128 



SCIENCE 



[N. S. Vol. XXXIII. No. 839 



based upon a few extremely rudimentary 

 experiences, which we make as very little 

 children and of which probably no adult 

 has any recollection. The fact that from 

 this basis men of genius have evolved won- 

 derful methods of dealing with numerical 

 relations should not blind us to another 

 fact, namely, that the observational basis 

 of mathematics is, psychologically speak- 

 ing, very minute compared with the ob- 

 servational basis of even a single minor 

 branch of biology. Moreover, mathematics 

 can at the utmost deal with only a very 

 few factors and can not give any compre- 

 hensive expression of the complex relations 

 with which the biologist has to deal. 

 While, therefore, here and there the mathe- 

 matical methods may aid us, we need a 

 kind and degree of accuracy of which 

 mathematics is absolutely incapable. For 

 our accuracy it is necessary often to have 

 a number of data in their correct mutual 

 relations presented to our consciousness at 

 the same time, and this we accomplish by 

 the visual image, Avhich is far more efficient 

 for this service than any other means of 

 which we dispose. When Ave wish to un- 

 derstand a group of complex related de- 

 tails, such as an anatomical structure, we 

 must see them, and if we can not see them 

 no accurate conception of the group can 

 be formed. With human minds consti- 

 tuted as they actually are, we can not an- 

 ticipate that there will ever be a mathe- 

 matical expression for any organ or even a 

 single cell, although formulte will continue 

 to be useful for dealing now and then with 

 isolated details. Moreover, biologists have 

 to do with variable relations, some of which 

 of course can be put into mathematical 

 form, but we find that even the simplest 

 variations become clearer to us when pre- 

 sented graphically. The value to every 

 student of science of the graphic method 

 has been immense. Biologists can work to 



advantage with quantitative methods, we 

 welcome the increasing use of measure- 

 ments in biology, we welcome the English 

 journal Biometrika, the organ of the meas- 

 uring biologists — but none the less we re- 

 fuse to accept the mathematical delusion 

 that the goal of biology is to express its 

 results in grams, meters and seconds. 

 Measurements furnish us with so-called 

 "exact" records, but the aim of science 

 goes beyond the accumulation of exact rec- 

 ords to the attainment of accurate knowl- 

 edge, and the accuracy of our knowledge 

 depends chiefly on what we see. The prac- 

 tise of science conforms to this principle, 

 the definite affirmation of which may prove 

 of continuing advantage. 



No class of records illustrates the value 

 of sight in science more impressively than 

 those made by instruments for registering 

 the time factor. The kymographion in- 

 vented by Carl Ludwig is the prototype of 

 many apparatus. In them all a succession 

 of events, like heart beats for example, 

 together with marks showing the time are 

 so registered that they can be seen simul- 

 taneously and thus readily compared. If 

 no such apparatus were available much of 

 our most important scientific knowledge 

 would not exist. To deprive mankind of 

 microscopes or telescopes would be hardly 

 a more serious blow to science. We do not 

 of course depend on our eyes for the notion 

 of time — for the congenitally blind per- 

 ceive time — ^but as soon as we wish to know 

 accurately the relation of changing events 

 to time intervals we depend upon having 

 them recorded in a visible form. It is the 

 practical acknowledgment of the superior- 

 ity of the eye as an agent to make clear the 

 correlation of data. 



When we refer to the history of modern 

 medical science we begin with the anatom- 

 ist Vesalius, because he reintroduced reli- 



