Re: art, shape, and symmetry

Michael Leyton has some ideas that I believe are leverageable for the
FIS agenda, and in fact my (now delayed) FIS position paper employs
some ideas which overlap, though in a way with which Leyton would
likely disagree.

The "Symmetry, Causality, Mind" book is probably not the best place
to start. The more recent, more readable "A Generative Theory of
Shape" is more accessible and can be read for free on-line. But as it
is more focused on a specific problem, you'll have a little more
extrapolation to do to apply it to our problem domain.

Leyton's notion is highly antirealist: cognition as bound in
representation; representation as bound in form; form understandable
in terms of generative states and state translations. The mechanics
of the translations are synthesized from the formal machinery of the
perceiver, focused on the apparent external primitive phenomenon of
"causality." These mechanics are constituted from categoric types in
the form of symmetry primitives. The primitives have shape metaphors.
The primitives are manipulatable by topological transforms on the
types, resulting in new types from fibre bundles. Examples are given
from the domain of cognition in the first book and shape grammar in
the second. This is the rough outline, but not how he would describe
it, I am sure.

Leyton's goal is not at all the same as that of FIS, though equally
ambitious. He has the luxury of focusing on the receiver, and is
developing causal mechanics where none really exist. FIS instead has
taken the job of focusing on the nature of the information token;
this is an area where an immensely popular theory already exists;
albeit with inadequacy in key areas. So we cannot be so cavalier in
avoiding the problems of how cognition colors world mechanics. And we
have to worry about "cognition" of things like cells and elementary
particles.

Independently, I have been working with some of the same mechanics.
My focus has been concerned with uncertainty where Leyton deals with
discreteness; and system context where he deals with objects. But we
have the same basic notions, notions which I will suggest in my paper
are useful for the FIS agenda (excepting the sorting out of semiotic
accounting):

-- a notion that information is always "situated" by the receiver
(requiring abandonment of first order logic and adoption of situation
logic)

-- a parsing of information by abstraction groups (namely by
context-defined categoric types from that situation)

-- a recognition that the most general flexible and leverageable type
primitives -- for the abstraction groups -- are at the symmetry
level. (This is a key religious preference that imputes a geometric
mechanic of complexity theory rather than the "statistical" basis of
the Santa Fe movement.)

-- an application of group theoretic functions to denote state
transforms of the types within the "messages." (This allows, I
suggest, the emergence of new "levels" of reality when certain
complexity thresholds are reached. So cellular dynamics can "emerge"
from particle physics.)

I hope to have a meaningful contribution by the time of the e-conference.

I am greatly encouraged to see Leyton's mechanics introduced into the
FIS discussion.

Best, Ted
Received on Mon Apr 8 17:49:39 2002