NATURE 



49 



THURSDAY, MAY 17, 1900. 



BIOLOGY AS AN ''EXACT'' SCIENCE. 

 The Grammar of Science. By Karl Pearson, M.A., 

 F.R.S., Professor of Applied Mathematics and 

 Mechanics, University College, London. Second Edi- 

 tion, revised and enlarged, with n figures in the text. 

 Pp. xviii + 548. (London: Adam and Charles Black, 

 1900.) 



THE sciences of life are marked off for practical pur- 

 poses from those concerned with inorganic matter 

 by obvious differences in the nature of the material with 

 which they respectively deal. But in addition to dis- 

 tinctions of this kind, it has been customary to look upon 

 biology as havmg a lower claim to the title of an 

 " exact " science than that enjoyed, for example, by 

 chemistry and physics. This view has been emphasised 

 by the practice of calling biology a merely " descriptive " 

 science, with a kind of implication that other sciences 

 are that and something more. The distinction, however, 

 is at best an artificial one, resting mainly on the fact that 

 the conditions of life are often so complex, and the data 

 so difficult of access, that the use of those quantitative 

 methods of induction which in other sciences have been 

 fruitful of important results, so far as biology is concerned 

 has to a great extent remained in abeyance. 



It could not be expected that this state of things 

 should be allowed to continue. " Every science," said 

 Stanley Jevons, " and every question in science, is first a 

 matter of fact only, then a matter of quantity, and by 

 degrees becomes more and more precisely quantitative." 

 In those parts of biology which come into relation with 

 chemistry and physics, the quantitative methods have 

 long since gained a footing. Physiology tends increas- 

 ingly to become a science of exact measurement, and 

 there is abundant scope for the exercise of mathematical 

 power in the investigation of its present data. With regard, 

 however, to many problems of what is known as " general 

 biology," especially those which gather round the central 

 doctrine of evolution, it is no doubt true that until recently 

 measurements have either not been applied at all, or 

 have been used only in the simplest and crudest form. 

 That general biology has now ceased to deserve the 

 reproach of neglecting quantitative methods is largely 

 due to the labours of Mr. Francis Galton, Prof. Weldon, 

 and Prof. Karl Pearson ; the way towards a greater pre- 

 cision of method having also been in some degree pre- 

 pared by other workers, such as Milne Edwards, J. A. 

 Allen and A. R. Wallace. 



In the second edition of his well-known " Grammar of 

 Science," Prof. Pearson has included two new chapters 

 which contain a semi-popular account of his recent work 

 on the mathematical aspects of evolutionary theory. The 

 ground covered is extensive, comprising quantitative 

 investigations of variation, correlation, selection in its 

 various forms, heredity and reversion. Those readers 

 who may be deterred by the length and elaboration of 

 Prof. Pearson's papers in the Proceedings and Philosophical 

 Transactions of the Royal Society will here find a clear 

 account of the various problems concerned, together with a 

 NO. 1594, VOL. 62] 



tolerably easy explanation of the mathematical processes in- 

 volved in their attempted solution, and a useful summary 

 of the results so far arrived at. The author states his 

 main position as follows : — 



" What we need in the theory of evolution is quantita- 

 tive measurement following upon precise definition of our 

 fundamental conceptions. Biologists, even as physicists 

 have done, must throw aside merely verbal descriptions, 

 and seek in future quantitative precision for their ideas." 



In the same spirit. Prof. Weldon remarked in his Pre- 

 sidential Address to Section D at the Bristol meeting of 

 the British Association : " Numerical knowledge of this 

 kind is the only ultimate test of the theory of natural 

 selection, or of any other theory of any natural process 

 whatever." That these dicta are substantially true will 

 hardly be questioned, though it may be objected to Prof. 

 Pearson that he somewhat overstates his case. AH con- 

 crete science is in its essence descriptive, and it is not 

 improbable that parts at least of biological study will 

 have to remain indefinitely in the condition of " merely 

 verbal description." It would appear, too, that in his 

 eagerness to denounce the putting forward of inadequate 

 hypotheses, the author allows himself to undervalue those 

 rough preliminary generalisations which have frequently 

 formed so useful a step in the completion of a great in- 

 duction. It is possible to attach too much importance 

 to Faraday's famous saying. If every " suggestive 

 thought" which has eventually turned out to be imper- 

 fect, or even erroneous, had been "crushed in silence" 

 instead of being given to the world, the cause of scientific 

 progress would have suffered. We must often, for prac- 

 tical purposes, be content to proceed by the method of 

 successive approximation. The work of Darwin himself 

 was only to a limited extent quantitative. 



Evolutionists of what may perhaps without offence 

 be called the " orthodox " type, will find Prof. Pearson's 

 attitude towards most controverted points sufficiently 

 correct. Thus, without denying the possibility of a 

 bathmic element in evolution, he does not countenance 

 the " inherent growth-forces " that find favour with Neo- 

 Lamarckians. Demonstration of the inheritance of 

 acquired characters he holds to be still wanting ; 

 tradition, on the other hand, is probably an important 

 factor in what are called the " instincts " of the lower 

 animals. He finds no quantitative evidence for tele- 

 gony, the occurrence of which alleged phenomenon 

 "seems both mechanically and physiologically incon- 

 ceivable." The reality of natural selection as a factor 

 in evolution is quantitatively demonstrable, and sexual 

 selection is rehabilitated. 



It would be impossible within the limits of ^notice 

 like the present to do justice to the lucidity of Prof. 

 Pearson's explanations, the ingenuity of his mathematical 

 devices, and the care with which he has avoided possible 

 sources of error in his calculations. Examples may be 

 found in his exposition of the technical terms "modal 

 value " and " standard deviation " ; in his determination 

 of the coefficient of regression ; and in his discussion of 

 the relative value of selective and non-selective death- 

 rates for organs of different sizes. Among the most 

 valuable of his suggestions are those on the importance 

 of correlation ; on selective mating in its various forms 



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