256 H. K. HARTLINE, F. RATLIFF AND W. H. MILLER 



simple, once the principle of mutual interdependence of the receptor unit 

 responses is recognized. This makes it possible to construct a useful formal 

 theory describing the inhibitory interaction succinctly. 



The value of such a theoretical formulation lies in the compactness with 

 which a number of experimental observations are described, and the insight 

 it gives into the understanding of relationships that, while inherently simple, 

 sometimes yield phenomena of considerable complexity. It has predicted 

 several experimental results. With the addition of simplifying assumptions, it 

 furnishes a semiquantitative explanation of experimental phenomena asso- 

 ciated with patterns of retinal illumination on the eye of Limulus. Apphed 

 with caution, it may be useful as a basis for hypothetical explanations of such 

 phenomena as brightness contrast and sensitivity to moving patterns in human 

 vision. 



Perhaps the aspect of greatest interest for this symposium is the value 

 this theory may have in furnishing a prototype for the construction of theories 

 of more complex interacting systems. For highly organized nervous centers, 

 basic principles may be difficult to establish by direct experiment, and patterns 

 of interaction may be extremely complex. In such cases it may be of value to 

 start with a simple model — one which possesses the merit that it describes 

 fairly faithfully an interacting system that actually exists in at least one 

 Hving organism. 



We have based the theory of the inhibitory interaction in the eye of 

 Limulus on postulates that have been derived inductively from certain empiri- 

 cal experimental observations. It would be much more desirable, of course, 

 to have a complete knowledge of the underlying mechanism of the receptor 

 unit and of the inhibitory process, and a complete description of the histo- 

 logical and functional interconnections of the interacting units. Undoubtedly, 

 such knowledge would permit the derivation of fundamental postulates on 

 which could be based an exact and rigorous theory of the interaction. In the 

 absence of such basic knowledge, the postulates can only be worked out 

 empirically, step by step, and of necessity still incompletely. 



The construction of the theory must begin with a search for a parameter 

 which, taken as the measure of the response of a receptor unit, yields a useful 

 measure of the degree of its inhibition. It is no surprise to physiologists that 

 the frequency of discharge, which seems a natural measure of a neuron's 

 response, should turn out to be the required parameter. However, this should 

 not necessarily be regarded as a consequence of any a priori considerations. 

 Some other aspect of the discharge might have been more useful in the con- 

 struction of an empirical theory of interaction: the magnitude of the time 

 interval between successive impulses, for example, or the logarithm of the 

 frequency. Less obvious is the experimental finding that it is the absolute 

 decrease in frequency, independent of its absolute level, that is the most 

 useful measure of the degree of inhibition exerted on a "test" receptor by a 



