8/3 THE HOMEOSTAT 



the field is stable, the four magnets move to the central position, 

 where they actively resist any attempt to displace them. If 

 displaced, a co-ordinated activity brings them back to the centre. 

 Other parameter-settings may, however, give instability; in which 

 case a ' runaway ' occurs and the magnets diverge from the central 

 positions with increasing velocity — till they hit the ends of the 

 troughs. 



So far, the system of four variables has been shown to be 

 dynamic, to have Figure 4/15/1 (A) as its diagram of immediate 

 effects, and to be state-determined. Its field depends on the 

 thirty-two parameters X and P. It is not yet ultrastable. But 

 the inputs, instead of being controlled by parameters set by hand, 

 can be sent by the switches S through similar components arranged 

 on a uniselector (or ' stepping-switch ') U. The values of the 

 components in U were deliberately randomised by taking the 

 actual numerical values from Fisher and Yates' Table of Random 

 Numbers. Once built on to the uniselectors, the values of these 

 parameters are determined at any moment by the positions of 

 the uniselectors. Twenty-five positions on each of four uni- 

 selectors (one to each unit) provide 390,625 combinations of 

 parameter- values . 



F represents the essential variable of the unit. Its contacts 

 close when and only when the output current exceeds a certain 

 value. When this happens, the coils G of the uniselector can be 

 energised, moving the parameters to new values. The power to 

 G is also interrupted by a device (not shown) that allows the power 

 to test F's contacts only at intervals of one to ten seconds (the 

 operator can adjust the frequency). Thus, if set at 3-second 

 intervals, at every third second the uniselector will either move to 

 new values (if F be receiving a current exceeding the limits) or 

 stay where it is (if F's current be within). 



8/3. That the machine described is ultrastable can be verified 

 by an examination of the correspondences. 



There are four main variables — the positions of the four magnets. 

 (There can, of course, be fewer if not all the units are used.) 

 These four represent both the environment and the reacting part 

 R of Figure 7/2/1, the allotment of the four to the two subsystems 

 being arbitrary. The relays F correspond to the essential 

 variables, and the physiological limits correspond to the currents 



103 



