ON THE PSYCHOLOGY AND NATURAL DEVELOPMENT OF GEOMETRY.
For the animal organism, the relations of the different parts of its own body to one another, and of physical objects to these different parts, are primarily of the greatest importance. Upon these relations is based its system of physiological sensations of space. More complicated conditions of life, in which the simple and direct satisfaction of needs is impossible, result in an augmentation of intelligence. The physical, and particularly the spatial, behavior of bodies toward one another may then acquire a mediate and indirect interest far transcending our interest in our momentary sensations. In this way, a spatial image of the world is created, at first instinctively, then in the practical arts, and finally scientifically, in the form of geometry. The mutual relations of bodies are geometrical in so far as they are determined by sensations of space, or find their expression in such sensations. Just as without sensations of heat there would have been no theory of heat, so also without sensations of space there would be no geometry; but both the theory of heat and the theory of geometry stand additionally in need of experiences concerning bodies; that is to say, both must pursue their inquiries beyond the
38ely disappear in the former. Sosikles of Corinth (Herodotus v. 92) asseverated that "sooner should the heavens be beneath the earth and the earth soar in the air above the heavens, than that the Spartans should lose their freedom." And his assertion, together with the tirades of Lactantiuso remark that physiologicalrans. Page 59.7.