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extended as space in three dimensions long, broad, and deep is one thing, but to be enduring as time before, now, and hereafter is different. Minkowski rashly predicted that space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. But in reality it is the substance of the whole world which on the one hand as extended long, broad, and deep, is the real space, and on the other hand as enduring before, now, and hereafter, is the real time; both of which are independent of one another but both dependent on the substance of the world, of which they are different attributes closely connected. Minkowski's hypothesis that space and time are doomed to fade away into mere shadows has led to a habit of reducing them into one single term 'space-time'. But the nearest to which we can reduce the close relation of space and time is space during time, as without time there could be no space.

V. FROM EUCLID TO EINSTEIN

SPACE DURING TIME

FROM The Times, JANUARY 7, 1922.

In The Times of the 4th inst., Mr. Clive E. Temperley has taken me to task over what appear to him some of the errors in my letter of December 24. Before I defend myself I must premise that, in my opinion, space is extended, long, broad, and deep, and is continuous without any intervals such as exist between numbers, or points, or finite bodies, which are discrete; that the immutable space common to the whole body of the universe and in which all finite bodies are, and rest or move, is to be distinguished from the mutable private spaces of finite bodies; and that Professor Einstein, in his book on

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Relativity, translated by Dr. Lawson, is not so convincing about common space as he is about private or local spaces. I proceed to meet my errors in the order of Mr. Temperley.

(a) While in my letter I said, in agreement with Professor Einstein, that, in spite of the negative result of the Michelson-Morley experiment, FitzGerald's suggestion of the contraction of a body in the direction of its motion has been calculated by Lorentz, Mr. Temperley, on the other hand, accuses me of reversing the order, on the ground that the negative result follows directly from Lorentz's equation. I answer by quoting from the translation of Professor Einstein's book (p. 53) the following statement of the order, which is the same as mine: "The experiment gave a negative result―a fact very perplexing to physicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that the motion of the body ' relative to aether produces a contraction of the body in the 'direction of motion.'

(b) While in my letter I said, in opposition to Professor Einstein, that the sun could not deflect the space between itself and the light, and that, even if it could, the deflected space could not deflect the light, because space is not a force, Mr. Temperley replies that, according to Einstein's mathematical conception of the universe, no force is required to cause this deflection. I answer that, in Appendix III, added to his book at the request of Dr. Lawson (p. 127), Professor Einstein did require the deflected space to produce this deflection in the following

sentence:

'It may be added that, according to the theory, half of this deflection is produced by the Newtonian field of attraction ' of the sun, and the other half by the geometrical modification ("curvature ") of space caused by the sun.'

Professor Einstein then did, perhaps unconsciously, require the supposed curvature of space to be a cause

producing half of the deflection, and thus converted space into being a force. In this sentence he contradicts the whole science of classical mechanics, which has, in the course of some twenty-four centuries, been the gradual work of Archimedes, Galileo, Newton, Maxwell, Thomson, and Tait, and has at length proved that space and time are the kinematic conditions, but force and energy are the kinetic causes which produce motion. Which of them would have admitted the statement that curved space is a cause of the deflection of light? Sad to say, Professor Einstein has added one more to the many examples of the modern tendency to supersede old truths by new paradoxes-without sufficient evidence.

(c) and (d) Under these two heads, which are really parts of one argument, Mr. Temperley, without quoting Professor Einstein's definition, either from the translation of his book (page 55) or from my letter, attacks my criticism of that definition out of other parts of Professor Einstein's book, and thus falls into the fallacy of ignoratio elenchi. In selfdefence, therefore, I must quote the definition for him from my letter, in which I said that Professor Einstein defines space as a three-dimensional continuum, composed of an indefinite number of points near enough one another to give a kind of apparent continuity. I answer that space cannot be both a three-dimensional continuum in the old and proper sense of being continuously extended and a continuum in the new and improper sense of being a continual series of discrete points, however close together; but that space can, on the one hand, be a three-dimensional continuum as continuously extended long, broad, and deep, and, on the other hand, can be measured by, but not composed of, a continual series of discrete points, which are not segments of extended space potentially divisible to infinity.

(e) While in my letter, in opposition to the hypothesis of a fourfold continuum and a space-time advocated by Minkowski and Einstein, I said that, in addition to the three straight lines of space at right angles to one another, no place could be found for a fourth straight line of time as a fourth coordinate in any diagram of the supposed fourfold continuum, Mr. Temperley replies that lengths in a time-co-ordinate appear in Einstein's equation, indicating the impossibility of including them in a diagram. I answer first, that it is no argument against me to point out the very defect which I pointed out-namely, the absence of time from a diagram when it ought ex hypothesi to be present; secondly, that he takes no notice of another fault, which I also pointed out, that time is not a line, and therefore has no lengths to lie in a space-time-coordinate; and thirdly, that he overlooks the consequence that the presence of a length of time in Professor Einstein's equation does not excuse its absence from a diagram of a supposed fourfold continuum, or guarantee the presence of a fourfold continuum of space-time in what Minkowski calls the world, but I call the body of the world.

Lastly, I submit that, whatever it may be called, the world, so far as it is continuous, is neither space plus time, nor space-time, nor any kind of union of space and time except space during time and divided by time, without which space would have no time to endure even for an instant.

VI. ARISTOTLE ON METAPHYSICS

METAPHYSICS AND PHYSICS

FROM The Times, MAY 2, 1922.

A hope has been expressed in your columns by Mr. Max Judge that Sir Oliver Lodge's letter of the 13th inst. will not be neglected. I share this hope, if

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ARISTOTLE ON METAPHYSICS

only an attempt is made to go to the bottom of the subject before Professor Einstein is allowed to confound pure mathematics and concrete physics, although they have been generally distinguished since the time of Aristotle, who long ago was the first to say, things mathematical are from abstraction, things physical from addition'.

Aristotle's primary philosophy, or metaphysics', as his commentators called it, is the science of things as things, and not of mere ideas or names. Its first principle is that all things as things are substances, or whole things, and reduces itself to three main propositions:

1. All things are substances, each of which is an individual, independent, determinate, whole thing, and a real subject of real predicates or attributes, each of which is a thing, yet not a whole thing, but something which, being quantitative, or qualitative, or relative, &c., is only something which a substance is, or, in other words, is a substance so far as that substance is quantitative, or qualitative, or relative, &c. As Aristotle pithily says, The same thing in a way is Socrates and Socrates musical.' Everything, therefore, is a substance both as itself a whole thing, and also as something quantitative, or qualitative, or relative, &c.

2. The most evident, the most knowable, and the most acknowledged substances are natural substances or bodies—e. g. earth and water, plants and animals, sun, moon, and stars, which are all investigated by what Aristotle was the first to call natural science or natural philosophy.

3. Over and above all other substances is God, the supernatural substance, who is animate, eternal, and best, and therefore, according to Aristotle, the prime mover as motive of Nature.

Such is Aristotle's science of things as things, containing the realism without materialism, which

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