Functional Geometry and the Determination of Pattern in Mosaic Receptors 387 



delay is different from zero, a delay cell. Such cells would have several possible 

 special applications. 



In the auditory system, a delay cell with binaural channels would be a useful 

 direction-indicator . 



In the retina, a second-stage delay cell like that in Fig. 4 would indicate a 

 particular image velocity-component in the plane of the paper, and could be 

 called a velocity detector cell. One with several inappropriate delays might be 

 sensitive to almost any motion or flicker. This may be one of the functions of 

 the widely branching horizontal cells that are so numerous at the periphery 

 of the retina, since this is a region particularly sensitive to motion. 



Velocity detector cells would give useful correction signals to the oculomotor 

 system. 



Under Operation 1, it is easy to see how delay cells with input channels 

 from retinal elements /, j, k might be preserved in the organism if their time 

 lags are in either the spatial sequence ijk or the sequence kji, but might atrophy 

 from disuse or at least rearrange their channels if their time lags are in any other 

 sequence. And the ijk delay cells would be a different group from the kji cells. 

 Such a principle of natural selection and differentiation might be applicable to 

 all types of second-stage and higher-stage cells. 



It may be profitable to examine these or other kinds of time-delay connections 

 in trying to make a model of color-vision, since it now appears that this may 

 involve a comparison of signals from cones at different times as the photo- 

 chemical substance in each one goes through some time sequence of spectral 

 transformations under illumination and perhaps under scanning. 



To summarize these exploratory notions, it appears that the types of neural 

 connections that would be useful for address determination, at least in an 

 artificial system, would include: difference cells; time-differential cells; null cells; 

 null-transmitter cells ; delay lines and delay cells ; and velocity-component cells. 



The outputs of such second and third-stage cells apparently can signal all 

 the self-congruences required in the basic operations of functional geometry. 

 All the geometrical patterns defined by local group theory congruences can be 

 signaled without using the retinal elements in any way except as null detectors. 



If natural selection favors those cells, together with their oculomotor 

 connections, which signal repeated self-congruences under scanning; then in the 

 mature organism each retinal cell will feed into many second-stage cells, each 

 of which expresses a useful functional relationship between that retinal cell 

 and some others. The address of the cell has indeed been determined. The 

 mature network-address becomes an expression cf the space-address. 



Evidently the functional geometry of scanning a pattern is a way of con- 

 verting its space congruences into identical time patterns. It therefore could 

 be said, as some have said (16), that in the mature organism the appearance 

 of a certain time pattern at a certain point in the network creates an 'expectation' 

 of its repetition at an adjacent point, and stimulates oculomotor and other 

 movements normally appropriate for the accurate fulfillment of this expectation. 



The accuracy of address-determination in these operations depends on 

 the temporal accuracy of the delay lines and not on the spatial structure, which 

 can be largely eliminated from the congruence signals, and therefore from the 

 perceived patterns. 



