412 Life and Letters of Francis Galton
widely separated from each other. I cannot describe better my sense of the importance 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 normal distribution in a general sort of way indicates that the differences between modal or what the biologists term 'normal' individuals are very small. But Mr Galton's Difference Problem enables us for the first time to appreciate quantitatively how much wider the differences are between the extreme (biologists' 'abnormal' or atypical individuals) and modal ('normal' or typical) individuals. Now the range of a distribution being somewhat about six times the standard deviation, we see that extreme individuals, even in a population of only 100, may be separated by as much as 1-,.th of the range, while modal individuals have only a difference of 2}th of the range and even individuals at the quartile only a difference of 2- th of the range. The relative differences become much greater in populations of several 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 emphasised as we pass 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 stages. We know this by experience-our Shakespeares, our Newtons, our Napoleons have no close compeers in the populations of their own generationsbut 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 resulta of competitive examinations, 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 individuality of extreme criminality, and the appalling differences in stupidity and imbecility at the lower end of the moral and intellectual scales, receive their, due statistical appreciation.
We stand in a better position to discriminate the pathological from the merely exceptional; mere isolation no longer leads us a 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 characters, 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 neighbours,-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 suggestiveness. Just as the continuous representation by a frequency curve is only an ideal representation of the observed facts, so we now reach an ideal representation of the actual discontinuity in the given population. As in the case of many physical investigations, so we find in statistical theory both continuous and discontinuous representations of the phenomena equally important and equally valid within the legitimate limits of interpretation."
Did Galton immediately recognise all that flowed from his treatment of the proper proportions of first and second prizes? Possibly not; he took some years to realise all that must eventually flow from his conception of correlation. But is not this failure to grasp immediately all that results from a new standpoint the essential peculiarity of the creative mind, whether it be that of a great scientist or of a great poet? Galton has 'himself so well described the workings of the exceptional mind that I need not labour this point$. The mine discovered by Galton more than twenty years ago is far
' Biometrika, Vol. i, p. 398.
2 See the first footnote on p. 236 of this volume. The inspiration is the product of the subconscious mind. The man who has reached a truth knows it to be true, wrote Spinoza truly