96 



NATURE 



[March i6, 191 i 



important than formerly. Science grows by the accretion 

 of ideas. Now, a great man has, let us say, twelve new 

 ideas, where a man of ability has one. If science gets 

 twelve new ideas, it matters little whether they come from 

 one man or from twelve. To a certain extent, numlx-rs 

 make a substitute for genius — but nothing probably will 

 • ver replace that type of great genius, to which we owe 

 most, the man who has a great thought, which no one 

 lias ever conceived before. 



The nineteenth century, in response \o the new con- 

 ditions which have arisen in its course, has added another 

 new standard for scientific memoirs — they must include a 

 conscientious consideration of recent and co-temporary 

 related work. Now the second step in science-making, 

 ;ifter recording the new original observations, so as to 

 make them accessible to others, is the collation of these 

 same observations into broad general results. The aim is 

 to eliminate the personal factor and to impart the character 

 of impersonal, absolute validity to the conclusions. 



In addition to the original memoirs, science profits by 

 1 large number of publications, almost all of which are 

 "f modern, often of very recent, creation. Broadly speak- 

 ing, their aim is to promote that collation which is begun 

 in the original memoirs. Germany is the home of most 

 of these undertakings, which are familiar to us under the 

 names of " Jahresberichte," " Centralblatter," and 

 " Hlrgebnisse." 



\\\' recognise in the present methods of recording and 

 collating scientific discoveries many adaptations which are 

 due, it seems to me, essentially to the mere increase in 

 the number of workers. But though the methods are 

 modified, the essential steps are the same : first, the record 

 of the individual personal knowledge ; secondly, the con- 

 version of the personal knowledge by verification and colla- 

 tion into valid impersonal knowledge; thirdly, the 

 systematic coordination and condensation of the con- 

 clusions. 



A defect — perhaps the most serious defect of our educa- 

 tion — arises from our failure to make our students 

 .ippreciate vividly the fundamental fact that science is 

 based on personal knowledge. Our students are allowed 

 to graduate from college, for the most part, without any 

 comprehension of this great truth. The best of them start 

 forth with a high reverence for the library, the place of 

 records, but quite unaware that a still higher reverence is 

 due to those who, by being the first to observe unknown 

 things, have founded the knowledge the records of which 

 the library keeps. 



The divergence between philosophy and science shows 

 itself most conspicuously in the personal mental attitude 

 which philosophy cherishes and science seeks to overcome. 

 Philosophers still discuss philosophers and their svstems, 

 scientific men pursue impersonal knowledge with such 

 ardour that they are apt to know little of the history of 

 science. 



The records which we have considered thus far are 

 those which serve to make the discoveries of individuals 

 available for others. So soon as the discoveries are 

 properly collated and sufficiently verified, they become per- 

 manent parts of science. Many definitions of science have 

 be.en given, and did time permit it might be profitable to 

 quote some of them— but is it not sufficient to define 

 science as knowledge which has acquired impersonal 

 validity? 



We must now attempt a general examination of the 

 records, which are used primarily to help the original 

 investigator, though often preserved to assist his 

 successors. The simplest form of record is the preserva- 

 tion of the actual specimen. Scientific museums are 

 essentially storehouses for such records. Most of them, 

 to be sure, maintain public exhibitions, which interest, 

 stimulate, and possibly instruct the public, but the precious 

 part of their collections comprises the objects possessed, 

 which have ser\-ed for some original discovery. Scientific 

 museums are ver>- modern ; nearly all those' in America 

 have been started within a few years. 



The progress of science is marked by the advance in the 

 ^^^ A "J.^'^'"^ research records. We" all admit, in other 

 words, that the progress of science depends partly on the 

 perfecting of old methods, but chiefly on the in<\-ention of 

 new ones. Despite the enormous variety in their nature 

 and aims, all our technical methods have this in common 

 NO. 2159, VOL. 86] 



— that their real purpose is to yield us nutrd*. Our 



microscopes, spectroscopes, measuring instrum' r" ' 



many another apparatus have indeed their priru 



in rendering possible observations which arc i...,. . 



with our unaided senses. They enlarge our field of 

 inquiry, and put precision within our reach. Yet their 

 usefulness is conditioned upon their enabling us to make 

 records which else would remain beyond our power. On 

 the other hand, there is a still larger class of apparatus 

 which are obviously designed to make records. What has 

 been said concerning apparatus might be repeated concern- 

 ing methods. 



It is remarkable that the vast majority of methods and 

 apparatus are contrived to furnish a visible result. Sight 

 has long been acknowledged by science as the supreme 

 sense. Perhaps the philosopher was right who asserted 

 that nothing is really known until it is presented in a 

 visible form. We biologists cannot deplore too frequently 

 or too emphatically the great mathematical delusion by 

 which men often of very great, if limited, ability, have 

 been misled into becoming advocates of an erroneous con- 

 ception of accuracy. Although I have expressed myself 

 on the subject before, its importance justifies recurring to 

 it. The delusion is that no science is accurate until its 

 results can be expressed mathematically. The error comes 

 from the assumption that mathematics can express com- 

 plex relations. Unfortunately, mathematics have a very 

 limited scope, and are based upon a few extremely rudi- 

 mentary 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 

 wonderful methods of dealing with numerical relations 

 should not blind us to another fact, namely, that the 

 observational basis of mathematics is, psychologically 

 speaking, very minute compared with the observational 

 basis of even a single minor branch of biology. More- 

 over, mathematics can at the utmost deal with only a 

 very few factors, and cannot give any comprehensive ex- 

 pression 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 \^ accomplish 

 by the visual image, which is far more efficient for this 

 service than any other means of which we dispose. When 

 we wish to understand a group of complex related details, 

 such as an anatomical structure, we must see them, and 

 if we cannot see them no accurate conception of the group 

 can be formed. 



With human minds constituted as they actually are, w-^ 

 cannot anticipate that there will ever be a mathematical 

 expression for any organ or even a single cell, although 

 formulae 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 presented 

 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 measurements in biology, we welcome 

 the English journal Biometrika, the organ of the measur- 

 ing biolc^ists— but none the less we refuse to accept the 

 mathematical delusion that the goal of biolc^y is to express 

 its results in grams, metres, and seconds. Measurements 

 furnish us with so-called " exact " records, but the ainr 

 of science goes beyond the accumulation of exact records 

 to the attainment of accurate knowledge, and the accuracy 

 of our knowledge depends chiefly on what we see. The 

 practice 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 simultaneously, and thus 

 readily compared. If no such apparatus were available, 

 much of our most important scientific knowledge would 



