Functional Geometry and the Determination of Pattern in Mosaic Receptors 389 



glanced past in a tenth of a second. These signals have a one-to-one corre- 

 spondence with Platonic properties of 'R-ness', 'Blackness', 'Largeness', and 

 so on. 



Of course, a pre-addressed network, might also give the same kind of infor- 

 mation that any of these neurons gives. Or it might give information trivial 

 or inscrutable for us, such as 'Slope of sharpest edge, 103° 8"; or 'Five corners, 

 two arcs concave to the left'. 



In fact, any neuronal output in any connected network could be thought 

 of as indicating some kind of pattern invariance. Jn this sense there are no 

 addresses to learn! But most of these invariances in an arbitrary synthetic 

 network would be worthless for biological survival. A major evolutionary 

 problem for non-addressed systems must have been the facilitation of principles 

 of connection leading to the appearance of cells, like the delay cell, capable 

 of perceiving useful invariances, color, velocity, topology, and so on. 



Every internal invariance or imposed relationship of signals in time and 

 space gives rise to essential redundancies that can be eliminated from the 

 higher-order signals with no loss of external invariance information. There 

 is a reduction by a factor of about 10^ between the 10^ elements of the retina 

 and the 10^ elements of the optic nerve. Possibly this represents the elimination 

 of some of the redundant scanning constancies of types such as those described 

 in Section III that are implicit in the oculomotor operations and in the con- 

 straints of the kinematic rotational metric. These regularities would then 

 acquire an inescapable a priori character so far as the higher operations of 

 the network are concerned. 



The external field may also contain many redundancies that are not impor- 

 tant in a given situation. For many purposes it suffices to know that the animal 

 is a wet, friendly dog, and we do not need the concurrent retinal information 

 that he is opaque and continuous and in contact with the sidewalk. 



We have not considered here how such an 'attention' to certain patterns 

 and suppression of others might take place. However, the facilitation of 

 signals through one neuron by means of a change of its sensitivity produced 

 by feedback from the 'expectations' of a higher-order neuron (representing 

 an earlier wet-dog experience pattern) may not be different in principle from 

 the facilitation of oculomotor tracking movements by feedback from the 

 'expectations' of second-stage or third-stage retinal velocity-detector cells. 

 It may be helpful in many problems to think of attention and expectation as 

 generalized tracking devices. 



The elimination, first, of field information that does not fit into the familiar 

 useful second-stage patterns or categories, then of the redundant internal 

 patterns, and finally of the temporarily unimportant and unattended-to external 

 patterns, shows qualitatively how and why information is consumed in the 

 course of abstracting invariances from a mosaic receptor (1). It is not lost 

 or damaged by transmission in the sense usually considered in single-channel 

 communication theory. Instead, it is used up, somewhat in the way that energy 

 is used up in doing mechanical work. More mosaic input information is 

 consumed in abstracting out a higher-level decision or invariance than in a 

 lower-level one. It is consumed in the sense that the detailed input information 

 is irrecoverable, non-reconstructable, from the output. Only by the almost 



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