BOOK II. § 4. Geometry and Kinematic. space" is conceived as figurable, in being conceived as comparable to "relative space." Now the lowest or most abstract degree of figuration, applicable to space in its entirety, is that given by the three Cartesian rectangular axes of co-ordinates, cutting each other at a single point, which have been already mentioned in Book I;-a figuration which is by no means adverse to the infinity of space, any more than the position of any present moment of time, between the two infinites of past and future, is adverse to the infinity or eternity of time. same case. We see, then, that concrete matter is not the only thing which at once is common ground to philosophy and science, and receives a different analysis from each. Time and Space, which are what I have called the formal element in the perception of objects, including matter, are in the All three are numerically identical, but analytically different, in science and in philosophy. It is this fact of difference in identity of their object-matter which enables science and philosophy to exist in harmony, and mutually support and supplement each other. And this fact it is the business of philosophy to establish, simply because it occupies the more central and commanding position of the two, and the only position from which both procedures can be discriminated and compared, as was set forth more fully in an earlier Chapter. At the same time it is only with the comparatively few fundamental conceptions of science that philosophy has to do. These it is bound, if possible, to bring into harmony with metaphysical analysis, thereby establishing the true relations BOOK II. CH. I. and Kinematic. which obtain between the two pursuits, and showing what use they may legitimately make of each other's results. The establishment of the Geometry difference in identity of their common basis implies that each must go its own way in building on that basis, according to the different analysis given of it by each. It is not for philosophy to re-write Euclid, construct vortex-atoms, weigh the ether, or trace the forces which pervade it, define Life, analyse neural energy, or discriminate from it the activity of an immaterial agent. The conceptions, problems, methods, and results of the two pursuits are all different, notwithstanding that the self-same experience is the object-matter and the source of both. I need hardly say, what will be obvious enough to scientific readers, that I have no pretension to write as an expert in any mathematical or physical science. My purpose in writing is merely to show how their fundamental conceptions harmonise with those of philosophy, originating, as they do, in the same experience differently treated. When science objectifies material existents separate one from another in space and in time, it is evident that this carries with it the necessity of separately objectifying time and space also, as the media in which the material existents have their being and operation. And this separate objectification of what are originally and essentially inseparable formal elements of perceptions involves a duplication of them in thought, which may be the source of much perplexity. For perceptions do not cease to have duration when we objectify duration as a medium in which perceptions exist and change; nor do visual and tactual perceptions BOOK II. § 4. cease to be extended, when we objectify space as the medium in which visible and tangible Geometry objects exist and move. Thus we have to be Kinematic. careful not to confuse the duration, or the space, and occupied by perceptions, or by material objects, with the duration, or the space, in or through which, as media, they are said to change or to move. For instance, when a body moves, it seems to carry with it that portion of space which it occupies, and yet at the same time to leave behind it an equal portion of now empty space; that is, the same portion of space seems both to move onwards and to remain stationary. This appearance, and the confusion of thought which it is liable to cause, are due to the separate objectification of space as a medium. But no confusion need be caused if we remember, (1) that time and space are not really duplicated by our separately objectifying them, and (2) that, when they are so objectified, they are eo ipso considered as wholly independent of the occupation or non-occupation of any of their parts by perception or by objects, and offer no resistance or hindrance whatever to any changes of content which take place within them. Thus the space occupied by a moving body just spoken of is successively and numerically identified, as the body moves, with different portions of space taken separately as a medium; or in other words, different portions of space as an independent medium become successively the portion occupied by the body as it moves. Thus pure or abstract time and space, objectified as separate existents or media, are images partly due to conceptual thought, additional modes whereby we represent more completely the one really existent durational and spatial panorama. BOOK II. § 4. Geometry and But since time and space really exist in the Kinematic. material things, as well as between and around them, and since moreover the divisions, which differences in content introduce into time and space, are a means whereby ideal divisions can be introduced into them by thought, such as mathematical instants of time, mathematical points, lines, surfaces, and angles in space, it follows that these ideal divisions may be made a means of measuring material things and their operations, as well as of measuring ideally time and space themselves as objective media. Exact measurement is the first and indispensable step towards the ascertainment of physical processes of every kind. From which again it follows, that pure geometry forms a sort of statical Logic of physics; and, founded upon geometry together with the notion of time-duration, Kinematic, the science of physical motion, abstracting from the question, what kinds of physical force are employed in producing motions, forms as it were the vestibule, first to Dynamic, and then to the still larger and more complex science of Energetic, which covers (in conception at least) all the forces of Nature, when these are apprehended as in actual concrete operation, or as Energies of several kinds. The fact of motion in the world of space and matter, though we may abstract from its connection with force, cannot be separated in thought from the facts of time and space, so soon as we draw Newton's distinctions above mentioned, between BOOK II. § 4. absolute and relative time, and between absolute and relative space. Four things are mentioned in Geometry that Scholium to the Definitions of the First Book Kinematic. of the Principia already cited, to which the same and distinction applies. The other two are absolute and relative Place, and absolute and relative Motion. And the definitions of the two kinds of place, and the two kinds of motion, are closely dependent upon those of the two kinds of space. Place," says Newton, "is a part of space." The place of a body is the part of space which it occupies. And this is absolute if taken in absolute space, relative if in relative; "pro ratione spatii, vel absolutus vel relativus." Upon this depend the definitions of the two kinds of motion. "Absolute motion is translation of a body from one absolute place to another; relative motion its translation from one relative place to another." Thus we see that figured space, motion, and direction, rate, and duration of motion, are conceptions which hang closely together, mutually involved, and as a whole may very well be treated in abstraction both from the kinds of Matter and from the kinds of Force, in which they occur, or upon which they depend. So treated they form an introduction to Dynamic, and have received the name of Kinematic. "We adopt," say the authors of a well known Treatise on Natural Philosophy, in their Preface, "the suggestion of AMPÈRE, and use the term Kinematics for the purely geometrical science of motion in the abstract." They devote to it in fact the first Chapter, occupying 200 pages, of their great work. The same course is followed 2 Treatise on Natural Philosophy, by Sir William Thomson (Lord Kelvin), F.R.S., and Peter Guthrie Tait. 2 vols. Cambridge. New Edition, 1879. |