9 8 SCIENCE PROGRESS 



servation of energy) on the uniform and unbroken experience 

 of mankind. But if any deduction of this kind could be valid, 

 it surely is not one which is based upon the infinity of time — a 

 theory which we cannot genuinely bring before consciousness 

 and which staggers every attempt to realise it. Let me pass, 

 however, from Dr. Johnstone's logic to his physics. 



In order that the second law of thermodynamics may be 

 reversed, he tells us, we must assume that at a given moment 

 in some portion of gas every molecule should happen to collide 

 with another molecule moving at the same velocity and in the 

 same straight line. In that case the direction of motion of 

 every molecule would be instantaneously reversed, while its 

 velocity would remain unaltered ; there would then occur a 

 reversal of sign in the second law of thermodynamics : entropy 

 would be diminished, instead of being increased. The chance 

 against such an event occurring is, as Dr. Johnstone rightly 

 observes, immeasurably great ; but, as he continues, time and 

 space are also immeasurably great, and we may therefore 

 suppose that the thing can actually happen. 1 Yet he does not 

 adequately realise the infinite improbability of the occurrence. 

 He says : " At any instant many of the molecules in a decilitre 

 of gas must be approaching each other in the same straight line 

 and with the same velocity." On the contrary, the odds against 

 two molecules approaching each other in the same mathematical 

 straight line is infinity to i. The odds against their moving 

 with a mathematically equal velocity is also infinity to i ; and 

 the odds against a combination of these two events is the square 

 of infinity to i. Further, the chance that all the molecules in 

 a decilitre of gas should fulfil these conditions at the same 

 moment is represented by a fraction of which the numerator 

 is i, and the denominator is infinity raised to a power equal 

 to twice the number of molecules in the gas ; and that we may 

 call for practical purposes infinity to the power of infinity. 



Seeing that it is Dr. Johnstone's object to throw doubt upon 

 the universal validity of the second law of thermodynamics, it 

 is not apparent why he should have selected a mode of argu- 

 ment which represents the odds against its being "violated" 

 as infinity to the power of infinity. No one has ever claimed 



1 Dr. Johnstone has an inveterate habit of cancelling out infinities on the two 

 sides of an equation. We know that twice infinity = 3 times infinity ; but we 

 cannot cancel infinities and say that 2 = 3. 



