22/2 



DESIGN FOR A BRAIN 



Then if du/dt = <5{</>(w, v, . . .)}, du/dt will be usually zero ; but 

 if the changes of w, v , . . . take </> through zero, then d(u) becomes 

 momentarily infinite and n will change by a finite jump. These 



Figure 22/2/2 : Field of the 3-variable system. 



representations are of little practical use, but they are important 

 theoretically in showing that a step-function can be represented 

 in the canonical equations. 



22/3. In an absolute system, a step-function will change value 

 if, and only if, the system arrives at certain states : the critical. 

 In Figure 22/2/2, for instance, all the points in the plane k = K 

 and to the right of the line x x = X are critical states for the step- 

 f unction k when it has the initial value K. 



The critical states may, of course, be distributed arbitrarily. 

 More commonly, however, the distribution is continuous. In this 

 case there will be a critical surface 



<f>(k t X{, . . . , X n ) = 

 which, given k, divides the critical from the non-critical states. 

 In Figure 22/2/2, for instance, the surface intersects the plane 

 k = K at the line x 1 = X. (The plane k = is not intersected by 

 it, for there are no states in this system whose occurrence will 

 result in k changing from 0.) 



Commonly <£ is a function of only a few of the variables of the 



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