2 54 ANDERSON 



three to four from each. Two samples each would establish the two straight 

 lines, one more each would confirm that hypothesis, and a fourth would make 

 doubly sure. 



There is of course no one right answer to such a problem as this. It is a 

 problem in applied mathematics. We are not dealing with a neat, circum- 

 scribed, made-up universe with simple rules and yes-or-no answers. We are 

 dealing with the actual world around us, imperfectly understood at best, in 

 which answers are matters of judgment. 



For all their efficiency, pattern data need rigorous mathematical thinking 

 for maximum scientific usefulness. Here we immediately reach an impasse. 

 The kinds of minds which deal effectively with both pattern data and 

 mathematical symbols are rare indeed, so rare that the connections of pattern 

 data to mathematics have scarcely been touched upon in print. Apparently 

 the fact that multiple- sense-impression data (i.e., pattern data) require (and 

 deserve) to be analyzed by appropriate and efficient methods was not pointed 

 out until 1954 (Anderson, 1954) and then only in connection with one spe- 

 cialized problem. Yet (as was then demonstrated) the same methods of 

 statistical analysis which deal so effectively with pointer readings — weights, 

 yields, frequencies — can be inefficient, if not positively misleading, when ap- 

 plied to pattern-data problems. 



The fundamental reason is not far to seek. The chief branch of applied 

 mathematics which has turned its attention to such problems is Statistics. 

 As its name suggests. Statistics grew out of the state's need to keep (and 

 eventually to analyze) its records: births, deaths, incomes, marriages; ex- 

 ports; and the like. Note that these are all single-sense-impression data. Each 

 separate statistic is a number and nothing more; none of them are pattern 

 data. To analyze these data, statisticians eventually got help from Probability, 

 from notions derived ultimately from relatively simple games of chance 

 (simple, that is, by comparison with chess or basketball). Probability's basic 

 ideas were first worked out either by gamblers of some mathematical com- 

 petence or by mathematicians who for one reason or another (friendship with 

 a gambler seems to have been the commonest) took an interest in the opera- 

 tion of gaming tables. Randomness and chance are therefore central concepts 

 of Statistics. To illustrate how basic such ideas are to statistical thinking, I 

 shall quote and comment briefly from a recent inaugural address (de Loor, 

 1954) by a prominent statistician, B. de Loor of the University of Pretoria. 

 He outlines the increasing role of Statistics in many fields of science and then 

 turns to generalizations about the basic problems of Statistics and (by im- 

 plication) of science. 



"Statistics," says de Loor, "is not interested in the individual." This is 

 certainly true of most statisticians of my acquaintance. Perhaps there is no 

 inherent reason why it should continue to be true for Statistics. Certainly 

 applied mathematicians are interested in the significant individual. Whether 



