May 9, 2005
On the discussion of data
regularity à
On the Stephenson Cyber Attack
Taxonomy à
Communication to Paul Werbos (and others)
from Paul Prueitt
In the BCNGroup’s recent delineation of a “second school of semantic science”, we have
found it essential to talk about response degeneracy [1]
as an essential element of formative and differential ontology [2]
. We see response degeneracy as
necessary to normal function/structure mappings that are, at least in
biological systems, many to many.
Definition of “response degeneracy”:
Many structures will perform the same function, and many functions can
be fulfilled by a single structure.
Also see notion of double articulation in linguistics
à
What does response degeneracy have to do with Wolfram’s claims ?
<quote from PW’s communication> Deep in chapter 9 of a New Kind of Science, Wolfram
claims in effect, that his "causal network automata" (CNA) can
regenerate the predictions of the left-hand side of the Einstein equation. In
other words, he claims that the pattern of dynamics implied by the Einstein
equations (including nonlinear curvature effects) for regions of space in which
T=0 is reproduced exactly as an emergent statistical result from his very
simple models. (There is an analogy here to the way the heat equation
represents emergent behavior from lumpier small things...) </>
US Einstein Institute founder, and a key member of the ecological
physics community Robert Shaw (Univ of Conn, psychology department), has talked
often about the anticipatory nature of event structures in particle physics.
Your discussion about Wolfram and your own views (as I have come
to understand them over the years) are moving in the direction of suggesting
that it is physics understood properly, and not merely biology, that is not
fully understood if all one has is Hilbert mathematics and first order
logics.
This is an old discussion that you and I have had over two
decades. We are both getting old.
The key concept that is missing, as Penrose might agree, is the
action of imposing “final” constraints on the merely algorithmic selection of
function at the moment that a structure is emerging in natural setting. This imposition of final constraints is seem
by me to be the interpretative act that Peirce talked about, and which is
central to the Peircean view that knowledge is only present in real time and is
only present if interpreted by a natural system.
Paul (W), as you know, I am not an important mind, as you are and
as Wolfram is, but through out my career as a mathematician and technologist, I
have focused my deep research on the emergence of function at the moment that
atoms are aggregated together to form a whole at a level of organization with a
different time scale that the scale at which the atoms exist. This is the stratified theory that I have
talked about.
I first encountered mathematical formalism regarding emergence in
the work I did with [3]
Kowalski and Gross (1988, 1992).
I discuss this work on “planar rotators” in Chapter one of my on line book,
in the context of Soviet era “applied semiotics”. This work is a pre-cursor to the work that my group is now doing
on the differential ontology framework, and the role that response degeneracy
has on human visual inspection of underdetermined ontology structure.
It has to be simpler that we think that it is.
Paul S Prueitt
[1] the term as G. Edelman uses this term in his Book Neural Darwinism).
[3]
Kowalski, J. ; Ansari, A. ; Prueitt, P. ; Dawes,
R. and Gross, G. (1988.) On Synchronization and Phase Locking in Strongly
Coupled Systems of Planar Rotators. Complex Systems 2, 441-462.
Kowalski,
J., Labert, G., Rhoades, B, & Gross, G. (1992). Neuronal Networks With
Spontaneous, Correlated Bursting Activity: Theory and Simulations. Neural
Networks, 5, 5, 805 - 822.