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Published online by Cambridge University Press: 14 March 2022
At a certain stage of advance in any science it may be well to re-examine and perhaps to rearrange its fundamentals. One seeks an ideal, logical order of development, which may or may not be the best pedagogical order. Many a high school beginner in physics has become acquainted with “force” as something that gets in between two bodies of matter and pulls them together or pushes them apart, like himself between two carts or like “magnetism” between two magnets. Whether or not this might ever be a proper view, the mature student of today will consider that for him, a knowledge of accelerations and strains, inter alia, is prerequisite to a knowledge of force.
1a In a paper on “The Scientific Conception of the Measurement of Time,” which was read before the Aristotelian Society on June I, 1885 (published in Mind for July 1885, vol. 10, pp. 347 to 362, especially p. 355 et seq.), E. Hawksley Rhodes distinguished as “independent” and “dependent” these two classes of sequences of events which are here distinguished as “extensive” and “trivial.” Inasmuch as his terminology seems to have been put to little or no use by others, I consider myself free not to employ it; a reason for not doing so in this instance is to avoid the implication of a causal relation which is carried by the word “dependent.” In my opinion, if authors on the subject of time as a basic concept had given closer attention to this well-reasoned paper, sound thinking on that subject would have been greatly promoted during the past fifty years.
1 Without pretense of annotating these allusions, a single reference will be given by way of example: See Bertrand Russell, On order in time, Cambridge Phil. Soc. Proc, Vol. 32 (May 1936), pages 216 to 228. This begins “Instants are mathematical constructions, not physical entities …”
2 H. N. Russell et al., Astronomy, Ginn & Co., Boston, 1926, Vol. I, Appendix, Table III.
3 Isaac Newton, Principia (Motte's translation, revised by F. Cajori), U. of Calif. Press, 1934, Book I, Scholium to Definitions, page 6.
4 Isaac Newton, Optics, G. Bell & Sons, London 1931, page 102 and context, also page xvii of Introduction by E. T. Whitaker.
5 Principles of Psychology, Holt, N. Y. 1890, Vol. II, pages 63, 64.
6 Hudson Hoagland, The Chemistry of Time, Philosophy of Science, 1934, Vol. I, pages 351-2.
7 Wells, Huxley & Wells, Science of Life, Doubleday, Doran & Co., N. Y., 1931, page 542.
8 Of course the perforations in the flange should be equally spaced. If this seems to violate our principle that space-metric considerations should be postponed, there are two replies: (1) To refuse consideration of this experiment at this stage would be like the case of the student who refused to wear his glasses when he began the study of mechanics, on the ground that he had as yet made no study of optics. The instructor may make the flange with its equally spaced perforations part of the “given”, and the student need have no concern as to how the perforations are distributed. (2) For the purposes of this experiment, general space-metric considerations could be evaded by directing the student to center the flange on a flywheel, to put enough torque on the flywheel to keep it at 501 rotations per 500 seconds, and to mark a place for a perforation on the flange at every fifth second.
9 H. A. Lorentz, Theory of Electrons, Teubner, Leipzig, 1916, page 197 and context.
10 Henri Poincaré, Foundations of Science, Science Press, New York, 1921, pages 227, 228.
11 H. N. Russell et al., Astronomy, Ginn & Co., Boston, 1926, Vol. I, pages 116, 117, 288, 289, 300.
12 H. N. Russell et al., Astronomy, Ginn & Co., Boston, 1926, Vol. I, pages 117, 289, 290.
13 See the paper by Philip Franklin, “What is topology?”, in Philosophy of Science, Vol. II (1935), pages 39 to 47.
14 An Examination of Sir William Hamilton's Philosophy …, 6th ed., Longmans, 1889, page 233 and context.
15 The Axioms of Projective Geometry, Cambridge Tract in Mathematics and Mathematical Physics, No. 4, 1913, page 5.