Mathematics and Mechanics

Within a certain kind of environment, an activity may be checked so that the only meaning which accrues is of its direct and tangible isolated outcome. One may cook, or hammer, or walk, and the resulting consequences may not take the mind any farther than the consequences of cooking, hammering, and walking in the literal — or physical — sense. But nevertheless the consequences of the act remain far-reaching. To walk involves a displacement and reaction of the resisting earth, whose thrill is felt wherever there is matter. It involves the structure of the limbs and the nervous system; the principles of mechanics. To cook is to utilize heat and moisture to change the chemical relations of food materials; it has a bearing upon the assimilation of food and the growth of the body. The utmost that the most learned men of science know in physics, chemistry, physiology is not enough to make all these consequences and connections perceptible. The task of education, once more, is to see to it that such activities are performed in such ways and under such conditions as render these conditions as perceptible as possible.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.

A marveilous newtrality have these things mathematicall and also a strange participation between things supernaturall, imortall, intellectuall, simple and indivisible, and things naturall, mortall, sensible, compounded and divisible.