3/11 AN INTRODUCTION TO CYBERNETICS 



an optical absorption, elasticity, shape, specific gravity, and so on 

 and on. Any suggestion that we should study "all" the facts is 

 unrealistic, and actually the attempt is never made. What is 

 necessary is that we should pick out and study the facts that are 

 relevant to some main interest that is already given. 



The truth is that in the world around us only certain sets of facts 

 are capable of yielding transformations that are closed and single- 

 valued. The discovery of these sets is sometimes easy, sometimes 

 difficult. The history of science, and even of any single investiga- 

 tion, abounds in examples. Usually the discovery involves the 

 other method for the defining of a system, that of listing the variables 

 that are to be taken into account. The system now means, not a 

 thing, but a list of variables. This list can be varied, and the 

 experimenter's commonest task is that of varying the list ("taking 

 other variables into account") until he finds a set of variables that 

 gives the required singleness. Thus we first considered the pendulum 

 as if it consisted solely of the variable "angular deviation from the 

 vertical"; we found that the system so defined did not give singleness. 

 If we were to go on we would next try other definitions, for instance 

 the vector: 



(angular deviation, mass of bob), 



which would also be found to fail. Eventually we would try the 

 vector: 



(angular deviation, angular velocity) 



and then we would find that these states, defined in this way, would 

 give the desired singleness (cf. Ex. 3/6/14). 



Some of these discoveries, of the missing variables, have been of 

 major scientific importance, as when Newton discovered the import- 

 ance of momentum, or when Gowland Hopkins discovered the 

 importance of vitamins (the behaviour of rats on diets was not 

 single-valued until they were identified). Sometimes the discovery 

 is scientifically trivial, as when single-valued results are obtained 

 only after an impurity has been removed from the water-supply, or 

 a loose screw tightened; but the singleness is always essential. 



(Sometimes what is wanted is that certain probabilities shall be 

 single- valued. This more subtle aim is referred to in S.7/4 and 9/2. 

 It is not incompatible with what has just been said: it merely means 

 that it is the probability that is the important variable, not the 

 variable that is giving the probability. Thus, if I study a roulette- 

 wheel scientifically I may be interested in the variable ''probability of 

 the next throw being Red", which is a variable that has numerical 

 values in the range between and 1, rather than in the variable 



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