The discovery of the laws which govern the interaction of the psychical elements is the task of a statics and a mechanics of representations.  The former investigates the equilibrium or the settled final state; the latter, the change, i.e. the movements of representations.  These names of themselves betray Herbart’s conviction that mathematics can and must be applied to psychology.  The bright hopes, however, which Herbart formed for the attempt at a mathematical psychology, were fulfilled neither in his own endeavors nor in those of his pupils, although, as Lotze remarks, it would be asserting too much to say that the most general formulas which he set up contradict experience.—­The unity of the soul forces representations to act on one another.  Disparate representations, those, that is, which belong to different representative series, as the visual image of a rose and the auditory image of the word rose, or as the sensations yellow, hard, round, ringing, connected in the concept gold piece, enter into complications [complexes].  Homogeneous representations (the memory image and the perceptual image of a black poodle) fuse into a single representation.  Opposed representations (red and blue) arrest one another when they are in consciousness together.  The connection and graded fusion of representations is the basis of their retention and reproduction, as well as of the formation of continuous series of representations.  The reproduction is in part immediate, a free rising of the representation by its own power as soon as the hindrances give way; in part mediate, a coming up through the help of others.  On the arrest of partially or totally opposed representations Herbart bases his psychological calculus.  Let there be given simultaneously in consciousness three opposed representations of different intensities, the strongest to be called a, the weakest c, the intermediate one b.  What happens?  They arrest one another, i.e. a part of each is forced to sink below the threshold of consciousness.[1]

What is the amount of the arrest?  As much as all the weaker representations together come to—­the sum of arrest or the sum of that which becomes unconscious (as it were the burden to be divided) is equal to the sum of all the representations with the exception of the strongest (hence = b + c), and is divided among the individual representations in the inverse ratio of their strength, consequently in such a way that the strongest (the one which most actively and successfully resists arrest) has the least, and the weakest the most, of it to bear.  It may thus come to pass that a representation is entirely driven out of consciousness by two stronger ones, while it is impossible for this to happen to it from a single one, no matter how superior it be.  The simplest case of all is when two equally strong representations are present, in which case each is reduced to the half of its original intensity.  The sum of that which remains in consciousness is always equal to the greatest representation.