380 John R. Platt 



potential and neural spike results obtained with steady-state illumination may 

 have to be reexamined for their relevance to the process of vision. 



Insects and amphibia and other lower orders seem to hold their heads and 

 eyes rigid for long periods. The need for scanning suggests this might permit 

 selective detection of moving objects in the field. (The insect eye perception 

 problem treated earlier was an artificial way of pointing up the general pattern 

 problem, and not an attempt to describe the real workings of the insect eye.) At 

 some point up the scale, a scanning tremor in the eye might have been an 

 evolutionary predecessor of wide-angle motion. 



(It is not only vision that requires 'scanning'. A variation of input stimulus 

 is needed to maintain sensitivity in touch and in smell. This strongly suggests 

 that a search be made for a similar mechanism in hearing, by which the 'sound 

 image' might be scanned up and down the basilar membrane to provide continual 

 change of stimulation, to prevent local fatigue, and to sharpen tonal discrimina- 

 tion.) 



B. Determination of Addresses 



In any field of study, it is always a hopeful sign to find two or more un- 

 explainable effects and not just one; for this opens up the possibility that the 

 two will explain each other. In the retina, we are confronted first with the 

 pattern-perception address-determination problem and then with the strange 

 importance of scanning. Putting these together, it appears that scanning might 

 be a particularly straightforward method for functional determination of 

 addresses in a non-addressed mosaic receptor. And this is functional geometry. 

 Several theorems suggest themselves. 



The Fundamental Operations 



1. Sequence of Elements — During random scanning over visual fields con- 

 taining some structure such as sharp discontinuities or boundaries, if retinal 

 elements /, y, k are triggered in similar patterns in succession far more often in 

 the time-sequences ijk or kji than in the sequences y/7:,yA:/, ikj, or kij, then: 



(la) there are some boundaries in the external field that are relatively stable 



during the scanning motion; 

 (lb) y lies on the image of a point in the field between the corresponding 



points for / and k ; and 

 (Ic) the eye movement for one of the sequences ijk is opposite to that for 



the other kji. 



2. Collinearity — During random scanning over visual fields containing sharp 

 boundaries, if all the elements in a certain large set fgh • • • k are excited simul- 

 taneously in the same way (d.c. ; or a.c, as by tremor across a boundary) and 

 if this excitation continues unchanged throughout a short drift movement, then: 



(2a) there is a linear boundary in the field; 



(2b) elements y^/j • • • A: lie on the image of that boundary; and 



(2c) the drift movement is parallel to that boundary. 



The photodetector inputs produced by tremor movement could provide a 

 gradient discrimination across the boundary which, when combined with drift, 

 as suggested in Fig. 1 for a curved line, could give an especially delicate deter- 

 mination of addresses (3). Thus, for cells distributed roughly along the image, 

 one traverse might produce firing in a reproducible sequence fkghjfigf • • •, the 



