Cybernetics of Epistemology - Understanding Understanding: Essays on Cybernetics and Cognition - page 234

Let me first use a pedagogical artifice in order to formulate the problem
of the computing of perceptual richness in such a way that in this new per-
spective the issue is seen from the viewpoint of the perceiving organism and
not—as usual—from the viewpoint of an observer who, seduced by his own
perception, always thinks he knows how “out there” looks, and who then
tries to figure out with micropipets in the nervous system of an organism
how “that of the outside” will look “in the inside.” Epistemologically
viewed, this constitutes a case of cheating, as the observer, so to speak, peeks
sideways for “answers” (his own world view) which he then will compare
will some cellular states of activity, from which alone our organism will have
to piece together its view of the world. However, how it does this, that is
the problem. 8
It is clear that every organism has a finite volume which is bounded by a
closed surface, a volume which is thread by an intricate system of “tubes.”
the latter surfacing at several places, let's say at “s” number of places. Onto-
genetically speaking, the surface is defined by the ectoderm and contains
all sensitive endorgans, while the interior is defined by the endoderm.
Topologically viewed, such a surface constitutes an orientable two-dimen-
sional manifold of genus p = (s + t)/2, with “t” indicating the number of “T-
connections” within the system of tubes. According to a well-known law of
topology, every closed and orientable surface of finite order is metrizable,
i.e. we can superimpose on the surface of each organism a geodetic co-
ordinate system, which in the immediate vicinity of each point is Euclidian.
I will call this system of coordinates “proprietary,” and I shall represent
the two coordinates x 1 , x 2 , which define a given point at the surface of this
Representative Unit Sphere with a single symbol x. This way I assure that
each sensory cell is given unambiguously a pair of coordinates that uniquely
apply to this organism.
According to an equally well-known law of topology, every orientable
surface of “p” is identical with the surface of a sphere of the same, which
means that we can show the sensitive surface of any organism on a sphere—
the “Representative Unit Sphere” [Figure 1]—so that each sensory cell of
the organism corresponds to a point on the Unit Sphere and vice versa. It
can easily be shown that the same considerations can also be used for the
interior.
It is clear that the Representative Unit Share remains invariant to all
deformations and movements of the organism. In other words, the pro-
prietary coordinates are principal invariants.
However, seen from an observer's point of view, the organism is em-
bedded in an Euclidian coordinate system (the “participatory” coordinate
system k 1 , k 2 , k 3 ,...or k, for short, as above, and he may well interpret the
relation x=F(k) as the “Formfunction”, F, or by also considering temporal
(t) variations x=B(k,t) as the Behavior Function B.
[Note: For non-deformable endo- or exo-skeletal) organisms is, of course,
F(x) = B(x,t) = 0. Moreover, because of (approximate) incompressibility we
have: