MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



(1938, 1942) , seems to simplify the terminology, since for us the junc- 

 tion is primarily of dynamical, not anatomical, significance. We de- 

 vote chapter i to the development of the postulates of our system, and 

 to the elaboration of a few elementary consequences. 



The second stage in the development of the theory consists in 

 the investigation of the properties of complexes of specified structure, 

 these properties being deduced from the postulated properties of the 

 units and from their interrelations in the structure. The bulk of Part 

 1 deals in a purely abstract manner with a number of different struc- 

 tures which are in some sense typical of those required by the appli- 

 cations, and considers the general problem of the reciprocal determi- 

 nations of the structural form and the dynamics. 



The final stage is the comparison of prediction with fact. A neu- 

 ral complex of particular structure is assumed to link the stimulus 

 to the response in a given class of cases. From this assumption, 

 a certain quantitative functional relation between stimulus and re- 

 sponse can be deduced. To the extent to which experience verifies the 

 prediction, we have confidence in our initial assumption and are jus- 

 tified in extending the range of our predictions. In general the func- 

 tional relations involve variables and parameters, each capable of 

 assuming values over a certain range, so that any such relation yields 

 predictions well beyond the actual range of verification. 



Whether or not verification occurs over some range, there must 

 somewhere occur a failure. This is because both our units and our 

 structures are of necessity over-simplified. But the failure is itself 

 instructive, for the trend of the deviations can yield insight into the 

 nature of the complications required for increasing the realism and 

 extending the range of applicability of our model. This is the theme 

 of Part II, in which deductions made on the basis of special struc- 

 tures are compared with data, where data are available. Unfortunate- 

 ly, even when data of a kind are available, these are not always well 

 adapted to our special purpose. The test of a specific theory gen- 

 erally requires the imposition of specific conditions upon the conduct 

 of the experiment, and when the theory is not available to the experi- 

 menter it is largely chance if these conditions are satisfied. Hence 

 some comparisons can be made only in the light of special assump- 

 tions, and too often no quantitative comparison at all is possible. It 

 is our hope in publishing this monograph that more experiments will 

 be planned to make these tests. 



In Part III we present the basis for an alternative development, 

 as laid down quite recently by McCulloch and Pitts (1943). The neu- 

 ronal dynamics as postulated by these authors is much more realistic, 

 but the deductions from them of laws of learning and conditioning, 



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