Fig. 12.—Probability curve with increased number of steps.
And with an infinite number, the steps would disappear altogether, leaving a perfectly smooth, flowing line, unmarred by a single step or break. It would be an absolutely continuous distribution.
If then, the results of all the tests that have been made on all mental traits be studied, it will be found that human mental ability as shown in at least 95% of all the traits that have been measured, is distributed throughout the race in various degrees, in accordance with the law of chance, and that if one could measure all the members of the species and plot a curve for these measurements, in any trait, he would get this smooth, continuous curve. In other words, human beings are not sharply divided into classes, but the differences between them shade off into each other, although between the best and the worst, in any respect, there is a great gulf.
If this statement applies to simple traits, such as memory for numbers, it must also apply to combinations of simple traits in complex mental processes. For practical purposes, we are therefore justified in saying that in respect of any mental quality,—ability, industry, efficiency, persistence, attentiveness, neatness, honesty, anything you like,—in any large group of people, such as the white inhabitants of the United States, some individuals will be found who show the character in question in a very low degree, some who show it in a very high degree; and there will be found every possible degree in between.
NORMAL VARIABILITY CURVE FOLLOWING LAW OF CHANCE
Fig. 13.—The above photograph (from A. F. Blakeslee), shows beans rolling down an inclined plane and accumulating in compartments at the base which are closed in front by glass. The exposure was long enough to cause the moving beans to appear as caterpillar-like objects hopping along the board. Assuming that the irregularity of shape of the beans is such that each may make jumps toward the right or toward the left, in rolling down the board, the laws of chance lead to the expectation that in very few cases will these jumps all be in the same direction, as is demonstrated by the few beans collected in the compartments at the extreme right and left. Rather the beans will tend to jump in both right and left directions, the most probable condition being that in which the beans make an equal number of jumps to the right and left, as is shown by the large number accumulated in the central compartment. If the board be tilted to one side, the curve of beans would be altered by this one-sided influence. In like fashion a series of factors—either of environment or of heredity—if acting equally in both favorable and unfavorable directions, will cause a group of men to form a similar variability curve, when classified according to their relative height.
The consequences of this for race progress are significant. Is it desired to eliminate feeble-mindedness? Then it must be borne in mind that there is no sharp distinction between feeble-mindedness and the normal mind. One can not divide sheep from goats, saying "A is feeble-minded. B is normal. C is feeble-minded. D is normal," and so on. If one took a scale of a hundred numbers, letting 1 stand for an idiot and 100 for a genius, one would find individuals corresponding to every single number on the scale. The only course possible would be a somewhat arbitrary one; say to consider every individual corresponding to a grade under seven as feeble-minded. It would have to be recognized that those graded eight were not much better than those graded seven, but the drawing of the line at seven would be justified on the ground that it had to be drawn somewhere, and seven seemed to be the most satisfactory point.
In practice of course, students of retardation test children by standardized scales. Testing a hundred 10-year-old children, the examiner might find a number who were able to do only those tests which are passed by a normal six-year-old child. He might properly decide to put all who thus showed four years of retardation, in the class of feeble-minded; and he might justifiably decide that those who tested seven years (i.e., three years mental retardation) or less would, for the present, be given the benefit of the doubt, and classed among the possibly normal. Such a procedure, in dealing with intelligence, is necessary and justifiable, but its adoption must not blind students, as it often does, to the fact that the distinction made is an arbitrary one, and that there is no more a hard and fast line of demarcation between imbeciles and normals than there is between "rich men" and "poor men."