Re: Next stage: Q4, Q5, Q6

Dear FISers:

John poses an excellent question:

>================================================
>A central hypothesis is that correspondence relations between
>algebraic species and organic species generate a robust basis for
>message specificity and sensitivity. I presuppose that category
>theory is a suitable mathematical framework for a general theory of
>communication.
>================================================
>
>Q5. Must this correspondence be such that organic species resemble
>computational "agents" as used in Alife programs, in which
>communication is fully formalized in terms of explicit rules
>("methods")?
>

It is not easy to respond directly to John's question. I will seek
to answer it from an engineering perspective and from a biological
perspective.
 
Communication in the sense that I use it in this extended abstract is
used as a relation among two or more systems; two or more domains of
reference. The process of organic communication in natural systems
admits multiple dynamics to form (biological plasticity or
adaptability or flexibility) . One type of dynamic can be called
"error" if one has created a norm that admits a variance from that
norm. Thus, organic communication can admit error in the process of
generating a message, in the process of transmitting the message or
in the process of responding to the message.

Formally, these are merely alternative dynamics within a living
system; the notion of "error" is a normative value imposed by an
external source. Note that in the case of the engineering
information of Shannon, one system generates a message, thus a "true"
message is said to exist. This "true" message becomes the basis of
the "encoding" prior to transmission and "decoding" after reception.
Shannon's theory thus creates a sequence of four systems, each with a
special task and the performance of that task can be evaluated in
terms of "true" or "false". By presupposing that each of the systems
for message generation, transmission, reception and interpretation
functions can be constructed exactly as needed to transmit a "truth
value", Shannon can introduce yet another system. This 5 th system
functions solely to create errors, but only errors in the
transmission process, leaving the other four systems to function
truthfully.

The utility of Shannon's system's engineering is without question.
 From an efficiency perspective, the efficiency of creating five
systems, (one solely for the purpose of making errors,) in order to
transmit a message would not normally be considered as good
engineering practise. The inefficiency of the design principle is
offset by the advantages gained from the efficiency of the
transmission process and the capability to transmit over unlimited
distances.

The natural history of living systems created an efficient form of
message transmission. The generating function is one set of organic
components. The transmitted message is another organic component.
The response generating function is still another set of organic
components. All of these functional components collaborate (work
together in a thermodynamic sense). The system functions locally.
This internal collaboration negates the need for a separate system to
generate errors. (From a cynical perspective, one could say modern
management methods are foreign to biological design. :-) )

For these reasons, I do not see a significant relation between the
"Alife" usage of agents and the sorts of generating functions used by
natural systems.

A second aspect of John's question concerns the nature of applied
mathematics. Within the framework of the axioms of category theory,
a wide range of mathematic systems (species) of logic have been
developed by PURE mathematicians. Traditionally, APPLIED
mathematicians have restricted the usage of mathematical species to a
few popular choices - such as linear vector spaces or highlighted a
particular aspect of one of the species used, for example group
theory or probability theory.

The natural emergence of organic communication appears to be
"spontaneous". I am not aware that any a priori restriction was
placed on either the organic species chosen to be transmitted or on
the mathematical species used to represent the organic species. In
separate work, I am describing the organic message in terms of a
novel mathematical species - a special form of a bipartite graph.
("Graph" here means a logical triplet - a set of nodes, a set of
edges and a set of ordered pairs that matches the edges and the nodes
to form a "network".) This mathematical species is rare; indeed, I
have not yet found a single reference to it in the mathematical
literature. But then, I have not conducted an exhaustive search.

I am uncertain as to the precise meaning of John's "fully formalized"
in the context of this question. If a system is formalized, it seems
to me that it is "fully formalized". Organic messages can flow in
living systems. Are living systems "fully formalizable"? Must all
messages be "fully formalized" before the system is formalized? This
terminology raises questions about physics and mathematics that are
not particularly germane to organic communication and the
collaborative efforts within the organic community. The prosperity
of the organic community need not be directly related to the
formalizability of the mathematical species chosen to describe the
dynamics. Indeed, I can imagine circumstances where a toxic chemical
is metabolized to generate a huge number of "errors" that are
transmitted throughout the systems. From a mathematical perspective,
such a toxic chemical would introduce a high level of
non-stationarity into the natural system. Nevertheless, the organism
may continue to prosper in the presence of a toxic compound, provided
other circumstances are sufficient to sustain a normal dynamic within
the organism. It is thus unclear how the mathematical / physical
notion of "formalizable" is related to biological / organic
communication or to the prosperity of life.

Perhaps someone else can suggest a reason why "formalizability " is
important in natural systems.

Cheers to all

Jerry LR Chandler

 
Received on Sat Jul 6 06:41:39 2002