Functional Geometry and the Determination of Pattern in Mosaic Receptors 379 



unlimited by the coarseness of the mosaic structure and the randomness and 

 uncertainty of cone locations. 



Functional geometry offers such a method, since it can generate indefinitely 

 high precision out of arbitrarily coarse materials crudely manipulated. With it, 

 the practical limitation in precision could be a very refined signal-to-noise 

 limitation, that is, an intensity-judgment-time limitation, as we shall see, and 

 not a coarse mosaic structure limitation. For the internal as well as the external 

 eye, it would be characteristic of biological systems to make use of such a 

 method, conceptually simple, operationally precise, making only minimum 

 demands on the accuracy of assembly, and capable of being driven to higher and 

 higher precision as needed under the pressure of natural selection. 



III. DETERMINATION OF ADDRESSES 



A. Scanning in Vision 



DiTCHBURN and co-workers (8-10), and Riggs and co-workers (11-12), have 

 shown that vision disappears unless the field is continuously scanned by the 

 eye. The scanning is normally provided by 'physiological nystagmus', or 'fixa- 

 tion tremor.' When a subject is fixating as steadily as possible, the following 

 eye movements are present : 



'(i) a tremor of amphtude of the order of 15 sec arc and frequency ranging 

 from 30 to 80 c.p.s. 



'(ii) a series of 'flicks' of up to 20 min arc occurring at irregular intervals 

 ranging from 0.03 sec to 5.0 sec. 



'(iii) slow drifts in the intervals between flicks.' (Ditchburn (9)). 



The movements are involuntary. They continue undiminished even when 

 an image has been stabilized on the retina, so that they do not seem to have 

 quantitative feedback character, at least for fixation of a point source ; but the 

 flicks do tend to produce recentering after the image begins to drift off" the fovea. 



The frequency, amplitude and sequence of the movements as presently 

 known would be consistent with assigning the tremor jerks to the successive 

 single neural spike inputs in the normal trains of spike pulses to the ocular 

 muscles ; with assigning drift to the unbalance between these jerks in opposed 

 muscles at slightly different spike frequencies; and with assigning flick to a 

 final sudden burst of spikes to the less active muscle which redresses the un- 

 balance and recenters the system. There is no vision during the flick movement. 

 This demonstrates an intimate oculomotor interaction with the retinal output, 

 complementary to the interaction which will be postulated later. 



When these movements are stopped by optically stabilizing the retinal image, 

 vision is lost within a second or two. It can be restored by flicker modulation 

 of the light intensity or by reintroduction of some image movement. 



The necessity for scanning in maintaining vision might have been anticipated. 

 It is probably no surprise to a biologist to find such a mechanism used to 

 counteract the effects of adaptation and fatigue in receptors that need to be 

 continuously sensitive; nor to a biochemist to find that the electrochemical 

 shock waves corresponding to nerve impulses are reduced in frequency as the 

 photochemical steady state is approached; nor to a physicist to find that a.c. 

 operation of a phototube is the best way to avoid d.c. drifting. Many retinal 



