THE ULTRASTABLE SYSTEM 8/8 



X is not stable in the region, and the representative point follows 

 the line to the boundary. Here (F) it meets a critical state 

 and a step-function changes value ; a new field, perhaps like II, 

 arises. The representative point is now at Y, and the line from 

 this point is still unstable in regard to the region. The point 

 follows the line of behaviour, meets a critical state at Z, and 

 causes a change of a step-function : a new field (III) arises. 

 The point is at Z, and the field includes a stable resting state, 

 but from Z the line leads further out of the region. So another 

 critical state is met, another step-function changes value, and 

 a new field (IV) arises. In this field, the line of behaviour from 

 Z is stable with regard to the region. So the representative 

 point moves to the resting state and stops there. No further 

 critical states are met, no further step-functions change value, 

 and therefore no further changes of field take place. From now 

 on, if the field of the main variables is examined, it will be found 

 to be stable. // the critical states surround a region, the ultra- 

 stable system is selective for fields that are stable within the region. 

 (This statement is not rigorously true, for a little ingenuity 

 can devise fields of bizarre type which are not stable but which 

 are, under the present conditions, terminal. A fully rigorous 

 statement would be too clumsy for use in the next few chapters ; 

 but the difficulty is only temporary, for S. 13/4 introduces some 

 practical factors which will make the statement practically true.) 



The Homeostat 



8/8. So far the discussion of step-functions and of ultrastability 

 has been purely logical. In order to provide an objective and 

 independent test of the reasoning, a machine has been built 

 according to the definition of the ultrastable system. This 

 section will describe the machine and will show how its behaviour 

 compares with the prediction of the previous section. 



The homeostat (Figure 8/8/1) consists of four units, each of 

 which carries on top a pivoted magnet (Figure 8/8/2, M in 

 Figure 8/8/3). The angular deviations of the four magnets from 

 the central positions provide the four main variables. 



Its construction will be described in stages. Each unit emits 

 a D.C. output proportional to the deviation of its magnet from 

 the central position. The output is controlled in the following 



93 



