With increase of population, the problem of the State becomes more and more pressing. There are many theories about the state. For the purpose of the moment it is important to realize that a state is the governing center of an accumulation of human beings—of time-binding powers—increasing exponential functions of time. These powers, though the same in kind, differ in degree and in respect of individuality. If they are to be united so as to constitute a whole, they must be given a common aim; they must, so to speak, be reduced to a common base; if they be respectively _X__m_, _Y__n_, _Z__p_, and so on, we can not unite them and compute the whole by adding the exponents; but if we give them a common base—a common aim or purpose—then we can readily represent the magnitudes of the whole constituted by them; if we take _X_ to be their common aim or base, then, if _Y_ = _aX_, _Z_ = _bX_, and so on, we shall have:
_X__m_ × _Y__n_ × _Z__p_ ... = _X__m_ × _a__n_ × _X__n_ × _b__p_ × _X__p_ ... = (_a__n_ × _b__p_ ...)_X__m+n+p_ ...
The last expression, where the parenthetical coefficient is the product of individualities, serves to represent the united powers of all in terms of _X_, the common base, purpose or aim.
Let us look at the matter in another way. One mechanical “horse-power” is less than the power of one living horse. One living horse can do more work than one mechanical horse-power, but in using more than one living horse at one time we get less work than by using the same number of mechanical horse-powers; the reason is very obvious. The mechanical horse-powers are the same in kind, equal, and constant, but living horses differ in character, they are not equal, and each one is a variable. Hence mechanical horse-powers can be added or multiplied arithmetically, but the powers of living horses can not, except very roughly; the living horses of a team interfere with each other; they do not pull together, as we say, and energy is lost.
The German mathematical philosophy or theory of the state did not express itself in just this way, but the foregoing gives a clue to it. Germany united the powers of living men and women and children; it gave them a common base; it gave them one common “social” mood and aim; they all became consolidated in service of that which is called the State; they studied and taught for the State; they worked, lived and died for the State: the State was their idol, King and God.