354 VI. ON PSYCHOPHYSIOLOGY
one, but we could not subtract three from two. Yet the structure of this world is such that a further development in the structure of the language was imperative. Thus, if an object moves in a given direction with the velocity two feet per second, and some external factor imparts to it a velocity of three feet per second in the opposite direction, the original direction of motion will be reversed, and the object will move with the velocity of one foot per second in the opposite direction. Or, to give another example, some one has two units of money and he buys something which costs three units of money. He is then in debt one unit.
Such facts necessitated the introduction of negative numbers and so made subtraction always possible. If the motion in one direction or the amount of money in our pocket was called 'plus two' units, and we subtract from it three units, the results were 'minus one', meaning a conventional reversal of direction, or sense, for motion, or a debt. instead of a possession, for money.
Experimental facts of division again necessitated the expansion of this language. Thus, fractions were introduced so as always to allow of linguistic division. The 'imaginary' number, was intro-
duced to allow, in all cases, the extraction of roots,. For a long 'time', the number was considered almost mystical, but, of late, when
a physicist or an engineer finds it in his equations, it is almost an unmistakable indication for him to look for some wave-motion in the world. More extended observation of the empirical world and structure required further structural adjustment of our languages.
In the vector calculus we have the so-called scalar product which obeys the ordinary laws of multiplication and a.b = b.a where the order of the factors is of no importance! The vector product does not follow these rules, as the order becomes important; thus, in a vector product, a.b = b.a. In the newer quantum mechanics, to account structurally for the experiments, still newer numbers were introduced. Instead of the old arithmeticalwe introduce new numbers
It is very significant that a similar linguistic evolution appears justifiable in the case of the function of the nervous system in general and in the structure and function of the conditional reactions in particular. As experience and theory show, the fundamental structures and functions we find in life are not 'plus' affairs, but represent some higher-degree functions of a non-additive character. The typical functioning of the human nervous system (time-binding) is represented by an exponential function of 'time'.13 Now we see that the reversal of the sign