hand to the stone, or from the stone to the hand; and, according to modern science, heat is nothing but the agitation of the molecules of a body. Finally, the organ begins playing, and again sound is nothing but the result of motions of the air striking on the drum of the ear.
Thus the endeavour to give a dynamical explanation of phenomena is the attempt to explain them by statements of the general form, that such and such a substance or body was in this place and is now in that place. Thus we arrive at the great basal idea of modern science, that all our sensations are the result of comparisons of the changed configurations of things in space at various times. It follows therefore, that the laws of motion, that is, the laws of the changes of configurations of things, are the ultimate laws of physical science.
In the application of mathematics to the investigation of natural philosophy, science does systematically what ordinary thought does casually. When we talk of a chair, we usually mean something which we have been seeing or feeling in some way; though most of our language will presuppose that there is something which exists independently of our sight or feeling. Now in mathematical physics the opposite course is taken. The chair is conceived without any reference to
anyone in particular, or to any special modes of perception. The result is that the chair becomes in thought a set of molecules in space, or a group of electrons, a portion of the ether in motion, or however the current scientific ideas describe it. But the point is that science reduces the chair to things moving in space and influencing each other's motions. Then the various elements or factors which enter into a set of circumstances, as thus conceived, are merely the things, like lengths of lines, sizes of angles, areas, and volumes, by which the positions of bodies in space can be settled. Of course, in addition to these geometrical elements the fact of motion and change necessitates the introduction of the rates of changes of such elements, that is to say, velocities, angular velocities, accelerations, and suchlike things. Accordingly, mathematical physics deals with correlations between variable numbers which are supposed to represent the correlations which exist in nature between the measures of these geometrical elements and of their rates of change. But always the mathematical laws deal with variables, and it is only in the occasional testing of the laws by reference to experiments, or in the use of the laws for special predictions that definite numbers are substituted.
The interesting point about the world as
thus conceived in this abstract way throughout the study of mathematical physics, where only the positions and shapes of things are considered together with their changes, is that the events of such an abstract world are sufficient to "explain" our sensations. When we hear a sound, the molecules of the air have been agitated in a certain way: given the agitation, or air-waves as they are called, all normal people hear sound; and if there are no air-waves, there is no sound. And, similarly, a physical cause or origin, or parallel event (according as different people might like to phrase it) underlies our other sensations. Our very thoughts appear to correspond to conformations and motions of the brain; injure the brain and you injure the thoughts. Meanwhile the events of this physical universe succeed each other according to the mathematical laws which ignore all special sensations and thoughts and emotions.