fact has any meaning for physics at all. It is because Einstein accepts a fact's conformity to law as essential to its relevancy for physics that he can logically unite his empirical convictions with an absorbing quest for the conditions which shall justify the reign of law in the world of relativity. When Einstein discovers his general formula for the fundamental laws of nature, a formula which holds good for all natural events, whatever be the special point of view, or special axes of reference adopted by the observer, he connects in his achievement the requirements of measurability and of invariancy alike. Starting from the conception of a measurable Euclidean straight line, relativistic theory takes us through its two levels-those of its restricted and generalised formulations-to the weird, but fascinating conception of a line-element, ds, the differential interval between two point-events in a spatio-temporal continuum, four-dimensional, non-Euclidean, dependent for its geometrical form on the conditions of the gravitational field within which it figures. This "interval," as the fundamental invariant of the relativist doctrine is the supremely real thing for it. It is, in its general form, non-intuitable, nonmeasurable, and yet is no inaccessible thing-in-itself, but intelligibly connected through appropriate gradings with what is intuitable and measurable, as its limiting cases.* Hence to grasp Einstein's idea of physical reality we must include in one scheme both its empiricist and its rationalist elements, the measurable fact accessible to sense and muscle, and the invariant accessible only to the mathematical mind. The latter connects continuously with the former. Like the Platonic Good, it is the abiding source of all that is intelligible in the physical world, but, unlike it, overflows into all the subworlds of apprehension without break of continuity, and under clear limitations which can be mathematically controlled and defined.

•Expressed in the light of the six equations in which Einstein's Gravitational Theory is embodied, it takes the form: ds = - drr der sin edo + jdt, where j=1—

2M

2

2

2 2

2 2

2

2

m being the mass of the attractive particle to which the gravitational field is due and r., the polar co-ordinates corresponding to the x, y, z in the standard expression for the interval element. Now let dt=0 and we get a formula for measured length which shows that in this "real" universe it is a function of the gravitational field. For any given value of m, the rod's real geodetic length (for it can no longer be straight, the geometry being non-Euclidean) will be a fixed amount, the same for all values of the co-ordinates r 0, 4, And if m=0 and .. j=1 the invariant takes the form proper to the restricted theory, and the measured length is Euclidean. There is therefore a continuous mathematical connection between the actual measure of the ruler taken under ordinary physical conditions and the leading Invariant of the General Theory, the real matrix of all physical reality. (Vide: Bolton, "An Introduction to the Theory of Relativity," ch. xviii).

Hans Reichenbach, in his "Relativitaets-theorie and Erkenntnis Apriori," Section viii. (Julius Springer, 1920), draws attention to the change in the object-concept brought about by the Theory of Relativity, and illustrates by reference to the concept of length. What we measure as length

So

must be stated in terms of some system of co-ordinates. stated it is a clearly-defined magnitude. But it is also subjective since the system of co-ordinates is arbitrarily chosen by the observer. "It is when, in addition, we supply the transformation formulae for every other system that our statement first wins a really independent meaning. The new method of the Theory of Relativity consists precisely in this, that through the transformation formulae the subjective assertion wins an objective meaning. What is ascertain

able is only the length as measured in some one system. And this is only one expression of the real relation. . . It is only when we supply in addition the transformation formulae that we eliminate the subjective, arbitrary influence of the reference system, and also reach at last a genuinely objective determination of the real" (id., pp. 92-93).

On this view the physically objective is reached only through mental considerations whereby a purely subjective starting-point is adequately compensated, and its subjectivity sifted away. The very meaning of the General Theory of Relativity is that metrics are much more than a mathematical measuring scheme for bodies: that they are in fact the form for conceptually presenting a body as an element in the material world (cf., id., pp. 97-98).

Now, it seems to me that this view, fine and suggestive as it is, does not take sufficient note of the fact that there is a -privileged, though not an absolute position from which the length relationship can be stated, namely, that in which the observer's view-point coincides with that of the object he proposes to measure, so that, for that position, variations due to differences of time and rate of relative motion do not arise: it is the position of the measuring-rod itself. Objectivity of the empirical kind is here secured through the sole agency of measurement, and apart from the accessory assistance of the transformation equations through which the findings of different observers may be interconnected, and results at one point of observation reduced to corresponding results obtainable at any other observation-point. It is true that measurement itself is a metrical relation, so that the relativist view that metrics is the key to matter is not hereby impugned, but objectivity and measurement are more intimately connected. The measure taken of a ruler by means of a measuring-rod reveals

the natural length of the ruler for all the purposes of physical science. And the measure includes no reference to a clock. It is true that the length will vary with, movement and in the direction of motion, and to ascertain the law according to which this variation takes place is of the utmost importance for reductions of measurements from one observer's viewpoint to another's. But the standard measurement will always be that obtained through the direct application of the measuring-rod, or, where such superposition is not possible, the nearest indirect equivalent, whatever that may be.

Further, the relativist concept of objectivity is incomplete apart from a reference to the "interval" or line-element as the fundamental invariant. It is only in relation to this invariant that the deeper objectivity and the part played by mathematics in discovering and defining it can be made clear. The measured length, on the relativist view, is necessarily an abstraction. For the measure is spatial only, and we are none of us allowed to forget Minkowski's dictum, uttered in 1908: "From henceforth space in itself, and time in itself, sink to mere shadows, and only a kind of union of the two preserves an independent existence."*

Summing up on the matter of the ruler's real length, we would suggest: first, that for all purposes of empirical application the real length is the natural length as discoverable through direct measurement, or its nearest mathematical substitute; second, that this natural length is none the less abstract and derivative: the space-shadow projected by a "world-line" whose law of being and of movement is given by an ideal invariant which, with mathematical rigour,, controls the metrics of the relativist world; and third, that through the principle of continuity the natural length as directly measured is connected with the ideal length as a world-line through a wonderful system of mathematical workmanship, so that the one participates in the other, the natural in the ideal, as its projection or partial manifestation. To grasp the natural length as a mathematically controlled projection from an unpicturable universe of world-lines is no easy challenge for the mind to meet, but owing mainly to the rigorous mathematical character of the invariants involved, the challenge opens up a view of intelligibly organized physical reality which should be an inspiration to truth-seekers for many years to come.

*Moritz Schlick ("Space and Time in Contemporary Physics," p. 66) points out that Minkowski's synthesis is itself "a mere shadow, an abstraction," and "only the oneness of space time and things has an independent existence."

34

STRIFE.
By

W. JETHRO BROWN, LL.D., D. Litt., President of the South Australian Industrial Board.

O

UR age, unique in so many of its problems and perplexities, presents as a dominant characteristic a spirit of revolt. Much of our unrest may be due either to

a paralysing complexity of environment, or to a protest against entanglement in a web of traditional conventionalisminnumerable tyrannies which tend, in quite superfluous ways, to rob life of its joy and zest. The more menacing forms of unrest centre around the possession of material things. In a maze of industrial discontent the individual seems to lose that sense of proportion which philosophy should teach or restore to him.

Reflection on such high matters brings to my mind a dialogue which, so far as I am aware, has not yet been published. It purports to have taken place between Socrates and one designated "Stranger." I am not able to vouch either for the authenticity of the dialogue or the propriety of the translation, if indeed translation it be. Socrates contributes little himself to the discussion, save by way of asking questions after the Socratic manner. The answers of the Stranger appear often naive, though not lacking plausibility and even at time a conscious or unconscious irony.

Socrates: It has come to my knowledge that in your country there are many great and wonderful things; but the nature of the mind is of more interest to me than inventions of science or the maladies of the body. Therefore am I more concerned to know whether it is indeed true that in Modernia, from whence by report you come, all men are free and possess that knowledge which is wisdom.

Stranger: All men indeed are free, O Socrates, since all men can vote for those who rule in the Assemblies, and in law no man is in bondage to another. As to whether they have the wisdom of which you speak it would ill become me to say, since 1 am but one of many. Yet do we deem ourselves wise. This has its advantage, since if a man be not wise, it is yet agreeable for him to think himself so. Yet, since opinions on many matters are often at variance, it follows that a man's freedom to think himself wise necessitates a freedom to think others who do not agree with him unwise. So have I heard it said that whilst many in our City have more

of information than their minds can apply (or, as a wit has put it, are too highly educated for their intelligence), there are others more fortunate, who, from choice or necessity, are not troubled with much learning, and therefore enjoy the advantage of being able to arrive at desired conclusions without their minds being confused by what has been said or may be said to the contrary. Now, of these two classes, the one often derides the other. Indeed, such expressions are common as "the pedantry of learning," and "the value of ignorance.' But whether these taunts be just I am at a

loss to say.

Socrates: But what say those who, since they are chosen for the Assemblies, may presumably be taken as wise, or at least learned?

Stranger: They say that the voice of the people is the voice of God. Therefore should the people be wise and the lawmakers most wise. Yet have I heard it said in Modernia that a man is most wise who counts himself such, provided he can speak loud enough to be heard, and be not too long in speech to try the patience of those who may chance to listen. I but repeat what is said.

Socrates: If what is said be the truth, it would seem as if the voice of wisdom were like to be drowned in the babel of tongues. But yet perhaps you may be able to tell me in what, apart from the knowledge of many secrets, have your people advanced beyond those whom I knew at Athens?

Stranger: In truth, O Socrates, I would rather you come to Modernia and judge for yourself. I am not learned enough in Athenian ways to answer your question. Yet have 1

noticed, even within the short span of my days on earth, that we have developed a great capacity for fighting over many things, and of worrying about anything. If I may speak of such matters, tradition says of you, O Socrates, that you would not oblige even your wife by quarrelling with her though she gave you much opportunity. Now with us, even though a man may not have a wife, he finds it easy to quarrel with almost anyone, and if he cannot find anything to worry about in his present, he can worry about what may happen next, when so many strange things happen day by day in one part of the earth or the other. Lest he should be so supine as to prefer repose, we have a great institution called the "Press." Now the chief function of the press would appear to be to collect from all the world information of disasters, plagues, famine, pestilence, and crime. You will agree that this shows that in some respects at least we have advanced towards a life of excitement.