Objects: Tokens for (Eigen-)Behaviors - Understanding Understanding: Essays on Cybernetics and Cognition - page 265

This is so because any infinitesimal perturbation ±Œ from an Eigenvalue
Obs i (i.e., Obs i ±Œ) will disappear, as did all other values of obs, except those
for which obs = Obs i , and obs will be brought either back to Obs i ( stable
Eigenvalue), or to another Eigenvalue Obs j ( instable Eigenvalue Obs i ).
In other words, Eigenvalues represent equilibria , and depending upon
the chosen domain of the primary argument, these equilibria may be
equilibrial values (“Fixed Points”), functional equilibria, operational equi-
libria, structural equilibria, etc.
(ii) that Eigenvalues Obs i and their corresponding operators COORD
stand to each other in a complementary relationship, the one implying the
other, and vice versa; there the Obs i represent the externally observable
manifestations of the (introspectively accessible) cognitive computations
(operations) COORD.
(iii) that Eigenvalues, because of their self-defining (or self-
generating) nature imply topological “closure” (“circularity”) (see Figures
2 and 3):

This state of affairs allows a symbolic re-formulation of expression (5);

() ∫

n

lim

COORD COORD

n Æ•

that is, the snake eating its own tail: cognition computing its own cognitions.

*****

Let there be, for a given operator COORD, at least three Eigenvalues

Obs 1 , Obs 2 , Obs 3 ,

FIGURE 2.