STEP-FUNCTIONS IN THE LIVING ORGANISM 10/6 



two values, the total number of fields available will be 2 n . This 

 number would have to be lessened in practical cases for practical 

 reasons, but even if it is only approximate, it still illustrates the 

 main fact : the number of fields is moderate when n is moderate, 

 but rapidly becomes exceedingly large when n increases. Ten 

 step-functions, for instance, will provide over a thousand fields, 

 while twenty step-functions will provide over a million. The 

 number of fields soon becomes astronomic. 



The following imaginary example emphasizes the relation be- 

 tween the number of fields and the number of step-functions 

 necessary to provide them. If a man used fields at the rate of 

 ten a second day and night during his whole life of seventy years, 

 and if no field was ever repeated, how many two-valued step- 

 functions would be necessary to provide them ? Would the 

 reader like to guess ? The answer is that thirty-five would be 

 ample ! Quantitatively, of course, the calculation is useless ; but 

 it shows clearly that the number of step-functions can be far less 

 than the number of fields provided. So if the human nervous 

 system produces a very large number of fields, we need not deduce 

 that it must have a very large number of step-functions. 



References 



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