MATHEMATICS AND THE SCIENCES — LASLEY 189 



Although many scientists feel, with Jeans, that the advent of 

 Plank's quantum mechanics has dethroned continuity and causation, 

 they in large measure share his belief that the appeal to a purely 

 statistical basis may be a cloak for ignorance and that cause and 

 effect of an unknown character may actually be in operation. 



DETERMINISM 



One would expect that questions about cause and effect should have 

 philosophical implications. There arise the old questions of deter- 

 minism and freedom. Determinism, according to Dantzig, "consists 

 of the assumption that, given any natural phenomenon, the various 

 features that characterize it are completely determined by its ante- 

 cedents. The present knowledge permits prediction of the future 

 course." "Each extension of the law of causation," says Jeans, 

 "makes belief in freedom more difficult." Pearson claims that "our be- 

 lief in determinism is the result of supposing sameness instead of 

 likeness in phenomena." Eddington asserts that "physics is no longer 

 pledged to a scheme of deterministic law." When asked why one 

 magnet repels another, Whitney replied, "By the will of God," and 

 added "science can enslave us, or it can make us free, but it is we who 

 make the choice." Others hold the view that our bodies and our 

 minds are as physical as inert matter, made of the same chemical ele- 

 ments to be found in the remote stars, subject to the same inevitable 

 laws; that the same determinism which holds for them holds also for 

 us. Compton, speaking at the University last November, refuted the 

 claim that man's actions depend on physical law. But he claimed it 

 a vital question for science to find out whether man's actions are 

 determined ; and if so, by what factors. He maintained that it is no 

 longer justifiable to use physical law as evidence against freedom. 



Into this confused picture comes mathematics with its law of aver- 

 ages and its probability theory. Almost within the last decade the 

 uncertainties of the situation have been amplified by Heisenberg into 

 an Uncertainty Principle, which says, "To any mechanical quantity 

 Q there corresponds another quantity P in such a way that the 

 product of the uncertainties in our knowledge of Q and of P can 

 never be less than a certain constant A, Plank's constant; hence the 

 more accurately we determine Q, the more ignorant we are of P." 

 In the Newtonian mechanics a knowledge of the position and of the 

 velocity of an electron at an instant determines the future position 

 of that electron, but Heisenberg assures us that we can never know 

 both. The more accurately we determine the position, the less accu- 

 rately we know the velocity; and vice versa. This concept of un- 

 certainty seems to put the coup de grace on determinism. But who 



