DECLINE OF DETERMINISM EDDINGTON 155 



tion and velocity of an electron are paired in this way. We can 

 fix the position with a probable error of 0.001 millimeters and the 

 velocity with a probable error of about 1 km per sec; or we can 

 fix the position to 0.0001 millimeters and the velocity to 10 km per 

 sec; and so on. We divide the uncertainty how we like but we 

 can not get rid of it. If current theory is right, this is not a question 

 of lack of skill or a perverse delight of Nature in tantalizing us, for 

 the uncertainty is actually embodied in the theoretical picture of the 

 electron; if we describe something as having exact position and 

 velocity we can not be describing an electron, just as (according to 

 Russell) if we describe a person who knows what he is talking about 

 and whether what he is saying is true we can not be describing a pure 

 mathematician. 



If we divide the uncertainty in position and velocity at time t-^ 

 in the most favorable way we find that the predicted position of 

 the electron one second later at time tz is uncertain to about 5 centi- 

 meters. That represents the extent to which the future position is 

 not predetermined by anything existing one second earlier. If the 

 position at time tn always remained uncertain to this extent there 

 would be no failure of determination.' But when the second has 

 elapsed we can measure the position of the electron to 0.001 milli- 

 meters or even more closely, as already stated. This accurate posi- 

 tion is not predetermined ; we have to wait until the time arrives and 

 then measure it. It may be recalled that the new knowledge is 

 acquired at a price. Along with our rough knowledge of position 

 (to 5 cms) we had a fair knowledge of the velocity; but when we 

 acquire more accurate knowledge of the position the velocity goes 

 back into extreme uncertainty. 



We might spend a long while admiring the detailed working of 

 this cunning arrangement by which we are prevented from finding 

 out more than we ought to know. But I do not think you should 

 look on these as Nature's devices to prevent us from seeing too far 

 into the future. They are the devices of the mathematician who has 

 to protect himself from making impossible predictions. It commonly 

 hapj^ens that when we ask silly questions, mathematical theory does 

 not directly refuse to answer but gives a noncommittal answer like 

 0/0 out of which we can not wring any meaning. Similarly when we 

 ask where the electron will be to-morrow, the mathematical theory 

 does not give the straightforward answer " It is impossible to say 

 because it is not yet decided " — because that is beyond the resources 

 of an algebraic vocabulary. It gives us an ordinary formula of 

 a;'s and y's, but makes sure that we can not possibly find out what 

 the formula means — until to-morrow. 



2 For the thing we failed to predict (exact position at time ta) would be meaningless. 



