This same proposition may be put on a broader basis.[37] "In so far as the differences in achievement found amongst a group of men are due to the differences in the quantity and quality of training which they had had in the function in question, the provision of equal amounts of the same sort of training for all individuals in the group should act to reduce the differences." "If the addition of equal amounts of practice does not reduce the differences found amongst men, those differences can not well be explained to any large extent by supposing them to have been due to corresponding differences in amount of previous practice. If, that is, inequalities in achievement are not reduced by equalizing practice, they can not well have been caused by inequalities in previous practice. If differences in opportunity cause the differences men display, making opportunity more nearly equal for all, by adding equal amounts to it in each case should make the differences less. "The facts found are rather startling. Equalizing practice seems to increase differences. The superior man seems to have got his present superiority by his own nature rather than by superior advantages of the past, since, during a period of equal advantage for all, he increases his lead." This point has been tested by such simple devices as mental multiplication, addition, marking A's on a printed sheet of capitals and the like; all the contestants made some gain in efficiency, but those who were superior at the start were proportionately farther ahead than ever at the end. This is what the geneticist would expect, but fits very ill with some popular pseudo-science which denies that any child is mentally limited by nature. 6. _Direct measurement of the amount of resemblance of mental traits in brothers and sisters._ It is manifestly impossible to assume that early training, or parental behavior, or anything of the sort, can have influenced very markedly the child's eye color, or the length of his forearm, or the ratio of the breadth of his head to its length. A measure of the amount of resemblance between two brothers in such traits may very confidently be said to represent the influence of heredity; one can feel no doubt that the child inherits his eye-color and other physical traits of that kind from his parents. It will be recalled that the resemblance, measured on a scale from 0 to 1, has been found to be about 0.5. Karl Pearson measured the resemblance between brothers and sisters in mental traits--for example, temper, conscientiousness, introspection, vivacity--and found it on the average to have the same intensity--that is, about 0.5. Starch gets similar results in studying school grades. Professor Pearson writes:[38]