Chapter VI: completes the preliminary course in the fundamentals of (1)

relativity by tying up together the findings of Chapter V. and those of Chapters III. and IV. It represents more or less of a last-minute change of plan; for while it had been the Editor's intent from the beginning to place the material of Chapters II.-V. in its present position, his preliminary impression would have been that the work of the present Chapter VI. would be adequately done by the essayists themselves. His reading of the essays, however, convinced him that it had not so been done--that with the possible exception of Mr. Francis, the essayists did not make either a serious or a successful effort to show the organic connection between the Special Theory of Relativity and the Minkowski space-time structure, or the utter futility of trying to reconcile ourselves to the results of the former without employing the ideas of the latter. So Chapter VI. was supplied to make good this deficiency, and to complete the mental equipment which the reader requires for his battle with the General Theory.

In laying down a set of general principles to govern the award of the prize, one of the first things considered by the Judges was the relative importance of the Special and the General Theories. It was their opinion that no essay could possibly qualify for the prize which did not very distinctly give to the General Theory the center of the stage; and that in fact discussion of the Special Theory was pertinent only so long as it contributed, in proportion to the space assigned it, to the attack upon the main subject. The same principle has been employed in selecting essays for complete or substantially complete reproduction in this volume. Writers who dealt with the Special Theory in any other sense than as a preliminary step toward the General Theory have been relegated to the introductory chapters, where such excerpts from their work have been used as were found usable. The distinction of publication under name and title is reserved for those who wrote consistently and specifically upon the larger subject--with the one exception of Dr. Russell, whose exposition of the Special Theory is so far the best of those submitted and at the same time so distinctive that we have concluded it will appear to better advantage by itself than as a part of Chapters III. and IV.

Following after Mr. Bolton's essay we have tried to arrange the various contributions, not at all in any order of merit, but in the order that will make connected reading of the book most nearly possible and profitable. Each essay should be made easier of reading by the examination of those preceding it; at the same time each, by the choice of ground covered and by the emphasis on points not brought out sharply by its predecessors, should throw new light upon these predecessors.

The reader will find that no two of the essays given thus in full duplicate or even come close to duplicating one another. They have of course been selected with this in view; each represents the best of several essays of substantially the same character. Not all of them require comment here, but concerning some of them a word may well be said.

Mr. Francis, we believe, has succeeded in packing more substance into his 3,000 words than any other competitor. Mr. Elliot has come closer than anybody else to really explaining relativity in terms familiar to everybody, without asking the reader to enlarge his vocabulary and with a minimum demand so far as enlarging his mental outlook is concerned. Were it not for certain conspicuous defects, his essay would probably have taken the prize. In justice to the Judges, we should state that we have taken the liberty of eliminating Mr. Elliot's concluding paragraph, which was the most objectionable feature of his essay.

Dr. Dushman chose for his title the one which we adopted for this book. It became necessary, therefore, for us to find a new title for his essay; aside from this instance, the main titles appearing at the heads of the various complete essays are those of the authors. The subtitles have in practically every instance been supplied editorially.

Dr. Pickering submitted two essays, one written from the viewpoint of the physicist, the other from that of the astronomer. To make each complete, he naturally found it necessary to duplicate between them certain introductory and general material. We have run the two essays together into a single narrative, with the elimination of this duplicated material; aside from this blue-penciling no alteration has been made in Dr. Pickering's text. This text however served as the basis of blue-penciling that of several other contestants, as indicated in the foot notes.

For the reader who is qualified or who can qualify to understand it, Dr. Murnaghan's essay is perhaps the most illuminating of all. Even the reader who does not understand it all will realize that its author brings to the subject a freshness of viewpoint and an originality of treatment which are rather lacking in some of the published essays, and which it will readily be understood were conspicuously lacking in a good many of the unpublished ones. Dr. Murnaghan of all the competitors has come closest to making a contribution to science as well as to the semi-popular literature of science.

In the composite chapters, the brackets followed by reference numbers have been used as the most practicable means of identifying the various individual contributions. We believe that this part of the text can be read without allowing the frequent occurrence of these symbols to distract the eye. As to the references themselves, the asterisk marks the contributions of the Editor. The numbers are those attached to the essays in order of and at the time of their receipt; it has been more convenient to use these than to assign consecutive numbers to the quoted essays. The several numbers identify passages from the essays of the following contestants:

10: Frederick W. Shurlock, Derby, England. 18: L. L. Whyte, Cambridge, England. 24: Prof. Moritz Schlick, University of Rostock, Germany. 30: C. E. Rose, M.E., Little Rock, Ark. 33: H. Gartelmann, Bremen, Germany. 35: Prof. Joseph S. Ames, Johns Hopkins University, Baltimore. 47: James O. G. Gibbons, East Orange. N. J. 82: Charles H. Burr, Philadelphia. 101: L. F. H. de Miffonis. B.A., C.E., Ottawa, Canada. 102: Charles A. Brunn, Kansas City. 106: J. Elias Fries, Fellow A.I.E.E., Birmingham, Ala. 114: Dean W. P. Graham, Syracuse University, Syracuse, N. Y. 115: Rev. George Thomas Manley, London. 116: Prof. J. A. Schouten, Delft, Netherlands. 121: Elwyn F. Burrill, Berkeley, Cal. 125: Dorothy Burr, Bryn Mawr, Pa. 130: C. W. Kanolt, Bureau of Standards, Washington. 135: Robert Stevenson, New York. 139: Leopold Schorsch, New York. 141: Dr. M. C. Mott-Smith, Los Angeles, Calif. 147: Edward A. Clarke, Columbus, O. 149: Edward A. Partridge, Philadelphia. 150: Col. John Millis, U. S. A., Chicago. 152: George F. Marsteller, Detroit. 156: D. B. Hall, Cincinnati. 165: Francis Farquhar, York, Pa. 178: Dr. George de Bothezat, Dayton, O. 179: Professor A. E. Caswell, University of Oregon, Eugene, Ore. 182: C. E. Dimick, New London, Conn. 186: Earl R. Evans, Washington, D. C. 188: Norman E. Gilbert, Dartmouth College, Hanover, N. H. 192: A. d'Abro. New York. 194: L. M. Alexander, Cincinnati. 197: Kenneth W. Reed, East Cleveland, O. 198: Prof. E. N. da C. Andrade, Ordnance College, Woolwich, England. 216: Professor Andrew H. Patterson, University of North Carolina, Chapel Hill, N. C. 220: Prof. Arthur Gordon Webster, Clark College, Worcester, Mass. 221: Walter van B. Roberts, Princeton University, N. J. 223: Paul M. Batchelder, Austin, Tex. 227: Prof. R. W. Wood, Johns Hopkins University, Baltimore. 229: E. P. Fairbairn, M.C., B.Sc., Glasgow. 231: R. F. Deimel, Hoboken, N. J. 232: Lieut. W. Mark Angus, U. S. N., Philadelphia. 235: Edward Adams Richardson, Kansas City. 263: Prof. William Benjamin Smith, Tulane University, New Orleans. 264: James Rice, University of London, London. 267: William Hemmenway Pratt, Lynn, Mass. 272: R. Bruce Lindsay, New Bedford, Mass. 283: Frank E. Law, Montclair, N. J.

In addition to the specific credit given by these references for specifically quoted passages, the Editor feels that he ought to acknowledge his general indebtedness to the competing essayists, collectively, for the many ideas which he has taken away from their text to clothe in his own words. This does not mean that the Editor has undertaken generally to improve upon the language of the competitors, but merely that the reading of all their essays has given him many ideas of such complex origin that he could not assign credit if he would.

TABLE OF CONTENTS

I.--The Einstein $5,000 Prize: How the Contest Came to be Held, and Some of the Details of Its Conduct. By the Editor 1

II.--The World--And Us: An Introductory Discussion of the Philosophy of Relativity, and of the Mechanism of our Contact with Time and Space. By various contributors and the Editor 19

III.--The Relativity of Uniform Motion: Classical Ideas on the Subject; the Ether and the Apparent Possibility of Absolute Motion; the Michelson-Morley Experiment and the Final Negation of this possibility. By various contributors and the Editor 47

IV.--The Special Theory of Relativity: What Einstein's Study of Uniform Motion Tells Us About Time and Space and the Nature of the External Reality. By various contributors and the Editor 76

V.--That Parallel Postulate: Modern Geometric Methods; the Dividing Line Between Euclidean and Non-Euclidean; and the Significance of the Latter. By the Editor 111

VI.--The Space-Time Continuum: Minkowski's World of Events, and the Way in Which It Fits Into Einstein's Structure. By the Editor and a few contributors 141

VII.--Relativity: The Winning Essay in the Contest for the Eugene Higgins $5,000 Prize. By Lyndon Bolton, British Patent Office, London 169

VIII.--The New Concepts of Time and Space: The Essay in Behalf of Which the Greatest Number of Dissenting Opinions Have Been Recorded. By Montgomery Francis, New York 181

IX.--The Principle of Relativity: A Statement of What it is All About, in Ideas of One Syllable. By Hugh Elliot, Chislehurst, Kent, England 195

X.--Space, Time and Gravitation: An Outline of Einstein's Theory of General Relativity. By W. de Sitter, University of Leyden 206

XI.--The Principle of General Relativity: How Einstein, to a Degree Never Before Equalled, Isolates the External Reality from the Observer's Contribution. By E. T. Bell, University of Seattle 218

XII.--Force Vs. Geometry: How Einstein Has Substituted the Second for the First in Connection with the Cause of Gravitation. By Saul Dushman, Schenectady 230

XIII.--An Introduction to Relativity: A Treatment in which the Mathematical Connections of Einstein's Work are Brought Out More Strongly and More Successfully than Usual in a Popular Explanation. By Harold T. Davis, University of Wisconsin 240

XIV.--New Concepts for Old: What the World Looks Like After Einstein Has Had His Way with It. By John G. McHardy, Commander R. N., London 251

XV.--The New World: A Universe in Which Geometry Takes the Place of Physics, and Curvature that of Force. By George Frederick Hemens, M.C., B.Sc., London 265

XVI.--The Quest of the Absolute: Modern Developments in Theoretical Physics, and the Climax Supplied by Einstein. By Dr. Francis D. Murnaghan, Johns Hopkins University, Baltimore 276

XVII.--The Physical Side of Relativity: The Immediate Contacts between Einstein's Theories and Current Physics and Astronomy. By Professor William H. Pickering, Harvard College Observatory, Mandeville, Jamaica 287

XVIII.--The Practical Significance of Relativity: The Best Discussion of the Special Theory Among All the Competing Essays. By Prof. Henry Norris Russell, Princeton University 306

XIX.--Einstein's Theory of Relativity: A Simple Explanation of His Postulates and Their Consequences. By T. Royds, Kodaikanal Observatory, India 318

XX.--Einstein's Theory of Gravitation: The Discussion of the General Theory and Its Most Important Application, from the Essay by Prof. W. F. G. Swann, University of Minnesota, Minneapolis 327

XXI.--The Equivalence Hypothesis: The Discussion of This, With Its Difficulties and the Manner in Which Einstein Has Resolved Them, from the Essay by Prof. E. N. da C. Andrade, Ordnance College, Woolwich, England 334

XXII.--The General Theory: Fragments of Particular Merit on This Phase of the Subject. By Various Contributors 338

I.

THE EINSTEIN $5,000 PRIZE

HOW THE CONTEST CAME TO BE HELD, AND SOME OF THE DETAILS OF ITS CONDUCT

BY THE EDITOR

In January, 1909, an anonymous donor who was interested in the spread of correct scientific ideas offered through the Scientific American a prize of $500 for the best essay explaining, in simple non-technical language, that paradise of mathematicians and bugaboo of plain ordinary folk--the fourth dimension. Many essays were submitted in this competition, and in addition to that of the winner some twenty were adjudged worthy of ultimate publication. It was felt that the competition had added distinctly to the popular understanding of this significant subject; that it had done much to clear up popular misconception of just what the mathematician means when he talks of four or even more dimensions; and that it had therefore been as successful as it was unusual in character.

In November, 1919, the world was startled by the announcement from London that examination of the photographs taken during the total solar eclipse of May 29th had been concluded, and that predictions based upon the Einstein theories of relativity had been verified. In the reaction from the long surfeit of war news an item of this sort was a thoroughly journalistic one. Long cable dispatches were carried in the news columns all over the world; Einstein and his theories were given a prominent place on the front pages day after day; leading scientists in great number were called upon to tell the public through the reportorial medium just what the excitement was all about, just in what way the classical scientific structure had been overthrown.

Instead of being a mere nine days' wonder, the Einstein theories held their place in the public mind. The more serious periodicals devoted space to them. First and last, a very notable group of scientific men attempted to explain to the general reader the scope and content of Einstein's system. These efforts, well considered as they were, could be no more than partially successful on account of the very radical character of the revisions which the relativity doctrine demands in our fundamental concepts. Such revisions cannot be made in a day; the average person has not the viewpoint of the mathematician which permits a sudden and complete exchange of one set of fundamentals for another. But the whole subject had caught the popular attention so strongly, that even complete initial failure to discover what it was all about did not discourage the general reader from pursuing the matter with determination to come to some understanding of what had happened to Newton and Newtonian mechanics.

THE DONOR AND THE PRIZE

In May, 1920, Mr. Eugene Higgins, an American citizen long resident in Paris, a liberal patron of the arts and sciences, and a lifelong friend of the Scientific American and its proprietors, suggested that the success of the Fourth Dimension Prize Contest of 1910 had been so great that it might be desirable to offer another prize in similar fashion for the best popular essay on the Einstein theories. He stated that if in the opinion of the Scientific American these theories were of sufficient importance, and the probability of getting a good number of meritorious essays were sufficiently great, and the public need and desire for enlightenment were sufficiently present, he would feel inclined to offer such a prize, leaving the conduct of the contest to the Scientific American as in the former event. It was the judgment of the editors of the Scientific American that all these provisos should be met with an affirmative, and that Mr. Higgins accordingly could with propriety be encouraged to offer the prize.

In his preliminary letter Mr. Higgins had suggested that in view of the apparent greater importance of the subject to be proposed for discussion by the contestants of 1920, the prize offered should probably be more liberal than in the former instance. This view met with the approval of the editors as well; but they were totally unprepared for the receipt, late in June, of a cablegram from Mr. Higgins stating that he had decided to go ahead with the matter, and that he was forwarding a draft for $5,000 to represent the amount of the prize. Such a sum, exceeding any award open to a professional man with the single exception of the Nobel Prize, for which he cannot specifically compete, fairly took the breath of the Editors, and made it immediately clear that the contest would attract the widest attention, and that it should score the most conspicuous success. It also made it clear that the handling of the contest would be a more serious matter than had been anticipated.

In spite of the fact that it would not for some time be possible to announce the identity of the Judges, it was felt that the prospective contestants should have every opportunity for extensive preparation; so the contest was announced, and the rules governing it printed as far as they could be determined on such short shrift, in the Scientific American for July 10, 1920. Several points of ambiguity had to be cleared up after this initial publication. In particular, it had been Mr. Higgins' suggestion that in the very probable event of the Judges' inability to agree upon the winning essay, the prize might, at their discretion, be divided between the contributors of the best two essays. This condition was actually printed in the first announcement, but the Post Office Department insisted upon its withdrawal, on the ground that with it in force the contestant would not know whether he were competing for $5,000 or for $2,500, and that this would introduce the "element of chance" which alone was necessary, under the Federal statutes, to make the contest a lottery. So this provision was replaced by one to the effect that in the event the Judges were not able to agree, the Einstein Editor should cast the deciding vote between the essays respectively favored by them.

The announcement attracted the widest attention, and was copied in newspapers and magazines all over the world. Inquiries poured in from all quarters, and the Einstein Editor found it almost impossible to keep himself supplied with proofs of the conditions and rules to mail in response to these inquiries. It was immediately clear that there was going to be a large number of essays submitted, and that many distinguished names would be listed among the competitors.

THE JUDGES

In the Scientific American for September 18, announcement was carried in the following words:

"We are assured with complete certainty that the competition for the five-thousand-dollar prize will be very keen, and that many essays will be submitted which, if they bore the names of their authors, would pass anywhere as authoritative statements. The judges will confront a task of extraordinary difficulty in the effort to determine which of these efforts is the best; and we believe the difficulties are such that multiplication of judges would merely multiply the obstacles to an agreement. It is altogether likely that the initial impressions of two or three or five judges would incline toward two or three or five essays, and that any final decision would be attainable only after much consultation and discussion. It seems to us that by making the committee as small as possible while still preserving the necessary feature that its decision represent a consensus, we shall simplify both the mental and the physical problem of coming to an agreement. We believe that the award should if possible represent a unanimous decision, without any minority report, and that such a requirement is far more likely to be met among two men than among three or five. At the same time, the bringing together of two men and the details of general administration of their work together are far simpler than if there were three or five. So we have finally decided to have but two judges, and in this we have the endorsement of all the competent opinion that we have consulted.

"The gentlemen who have consented to act as Judges are Professors Leigh Page and Edwin Plimpton Adams, of the departments of physics of Yale and Princeton Universities, respectively. Both are of the younger generation of physicists that has paid special attention to those phases of mathematics and physics involved in the Einstein theories, and both have paid special attention to these theories themselves. We are gratified to be able to put forward as Judges two men so eminently qualified to act. We feel that we may here appropriately quote Professor Page, who says in his acceptance: 'As the large prize offers a great inducement, I had thought of entering the contest. However I realize that not many people in this country have made a considerable study of Einstein's theory, and if all who have should enter the contest, it would be difficult to secure suitable Judges.' Without any desire to put the gentleman in the position of pleading for himself, we think this suggests very well the extent to which the Scientific American, the contestants, and the public at large, are indebted to Professors Page and Adams for their willingness to serve in the difficult capacity of Judges."

It might appropriately have been added to this announcement that it was altogether to the credit of science and the scientific spirit that the first two gentlemen approached with the invitation to act as Judges were willing to forego their prospects as contestants in order thus to contribute to the success of the contest.

THREE THOUSAND WORDS

Of the conditions, the one which evoked most comment was that stating the word limit. This limit was decided upon after the most careful discussion of the possibilities of the situation. It was not imagined for a moment that any contestant would succeed in getting within 3,000 words a complete discussion of all aspects of the Special and the General Theories of Relativity. It was however felt that for popular reading a single essay should not be much if any longer than this. Moreover, I will say quite frankly that we should never have encouraged Mr. Higgins to offer such a prize if we had supposed that the winning essay was the only thing of value that would come from the contest, or if we had not expected to find in many of the other essays material which would be altogether deserving of the light. From the beginning we had in view the present volume, and the severe restriction in length was deliberately imposed for the purpose of forcing every contestant to stick to what he considered the most significant viewpoints, and to give his best skill to displaying the theories of Einstein to the utmost advantage from these viewpoints. We felt that divergent viewpoints would be more advantageously treated in this manner than if we gave each contestant enough space to discuss the subject from all sides; and that the award of the prize to the essay which, among other requirements, seemed to the Judges to embody the best choice of material, would greatly simplify the working of the contest without effecting any injustice against those contestants who displayed with equal skill less happily chosen material. Perhaps on this point I may again quote with profit the editorial page of the Scientific American:

"An essay of three thousand words is not long enough to lose a reader more than once; if it does lose him it is a failure, and if it doesn't it is a competitor that will go into the final elimination trials for the prize. If we can present, as a result of the contest, six or a dozen essays of this length that will not lose the lay reader at all, we shall have produced something amply worth the expenditure of Mr. Higgins' money and our time. For such a number of essays of such character will of necessity present many different aspects of the Einstein theories, and in many different ways, and in doing so will contribute greatly to the popular enlightenment.

"Really the significant part of what has already appeared is not the part that is intelligible, but rather the part that, being unintelligible, casts the shadow of doubt and suspicion on the whole. The successful competitor for the prize and his close contestants will have written essays that, without any claim to completeness, will emphasize what seems to each author the big outstanding feature; and every one of them will be intelligible. Together they will in all probability be reasonably complete, and will retain the individual characteristic of intelligibility. They will approach the various parts of the field from various directions--we could fill this page with suggestions as to how the one item of the four-dimensional character of Einstein's time-space might be set forth for the general reader. And when a man must say in three thousand words as much as he can of what eminent scientists have said in whole volumes--well, the result in some cases will be sheer failure, and in others a product of the first water. The best of the essays will shine through intelligent selection of what is to be said, and brilliant success in saying it. It is to get a group of essays of this character, not to get the single essay which will earn the palm, that the prize is offered."

THE COMPETING ESSAYS

At all times after the first announcement the Einstein Editor had a heavy correspondence; but the first real evidence that the contest was under way came with the arrival of the first essay, which wandered into our office in the middle of September. About a week later they began to filter in at the rate of one or two per day--mostly from foreign contestants who were taking no chances on the mails. Heavy returns did not commence until about ten days before the closing date. The great avalanche, however, was reserved for the morning of Monday, November 1st. Here we had the benefit of three days' mail; there were about 120 essays. Among those which were thrown out on the ground of lateness the honors should no doubt go to the man who mailed his offering in The Hague on October 31st.

Essays were received in greater quantity from Germany than from any other foreign country, doubtless because of the staggering value of $5,000 when converted into marks at late 1920 rates. England stood next on the list; and one or more essays were received from Austria, Czechoslovakia, Jugoslavia, France, Switzerland, the Netherlands, Denmark, Italy, Chile, Cuba, Mexico, India, Jamaica, South Africa and the Fiji Islands. Canada, of course, contributed her fair share; and few of our own states were missing on the roll-call.

The general level of English composition among the essays from non-English-speaking sources was about what might have been expected. A man may have a thorough utilitarian knowledge of a foreign tongue, but when he attempts intensive literary competition with a man who was brought up in that tongue he is at a disadvantage. We read French and German with ease and Spanish and Italian without too much difficulty, ourselves; we should never undertake serious writing in any of these languages. Not many of the foreign contributions, of course, were as ludicrous as the one we quote to some extent in our concluding chapter, but most of them were distinctly below par as literary compositions. Drs. De Sitter and Schlick were the notable exceptions to this; both showed the ability to compete on a footing of absolute equality with the best of the native product.

We dare say it was a foregone conclusion that many essays should have been over the limit, and that a few should have been over it to the point of absurdity. The winning essay contains 2,919 words, plus or minus a reasonable allowance for error in counting; that it should come so far from being on the ragged edge should be sufficient answer to those who protested against the severity of the limitation. One inquirer, by the way, wanted to know if 3,000 words was not a misprint for 30,000. Another contestant suggested that instead of disqualifying any essay that was over the line, we amputate the superfluous words at the end. This was a plausible enough suggestion, since any essay able to compete after such amputation must necessarily have been one of extreme worth; but fortunately we did not have to decide whether we should follow the scheme. Perhaps twenty of the essays submitted were so seriously in excess of the limit that it was not even necessary to count their words in detail; most of these offenders ran to 3,500 words or thereabouts, and one--a good one, too, from which we use a good deal of material in this volume--actually had 4,700. On the other extreme were a few competitors who seemed to think that the shortest essay was necessarily the best, and who tried to dismiss the subject with 500 or 1,000 words.

By a curious trick of chance there were submitted in competition for the prize exactly 300 essays. Of course a few of these did not require serious consideration--this is inevitable in a contest of such magnitude. But after excluding all the essays that were admittedly not about the Einstein theories at all, and all those whose English was so execrable as to make them quite out of the question, and all those which took the subject so lightly as not to write reasonably close to the limit of 3,000 words, and all those which were given over to explanation of the manner in which Einstein's theories verify those of the writer, and all those in which the writer attempted to substitute his own cosmic scheme for Einstein's--after all this, there remained some 275 essays which were serious efforts to explain in simple terms the nature and content and consequences of Special and General Relativity.

LOOKING FOR THE WINNER

The Einstein Editor was in sufficiently close touch with the details of the adjudication of the essays to have every realization of the difficulty of this work. The caliber of the essays submitted was on the whole high. There were many which would have been well worthy of the prize in the absence of others that were distinctly better--many which it was not possible to eliminate on the ground of specific faults, and which could only be adjudged "not the best" by detailed comparison with specific other essays. It was this detailed comparison which took time, and which so delayed the award that we were not able to publish the winning essay any sooner than February 5th. Especially difficult was this process of elimination after the number of surviving essays had been reduced to twenty or less. The advantages of plan possessed by one essay had to be weighed against those of execution exhibited in another. A certain essay had to be critically compared with another so like it in plan that the two might have been written from a common outline, and at the same time with a third as unlike it in scope and content as day and night. And all the time there was present in the background the consciousness that a prize of $5,000 hung upon the decision to be reached. For anyone who regards this as an easy task we have no worse wish than that he may some day have to attack a similar one.

We had anticipated that the bulk of the superior essays would be among those received during the last day or two of the contest; for we felt that the men best equipped to attack the subject would be the most impressed with its seriousness. Here we were quite off the track. The seventeen essays which withstood most stubbornly the Judges' efforts at elimination were, in order of receipt, numbers 8, 18, 28, 40, 41, 43, 92, 95, 97, 130, 181, 194, 198, 223, 267, 270, 275: a fairly even distribution. The winner was the 92nd essay received.

The Judges held their final meeting in the editorial office on January 18, 1921. The four essays which were before the committee at the start of the session were speedily cut to three, and then to two; and after an all-day session the Judges found themselves conscientiously able to agree on one of these as the best. This unanimity was especially gratifying, the more so since it by no means was to be confidently expected, on a priori grounds, that it would be possible of attainment. Even the Einstein Editor, who might have been called upon for a final decision but wasn't, can hardly be classed as a dissenter; for with some slight mental reservations in favor of the essay by Mr. Francis which did not enter the Judges' final discussion at all, and which he rather suspects appeals more to his personal taste than to his soundest judgment, he is entirely in accord with the verdict rendered.

The fact that the prize went to England was no surprise to those acquainted with the history of Einstein's theories. The Special Theory, promulgated fifteen years ago, received its fair share of attention from mathematicians all over the world, and is doubtless as well known and as fully appreciated here as elsewhere. But it has never been elevated to a position of any great importance in mathematical theory, simply because of itself, in the absence of its extension to the general case, it deserves little importance. It is merely an interesting bit of abstract speculation.

The General Theory was put out by Einstein in finished form during the war. Owing to the scientific moratorium, his paper, and hence a clear understanding of the new methods and results and of the sweeping consequences if the General Theory should prevail, did not attain general circulation outside Germany until some time in 1918 or even later. Had it not been for Eddington it is doubtful that the British astronomers would have realized that the eclipse expeditions were of particular consequence. Therefore at the time of these expeditions, and even as late as the November announcement of the findings, the general body of scientific men in America had not adequately realized the immense distinction between the Special and the General Theories, had not adequately appreciated that the latter led to distinctive consequences of any import, and we fear in many cases had not even realized explicitly that the deflection of light and the behavior of Mercury were matters strictly of the General and in no sense of the Special Theory. Certainly when the American newspapers were searching frantically for somebody to interpret to their public the great stir made by the British announcement that Einstein's predictions had been verified, they found no one to do this decently; nor were our magazines much more successful in spite of the greater time they had to devote to the search. In a word, there is not the slightest room for doubt that American science was in large measure caught asleep at the switch--perhaps for no reason within its control; and that American writers were in no such favorable case to write convincingly on the subject as were their British and continental contemporaries.

So it was quite in accord with what might have been expected to find, on opening the identifying envelopes, that not alone the winning essay, but its two most immediate rivals, come from members of that school of British thought which had been in contact with the Einstein theories in their entirety for two years longer than the average American of equal competence. This riper familiarity with the subject was bound to yield riper fruit. Indeed, had it not been for the handicap of writing in a strange language, it is reasonable to assume that the scientists of Germany would have made a showing superior to that of either Americans or British--and for the same reason that Britain showed to better advantage than America.

THE WINNER OF THE PRIZE

Mr. Bolton, the winner of the big prize, we suppose may fairly be referred to as unknown in a strict scientific sense. Indeed, at the time of the publication of his essay in the Scientific American nothing could be learned about him on the American side of the water beyond the bare facts that he was not a young man, and that he had for a good many years occupied a position of rank in the British Patent Office. (It will be recalled that Einstein himself was in the Swiss Patent Office for some time.) In response to the request of the Scientific American for a brief biographical sketch that would serve to introduce him better to our readers, Mr. Bolton supplied such a concise and apparently such a characteristic statement that we can do no better than quote it verbatim.

"I was born in Dublin in 1860, but I have lived in England since 1869. My family belonged to the landed gentry class, but I owe nothing to wealth or position. I was in fact put through school and college on an income which a workman would despise nowadays. After attending sundry small schools, I entered Clifton College in 1873. My career there was checkered, but it ended well. I was always fairly good at natural science and very fond of all sorts of mechanical things. I was an honest worker but no use at classics, and as I did practically nothing else for the first four years at Clifton, I came to consider myself something of a dunce. But a big public school is a little world. Everyone gets an opportunity, often seemingly by accident, and it is up to him to take it. Mine did not come till I was nearly 17. As I was intended for the engineering profession, I was sent to the military side of the school in order to learn some mathematics, at which subject I was then considered very weak. This was certainly true, as at that time I barely knew how to solve a quadratic, I was only about halfway through the third book of Euclid, and I knew no trigonometry. But the teaching was inspiring, and I took readily to mathematics. One day it came out that I had been making quite a good start with the differential calculus on my own without telling anybody. After that all was well. I left Clifton in 1880 with a School Exhibition and a mathematical scholarship at Clare College, Cambridge.

"After taking my degree in 1883 as a Wrangler, I taught science and mathematics at Wellington College, but I was attracted by what I had heard of the Patent Office and I entered it through open competition in 1885. During my official career I have been one of the Comptroller's private secretaries and I am now a Senior Examiner. During the war I was attached to the Inventions Department of the Ministry of Munitions, where my work related mainly to anti-aircraft gunnery. I have contributed, and am still contributing to official publications on the subject.

"I have written a fair number of essays on various subjects, even on literature, but my only extra-official publications relate to stereoscopic photography. I read a paper on this subject before the Royal Photographic Society in 1903 which was favorably noticed by Dr. von Rohr of Messrs. Zeiss of Jena. I have also written in the Amateur Photographer.

"I have been fairly successful at athletics, and I am a member of the Leander Club."

That Mr. Bolton did not take the prize through default of serious competition should be plain to any reader who examines the text from competing essays which is to be found in this volume. The reference list of these competitors, too, supplemented by the names that appear at the heads of complete essays, shows a notable array of distinguished personalities, and I could mention perhaps a dozen more very well known men of science whose excellent essays have seemed a trifle too advanced for our immediate use, but to whom I am under a good deal of obligation for some of the ideas which I have attempted to clothe in my own language.

Before leaving the subject, we wish to say here a word of appreciation for the manner in which the Judges have discharged their duties. The reader will have difficulty in realizing what it means to read such a number of essays on such a subject. We were fortunate beyond all expectation in finding Judges who combined a thorough scientific grasp of the mathematical and physical and philosophical aspects of the matter with an extremely human viewpoint which precluded any possibility of an award to an essay that was not properly a popular discussion, and with a willingness to go to meet each other's opinions that is rare, even among those with less ground for confidence in their own views than is possessed by Drs. Page and Adams.

II.

THE WORLD--AND US

An Introductory Discussion of the Philosophy of Relativity, and of the Mechanism of Our Contact with Time and Space

BY VARIOUS CONTRIBUTORS AND THE EDITOR

From a time beyond the dawn of history, mankind has been seeking to explain the universe. At first the effort did not concern itself further probably than to make a supposition as to what were the causes of the various phenomena presented to the senses. As knowledge increased, first by observation and later by experiment also, the ideas as to these causes passed progressively through three stages--the theological (the causes were thought to be spirits or gods); the metaphysical (the causes were thought in this secondary or intermediate stage to be some inherent, animating, energizing principles); and the scientific (the causes were finally thought of as simply mechanical, chemical, and magneto-electrical attractions and repulsions, qualities or characteristics of matter itself, or of the thing of which matter is itself composed.)

With increase of knowledge, and along with the inquiry as to the nature of causes, there arose an inquiry also as to what reality was. What was the essential nature of the stuff of which the universe was made, what was matter, what were things in themselves, what were the noumena (the realities), lying back of the phenomena (the appearances)? Gradually ideas explaining motion, force, and energy were developed. At the same time inquiry was made as to the nature of man, the working of his mind, the nature of thought, the relation of his concepts (ideas) to his perceptions (knowledge gained through the sense) and the relations of both to the noumena (realities).]283

[The general direction taken by this inquiry has been that of a conflict between two schools of thought which we may characterize as those of absolutism and of relativism.]* [The ancient Greek philosophers believed that they could tap a source of knowledge pure and absolute by sitting down in a chair and reasoning about the nature of time and space, and the mechanism of the physical world.]221 [They maintained that the mind holds in its own right certain concepts than which nothing is more fundamental. They considered it proper to conceive of time and space and matter and the other things presented to their senses by the world as having a real existence in the mind, regardless of whether any external reality could be identified with the concept as ultimately put forth. They could even dispute with significance the qualities which were to be ascribed to this abstract conceptual time and space and matter. All this was done without reference to the external reality, often in defiance of that reality. The mind could picture the world as it ought to be; if the recalcitrant facts refused to fit into the picture, so much the worse for them. We all have heard the tale of how generation after generation of Greek philosophers disputed learnedly why and how it was that a live fish could be added to a brimming pail of water without raising the level of the fluid or increasing the weight; until one day some common person conceived the troublesome idea of trying it out experimentally to learn whether it were so--and found that it was not. True or false, the anecdote admirably illustrates the subordinate place which the externals held in the absolutist system of Greek thought.]*

[Under this system a single observer is competent to examine a single phenomenon, and to write down the absolute law of nature by referring the results to his innate ideas of absolute qualities and states. The root of the word absolute signifies "taking away," and in its philosophical sense the word implies the ability of the mind to subtract away the properties or qualities from things, and to consider these abstract qualities detached from the things; for example, to take away the coldness from ice, and to consider pure or abstract coldness apart from anything that is cold; or to take away motion from a moving body, and to consider pure motion apart from anything that moves. This assumed power is based upon the Socratic theory of innate ideas. According to this theory the mind is endowed by nature with the absolute ideas of hardness, coldness, roundness, equality, motion, and all other absolute qualities and states, and so does not have to learn them. Thus a Socratic philosopher could discuss pure or absolute being, absolute space and absolute time.]121

GETTING AWAY FROM THE GREEK IDEAS

[This Greek mode of thought persisted into the late Middle Ages, at which time it was still altogether in order to dispose of a troublesome fact of the external world by quoting Aristotle against it. During the Renaissance, which intellectually at least marks the transition from ancient to modern, there came into being another type of absolutism, equally extreme, equally arbitrary, equally unjustified. The revolt against the mental slavery to Greek ideas carried the pendulum too far to the other side, and early modern science as a consequence is disfigured by what we must now recognize as gross materialism. The human mind was relegated to the position of a mere innocent bystander. The external reality was everything, and aside from his function as a recorder the observer did not in the least matter. The whole aim of science was to isolate and classify the elusive external fact. The rôle of the observer was in every possible way minimized. It was of course his duty to get the facts right, but so far as any contribution to these was concerned he did not count--he was definitely disqualified. He really played the part of an intruder; from his position outside the phenomena he was searching for the absolute truth about these phenomena. The only difference between his viewpoint and that of Aristotle was that the latter looked entirely inside himself for the elusive "truth," while the "classical" scientist, as we call him now, looked for it entirely outside himself.

Let me illustrate the difference between the two viewpoints which I have discussed, and the third one which I am about to outline, by another concrete instance. The Greeks, and the medievals as well, were fond of discussing a question which embodies the whole of what I have been saying. This question involved, on the part of one who attempted to answer it, a choice between the observer and the external world as the seat of reality. It was put in many forms; a familiar one is the following: "If the wind blew down a great tree at a time and place where there was no conscious being to hear, would there be any noise?" The Greek had to answer this question in the negative because to him the noise was entirely a phenomenon of the listener. The classical scientist had to answer it in the affirmative because to him the noise was entirely a phenomenon of the tree and the air and the ground. Today we answer it in the negative, but for a very different reason from that which swayed the Greek. We believe that the noise is a joint phenomenon of the observer and the externals, so that in the absence of either it must fail to take existence. We believe there are sound waves produced, and all that; but what of it? There is no noise in the presence of the falling tree and the absence of the observer, any more than there would be in the presence of the observer and the absence of the tree and the wind; the noise, a joint phenomenon of the observer and the externals, exists only in their joint presence.

RELATIVISM AND REALITY

This is the viewpoint of relativism. The statue is golden for one observer and silver to the other. The sun is rising here and setting in another part of the world. It is raining here and clear in Chicago. The observer in Delft hears the bombardment of Antwerp and the observer in London does not. If they were to be consistent, both the Greek and the medieval-modern absolutist would have to dispute whether the statue were "really" golden or silver, whether the sun were "really" rising or setting, whether the weather were "really" fair or foul, whether the bombardment were "really" accompanied by loud noises or not; and on each of these questions they would have to come to an agreement or confess their methods inadequate. But to the relativist the answer is simple--whether this or that be true depends upon the observer. In simple cases we understand this full well, as we have always realized it. In less simple cases we recognize it less easily or not at all, so that some of our thought is absolutist in its tendencies while the rest is relativistic. Einstein is the first ever to realize this fully--or if not this, then the first ever to realize it so fully as to be moved toward a studied effort to free human thought from the mixture of relativism and absolutism and make it consistently the one or the other.

This brings it about that the observed fact occupies a position of unexpected significance. For when we discuss matters of physical science under a strictly relativistic philosophy, we must put away as metaphysical everything that smacks of a "reality" partly concealed behind our observations. We must focus attention upon the reports of our senses and of the instruments that supplement them. These observations, which join our perceptions to their external objects, afford us our only objective manifestations; them we must accept as final--subject always to such correction as more refined observations may suggest. The question whether a "true" length or area or mass or velocity or duration or temperature exists back of the numerical determination, or in the presence of a determination that is subject to correction, or in the absence of any determination at all, is a metaphysical one and one that the physicist must not ask. Length, area, mass, velocity, duration, temperature--none of these has any meaning other than the number obtained by measurement.]* [If several different determinations are checked over and no error can be found in any of them, the fault must lie not with the observers but with the object, which we must conclude presents different values to different observers.]33

[We are after all accustomed to this viewpoint; we do not demand that Pittsburgh shall present the same distance from New York and from Philadelphia, or that the New Yorker and the Philadelphian come to any agreement as to the "real" distance of Pittsburgh. The distance of Pittsburgh depends upon the position of the observer. Nor do we demand that the man who locates the magnetic pole in one spot in 1900 and in another in 1921 come to a decision as to where it "really" is; we accept his statement that its position depends upon the time of the observation.

What this really means is that the distance to Pittsburgh and the position of the magnetic pole are joint properties of the observer and the observed--relations between them, as we might put it. This is obvious enough in the case of the distance of Pittsburgh; it is hardly so obvious in the case of the position of the magnetic pole, varying with the lapse of time. But if we reflect that the observation of 1900 and that of 1921 were both valid, and both represented the true position of the pole for the observer of the date in question, we must see that this is the only explanation that shows us the way out.