If, therefore, there is any truth in the belief of the old Greek philosophers and of some modern historians that the study of mathematics has its origin in the observed movements of the stars, the progress is of the same nature as that which we noticed at the end of the last chapter. Is it too fanciful to picture to ourselves how, drawn into the minds of a few men, the relative positions and movements of the stars gradually developed a more and more independent life there until, with the rise in Europe first of trigonometry and then of algebra, they detached themselves from the outside world altogether? And then by a few great men like Copernicus, Kepler, Galileo, Newton, these abstract mathematics were re-fitted to the stars which had given them birth, and the result was that cosmogony of infinite spaces and a tiny earth in which our imaginations roam to-day? When the Aryan imagination had at last succeeded in so detaching its “ideas” about the phenomena of the universe that these could be “played with,” as mathematicians say, in the form of an equation, then, no doubt, it was a fairly easy matter to turn them inside out. The alterations wrought in the meanings of many of our common words by this revolution of physical outlook are not difficult to perceive and yet not easy to realize. As the discoveries of Kepler and Galileo slowly filtered through to the popular consciousness, first of all simple words like _atmosphere_, _down_, _earth_, _planet_, _sky_, _space_, _sphere_, _star_, _up_, ... underwent a profound yet subtle semantic change. And then, in the eighteenth century, as Newton’s discoveries became more widely known, further alterations took place. _Weight_,[39] for instance, acquired a new significance, differing from _mass_, which also changed, having formerly meant simply a lump of matter.[40] _Gravity_,[41] (from the Latin ‘gravitas’ ‘heaviness’) took on its great new meaning, and the new words _gravitation_ and _gravitate_ were formed, the later being soon adapted to metaphorical uses. If we cared to examine them closely enough, we should probably find that from this point a certain change of meaning gradually spread over all words containing the notion of attraction, or ideas closely related to it. The twin phenomena of gravitation and magnetism, contemplated by most of us at an early age, and impalpably present in the meanings of so many of the words we hear spoken around us, make the conception of one lifeless body acting on another from a distance easy and familiar.[42] But the very word _attraction_ (from the Latin ‘ad-trahere’, ‘to draw’ or ‘drag towards’) may well serve to remind us that until the discovery of gravitation this conception must have been practically beyond the range of human intellection. There was formerly no half-way house in the imagination between actual dragging or pushing and forces emanating from a living being, such as love or hate, human or divine, or those “influences”