412 Life and Letters of Francis Galton 



widely separated from each other. I cannot describe better toy sense of the 

 imjxirtiince of Galton's Difference Problem than by citing, with but slight 

 additions, the words I used about it more than twenty years ago': 



"Now, of course, the noruial distribution in a general sort of way indicates that the 

 di f fb r encee between modal or what thu hiologiHts term 'normal' indiviiiualsare very small. But 

 Mr Oalton'a Difference Problem enables us for the first time to appreciate quantitatively how 

 much wider the differences are between the extreme (biologists' 'abnormal' or atypical indi- 

 viduals) and modal ('normal' or typical) individuals. Now the range of a distribution being 

 ■omewhat about six timas the standard deviation, we see that extreme individuals, even in a 

 population of only 100, may be separated by as much as ,'.th of the range, while modal indi- 

 viduals have only a difference of ^li^th of the range and even individuals at the (juurtile only 

 » difference of jgoth of the range. The relative differences become much greater in populations 

 of aeventl millions. 



It is not possible to pass over the general bearing of such results on human relations. If 

 we define 'individuality' as difference in character between a man and his immediate compeers, 

 we see how immensely individuality is empha.sised as we pasii from the average or modal 

 individuals to the exceptional men. Differences in ability, in power to create, to discover, to 

 rule men do not go by uniform stagea We know this by experience — our Shakespeares, our 

 Newtons, our Napoleons have no close compeers in the populations of their own generations — 

 but we see a reason for the gulf which separates the genius from ourselves, the phenomenon 

 flows from a characteristic and familiar chance distribution. We ought not to be surprised, as 

 we frequently are, at the results of competitive examination.s, where the difference in marks 

 between the first men is so much greater than occurs between men towards the middle of the 

 list. In the same way the marked iiidividuality of extreme criminality, and the appalling 

 diffsrenoes in stupidity and iraliecility at the lower end of the moral and intellectual scales, 

 receive their due statistical ap])reciation. 



We stand in a better position to discriminate the pathological from the merely exceptional; 

 mere isolation no longer leads us & priori to question the position of an outlying observation or 

 of an exceptional individual. 



In short Galton 's Difference Problem leads us to look upon samples of populations, and even 

 on populations themselves, no longer as arrays of individuals with continuously varying charac- 

 ters, but as systems of discrete units. We see discontinuity in every sample and in every 

 population. We obtain a new and most valuable conception of a normal or standard population. 

 It is one in which each individual is separated from his immediate neighlwurs, — when the whole 

 is arranged according to any character, — by definite calculable intervals. These intervals are, 

 of course, the average intervals which would be found by taking the mean of many such samples 

 or populations, but they are none the less of extreme suggestivene.ss. Just as the eontinuout 

 representation by a frecjuency curve is only an ideal representation of the observed facts, so we 

 now reach an ideal representation of the actual discontinuity in the given ]>opulation. As in the 

 case of many physical investigations, so we find in statistical theory lx)th continuous and dis- 

 continuous representiitions of the phenomena equally important and e<)UHlly valid within the 

 legitimate limits of interpretation." 



Did Galton immediately recognise all that flowed from his treatment of 

 the projKjr proportions of first and second prizes? Poasibly not; ho took 

 some yeai-8 Uj realLse all that must eventually flow from his conce|)tion of 

 correlation. But is not this failure to grasp immediately all that results from 

 a new stand])oint the essential peculiarity of the creative mind, whether it 

 |je that of a great scientist or of a great poet ? Galton has himself so well 

 descriljed the workings of the exceptional mind that I need not labour this 

 jK)int'. The mine discovered by Galton more than twenty years ago is far 



' Biometrika, Vol. I, p. 398. 



* Bee the first footnote on p. 236 of this volume. The inspiration is the product of the 

 sulxx>nacious mind. The man who has reached a truth knows it to be true, wrote Spinoza truly 



