Differentiation

Abstract

Science begins with observation. At first the observations may be only crude and tentative: more of one thing seems always to be accompanied by more of another (direct variation), or, perhaps, by less of the other (inverse variation). Once a science has established ways of measuring its central attributes (measuring temperature was a major achievement of early physical science) the primary observations become expressible as formulas, relating quantities. That is, attributes become quantities via measurement, and the science, or part of it, emerges from the qualitative stage to a quantitative stage, amenable to mathematical descriptions. The fundamental laws of the science are expressed by formulas.