4/2 DESIGN FOR A BRAIN 



result is that if any transient disturbance cools or overheats the 

 bath, the thermostat brings the temperature back to the usual 

 value. By this return the system demonstrates its stability. 



4/2. An important feature of stability is that it does not refer 

 to a material body or ' machine ' but only to some aspect of it. 

 This statement may be proved most simply by an example showing 

 that a single material body can be in two different equilibrial 

 states at the same time. Consider a square card balanced exactly 

 on one edge : to displacements at right angles to this edge the 

 card is unstable ; to displacements exactly parallel to this edge 

 it is, theoretically at least, stable. 



The example supports the thesis that we do not, in general, 

 study physical bodies but only entities carefully abstracted from 

 them. The concept of stability must therefore be defined in 

 terms of the basic primary operations (S. 2/3). 



4/3. Consider next a corrugated surface, laid horizontally, with 

 a ball rolling from a ridge down towards a trough. A photograph 

 taken in the middle of its roll would look like Figure 4/3/1. We 

 might think of the ball as being unstable because it has rolled away 

 from the ridge, until we realise that we can also think of it as 

 stable because it is rolling towards the trough. The duality shows 



we are approaching the concept in the 

 wrong way. The situation can be made 

 clearer if we remove the ball and consider 

 only the surface. The top of the ridge, 

 as it would affect the roll of a ball, is 

 now recognised as a position of unstable 

 equilibrium, and the bottom of the 

 trough as a position of stability. We 

 now see that, if friction is sufficiently 

 marked for us to be able to neglect 

 momentum, the system composed of 

 the single variable 4 distance of the ball laterally ' is absolute and 

 has a definite, permanent field, which is sketched in the Figure. 



From B the lines of behaviour diverge, but to A they converge. 

 We conclude tentatively that the concept of ' stability ' belongs not 

 to a material body but to a field. It is shown by a field if the lines 

 of behaviour converge. (An exact definition is given in S. 4/8.) 



44 



Figure 4/3/1. 



