188 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1941 



CAUSATION 



Jeans maintains that the "steady onward flow of time is the essence 

 of the cause and effect relation." It is but natural, then, that when 

 continuity is in question, causation should take its place under the 

 microscope of scientific scrutiny. There is more at issue than the 

 mere post hoc ergo propter hoc argument. We are so used to draw- 

 ing inferences from data, that it is hard to realize on what flimsy 

 grounds many of our conclusions rest. It is hard, too, to see how 

 we may do intellectual business at all without the ability to infer 

 effect from cause. The great seventeenth century of Galileo and 

 Newton encouraged the scientist to think of causation as something on 

 which he could definitely rely. Modern physics takes the position, so 

 ably formulated by Pearson, that causation is intelligible only in the 

 perceptual sphere as "antecedence in a routine of sense impressions." 



With the precision of measurement in studying natural phenomena 

 came the realization of the statistical character of those measure- 

 ments. Into the relations connecting the numbers arising in this 

 way began to enter questions of doubt. The descriptions of the phe- 

 nomena exhibited by the relations were seen to be more exact than 

 the uncertainty of the data warranted. It began to appear that the 

 descriptions described little more than what Weyl has called "statisti- 

 cal regularities." Pearson has put it thus bluntly, "In the order of 

 perceptions no inherent necessity can be demonstrated * * * 

 necessity has a meaning in the field of logic, but not in the universe 

 of perception * * * causation is neither a logical necessity, nor 

 an actual experience," 



This position seems at first glance to be at variance with the "if 

 this, then that" of mathematical disciplines. The causation which 

 inheres in logic, whose presence we so naively hope for in our scientific 

 thinking, seems actually to emerge in the tenets of the mathemati- 

 cian. How, then, may the scientist fit data patently statistical in 

 character into mathematical form, clearly nonstatistical in character? 

 If, as Pearson claims, "contingency and correlation replace causation 

 in science," how does the mathematical equation tell us a true story of 

 natural phenomena? Pearson answers this in part by saying, "Con- 

 tingency is expressed in a table with cell-dots forming a band. This 

 band viewed through an inverted telescope gives a curve. This curve 

 is the mathematical function." 



In the language of the mathematician, the scientific relation ap- 

 proaches the mathematical formulation asymptotically. Perhaps a 

 more nearly correct statement is that both the scientific data and the 

 mathematical description near each other in a process of successive 

 approximation which would warm the heart of a Poincare. 



