NATURAL HISTORY, STATISTICS, AND APPLIED MATHEMATICS 257 



mathematicians of my acquaintance. It has, however, when appHed to num- 

 ber data, produced results of such theoretical and practical importance that 

 most thoughtful statisticians have been caught up in the busy burgeoning 

 of their own discipline. Few statisticians indeed have, in the last few decades, 

 had quiet moments in which to inquire into the limitations imposed upon 

 their techniques by their own attitudes. They have been too busy with new 

 disciples. ("God," as Renan remarked about St. Peter, "tests his saints by 

 sending them disciples.") 



So widespread has been the use and misuse of modern Statistics in biology 

 and agriculture that it would be a simple matter to find illustrations of its 

 inefficiency with pattern data in almost any journal in those fields. Com- 

 petent statisticians are well aware that their beautifully precise methods are 

 continually misapplied by scholars who learned them by rote and only 

 halfway understand them. What I am concerned about, however, is a far 

 graver matter; it is a basic maladjustment between natural history and 

 mathematics. I am therefore deliberately choosing an example from the work 

 of one of the ablest scholars in the field of Maize Genetics in his generation. 

 Given the initial assumption (which would be concurred in by most American 

 agronomists and by many able statisticians) that modern statistical methods 

 are appropriate for pattern data (multiple-sense-impression problems), his 

 facts were recorded with precision and the calculations were carried out with 

 professional circumspection. Nor is it strange that E. W. Lindstrom, from 

 one of whose minor investigations I am drawing my final example, should 

 have been led astray in this initial assumption. Partly as the result of his 

 own efforts (he was department head, vice-dean of the graduate school, in- 

 fluential as teacher, scholar, and administrator), several of his ablest col- 

 leagues were either first-rate statisticians or facile in the use of Statistics. 

 He was simultaneously a maize geneticist and a successful corn breeder (the 

 inbred lines he developed made a real contribution to modern hybrid corn). 

 Both in Genetics and Plant Breeding he had seen the revolutionary effects 

 of Statistics properly applied to number data. He and his statistically 

 trained colleagues were far too busy with neophytes to sit down and conduct 

 a searching inquiry as to the proper limits of the new techniques they were 

 teaching. 



But the point remains that like anyone, eminent or obscure, who applies 

 traditional statistical methods to good pattern data, he was making a mistake. 

 At the very least, such methods are inefficient for such problems. At the 

 worst, as in this instance, they give the wrong answer, yet give it with such 

 an air of objective precision and professional competence that the world as 

 a whole is fooled. If such a man can make such a mistake, is it not time for 

 a rigorous examination of the field between Natural History, Statistics, and 

 Applied Mathematics? 



This illustration is from one (1940) of Lindstrom's minor investigations 



