The Two Knights and Alice

THE UNIVERSITY OF TORONTO QUARTERLY THE TWO KNIGHTS AND ALICE* A. ·E. FooT Until the end of the last century.) the task of the men ln the vanguard of scientific research was to answer clear and definite questions :-W~at is a glacier? How are the carbon atoms joined together in a molecule of benzene? What connecti.on is there between chemical action and the passage of electricity through a solution? The answers were eminently satisfactory and secured for the answerers with their experimental skill a lasting fame. But times have changed. Sir James Jeans tells of a clear and definite question that secured.) in the Michelson-M~rley experiment.) an answer that was pure nonsense. The reaction of science to this momentous incident was slow but of profound significance; it will be particularly appreciated by members of the teaching profession with their familiar readiness to complain of the stupidity of ~heir pupils in answering questions. I~ was the question and not the answer that was at fault. Since that time the effort to paint in a background to the stage of the universe (on which the performance of the actors was already pretty well known) has rested with the men who have studied the nature of the questions that must be asked of the physical world. , When the electron was first introduced to the general public in I 897, it seemed to be a satisfactory sort of marble to form a basis for the construction of matter. But the mathematicians have shown that it must be futile to inquire simultaneously of ah electron both its position and its velocity. And the mathematicians have shown. that when we ask many other questions about the begin:- *The New Background of Science, by Sir James Jeans, F.R.S., Cambridge University Press (Macmillans in Canada, $2.00). The Expanding Unioerse, by Sir Arthur Eddington, F.R.S., Cambridge University Press (Macmillans in Canada, $1.50). 122 REVIEWS ning and end of the world, its size and its structure, we are only behaving as loyal successors to Charles II in his demands of the Royal Society. It is said that the layman's school education in mathe- .rnatics contains no discussion of material that has been developed since 168o; it is unlikely, therefore, that many of the tens of thousands who have cultivated the habit of reading Professor Jeans's la'st books will understand any of the mathematical formulae in chapters v and vi. And such is the mistrust of the educated mind in the application of a formula of which the derivation is concealed, that, on reading the conclusions in chapters vii and viii, the reader may feel like an English matron when presented with the product of a clever French cook: it may be good, but did it really start from good butcher's meat? In the same way the formula of a synthetic organic dye may appear to the chemist to illuminate for a lay audience the method of its manufacture and use; but experience shows that a lay audience will dismiss it as a jumble of meaningless symbols. Professor Jeans inevitably leaves hi·s readers suspended by a thread between two stools. The·first stool is one of the sort to which they may be accustomed; the legs are · decorated with a variety of homely illustration and analogy. -The carving and symbolism of these is not quite so apt as that to which readers of Professor Eddington are accustomed: photons are not very much like potatoes; but there is nothing which <;ioes not keep a :firm contact with familiar ideas. But the other stool appears to have nothing recognizable to the lay1nan as a leg at all. A mathematician may attempt to persuade us that unit diagonal matrices, operators, and the equations of vvave mechanics are solid wood, but they have to be attached to the seat by the mathematician's universal nail-the square root of minus I. The reader 'may have 123 THE UNIVERSITY OF TORONTO QUARTERLY the same distaste for trusting himself to the stool as a novice in the mountains for an unroped excursion along steps on an ice-wall, even with the assurance from a guide of unimpeachable reliability that it is perfectly safe. The suspending thread is a philosophical one, and it is the chief merit of the book that ·its origin is clearly traced. With extensive quotation the strands provided by Plato, Descartes, Newton, Kant, Bradley, Planck, Whitehead, and others,·are interwoven into a new and satisfactory rope. It is not only the price and the size which will bring a greater number of readers through The Expanding Universe. Being the enlarged version of a single lecture, it unrolls itself as a single film rather than as a group of pictures of related objects taken from a variety of angles. The scope of this book is quite different, but it is natural to consider it at the same time as that of Professor Jeans since it will attract the same kind of reader in the same kind of mood. An expert reporter has been engaged on the reconstruction of an incident, which he refers to as a crime. We must pass over the implications of Sir Arthur Eddington 's suggestion that the existence and evolution of the universe is of a criminal nature. He uses this analogy because crime is one of the few occurrences in life that stimulate the interest of the average man. He first makes a clear statement of the observational data, and at orice answers all the questions which an intelligent but ignorant audience would ask. He states the law of the recession of the galaxies; and in the same first chapter he answers all these questions:How is the distance of a galaxy measured? How is its velocity found? How many galaxies have been thus examined? Are all galaxies receding? Why did you not 124 REVIEWS tell us about this in The Nature of the Physical World? Will more galaxies be discovered? Is there any limit to their measured distance from us? Is there ·any independent evidence for the remarkable circumstances that you relate? What degree of accuracy can be claimed for the measurements? We leave chapter i with a clear idea of the due on which the detectives are working, and in chapters ii and iii we are given a picture of one way in which such a crime may have been committed and the conceivable future consequences of the existence of such a criminal. The reader is given just that stimulus to the imagination which brings the Sunday newspapers their million-circulations . There is a picture which he can visualize; a pimply rubber balloon, a pin standing on its head, a twisted ring of blotting paper with a series of blots. These analogies seem ·to carry us definitely a stage further than the clue; and that is the reason that Professor Eddington gives us more intellectual pleasure than we derive from Professor Jeans's potatoes or railway tickets or even his search for John Smith. Fortunately for the inexpert reader, Professor Eddington does not involve us in the motive for the crime. He knows that we are not trained psychologists (that is to say, mathematicians), and he appreciates that we cannot understand the only language in which their conclusions can be expressed. But although the reporter has told a very attractive story, it seems to be possible that the Scotland Yard men will be saying: "That may well please your registered readers, but some of our men have other ways of interpreting the clues, perhaps not so startling nor so artistic, but we have to consider a court of law and a jury; and this is not Hollywood." Moreover, the Scotland Yard men proverbially have big boots and no emotiohs; they 125 THE UNIVERSITY OF TORONTO QUARTERLY are likely to look with mistrust on a story told by a man who is capable of ~'dislike of an in1putation," "aesthetic feeling," "disposition to blame," or even "an uneasy feeling." In the last .chapter we are shown that there is a link between the very large and the very small. The link is disclosed by means of symbols and equations that are of a'pattern familiar to the laytnan, and we are left with a consciousness of the significance of two nu1nhers, 79 and 137; these are just the sort of numbers that would havebeen selected by the \iVhite Queen, who, after all, was the real prophetess of relativity. -And, like Alice, we emerge from the book feeling the richer from our experience of a world in which ideas are connected together by arguments expressed with a ~onvincing assurance but with results that make us gasp alittle: "And if you take one from 365," said Humpty Dumpty ''what remains?" "364, of course," said Alice. "That shows that there are 364 days when you might get un-birthday presents-" - "Certainly;• said Alice. "And only one for birthday presents. There's glory for you!•' "I don•t know what you mean by 'glory'," Alice said. Humpty Dumpty smiled contemptuously. "Of course you don't-till I tell you. I meant