard wrote:
A quick comment on "reversible mappings" versus
"time reversibility". I do not want to see what I communicated before
over-stated.
Fair enough. And I too owe a little clarification on the physics side.
You also said:
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, EM 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).
In actuality -- there are at least four different major, well-known mainstream ways to formulate Quantum Field Theory (QFT). QFT has superseded the earlier work done on Schrodinger's original equation. These are viewed as more or less equivalent, but in the absence of a truly rigorous definition of any of them, I would not endorse the common view that they have been proven to be equivalent.
The oldest, still-valid version is the canonical version. Many view the canonical version as the belief that nature is governed by the "modern Schrodinger equation:
psi-dot = i H psi,
where psi is a wave function and H is a Hamiltonian operator.
The fascinating thing is that this system is time-symmetric.
More precisely -- for the H corresponding to the standard model of physics, the dynamics are exactly symmetric with respect to time reversal T. A key part of my argument in the backwards-time interpretation is that we need to take this symmetry seriously. If we do... we can drastically simplify the representation of the system, and get away with real fields over Minkowski space without losing anything (actually gaining something).
Richard said:
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.
OK, so trying to get a new model of nature is a job for someone else. The challenge you want to address is how to build a general reasoning system able to handle that testbed problem just as one example. That's clear.
Richard said:
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.
Here it gets a bit fuzzy. To begin with, it is very clear you are saying that your informational encoding should not be called "mathematics." The semantics distinction over words used, like “mathematics”, are interesting, but perhaps a distraction for now. [1]
But I strongly believe that a combination of serious mathematics and human minds are the only really serious hope we have of getting out of the ruts we are now stuck in, with regard to this testbed.
I would agree that mathematics alone, without an insightful enough human to use it, would not be enough. And I would even agree that lack of resources is a major barrier to understanding this stuff before we accidentally kill ourselves with it.
But is that what you are saying? And I don't see how this new semantic tool would help.
Richard said:
Self-consistency without
Ocham's razor ("no repetition beyond necessity" e.g. information
bandwidths) is mathematics fatal deficiency. It can be partially rectified, but
so far has not.
Mathematical physicists certainly have heard of Occam's Razor, and do their best to use it often. It is not at all a fatal flaw in mathematics per se. It's a "flaw" only in the sense that "disembodied mathematics," used by people who never heard of Occam's Razor, would be a problem. Your criticism reminds me a bit of those Bayesians who wanted to can existing regression packages, on grounds that they MUST have a mechanical mechanism to input prior probabilities from users; in actuality, convolution of priors and posteriors in our complex nonlinear world can be done best by having intelligent nonlinear humans there to do the convolution, starting form more standardized and objective measures, in the usual applications that econometrics deals with. [2] Likewise here.
In the meantime the issue we [3] 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.
We are very, very far away from being able to dispense with human reasoning in these difficult realms. Lots of nice general principles about how to design truly superhuman reasoning systems have been enunciated here and there, sometimes necessary principles in some sense, but never sufficient.
Best of luck,
Paul