DECLINE OF DETERMINISM EDDINGTON 153 



worth inquiring; the main point is that green-cheeseism like deter- 

 minism is a conjecture that we have no reason for entertaining. 

 Undisprovable hypotheses of that kind can be invented ad lib. 



PRINCIPLE OF UNCERTAINTY 



The mathematical treatment of an indeterminate universe does 

 not differ much in form from the older treatment designed for a 

 determinate universe. The equations of wave mechanics used in 

 the new theory are not different in principal from those of hydro- 

 dynamics. The fact is that since an algebraic symbol can be used to 

 represent either a known or an unknown quantity, we can symbolize a 

 definitely predetermined future or an unknown future in the same 

 way. The difference is that whereas in the older formulae every 

 symbol was theoretically determinable by observation, in the present 

 theory there occur symbols whose values are not assignable by 

 observation. 



Hence, if we use the equations to predict say the future velocity of 

 an electron the result will be an expression containing besides known 

 symbols a number of undeterminable symbols. The latter make the 

 prediction indeterminate. I am not here trying to prove or explain 

 the indeterminacy of the future; I am only stating how we adapt 

 our mathematical technique to deal with an indeterminate future. 

 The indeterminate symbols can often (or perhaps always) be ex- 

 pressed as unknown phase angles. When a large number of phase 

 angles are involved we may assume in averaging that they are 

 uniformly distributed from 0° to 360'', and so obtain predictions 

 which could only fail if there has been an unlikely coincidence of 

 phase angles. That is the secret of all our successful prophecies; 

 the unknowns are eliminated not by determinate equations but by 

 averaging. 



There is a very remarkable relation between the determined and 

 the undetermined symbols which is known as Heisenberg's prin- 

 ciple of uncertainty. The symbols are paired together, every 

 determined symbol having an undetermined symbol as partner. I 

 think tliat this regularity makes it clear that the occurrence of 

 undetermined symbols in the mathematical theory is not a blemish; 

 it gives a special kind of symmetry to the whole picture. The 

 theoretical limitation on our power of predicting the future is seen 

 to be systematic, and it can not be confused with other casual 

 limitations due to our lack of skill. 



Let us consider an isolated system. It is part of a universe of 

 inference, and all that can be embodied in it must be capable of 

 being inferred from the influence which it broadcasts over its 

 surroundings. Whenever we state the properties of a body in terms 



