THE ULTRASTABLE SYSTEM 8/9 



caused a down stroke in 1 after R v showing that the action 2 — ► 1 

 had been reversed by Jhe uniselector. This reversal compensated 

 for the reversal of 1 — > 2 caused at R v 



At R 2 the whole process was repeated. This time three uni- 

 selector changes were required before stability was restored. A 

 comparison of the effect of Z) 3 on 1 with that of D 2 shows that 

 compensation has occurred again. 



The homeostat can thus demonstrate the elementary facts of 

 ultrastability. 



8/9. In what way does an ultrastable system differ from an 

 ordinary stable system ? 



In one sense the two systems are similar. Each is assumed 

 absolute, and if therefore we form the field of all its variables, 

 each will have one permanent field. Given a region, every line 

 of behaviour is permanently stable or unstable (see Figure 7/8/1). 

 Viewed in this way, the two systems show no essential difference. 

 But if we compare the variables of the stable system with only 

 the main variables of the ultrastable, then an obvious difference 

 appears : the field of the stable system is single and permanent, 

 but in the ultrastable system the phase-space of the main vari- 

 ables shows a succession of transient fields concluded by a terminal 

 field which is always stable, The distinction in actual behaviour 

 can best be shown by an example. The automatic pilot is a 

 device which, amongst other actions, keeps the aeroplane hori- 

 zontal. It must therefore be connected to the ailerons in such 

 a way [that when the plane rolls to the right, its output [must 

 act on them so as to roll the plane to the left. If properly joined, 

 the whole system is stable and self-correcting : it can now fly 

 safely through turbulent air, for though it will roll frequently, 

 it will always come back to the level. The homeostat, if joined 

 in this way, would tend to do the same. (Though not well 

 suited, it would, in principle, if given a gyroscope, be able to 

 correct roll.) 



So far they show no difference ; but connect the ailerons in 

 reverse and compare them. The automatic pilot would act, 

 after a small disturbance, to increase the roll, and would persist 

 in its wrong action to the very end. The homeostat, however, 

 would persist in its wrong action only until the increasing devia- 

 tion made the step-functions start changing. On the occurrence 



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