+51. Class; race; group solidarity.+ If the group which is classified is a large one, and especially if it is a genetic unit (race, tribe, or nation), there are no gaps in the series. Each individual falls into his place by virtue of his characteristic differences. Just as no two are anthropologically alike, so we may believe that no two are alike or equal in societal value. That all men should be alike or equal, by any standard whatever, is contrary to all the facts of human nature and all the conditions of human life. Any group falls into subdivisions, the members of each of which are approximately equal, when measured by any standard, because the classification is imperfect. If we make it more refined, the subdivisions must be subdivided again. We are in a dilemma: we cannot describe mankind at all without categories, and if we go on to make our categories more and more exact, each one of them would at last contain only one person. Two things result which are practically important, and which furnish us with scientific concepts which we can employ in further study: (1) The classification gives us the notion of the relative position of one, or a subdivision, in the entire group. This is the sense of "class."[70] (2) The characteristic differences furnish the notion of individuality and personality. The concept of a race, as the term is now used, is that of a group clustered around a mean with respect to some characteristic, and great confusion in the use of the word "race" arises from the attempt to define races by their boundaries, when we really think of them by the mean or mode, e.g. as to skin color. The coherence, unity, and solidarity of a genetic group is a very striking fact. It seems to conceal a play of mystic forces. It is, in fact, no more mysterious than the run of dice. The propositions about it would all become, in the last analysis, identical propositions; e.g. it is most probable that we shall meet with the thing which is present in the greatest number; or, it is most probable that the most probable thing will happen. In the middle of the nineteenth century, when attention was first called to the solidarity and internal correlations of groups, especially if they were large and genetic, it was believed that occult and far-reaching laws had been discovered. That opinion has long been abandoned. If there are four dice in a box, each having from one to six dots on its faces, the chance of throwing four sixes is just the same as that of throwing four ones. The mean of the sums of the dots which may fall uppermost is fourteen, which can be produced by one hundred and forty-six throws. Suppose that the components of social value are four,--intellectual, moral, physical, economic,--represented by the four dice, and that the degrees are represented by the dots. We should get four sixes once in twelve hundred and ninety-six throws. Of the one hundred and forty-six throws which give the mean fourteen, seventy-two show one six up.