February i6, 1899] 



NA TURE 



369 



Is Natural Selection all Metaphor? 



The Duke of Argyll, in his reply to Mr. Herbert Spencer, 

 says " in the Darwinian theory there is no selector" (Nature, 

 February 2, p. 317). Though we have not yet discovered a 

 principle or factor which plays the part of the breeder in 

 nature, it by no means follows that " natural selection " is "all 

 metaphor," nor yet, as has been often stated, an altogether mis- 

 leading phrase. The role of the breeder or artificial selector is, 

 I believe, often misunderstood. If we consider what the art of 

 breeding mainly consists in, we may come to the conclusion that 

 even the phrase ' ' artificial selection " is, to a considerable extent , 

 misleading and metaphorical. It seems to me the art of breeding 

 consists mainly in two things, viz. (i) producing prepotency, and 

 (2) preventing intercrossing. Prepotency is produced and main- 

 tained by inbreeding. The object of preventing intercrossing 

 is to arrest, as far as possible, variation and reversion. If it can 

 be shown that in nature prepotency often arises either as a sport 

 or through inbreeding, and that prepotency by arresting the 

 "swamping effects of intercrossing" plays the part of the 

 fences of the breeder and the cages of the fancier, we shall be 

 justified in looking upon prepotency as a " selector," and in 

 finding more than metaphor in the phrase " natural selection." 

 We already know that amongst insects a sport may displace the 

 parent form ; and if, instead of searching for evidence of inter- 

 sterility as suggested by Romanes, we search diligently for 

 evidence of prepotency, we may ere long discover the " selector " 

 — the factor that in nature, under the control of utility, plays the 

 part of the breeder. J. C. Ewart. 



Geometry versus Euclid. 



To a great many people the assertion that the teaching of 

 geometry from Euclid's book in the schools — and especially in the 

 preparatory schools — is a positive hindrance to the teaching of 

 science will be regarded as paradoxical, if not, indeed, erroneous. 

 Vet I do make the assertion ; and I base my confidence in its 

 truth mainly on the experience which I have gained as an 

 examiner of boys who have finished their school education. 



Geometry is about the oldest of the sciences, and Euclid's 

 venerable work bears all the characteristics of a book compiled 

 at a remote time when such science as existed was a kind of 

 mysterious possession in the hands of a few experts to whom 

 intricate technicality cf language was (as Swift would say) a 

 principle of great emolument. The inventor of a new science 

 is only too prone to build it up with an elabor.ate and technical 

 system of definition and nomenclature, hoping thereby to 

 emphasise its importance and to cultivate a wholesome awe in 

 the uninitiated. In this way is established a particular kind of 

 jargon which becomes distinctive of the science, and of its 

 professional exponents. 



The growth of such a system is well exemplified in other 

 domains than that of science. For example, there is not, I 

 think, any game in vogue in England which possesses such an 

 elaborate technical jargon as tliat of golf, and the rule which is 

 always observed in such matters is here strictly recognised — 

 viz. the less the intrinsic merit of the subject, the more elaborate 

 the accompanying jargon. 



We are all very familiar with the Euclid jargon. Some of us, 

 indeed, have somehow come to believe that no proof of a 

 proposition can possibly be valid unless it is presented in this 

 orthodox form. 



A modern Euclid for the use of schools is sometimes a model of 

 soul-destroying systematisation. I have before me such a work in 

 which the process of arriving al the conclusion that two angles 

 of a triangle are equal if the sides opposite to them are equal, 

 reminds me of the process of walking across a lawn over the 

 surface of which have been stretched innumerable threads in 

 various directions for the purpose of tripping up the unwary. 



The number of heads under which a well-taught modern boy 

 will arrange the most simple proposition is wonderful : " general 

 enunciation," "particular enunciation," " hypothesis," " con- 

 struction," " demonstration," " conclusion " must all figure, or 

 else the proof is "no good." Only a boy who has been care- 

 less says, "if two triangles have three sides of the one equal to 

 three sides of the other, the triangles are equal in all respects " 

 — a very simple truth which I received once in the following 

 form from a boy who was much more careful of the orthodox 

 jargon : "if two triangles have two sides of the one respectively 

 equal to two sides of the other, each to each, and likewise also 



NO. 1529, VOL. 59] 



their bases, or third sides, equal, then shall the three angles of 

 the one triangle be equal to the three angles of the other triangle, 

 and the triangles shall be equal in every respect." 



Observe that in the Euclid jargon nothing ever simply "is" 

 — it always " shall be." 



In finding fault with Euclid as a book for beginners I have, 

 of course, no right to charge it with the enormous number of 

 definitions, and the dissertations on the various kinds of pro- 

 positions ("positive," " contra-positive," &c.) which some of 

 the school-books set right in front of the beginner before the first 

 proposition of the first Book is reached. 



.Still, it is by no means the paragon of logical clearness that 

 it is commonly alleged to be. Take, for instance, its very first 

 definition : "a point is that which has no parts." This is an 

 excellent definition of absolute nonentity, but not of anything 

 that can be pictured in the mind. Some editors of Euclid, 

 feeling that there is something wanting in this definition, have 

 (they think) vastly improved it by saying that "a point is that 

 which has position but no magnitude " — as if position is more 

 easily grasped than /«'«/. Then again (still at the threshold of 

 the subject) the beginner is taught to believe that he is getting a 

 very definite conception of a right line in the definition, "a 

 right line is that which lies evenly between its extreme points " 

 — as if the meaning of " evenly" is at once beyond question. 



But of all the elementary conceptions in Euclid that of an 

 angle is the one which most puzzles a beginner, and remains un- 

 realised for the longest time. "An angle is the inclination 

 of two straight lines to one another." Here again we have 

 one obscure term defined by another equally obscure ; and we 

 know by experience that, unless the conception is presented in 

 a very different way, the ob.scurity will be permanent. 



Moreover, it is possible to point out a self-contradiction in 

 Euclid. Thus his definition of a circle makes it to be a disc — 

 "a circle is a plain figure hounded by one line called the cir- 

 cumference"— so that, clearly, the whole of the space inside (or, 

 possibly, outside) the circumference is the circle, whose mere 

 boundary is the circumference ; and, if so, two circles can, of 

 course, intersect in an infinite number of points — over an ex- 

 tensive area, in fact ; but this is contradicted by Euclid in the 

 tenth proposition of Book HI., according to which one circle 

 cannot intersect another in more than two points. 



These, it may be admitted, are comparatively minor con- 

 siderations, and the defects might be corrected by judicious 

 teaching. 



It is chiefly in the way in which the fifth and sixth Books of 

 Euclid are apprehended by boys that the necessity for a change 

 in the system of teaching is to be seen. 



Those mediieval technicalities "duplicate ratio," "sub- 

 duplicate ratio," " sesquiplicate ratio," and some others are 

 drummed into the heads of boys as if they were terms of the 

 utmost scientific importance. What mathematician ever uses 

 such terms, or even thinks of them in his investigations? 



The simple and extremely important fact that the areas of 

 two similar figures are to each other as the squares of cor- 

 responding linear dimensions is presented to the beginner in the 

 nineteenth proposition of the sixth Book in the words "similar 

 triangles are to one another in the duplicate ratio of their 

 homologous sides " — a statement which is singularly deficient 

 in accuracy inasmuch as it omits to say precisely what two 

 qualities or quantities connected with the triangles are thus 

 related (colours, shapes, sizes, or what ?) ; and the result is 

 absolute confusion in the minds of a very large number of boys. 



Let me illustrate this by a few bona fide examples. In reply 

 to the question, "What are similar triangles, and what is the 

 relation between their areas ? " the following answers were 

 received : — 



(1) A triangle is similar to another triangle when their sides 

 are proportional, and when the homologous sides of one are in 

 duplicate ratio to the homologous sides of the other. 



(2) If two triangles have the sides about an angle in each 

 proportional and the other angles of the same affection, the 

 triangles are similar. Similar triangles are proportional to the 

 bases on which they stand, and are to one another in the dupli- 

 cate ratio of their homologous sides. 



(3) Similar triangles are those which are equal in area to each 

 other and are in the same proportion to each other as the 

 duplicate ratio of their homologous sides. 



(4) When the angles are sim.ilar the areas are similar, wher> 

 the areas are similar the angles are similar, when the sides are 

 similar the areas are similar. 



