190 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1941 



shall say that the very law of averages which replaces determinism 

 may not itself be as great a despot as the dictator which it displaces? 

 May there not be still a new determinism dominated by probability, 

 just as there may be a new causation whose source is unknown to us? 

 Or shall we, with Compton and others, align ourselves with freedom 

 because, as he says, "I find reason to believe in freedom, and wish 

 to find whether such freedom is consistent with the recognized laws 

 of physics." It would be a fine irony, indeed, if science, the greatest 

 liberator of men's minds, denied to itself that freedom which it has 

 so unstintingly given to mankind. 



LAW 



This outlook brings us to consider our ideas of law anew. When 

 we say law, what do we mean ? Do we think of brass buttons and a 

 uniform? Do we think of statutes to which as citizens we owe 

 obedience ? Do we think of natural law, such as Newton's universal 

 law of gravitation, or of mathematical law, such as Gauss' law of 

 quadratic reciprocity, or of the philosopher's definition: "Law is 

 Unity in action difference"? 



Weyl tells us that the mathematical lawfulness of nature "is a rev- 

 elation of Divine reason." "The world," he says, "is not a chaos, but 

 a cosmos harmoniously ordered by inviolable mathematical laws." 

 We speak of Boyle's law for a perfect gas, of Kepler's three laws of 

 planetary motion, of Dalton's law of multiple proportions and many, 

 many other laws. The scientist maintains that his chief concern is 

 the discovery of nature's laws. Just what does he mean by that? 

 Is civil law one thing, and natural law another? Does law mean 

 one thing to some of us, and quite another thing to others of us? 

 Or, is there a philosophic pattern behind all law? 



In trying to understand the world we live in we observe and we 

 experiment. We assume the validity of sense perception. We as- 

 sume that normal human beings observe and experiment in much the 

 same way. If we have ever listened to witnesses testify in court, we 

 know just how much of an assumption that is. And furthermore, 

 what, pray, is a normal human being? Many of us feel that all the 

 knowledge that we obtain of natural phenomena comes through the 

 senses, despite Pearson's continued insistence that in thinking we deal 

 not only with sense impressions but with stored-up opinions of for- 

 mer sense impressions. We measure with all the uncertainties at- 

 tendant thereto; we think, or try to, amid all the doubts above 

 mentioned as to continuity and causation and determinism weighing 

 upon us. How in this atmosphere can we get at law ? 



The mathematician stands serene in his confusion. To him law is 

 simply the matter of an invariant under a set of transformations. 



