A THEORY OF COLOR- VISION 91 



to specify it, then a three-dimensional array of synapses is required. 



In speaking- of one-dimensional and three-dimensional arrays we 

 are not referring 1 to their actual spatial distribution in the cortex, 

 since manifestly all synapses are distributed in three spatial dimen- 

 sions. We refer only to an abstract mode of classifying all the syn- 

 apses in question. In the case of the discriminating mechanism of 

 chapter ix, each synapse of the discriminating center is character- 

 ized by a certain h in such a way that given any interval bounded by 

 the numbers h' and h" , it is possible to say unambiguously of any 

 given synapse whether its associated h does or does not lie within this 

 interval. In the mechanism now to be discussed, of which we say that 

 the synapses form a three-dimensional array, each synapse is char- 

 acterized by the set of three parameters S x , S 2 , and S 3 and given any 

 set of these intervals Si to Si", we can say unambiguously of any 

 synapse that each Si associated with it does or does not lie upon the 

 interval from S h ' to Si". 



We shall now describe a mechanism which generalizes that of 

 chapter ix and provides the segregation of pathways required for 

 the discrimination of colors. While it may not be the simplest one 

 possible, it does possess the necessary qualitative properties and no 

 other mechanism has been proposed which does. We follow Helm- 

 holtz and assume three types of retinal receptors, each connected to 

 all the synapses of the three-dimensional array constituting the 

 "color-center." We utilize the three-receptor hypothesis because it is 

 convenient, not because we are necessarily convinced that it is "true." 

 We consider a small region of the retina only, containing one of each 

 of the three primary receptors, and we disregard the problem of 

 spatial localization or other attributes of the sensations which accom- 

 pany the stimulation of these receptors, confining ourselves exclu- 

 sively to the sensation of color. Admittedly the other attributes de- 

 mand explanation, but we regard the problems as distinct. 



The spatial arrangement required of the synapses at the color- 

 center is highly arbitrary, and while we imagine a specific spatial 

 localization of the various synapses this is for convenience of de- 

 scription only. With this understood, we suppose: ( 1 ), each primary 

 receptor is associated with a particular one-dimensional array, or 

 axis, of synapses, the three axes being mutually orthogonal and all 

 concurrent at a point O; (2), the stimulation of the i-th primary re- 

 ceptor in the amount Si occasions the production of a throughout the 

 color- center, the density being greatest all along its associated axis 

 and being everywhere a function a, (Si , P) of Si and of the assumed 

 position P; (3), as a function of position <n depends upon two para- 

 meters only, the distance r = OP , from 0, and the angle d t between 



