[Math Lair] The Search for Truth: Chapter VIII: Through the Tunnel

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Chapter VIII



A DETAILED account of what is known of the great library at Alexandria (Egypt) would read like a sardonic parody on western culture. In miniature the history of that vast collection of learned books reflects everything from the decline and fall of Greek thought to the rise and supremacy of religious intolerance in the Middle Ages, and there is even one episode mirroring the burning of the library at Louvain, Belgium, in 1914, for reasons of "military necessity." We need touch only a few of the high spots.

The city of Alexandria was founded in the Fourth Century B.C. by Alexander, commonly called the great, just as "the glory that was Greece" turned its face from the sun, hesitated for a splendid moment or two, and prepared for the long plunge to second-rateness and death.

To Ptolemy Soter (B.C. 323–285) fell the task of administering the vast estate which slipped from Alexander's bloody and drunken hands when the great conqueror of the world finally succeeded in drinking himself to death in his early thirties. Ptolemy was an enlightened man, in spite of his past record as one of Alexander's generals. In his ambition to make Alexandria queen of civilization, Ptolemy invited all the learned men of Greece who would come to settle in Alexandria and found a great institution for scientific and literary research. As the scholars could not get along without books, Ptolemy order his agents to scour Greece and Barbaria for the best to be had. It is said that he did not stop at the best; examples of all written books were to be sought out and conveyed to Alexan­dria. The city became the home and refuge of Greek culture for a thousand years.

Thus originated the great library, the center of a huge hive of scientists (in the Aristotelian sense), mathematicians (in the great first period, Euclid, Archimedes, and Apollonius all lectured at Alexandria) and literary scholars (for the most part niggling commentators). Although the first flush of glory quickly faded, the library at any rate remained first class, and the buildings were magnificent. The whole institution in its second period was not unlike some of the greater modern universities into which tens of millions have been poured for bricks, books, and gadgets, and literally thousands for brains. The only things the humming Institute for Research near the mouth of the Nile lacked in its decline were a winning football team and a peppy college (or varsity) yell. Its proximity to a fine river might have suggested rowing, but the second-rate thinkers of the later Alexandrian school missed their opportunity in this as in other sports. At the peak of its heterogeneous glory the library is said to have contained seven hundred thousand books. That was about two thousand years ago. For all of 500 years the huge institute slowly rotted.

The second of the great librarians entrusted with the treasures of the already hypertrophied library was a. Greek by the name of Callimachus, well known also in other connections, as a sort of poet. There is always something of the kleptomaniac and pack-rat about the really great librarians, and Callimachus was one of the greatest. Like a millionaire who unexpectedly finds himself with twenty-four idle hours per diem on his hands, Callimachus suddenly decided that he must do something for the world at large, to justify his own existence and lend to his hitherto hit-or-miss acquisition of everything under the sun an air of gentlemanly humanitarianism. He swore by all the gods of Greece, Egypt, and the Euphrates valley to acquire every word by, of, or about Aristotle that had ever been committed to anything less impressionable than air. He would bequeath to posterity the greatest collection of Aristoteliana that had ever been gathered together, or could ever be gathered together. By the time he, Callimachus, was through, other collectors might comb the second-hand bookstalls of the world, and thumb the advance catalogues of the most exclusive dealers for generations till their thumbs were worn out, and find no scrap of Aristotle.

Callimachus began by purchasing Aristotle's own library. It is said that two hundred camels alone had their backs broken during the transport of the books from the quay to the library. Callimachus realized his ambition almost to the last commentary on the last of Aristotle's voluminous treatises on logic, and therein lies the germ of one of the richest jokes in history. Had not the acquisitive Callimachus failed of his ambition, it is quite possible that the quibbling logicians and eager seekers after ecclesiastical truth in the Middle Ages would not have made the colossal spectacles of themselves that they did. Just one book more in Callimachus' vast collection, and the mediaeval logicians would have been spared no end of hard labor and humiliation. We shall drop in on them later at their banquet of cold crow.

All went well with the library till the greatest soldier of them all, Julius Caesar, during the siege of Alexandria, set fire to the finer of the two buildings housing the books. The better part of the huge collection of books went up in smoke. Caesar, however, was not to blame for this mishap. He personally did not apply the torch, and the whole regrettable incident was laughed off by the Romans after the conclusion of peace as just one of those little things which must happen every now and then in the exigencies of military necessity. Through Anthony (the lover lampooned by Shakespeare), Caesar tendered his sincere regrets to Cleopatra, and very handsomely presented her with a fourth-rate library, acquired by his legions elsewhere, as a substitute for what had been lost in the etiquette of military necessity. Cleopatra's speech of acceptance and thanks has been lost. But we can imagine its tenor, for Cleopatra seems to have had more wit in her slim little finger than her quarrelsome suitors had in both of their thick bodies combined.

From the death of Caesar in B.C. 44 till the rise of Christianity the restored library continued to grow and to fulfill the functions which libraries are supposed to fulfill in times of peace. This comparatively tranquil period was the long twilight before the darkness of the Middle Ages swooped down and blotted out the glory of Greece forever. In that lingering twilight generation after generation of contented scholars passed their lives in the shadow of the great library, worshipping Plato and Aristotle and Euclid, and editing interminable footnotes to the endless footnotes of their predecessors, who in their turn had commented upon comments upon Plato and Aristotle and Euclid.

Into this harmless asylum of the learned the beetle-brewed champions of the gentle Jesus Christ, ably whipped on by their sanctified and progressive bishop, Theophilus, muscled their rude way in 389 A.D. Learning and wisdom and everything connected with them were abhorrent to these staunch Fundamentalists of the Fourth Century. They registered their disapproval of books by pillaging the library and strewing its priceless contents broadcast over the gutters and open sewers of Alexandria. In 415 A.D. the worthy descendants of these same Christians, again ably aided and abetted by their spiritual pastors, added an emphatic footnote to what their fathers had done, protesting in no mistakable terms against the impiety of knowledge and the damnableness of unsanctified, non-sectarian wisdom. They haled the pagan Greek woman mathematician Hypatia from her lecture hall, dragged her through the filthy streets to their holy cathedral and, while she yet lived, tore her limb from limb before the cross of Christ.

Hypatia however did not die till 1853. In that year of gestating Darwinism and evolution, Charles Kingsley (once private chaplain to Queen Victoria and author of the novel Hypatia), in his understandable eagerness as a clergyman to prove that there never was any conflict between theology and enlightenment, that there is no such conflict, and that there never will be any such conflict, asserted that embraced the faith of her murderers just before her flesh stopped quivering.

The death of Hypatia is sometimes taken as the end of the great research institute by the Nile. The library survived her. It even continued to grow unhealthily, like the beard of a corpse. But it was dead, and the scholarship around it was decaying. A new faith was needed to breathe fire into the cold and languid spirit of Greek learning.

Alexandria, was still great. In the Seventh Century it is reported to have had well over 40 churches, 4000 public or semipublic baths, and 40,000 houses of prostitution. Such a prize could not fail to tempt the new and vigorous faith of Islam. In 642, after a siege of fourteen months, during which the beleaguered Christians ate starved dogs and "drank the stale of horses," just as the hardier Romans before them had done, the city capitulated to the infidel Arabs.

The commander of the victorious armies was amazed and delighted at what he found within the city walls. The moment he and his men had appeased their military necessities in the 4000 baths and elsewhere, the worthy soldier sat down to write out a lengthy inventory of all the loot, for immediate despatch to the Caliph Omar. (In passing, why is it that all sheiks are called Omar?) In a postscript to the inventory the good commander asked what in hell he was to do with all the books that had so suddenly fallen into his unaccustomed hands. He was referring, of course, to the great library.

The reply was long in coming, but when it finally did arrive it supplied the world with its one immortal classic of the Aristotelian logic. The reply was substantially as follows.

"Dear General:

Allah be with you. There is but one God, and Mohammed is his prophet. Don't believe a word of what those lying Christians tell you. Now, about this infernal library you say you have captured. As I see it, the whole matter is as simple as A.B.C. There are only two possibilities about those books:

(1) Either they contain matters which are not in our Bible (the Koran);

(2) Or they contain only what is already in our Bible;

"If (1) is true, then (2) is false; if (2) is true, then (1) is false.

"But you know as well as I do, my dear fellow, that our Bible contains all the truth there is. It follows, then, that if (i) is true, those books contain lies. Hence they should be destroyed.

"Let us now suppose, on the other hand, that (a) is true. Then those books are entirely unnecessary. It follows again that they should be destroyed, as there are too many books in the world already. Besides, what use would any sane human being have for them when he could get everything out of our One Book? And carry it in his turban, to boot.

"So, as I said before, it is as easy as falling off a horse. The books must be destroyed. From what you tell me of the baths, I judge that the water is insufficiently heated. Why not have the books carted over to the baths and stoked into the furnaces? It should keep some of the younger men out of mischief for a month or two anyway. Please consider this an order.

"Allah be with you till we meet again.

Yours as ever,

Omar, Caliph."

"P.S. I have not told your wife what you wrote about the baths (!), nor will I, as I may be running down to Alexandria myself one of these days. Women talk so, and what one knows another guesses.


Callimachus himself could have found no fault with Omar's essay in Aristotle's logic.

It is said that it took all of eight months to burn up the books by feeding them night and day into the furnaces required to keep 4000 baths—many of them huge swimming tanks—as hot as the Arabs liked them. This burning of the Alexandrian library, the greatest collection of books ever brought together in antiquity, is usually rated as one of the world's major calamities.

Now, was it a calamity? If it has taken the world 1700 years to begin to recover from the scraps of Greek wisdom preserved for the world by the Arabs and others, how long would it have taken scholars to get through and digest the 700,000 books in the Alexandrian library? And would the world have been sicker or better than it is now had it attempted to swallow such a Gargantuan feast? Having no opinion one way or the other, I pass on to a milder modern instance of the same sort of thing. It must not be hastily concluded from what follows that all mathematicians are insane; some are not.


One of the most brilliant of the younger generation of mathematicians was asked, about five years ago, what steps he would advise being taken to advance mathematical invention throughout the world. His reply can be anticipated by anyone who knows of an incident that had happened about a year before the momentous question was put. A not-so-brilliant fellow countryman of the budding genius had submitted to the genius for criticism a laboriously executed piece of mathematical research on which he had sweated for three years. Eight months passed without a word from the nearly great young genius. Unable to stand the suspense any longer, the stewing plodder wrote a humble note to the other, asking him whether he had ever received the work and, if he had, what he thought of it. Almost by return mail he got a reply.

"Dear Mr.....: I received the copy of your work just as I was about to board a steamer for Stockholm. I tried to read your stuff, but it was so bad that I threw it into the North Sea. I am glad to hear that your job depends upon receiving a favorable opinion of your work from me, for now I am sure that you will starve to death as you deserve. Yours very truly,...."

The answer to the original question can now be guessed: "Burn all the mathematical books in the world. If you have not time enough for that, be sure that you burn all the classics, at least." The seriousness of this proposal for more than one eminent living mathematician can be imagined when we recall that some of the greatest classics in mathematics are less than twenty-five years old.

There is a lot in the somewhat startling proposal of this flaming young genius. First there is the obvious overcorrection of his own inferiority complex. He is brilliant beyond a doubt, according to those who should know. But it is his tragedy to have missed first-rateness by half a hair's breadth, and he has had to content his morbid desire for fame with only a very high second class. It is a familiar enough tragedy. During the past half century there must have been at least ten men who apparently could have been Einstein; actually, however, only one had everything that was necessary to invent the theory of relativity. The other nine would have done it if they had had it in them, for they lacked no opportunity to do their best. But when all this is said, there appears to be a hard nub of truth in the young man's impossible counsel of perfection.

In literature it does seem to be possible to do some things once and for all. What would we not give now for the last sheaf of Sappho's poems that went to warm the bath water of the infidels? But the lesson of history in mathematics and in rigorous thinking generally seems to be different. Nothing in those fields is ever done; it is always being done. The best of one century is likely to appear flat and rather trivial, if not indeed almost wholly nonsensical, to the more critical taste of the succeeding century and, as a matter of fact, it is usually a waste of time to read "classics" in mathematics or science after they have been superseded. Many great works are out of date before they leave the printer. Sometimes it is worse than a waste of time to attempt mastering the classics; it is a positive detriment to clear thinking. For only an exceptionally skeptical mind can maintain its judicial disbelief in what is demonstrably false when a subtly fallacious argument is developed with all the superb skill of the old masters, who did not know they were lying, but who nevertheless lied with incomparable genius.

The classics are not the sort of stuff that can safely be put into the hands of those to whom reverence for great names and respect for authority are virtues. The minds of the old master) were as keen and as powerful as those of the new. What chance has an ordinary mortal, ignorant of most of what has been done since the old masters turned to dust, when he guilelessly pits his understanding against theirs? There are better guides; why not follow them from the beginning, till they too lose their way? We shall all be lost in the end, but we shall have got farther if we start where the last. man died, instead of wasting the fresh hours of the morning in silly attempts to dig up his great grandfather and put him on his feet again.

Not to label a specific instance, for that would be like awarding the booby prize to one of many where all are equally worthy, I should like nevertheless to sketch the career of one great modern classic of deductive reasoning. It is a massive and formidable work, and its influence on the critical development of straight thinking has been tremendous. The work however dropped from the press stillborn. It had been killed by a more profound work in the same direction before its first page was set up in type. Those who had labored for years to bring one era of exact thought to perfection and to found a new epoch, were wholly unaware of the skeptical (and yet creative) approach of the obscure competitor whose first half dozen printed pages nullified their colossal effort and made of it one of the most conspicuous {utilities in the history of human thought. The great and massive work was duly published, spoken highly of by all who were competent to speak, and read, possibly, by half a dozen. As the years passed, both the respect in which the work was held and the number of men who were willing to take five years off really to read it, increased slowly but steadily. Among those who had not read the work and who, perhaps, lacked the peculiar training which a reading demanded, the reputation of the epoch-making treatise rose rapidly. But those who had spent five years or more at the hard labor of trying to digest what the treatise really said about straight thinking, became more and more puzzled. Was this the real stuff, as they had thought at first, or was it merely another nebulous monument to that mystical moonshine which philosophers call Truth? They could not decide, and put the massive work aside, to gather dust but not light, till a more aggressive crop of skeptics should arrive. In due time these arrived. Instead of trying to correct the old errors, however, the newcomers blithely ignored the greak work entirely, and followed the lead of the obscure man whose labors had killed the masterpiece before it was born.

If that were the whole story we could say that the ending was a happy one after all. Not much time was wasted in trying to follow a false lead, and the more promising course was taken before a horde of objectors could kick up the usual clouds of dust to obscure the new way. But unfortunately it was not the end of the story. What actually happened is like an echo of Alexandria or, if anyone wants a more modern example, like the undying reverberations from the explosion of the erroneous ideas of the great philosopher Kant on what geometry is all about and its supposed relation to "truth."

The massive work, abandoned or ignored by professionals in its field, became a classic in philosophy, particularly in that department of philosophy which concerns itself with the foundations of science and of mathematics, and which undertakes to "evaluate" these comparatively non-gaseous products of hu­man restlessness. Because this longest chain of deductive reasoning in history does not demonstrate, and because it conceals inconsistencies which cannot be removed or reconciled by the means to which the great work restricted itself, therefore it is an inexhaustible matrix of philosophical mares' nests and, as such, will no doubt continue to supply wrangling generations for centuries to come with controversies as futile as those which it has engendered in the generation just closing.

This short history of one masterpiece is typical of many—in the field of science. First the work is honored as it should be; then, possibly, it is understood critically by a few; next it ceases to command either the attention or the respect of those who are accessible to new ideas; then gradually it is shelved and forgotten by specialists in the field of its enquiry; and then, much later, historians of science note it in passing, with an impartial statement of the influence (if any) which it had on its own times and on the development of its field. Finally, somewhere in one of the later stages of its descent into the abyss, the philosophers of science discover the work and tell the world that this is what the mathematicians and the scientists tell us is true. Some great works go even lower, and suffer a horrible sort of "second death"—the damnation of the mediaeval theologians—and are trumpeted with all their pathetic absurdities from fashionable and progressive pulpits as the latest and truest pronouncements of "science" to sustain a tottering prestige. It would be more decent to let the poor things die.

This seems to be as proper a place as any to record a revised version of a very old gibe at philosophers. This version is already classic on the Pacific Coast, where it originated, but possibly it is not so well known elsewhere. A professor of philosophy and an extremely scholarly theologian had been arguing for hours over the philosophy of science when the theologian, finding himself cornered, repeated the old simile likening a philosopher to a blind man in a pitch dark cellar looking for a black cat that isn't there. "Yes," said the pro­fessor, "and if the hunting philosopher happened also to be a theologian, he would find the cat." The discussion ended abruptly.

We are almost through the tunnel which leads from the golden age of Greece to the morass of the Middle Ages in Europe. The thread has not been lost; if anything it has been thickened into a stout rope. Let us see what use the men of the morass made of that rope, remembering always that they were seeking truth, just as some of us are, and that they looked for it in the finest quibbles of the game of deductive reasoning. Their achievements in other arts and sciences are of no importance for our narrow purpose. As with Egypt and Greece, we must leave all but the one kind of "truth-seeking" aside, or we shall never get to the end and appreciate our own perplexities.

*   *   *   *   *

Some who read history for pleasure get their keenest enjoyment out of the judgments which the liberal historian passes on all the actors who strut or stumble across his toy stage. Others get their fun out of sizing up the historian by noting the sort of judgments he passes. When, for instance, the historian disapproves of George, Duke of Clarence, who chose to drown himself in "a butt of malmsey" when given the privilege of choosing the manner of his execution, we must conclude, I think, that the historian never tasted malmsey. But when the enthusiastic historian lets his rhetoric run away with him in eulogizing the death of good King John from "a surfeit of peaches and beer," we know at once that the historian is thoroughly unreliable and that his judgments are worthless; for it is simply impossible for any human body to hold peaches and beer enough to do itself an irreparable injury.

The history of science can be made entirely impartial, and perhaps that is what it should be, by merely recording who did what, and leaving all "evaluations" to those who like them. To my knowledge there is only one history of ancient ti6c subject (Dickson's, of the Theory of Numbers) which has been written in this coldblooded, scientific way. The complete success of that unique example admitted by all who ever have occasion to use such a history in their work—seems to indicate that historians who draw morals should have their own morals drawn.

The purpose of the foregoing remarks is to forewarn the reader that he must form his own conclusions on some of the rather controversial episodes to follow. Into no discussion of the evolution of thinking would I inject my own opinion, even if it were the quite reasonable one that respect for intellectual authority and uncritical reverence for the tradition of great minds, instead of being virtues, are two of the most pernicious vices to which education hardens us.