7/5' DESIGN FOR A BRAIN 



intense and the ball fast-moving, then the ball will suddenly move 

 to B. And here it will remain, however high A becomes and 

 however low B. So, if the parameter changes steadily, the 

 lateral position of the ball will tend to step-function form, ap- 

 proximating more closely as the passage of the ball for a given 

 degree of slope becomes swifter. 



The possibility need not be examined further, for no exact 

 deductions will be drawn from it. The section is intended only 

 to show that step-functions occur not uncommonly when the 

 system under observation contains fast-acting components. The 

 subject will be referred to again in S. 10/5. 



Critical states 



7/5. In any absolute system, the behaviour of a variable at any 

 instant depends on the values which the variable and the others 

 have at that instant (S. 2/15). If one of the variables behaves as 

 a step-function the rule still applies : whether the variable remains 

 constant or undergoes a change is determined both by the value 

 of the variable and by the values of the other variables. So, 

 given an absolute system with a step-function at a particular value, 

 all the states with the step-function at that value can be divided 

 into two classes : those whose occurrence does and those whose 

 occurrence does not lead to a change in the step-function's value. 

 The former are its critical states : should one of them occur, the 

 step-function will change value. The critical state of an electric 

 fuse is the number of amperes which will cause it to blow. The 

 critical state of the ' constant of proportionality ' of an elastic 

 strand is the length at which it breaks. 



An example from physiology is provided by the urinary bladder 

 when it has developed an automatic intermittently-emptying 

 action after spinal section. The bladder fills steadily with urine, 

 while at first the spinal centres for micturition remain inactive. 

 When the volume of urine exceeds a certain value the centres 

 become active and urine is passed. When the volume falls below 

 a certain value, the centre becomes inactive and the bladder refills. 

 A graph of the two variables would resemble Figure 7/5/1 . The 

 two- variable system is absolute, for it has the field of Figure 7/5/2. 

 The variable y is approximately a step-function. When it is at 0, 

 its critical state is x = X 2 , y = 0, for the occurrence of this state 



84 



