[Math Lair] The Search for Truth: Chapter II: Case Histories

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Chapter II



LEST the above subtitle rouse unwarranted suspicions in the mind of anyone, I give him or her my solemn assurance that I have never been inside a lunatic asylum, either as guest or observer. Indeed it seems to me that a trip to the asylum in these depressed times is rank extravagance and quite unnecessary. There is so much to be seen on the outside.

No one man is competent to prescribe for all the fatty degeneration of the intellect which characterizes our times; the utmost anyone can hope to do is to apply to himself that most excellent advice, "Physician heal thyself." But, as any physician knows, even the best attempts at doctoring oneself are apt to end in ludicrous disaster. Before an illness can be helped something must be understood about it, and one of the accepted ways of understanding a disease is to study it in the laboratory or hospital. By helping to heal others the physician accumulates a rich store of experience which may some day help others to save his own life.

Applying this to the distressing degeneration mentioned, I concluded that the safest insurance against the disease is probably an impartial, disinterested study of a few of the most aggravated cases available. By a detached scrutiny of muddied thinking we may not unreasonably hope to keep our own heads cool and clear. Anyhow, it is less dangerous than deliberately muddling ourselves just to see how it feels. Good gin is cheaper, and the effect wears off sooner.

In this first case I had the able assistance of an extraor­dinarily acute woman, whom I shall call Toby. Through no fault of her own, Toby happened at the time to be suffering from a hypothyroid condition. Her balky thyroid made her feel as if her neck were a yard, long and her head somebody's else's business. At the lowest point of her illness she confused herself with Alice in one of the adventures in Wonderland, and nothing will now convince her that Lewis Carroll was not hypothyroid when he imagined the neck-stretching episode.

The elongated neck was only a minor part of Toby's distress. Ordinary honest print, whether in newspapers or books, or on highway signs, began to do all sorts of queer things whenever the groggy Toby glanced in its direction. What happened to dishonest advertising under Toby's inspired vision is a modern miracle: the lies shimmered like a landscape in a heat haze, the letters melted into new shapes and rearranged themselves, and the lying advertisement blurted out the truth it had been skillfully devised to conceal. Had this gifted woman lived in the fourteenth Century, she undoubtedly would have been canonized and immortalized in stained glass for her unerring ability to discern the truth behind a thick blather of propaganda. One example to substantiate this claim must suffice.

In the town where Toby lives there is a very flashy sort of general food store which caters to the snobbish trade—the kind of customer who thinks she is being cheated unless the high-hat tradesman charges her an outrageous price for an inferior brand of goods which could be picked up for next to nothing half a block down the street. One boast which this store for the c.lite made in its Halloween advertising read, "You will And our catering department packed with suitable goodies." The honest thyroid caused Toby to see, instead of "suitable goodies," the absolute truth, "gullible boobies."

Impressed by this remarkable exhibition of glandular clairvoyance, I begged Toby's assistance in understanding what had seemed to me to be a brilliantly muddled set of lectures by one of the most eminent churchmen of our generation. Toby de­murred at first, on the ground that she might do the good man an injustice in her queer psychic condition. But finally she consented, when I pointed out that she, with her elongated neck, stood a good chance of intercepting some of the shots which had gone clean over my head. The lectures in question were published in 1933 under the title God and the Astronomers: containing the Warburton Lectures 1931—33. By the Very Reverend Dean Inge. The lectures fill 308 pages. It may be necessary first to introduce the Dean.

Dean Inge is the Dean of St. Paul's Cathedral, London. In the British press he is often referred to as "the gloomy dean." This nickname the Dean brought down upon his own pate by his blunt outspokenness on a variety of topics, embracing practically everything from St. Paul and birth control to Cardinal Newman and immortality. The Dean recognizes, of course, that if birth control were pushed to its logical conclusion all discussions of immortality would become purely academic, so he does not, I believe, advocate extreme measures. From his Outspoken Essays, no less than from his recent attempt to reconcile God and the astronomers, it is plain that the Dean is a sincere seeker after truth. "Seek, and ye shall find" seems to be his motto. It may succeed in theology; in science it doesn't always work out as it should. The earnest seeker too often tumbles head first into a mare's nest.

Dean Inge takes life very seriously—too seriously, perhaps. Being as innocent as an unweaned babe of any scientific training, and lacking that instinctive tact which enables less seriously minded mortals to laugh off any particularly gloomy scientific prophecy, the Dean also takes science seriously, especially where it seems to impinge on that nebulous happy hunting ground of the philosophers and metaphysicians, the theory of "values"—human, ethical, moral, social, religious, or whatnot. We leave the Dean here and return to Toby.

One really good sniff at the title of the lectures was enough to whet Toby's appetite for the whole juicy gobbet. Scenting

her proper meat, she grabbed God and the Astronomers and settled down to devour it. From the studious silence pervading the room I judged that she was getting her teeth into it, and when presently she began to growl occasionally, like a dog with a refractory bone, I knew that she was. Her musings became coherent.

"Now what the devil does he mean by that?" she muttered.

"By what?" I asked. "But a lady is not supposed to swear in the presence of a Dean."

"He says the astronomers tell us—," and she proceeded to skim off a few of the choicer chunks of preposterous bosh bobbing here and there, all plainly labelled with the trademark "astronomy," in the tepid stew of Victorian moralizing and twice warmed-over homiletics. "The astronomers ?" she snorted "What astronomers? And how many of them?"

I tried to pacify her by pointing out that the good Dean had perfect right to cite "the astronomers" as authority for his ill digested hash of popular astronomy. He had in fact quoted precisely two, and those two the pair whose names—outside of professional astronomical circles—are synonymous with the whole vast domain of modern astronomical and astrophysical research. That these two frequently stage a sort of dignified scientific knock-down and drag-out prize fight to the unbounded delight of the hard-boiled and hard-headed professional scientific world in general, contradicting one another flatly on matters of high speculation, does not seem to have bothered the accommodating Dean at all. Like an ancient Egyptian hierophant reconciling the nonsensical contradictions of some absurd trinity, the Dean has integrated A's heated assertion "I tell you it is so," and B's equally positive denial "I tell you it isn't," into a transcendental sort of supersense in which white is black but black is not white. But to return to Toby.

My efforts to avert a war were wasted. The fight was on. Toby had all the ammunition, and she knew how to spend it with deadly effect. Her biggest gun was undoubtedly the fact that she herself is well acquainted with several astronomers, almost any two of whom are rated by their fellow astronomers as more deserving than the Dean's pair of deuces of being designated as "The astronomers"—if it were desirable or profitable to draw such snobbish distinctions in a science where all the honest workers are deeply conscious of their ignorance and correspondingly cautious.

The development of this line of attack was unanswerable. Toby had listened to too many discussions between these men when they were talking shop in plain English, and never once had she heard one of them get off anything even faintly resembling what the Dean would have her believe it is that "the astronomers" tell us. All of these discussions, by the way, had taken place when Toby's thyroid was in perfect working order, which may or may not have been an advantage. Even the least devout astronomer will bear watching occasionally, for have we not Young's assurance that "An undevout astronomer is mad"?

It seemed to me that the learned Dean was getting rather more than he deserved. To restore a juster balance I reminded Toby of Shelley's "Life, like a dome of many-colored glass, stains the white radiance of eternity," and transposed it, in an obvious way, to explain the Dean's understandable muddle as to exactly what the astronomers are trying to get through his ecclesiastical head. Some of this is reproduced in a later chapter on "Old Clo'." Here it is enough to state that my attempt to restore peace and justice brought about my annihilation—in that particular battle.

"Very well," the outraged Toby snapped, "if he knows nothing about physics or astronomy or mathematics, what business has he speculating about them in public> I call it an indecent exposure of ignorance." She was getting quite excited. "Think of all the people who will read what he tells them the astronomers tell us, and believe it on his say-so. What in the name of high Heaven will they make of all this slushy mysticism? What does he want them to make of it?"

Like many another Amazon in an argument, Toby here gave her intuition its head and galloped full tilt into personalities which may all have been true enough, but which did not advance her thesis appreciably. In fact I had difficulty in understanding exactly what her thesis was. One thing seemed clear. Either she had understood the purpose of the book too well, or I had missed it completely.

Toby's biggest bombshell was reserved for the last. "If the devil can cite scripture for a purpose, and if the good Dean can take the name of astronomy in vain, I don't see why I shouldn't meet him on his own ground—right in the parish where he lives—and remind him of something that was said by his own Master about those who mislead innocent or unsuspecting people." I guessed what was coming, and ducked. Toby quoted it from memory, so I trust it is accurate. "Whoso shall offend one of these little ones.... it were better for him that a millstone were hanged about his neck, and that he were drowned in the depth of the sea. Woe unto the world because of offences! For it must need be that offences come; but woe to that man by whom the offence cometh!"

That ended it. Being the stronger physically, I confiscated God and the Astronomers and consigned it to the flames of a roaring hot oakwood fire. As the flames took hold of the sacrifice, Toby pronounced the benediction. What she said about the "suitable goodies" purveyed under misleading trademarks by good, well intentioned men to those innocent souls who will swallow anything, provided the trademark is right and the price impertinent enough, made the flames blush.

Much of what she said had a certain bitter truth about it. She declared that the buyer pays only by giving up a substantial part of his common sense, and is not out any appreciable amount in hard cash. Nevertheless he pays—through the nose, is a rule. For it is not in human nature to parade oneself as a gullible booby, eager to swallow all the doubtful merchandise passed out over the counter by men who admit that they do not know what they are selling, even if one is of that dull stripe. It seems to follow that the payment is exacted under something perilously close to false pretenses, and is not made willingly; certainly no one would make such ridiculous purchases with his eyes open.

Who then profits? Not the buyer. And to rub in their excusable misfortune, the law informs those who have had no chance to form an independent judgment of their own on the stuff they are offered that it is the buyer, rather than the seller, who is cautioned to beware. In short they are told to swallow the tainted sacrament they have paid for, to wash it down with liberal draughts of the quack medicine that is given away with each purchase, and to like it. Their only hope is to become thoroughly sick of the stuff' before they poison themselves.

All of this, and much more, Toby managed to get out of her system before the last blue fame from the roasted book flickered up the chimney with a devilish leer of triumph. It was gone, but it knew it would not be forgotten. Anyhow, it inspired Toby's cordial collaboration on the chapter headed "Science and Religiosity."

Toby sat gazing half wistfully at the fire. I suspected her of feeling contrite for some of the things she had said about God and the Astronomers.

"I should like to see the Dean face to face for a minute or two," she sighed.

"Surely you wouldn't expect him to turn the other cheek—Christian though he is—after some of the slaps you gave his perfectly good book?"

"No," she admitted. "But if he'd turn his back for a half a second I'd know what to do."

She was still unrepentant. If more women would have an occasional bout with their thyroids, the world would be a livelier place to live in.


Anyone who cannot take a joke has no business taking any­thing from anyone. But sometimes even the best of jokes can do a deal of mischief, and unless I miss my guess, one of Mr. H. G. Wells' choicest pieces of humor has already done much more than its witty author ever intended it should.

Having had much first hand experience of both the American and the English senses of humor, I have come to believe that English writers would please their American readers more if they would carefully label their jokes. We may as well confess that we do not get them until it is too late to do anything about it. What the late Lord Balfour, for instance, did to us on his visit to the United States in 1917 (or was it 1918?) is only now beginning to dawn on us. And we, who have always prided ourselves on our sense of humor, could kick ourselves for very shame. Our conceit has cost us many a good laugh.

The best joke Mr. Wells ever made was so rich that he allowed himself the luxury of repeating it in his 1933 book, The Shape of Things to Come. With that fascinating forecast as a whole we have no concern here, except possibly to commend it to the attention of all Pollyannas. The joke alone is relevant. lay a brilliant device, Mr. Wells makes it possible for his Dr. Philip Raven to read the "history" of the future. That device is the application to fiction of Mr. J. W. Dunne's Experiment with Time which was published in 1927.

Mr. Dunne is remembered in aeronautical circles as the inventor of one of the oddest flying machines ever imagined by the wit of man. I do not know whether the thing ever actually got its legs off the ground. However, that is of no importance here. Mr. Dunne's theory of time holds that time is "the fourth dimension," just as Einstein's theory does—but there is a difference between Einstein and Dunne.

The theory further holds that human beings in their sleep move freely along this fourth time dimension, and so are enabled to foresee the future. Not that their foresight enables them to do anything about what they see; they have to see it and lump it like dumb boobies, no matter how unpleasant it may be. Otherwise, it wouldn't be the future, and their vision would have been a mere common nightmare. Knowing that the onrushing express is about to hurl them into eternity like so many squashed flies, they just have to sit on the track. The gorgeous muddles on free will and human destiny which the theory offers to the enthusiastic speculator are obvious. They beat even those suggested by the quantum theory with its much discussed "indeterminacy principle." In the fact the whole theory is obvious. A child could understand it.

Mr. Wells now reminds us that he was so smitten with Dunne's theory that in 1927 he advertised it in one or two articles which were widely syndicated in the press of the world. That was just Mr. Wells' little joke. His own Time Machine of 1898 was a much more amusing and prophetic performance than Dunne's Experiment with Time. Good judges rate it as one of the world's great imaginative short stories, and Mr. Wells could have used it instead of the other without undue immodesty.

The joke caught on, disastrously. The syndicated articles never came my way until about two years ago, when a friend—not all my friends are that way—besought me to read both them and Dunne's book.

A word or two about this friend, to bring out the point of all this. My friend is a highly educated man, with a brilliant mind, and moreover his education was strictly scientific after he left school and began studying for his profession. In his own specialty he stands at the very top, and it is no exaggeration to say that his reputation, in his specialty, is nation-wide. By his spectacular successes he has more than earned every bit of fame he has acquired, to say nothing of the money. For obvious reasons I cannot state what his profession is, or I should give the man away completely, and I have no desire to do that, as he is a thoroughly decent sort. His education, I remarked, was severely scientific. But, after the school stage, it included not a single word about mathematics. In the scientific profession for which he was training no mathematics is used.

This brings us to the point of what is to follow immediately. We may expect an occasional ecclesiastic or literary man to be rather naïve about elementary mathematics, and to believe more than the mathematics of a situation proves. But it comes as a bit of a, jolt to find a scientifically trained man, practising a scientific profession, swallowing the most outrageous nonsense about mathematical ideas as if it were the revealed word of God. Mathematical laymen (and some mathematicians, too) have altogether too much awe and respect for mathematical reasoning, or for what non-mathematicians, including the majority of scientific speculators, imagine mathematical proof to be. Not even a long and arduous scientific training can make a man anything but a pathetic gull concerning the "truth" of mathematics, unless that education has also included some mathematics of the modern period—say of the past 35 or 50 years. We shall come back to this later.

My friend begged me to read Dunne's book and Wells' articles on it. He was anxious to have the opinion of someone with a mathematical training on the soundness of Dunne's theory. He was not interested in anyone's opinion of the work as an interesting fantasy; what he insisted upon was a cold-blooded estimate of Dunne's theory as a contribution to science and sanity.

Well, he got it, and he hasn't called on me since. Any other man with a modicum of mathematics and some common sense would have given him exactly the same estimate, although possibly in politer language. I feel strongly about these things, and when I see an intelligent man making a damned fool of himself over them, I spare no pains to tell him what he is doing.

Dunne's theory (and Wells' endorsement of it) is as hopeless a muddle of woolly thinking by means of metaphors and farfetched analogies as any of the more childish efforts of the perpetual motion cranks to do the impossible. Yet my. friend had been irretrievably converted to a wishy-washy spiritualistic mysticism by the book and the articles, and nothing in heaven, earth, or reason can shake his faith that he holds in his hand the magic key to the past, the present, and the future. His reason admitted readily the craziness of the theory; his faith impelled him to counter every destructive argument with the ecstatic affirmation, "But, we move along time in the fourth dimension."

Only once did his faith waver. "Perhaps after all," he mused, "I am suffering from a 'fixed idea.'" But this disturbingly rational thought was brushed aside as immaterial, and he continued to glide evenly along time in the fourth dimension.

This pathetic case is responsible for the chapter on "The Fourth Dimension." That alluring dimension, since Einstein's theory popularized the sound but not the sense of it, has done its part in keeping the nut houses full. But there is a limit, and the taxpayer cannot be expected to support an ever growing army of selfmade philosophers indefinitely.

It so happens that as I write this a series of lectures, open to the public at a not too modest fee, is being given by a lady at one of the luxury hotels of Southern California. The hotel is situated in the same town that fosters two of the best known scientific research organizations in America. In each of those research organizations the fourth, fifth, sixth, and nth dimensions are far commoner than flies. The perfectly sensible meaning of these dimensions is bandied about all day, and an occasional public lecture (no fee) makes the facts about "dimensions" free to anyone who cares to listen. From a circular letter I learn that the lecturing lady is explaining to the patrons of the hotel, also to any others who will pay the fee, exactly how "the fourth dimension" will enable them to live so that they may recapture the virility of their prime, their evaporated dividends, their estranged husbands or wives, and their fugitive faith in God. The name of Einstein is mentioned as a worker in the fourth dimension whose great authority is sufficient guarantee of the scientific soundness of the lady's offering. Her lectures are very well attended indeed, and she has also delivered her fourth-dimensional talks before one of the more intellectual Lord Rayleigh never had the popular following of Dean Inge or Mr. Dunne, so I may be pardoned for saying who he was. In brief, he was one of the outstanding physicists of the Nineteenth and Twentieth Centuries. The first time the Nobel prize in physics was awarded, it went to Rayleigh. His dates are i 84.2,— 1919 and his first popular fame came with his discovery of the unsuspected element argon in the atmosphere. To those who could follow his work, one of his distinguishing traits was his ability to get the maximum substance out of an investigation with a minimum of mathematics. He understood his tools thoroughly, including the English language, and he never wasted a motion, a symbol, or a word. Every scientist in the world knows who Rayleigh was (and is, for his work lives), and

women's clubs of the vicinity. These things may sound incredible, but they are facts. Sometimes we marvel at the coexistence in the same world today of races just emerging from the most primitive savagery dike the Bushmen of Australia) and others who have conquered the air and communicate by wireless over vast distances. Thousands of years separate them. But do we need to go to Australia For a striking comparison? Barely two miles separate the hotel and the research organizations. The fourth dimension would seem to,need some pretty direct handling.

Before leaving Dunne's theory, I should. like to offer a suggestion to any prospective convert. Freud may be as wet as some of his rivals say he is, but for all that his analysis works miracles with a certain type of dream. Try it out on the dream in the Experiment with Time which describes those poor factory girls trapped by the fire. Then, if you don't see through the whole experiment, you are greener than you have any business being in this sexy day and age. I cannot reproduce the dream here, as no wideawake censor would pass it outside of a medical treatise.


Lord Rayleigh never had the popular following of Dean Inge or Mr. Dunne, so I may be pardoned for saying who he was. In brief, he was one of the outstanding physicists of the Nineteenth and Twentieth Centuries. The first time the Nobel prize in physics was awarded, it went to Rayleigh. His dates are 1842–1919, and his first popular fame came with his discovery of the unsuspected element argon in the atmosphere. To those who could follow his work, one of his distinguishing traits was his ability to get the maximum substance out of an investigation with a minimum of mathematics. He understood his tools thoroughly, including the English language, and he never wasted a motion, a symbol, or a word. Every scientist in the world knows who Rayleigh was (and is, for his work lives), and honors him for his character no less than for the great mass of first rate work he did.

In appearance Rayleigh was typically British, as solid as they make them. He might have posed for the portrait of a conservative banker—till the banks began blowing up in the recent unpleasantness. All the more surprising then was his semidetached membership in the Society for Psychical Research, but this was only evidence of his absolute fair-mindedness toward any unsettled question on which thoughtful men might entertain a not wholly irrational doubt. His retiring presidential address to the Society in 1919, reprinted in his collected works, volume 6, p. 642, makes good reading even today. If the spook hunters found their president's farewell remarks rather like a bucketful of icewater on their ebullient enthusiasm it nevertheless was admitted by all to be absolutely fair and in keeping with what a man of Rayleigh's quiet honesty would and could say. There was no bluff or nonsense about Rayleigh.

These remarks should suffice to give some idea of the man's standing in the world of science. For a more adequate picture I must refer the reader to Rayleigh's Life by his son, or to any reputable physicist.

Hear now what this great scientist had to say about science. Although it is nearly fifty years since Rayleigh said these things in his retiring address as president of the British Association for the Advancement of Science, they still embody the creed of most workers in science today. The italics are mine.

"Men who devote their lives to investigation, cultivate a love of truth for its own sake, and endeavor instinctively to clear up, and not, as is too often the object in business or politics, to obscure a difficult question. So far the opinion of a scientific worker may have a special value; but I do not think that he has a claim, superior to that of other educated men, to assume the attitude of a prophet. In his heart he knows that underneath the theories that he constructs there lie contradictions which he cannot reconcile."

"In his heart—" yes. But seldom in his mouth. Often, when about to be bamboozled by the pop and splutter of great generalizations on the alleged present state and probable destiny of man and the universe going on all around me, I have comforted myself with Rayleigh's quiet assurance that the vociferous gentlemen with the Jehovah. complexes may, after all, be talking through their hats. They have done so before; why not this time, too? Whether they are or not, some of their prophetic utterances and their sweeping damnations of everyone and everything disagreeing with their cocksure dogmas, coupled with the scientific Rayleigh's remarks on the scientist as prophet, inspired the chapter in the sequel on "The Priesthood of Science."

With these preliminaries out of the way, we can begin unravelling the thread. A complete account of the history of exact thinking is out of the question in any reasonable compass, It is also far beyond the powers of any one man to undertake. What a. thoroughgoing study would demand can be guessed from skimming a few of the relevant pages in Sarton's Introduction to the History of Science. Notice the word "Introduction." There are already three massive volumes of it.

Compared to any such task, our own is modest in the extreme. In no sense are the following chapters intended for specialists in anything; they are meant only as an appetizer for stronger meat which, when thoroughly digested, will make the consumer of it as lusty as a lion and as independent as the proverbial hog on ice when told, even on the highest authority, to swallow any particular brand of bosh, even the most widely advertised. If only we can think for ourselves, and form a just estimate of our efforts, we shall be immune to all the craft and subtlety of the half-cocked enthusiasts.

Let us see first what induced human beings to make a conscious effort to think consistently. As already remarked, the earliest definitely recorded evidence of close, abstract reasoning has in it more than a hint of difficulties not yet fully resolved. Fundamental questions arose at the very start. They may not have been recognized as such, or they may have escaped notice entirely. Nevertheless they were inherent, as we shall see, in what was actually done.

Although the following chapters roughly follow the chronological order in the history of exact thinking, they can be taken in almost any order that suits the reader's taste.