Unfortunately this was not easy, for the advance from pure mathematics to physics, from a study of the nature of pure mathematical conceptions to an inquiry into the laws of falling bodies, implied a change whose nature was not clear to the men who had themselves made the advance. A conflict arose between those who thought more of the fact that knowledge, to be certain, must be capable of mathematical expression, and those who thought more of the basis of experiment and observation on which the new sciences depended, who remembered that these sciences began when Galileo, instead of thinking in the abstract how bodies ought to fall, dropped bodies of different weights from the top of the leaning tower of Pisa and observed what actually happened. Descartes was the great representative of the first school. He began by insisting on the difference between mathematical truth which could be, as he said, clearly and distinctly conceived, and ordinary opinion about things which was full of guesswork and imagination. Scientific knowledge was possible, he thought, only by apprehending the real or primary qualities of things which were mathematical, in contradistinction to their secondary qualities--their colour, smell, &c.--which were less real. Thence he came to think that the real world was mathematical in nature, like a huge, intricate geometrical figure. The elements of mere fact, in our present knowledge, its dependence on observation and experiment, he thought of as temporary defects which the progress of science would remove. What we ordinarily call perception, indeed, in the sense of awareness of things in time and space, was described by Descartes’ successors as confused thinking. Our knowledge of the world would, it was hoped, become a vast mathematical system, all the detail and complexity of which would be rigorously deducible from a few central truths.