The A B C of Relativity

and in doing so has taken us nearer and nearer to bare structure, which is the mathematician’s goal—not because it is the only thing in which he [Pg 229] is interested as a human being, but because it is the only thing that he can express in mathematical formulæ. But far as we have traveled in the direction of abstraction, it may be that we shall have to travel further still. In the preceding chapter, I suggested what may be called a minimum definition of matter, that is to say, one in which matter has, so to speak, as little “substance” as is compatible with the truth of physics. In adopting a definition of this kind, we are playing for safety: our tenuous matter will exist, even if something more beefy also exists. We tried to make our definition of matter, like Isabella’s gruel in Jane Austen, “thin, but not too thin.” We shall, however, fall into error if we assert positively that matter is nothing more than this. Leibniz thought that a piece of matter is really a colony of souls. There is nothing to show that he was wrong, though there is also nothing to show that he was right: we know no more about it either way than we do about the flora and fauna of Mars. To the non-mathematical mind, the abstract character of our physical knowledge may seem unsatisfactory. From an artistic or imaginative [Pg 230] point of view, it is perhaps regrettable, but from a practical point of view it is of no consequence. Abstraction, difficult as it is, is the source of practical power. A financier, whose dealings with the world are more abstract than those of any other “practical” man, is also more powerful than any other practical man. He can deal in wheat or cotton without needing ever to have seen either: all he needs to know is whether they will go up or down. This is abstract mathematical knowledge, at least as compared to the knowledge of the agriculturist. Similarly the physicist, who knows nothing of matter except certain laws of its movements, nevertheless knows enough to enable him to manipulate it. After working through whole strings of equations, in which the symbols stand for things whose intrinsic nature can never be known to us, he arrives at last at a result which can be interpreted in terms of our own perceptions, and utilized to bring about desired effects in our own lives. What we know about matter, abstract and schematic as it is, is enough, in principle, to tell us the rules according to which it produces perceptions and feelings in ourselves; and it is upon these rules that the practical uses of physics depend. [Pg 231] The final conclusion is that we know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power. THE END Footnotes: [1] A contemporary Chinese ode, after giving the day of the year correctly, proceeds: “For the moon to be eclipsed Is but an ordinary matter. Now that the sun has been eclipsed, How bad it is.” [2] I shall define “interval” in a moment. [3] So long as he has no considerable acceleration. The treatment of acceleration belongs to the general theory of relativity. [4] This does not mean that its velocity is increasing, but that it is changing its direction. The only sort of motion which is called “unaccelerated” is motion with uniform velocity in a straight line. [5] See his Space, Time, Matter, Methuen, 1922. [6] Although “force” is no longer to be regarded as one of the fundamental concepts of dynamics, but only as a convenient way of speaking, it can still be employed, like “sunrise” and “sunset,” provided we realize what we mean. Often it would require very roundabout expressions to avoid the term “force.” [7] See Eddington, The Mathematical Theory of Relativity, Cambridge University Press, 2d edition, p. 128. [8] This is subject to the explanations given below as regards conservation of energy. [9] Mathematical Theory of Relativity, p. 135. [10] On this subject, see the present author’s A.B.C. of Atoms, chaps. VI and XIII. [11] Op. cit. § 60. [12] See Eddington, Space, Time and Gravitation, p. 162ff. [13] “Isotropy” means being similar in all directions—e.g., that a foot rule is as long when it points north as when it points east. [14] Mathematical Theory of Relativity, p. 238. [15] Mathematical Theory of Relativity, pp. 37-38. Italics in the original. [16] For the definition of “structure,” see the present author’s Introduction to Mathematical Philosophy. Transcriber’s Notes: The cover image was created by the transcriber, and is in the public domain. The illustrations have been moved so that they do not break up paragraphs and so that they are next to the text they illustrate. Typographical and punctuation errors have been silently corrected. *** END OF THE PROJECT GUTENBERG EBOOK 67104 ***