DESIGN FOR A BRAIN 7/16 



usually follow the bee's movements into the details of the wing 

 going up and down, neither does he follow the changes that 

 correspond to the bee's being a little older after the day's work. 

 The changes of wing-position are ignored as being too fast, only 

 an average being noticed, and the changes of age are ignored as 

 being too slow, the values being treated as approximately con- 

 stant. Thus, whether a variable of a real object behaves as a 

 step-function cannot in general be decided until the details of the 

 method of observation is specified. 



The distinction is illustrated in Figure 7/15/1 in which 

 x = tanh t has been graphed. If observed from t = — 2 to 

 t = -J- 2, the graph has form A, and is obviously not of step- 

 function form. But if graphed from t = — 100 to t = +100, 

 the result is B, and the curve is approximating to the step-function 

 form. 



7/16. As a second example, consider the Post Office type relay. 

 If observed from second to second the conductivity across its 

 contacts varies almost exactly in step-function form. If, how- 

 ever, the conductivity is observed over microseconds, the values 

 change in a much more continuous way, for the contacts can now 

 be seen to accelerate, decelerate, and bounce with a graceful and 

 continuous trajectory. And if the relay is observed over many 

 years and the conductivity plotted, the curve will not be flat 

 but will fall gradually as oxidation and wear affect the contacts. 

 We have here yet another example of the thesis that specifying 

 a real object does not uniquely specify the system or the behaviour 

 (Ss. 2/4 and 6/2). A question such as ' Is the behaviour of the 

 Post Office relay really of step-function form ? ' is improperly put, 

 for it asks about a real object what is determined only by the 

 system, which must be specified. (The matter is taken up again 

 in S. 9/10.) 



7/17. Behaviour of step-function form is likely to be seen when- 

 ever we observe a ' machine ' whose component parts are fast- 

 acting. Thus, if we casually alter the settings of an unknown 

 electronic machine we are not unlikely to observe, from time to 

 time, sudden changes of step-function form, the suddenness being 

 due to the speed with which the machine changes. 



A reason can be given most simply by reference to Figure 4/3/1 . 



90 



