Thoughts and Notes on Cognition - Understanding Understanding: Essays on Cybernetics and Cognition - page 182

FIGURE 6. Geometry of the sensory field for a specific sensor r x0 susceptible to an
agent D distributed over environmental space.
2.251 In some cases it is possible to compute the spatial distribution
of an agent from the known distribution of its effects along a closed surface
of given shape. For instance, the spatial distribution of an electrical poten-
tial V x has a unique solution by solving Laplace's equation
D V = 0
for given values V x along a closed orientable surface (electric fish). Other
examples may be cited.
2.252 In some other cases it is possible to compute the spatial dis-
tribution of an agent from its effects on just two small, but distinct regions
on the body. For instance, the (Euclidean, 3- D ) notion of “depth” is com-
puted by resolving the discrepancy of having the “same scene” represented
as different images on the retinas of the two eyes in binocular animals
(Fig. 7). Let L ( x , y ) be a postretinal network which computes the relation
“ x is left of y .” While the right eye reports object “ a ” to be to the left of
“ b ,” ( L r [ a , b ]), the left eye gives the contradictory report of object “ b ” being
to the left of “ a ,” ( L 1 [ b , a ]). A network B which takes cognizance of the dif-
ferent origin of signals coming from cell groups { r x } r and { r x } 1 to the right