NATURAL HISTORY, STATISTICS, AND APPLIED MATHEMATICS 255 



such problems belong in another field of Applied Mathematics and must 

 forever be excluded from the domain of Statistics is a relatively trivial 

 quibble. It is a fact that in many kinds of scientific work and even when 

 dealing with precise mathematically analyzed data, an individual may be 

 highly significant. A single electron track on a photographic plate (Physics), 

 a single erratic boulder (Glacial Geology), a single crossover between two 

 closely linked genes (Genetics) are examples from three fields of science of 

 individuals which might be the decisive evidence in critical experiments. 



"In many cases individuals behave at random," says de Loor. Most cer- 

 tainly not. We do not live in that kind of a world. In our ignorance, in our 

 imperfect understanding of some factors (and our complete ignorance of 

 even the possibility of knowing about others), it may seem to us as if in- 

 dividuals — plants, molecules, insects, or microscopic particles, as the case 

 may be — are behaving at random. The better we understand any particular 

 problem, the less do we have to assign random behavior to any of the factors 

 in it. 



"Certainties barely exist for him," says de Loor, speaking of the statistician. 

 With efficient pattern data, efficiently analyzed, the scientist may be as cer- 

 tain as it is possible to be. In the example of the former fence line in the 

 woods, I am as certain as if I had been there that one property was cut 

 over a considerable number of years ago and the other was not. Furthermore, 

 any competent naturalist given the same assignment would come to the same 

 conclusion. How certain can you get? Remember what Thoreau said about 

 circumstantial evidence? "Sometimes," he said (and let me remind you that 

 Thoreau was accustomed to using pattern data and to pondering deeply over 

 it), "circumstantial data can be very convincing, as when you find a minnow 

 in the can of milk!" 



In the introduction to his inaugural address de Loor pointed out the ever- 

 increasing role of Statistics in modern science. He said (and here I agree 

 with him wholeheartedly), "Its development has been phenomenal especially 

 during the last two decades. To express it in terms of modern physics, a chain 

 reaction has been set up and is making its influence felt in nearly every 

 sphere of human activity." He then cites examples from nuclear physics, 

 agricultural research, meteorology, medicine, social sciences, quality control, 

 operations research, economics, and even from philology. In all the examples 

 of which I have some knowledge, where Statistics has been an unqualified 

 success, it has been with problems dealing with numbers (single-sense- 

 impression data), usually pointer readings. In Agronomy it has revolution- 

 ized comparative-yield tests, even more in the way they are laid out than in 

 the way in which the data are organized after they have been gathered. In 

 Genetics it has simplified and codified the calculation of linkage data. (It 

 should specifically be pointed out that the outstanding contributions of 

 Sewall Wright to the fields of developmental and of population genetics owe 



