78 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



stimuli are all low in intensity, the linear expressions may be re- 

 garded as the first terms of Taylor expansions. Additional cross- 

 connections could be introduced into the mechanism, either inhibitory 

 or excitatory in character, but the essential features would not be 

 changed nor the metric of the space greatly modified. In particular, 

 it is important to note, the arbitrariness is inherent in the nature of 

 the experiment and can only be removed by further experiment or 

 observation of a different kind. 



In chapters vi and vii we considered the process at a single syn- 

 apse terminating one or more afferent chains, and related this to 

 various sequences of stimulus and response. In all these sequences 

 there was but a single response, however complex in form, dependent 

 upon the variation of the single a , evoked by a single, simple or com- 

 plex stimulus, and perhaps modified, in degree or in the time of its 

 occurrence, by other stimuli. In this and the preceding chapters we 

 have considered two or more synapses with as many afferents, ter- 

 minating afferent chains from various receptors. The structures were 

 associated with classes of sequences of stimulus and response of the 

 following sort. Each of a group of stimuli, simple or complex, when 

 presented in isolation can evoke a certain characteristic response, 

 whereas the concurrence of these stimuli modifies the separate re- 

 sponses by enhancing, reducing, or even preventing them. We have 

 by no means exhausted the possible applications of the various struc- 

 tures ; by varying the assumed relations among the parameters an al- 

 most countless variety of sequences is suggested. For example we 

 have been considering only the case of crossing inhibition and have 

 mentioned only in passing the possibility of having crossing excita- 

 tion, a mechanism that would mediate sequences of a quite different 

 sort. Numerous possible complications are easily suggested. The re- 

 sponse to a given stimulus might be modified, not directly by another 

 external stimulus but by the response to that stimulus, this calling 

 for a connection running from the second effector back to some point 

 in the afferent chain leading to the first effector. Circuits of the type 

 discussed in chapter iv might be introduced at various points and their 

 effects studied and related to observable sequences. 



The procedure of starting with the simpler structures and seek- 

 ing applications thereof has this decided advantage, that we can feel 

 assured that the postulated mechanism is not more complicated than 

 necessary for mediating the adduced sequence. Thus if one stimulus 

 can in any way modify the response evoked by the isolated occurrence 

 of another, then some connection must lead from the first receptor 

 to the effector for that response, whether the connection is direct, 

 through the spinal cord only, or indirect, through the thalamus, or 



