9/6 AN INTRODUCTION TO CYBERNETICS 



composed of three populations (if large enough to be free from 

 sampling irregularities) is determiuate, although the individual 

 insects behave only with certain probabilities. 



To follow the process in detail let us suppose that we start an 

 experiment by forcing 100 of them under the pebbles and then 

 watching what happens. The initial vector of the three populations 

 {dg, dyy, dp) wIll thus be (0, 0, 100). What the numbers will be at 

 the next step will be subject to the vagaries of random sampling; 

 for it is not impossible that each of the hundred might stay under 

 the pebbles. On the average, however (i.e. the average if the whole 

 100 were tested over and over again) only about 12-5 would remain 



lOO 



Ol Z-5456789 <^ 



TUiic (step) 



Fig. 9/6/1 



there, the remainder going to the bank (12-5 also) and to the water 

 (75). Thus, after the first step the population will have shown 

 the change (0, 0, 100) -> (12-5, 75, 12-5). 



In this way the average numbers in the three populations may be 

 found, step by step, using the process of S.3/6. The next state is 

 thus found to be (60-9, 18-8, 20-3), and the trajectory of this system 

 (of three degrees of freedom — not a hundred ) is shown in Fig. 9/6/1. 



It will be seen that the populations tend, through dying oscillations, 

 to a state of equUibrium, at (44-9, 42-9, 12-2), at which the system 

 will remain indefinitely. Here "the system" means, of course, 

 these three variables. 



It is worth noticing that when the system has settled down, and is 

 practically at its terminal populations, there will be a sharp contrast 

 between the populations, which are unchanging, and the insects, 

 which are moving incessantly. The same pond can thus provide 

 two very different meanings to the one word "system". ("Equili- 

 brium" here corresponds to what the physicist calls a "steady state".) 



168 



