Tuesday, July 25, 2017

Edgar Allen Poe the Mathematician 1907

Poe as a Mathematician by Harry Thurston Peck 1907

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Of those who admire Edgar Allan Poe, some admire him chiefly as a poet, while others admire him chiefly as a writer of prose. If we analyse both his poetry and his prose, and try to understand the true nature of his genius, we shall find that fundamentally he was first of all a mathematician.

Now most persons think of a mathematician as a mere vulgar weigher and measurer and calculator — a very prosaic person, utterly devoid of all imagination. Poe himself seems to have held this view; for in one of his most famous stories—The Purloined Letter—he makes his ingenious hero, Dupin, say of another character: "As a mere mathematician, he could not have reasoned at all." And then he goes on to remark that because the person in question was both a poet and a mathematician, he could reason well, and was, therefore, a very dangerous opponent.

Yet Poe, of all men, should have known that imagination is just as necessary to a really great mathematician as it is to a lyric poet, since the great mathematician does not limit his speculations to finite truths, but passes into transcendental regions of thought, where finite truths have no validity- In other words, it is wrong to say, as Poe does, that a mathematician may be a poet. Rather is it true that a great mathematician must have many of those qualities of mind which make a poet. It is only thus that he can rise above the finite to the infinite, and form those bold conceptions which do not, indeed, belong to arithmetic and to the theorems of Euclidean geometry, but which are absolutely vital to the higher mathematics.

That Poe's natural bent was mathematical is seen in many facts. Even in his early youth, when he was a cadet at West Point—he was then only nineteen years of age—it was recorded of him by a friend, "He had a wonderful aptitude for mathematics." Toward the end of his life, disregarding all that he had previously written as being relatively unimportant, he planned his so-called prose poem, Eureka, which he said and thought to be his strongest claim upon the remembrance of posterity. He went to Mr. Putnam, the publisher, all quivering with excitement, and declared that this prose poem was of momentous interest, and that a first edition of fifty thousand copies, if Mr. Putnam would publish it, would be only a small and inadequate beginning. Remember that in those days publishers regarded an edition of two thousand copies as a large one, and it will be plain that Poe really thought this book to be his greatest work. In his preface to it he declares Eureka to be "an art product," and says that only as a poem does he wish it to be judged after he is dead.

Now, what is this Eureka, on which Poe desired to rest his final reputation? It is a work of minutely analytical reasoning of the most abstract character, intended to explain the process of creation and the constitution of the universe. In it, like some ancient Greek—Empedocles or Leucippus, for example—he discourses of primordial atoms thrown off in a number directly proportioned to the surface of the particular sphere which they had occupied; and he argues that since the surfaces were directly proportioned to the squares of their distances from the centre, the radiating force was directly proportioned to the squares of the distances to which the several atomic showers were driven. Poe then assumes a recoil of the atoms and a tendency which represents the mutual attraction of atoms with a force inversely proportioned to the squares of the distances. Again, in some still later papers, he busies himself with a mathematical explanation of Kepler's planetary laws, and with certain mathematical deductions from Newton's theory of gravitation.

In all this complex speculation who discovers the author of The Bells, The Raven, and The Haunted Palace? Who readily detects the mind which constructed the story of The Gold Bug, or The Purloined Letter, or The Murders in the Rue Morgue? Apparently very few. Even Professor Woodberry, in his admirable biography, explains these scientific labours as "showing how egregiously genius may mistake its realm." Yet they certainly do show that Poe felt a powerful impulse toward mathematics and the related sciences. As I see them, the same qualities which appear in Eureka are the qualities which are conspicuous in his poetry, and no less so in the stories which every one had read, though no one reads Eureka. In the present chapter I have nothing to do with the poems; but I venture to propound the thesis that both the merits and the defects of Poe's short stories are largely traceable to the fact that their author was before all else a mathematician, with a mathematician's mind and temperament.

Let us take a few of these short stories by way of illustration. First of all, there is The Purloined Letter, of which the hero, Auguste Dupin, is a man saturated with mathematical knowledge, even-though he has a species of contempt for algebraists and geometricians. To him comes the prefect of police, begging his assistance to recover a letter which is known to be in the possession of a minister of state, and which is probably in the house of the minister; yet which the most minute ransacking of the house by the police has failed to bring to light. Every inch of space in every room has been examined. The legs of the chairs and the cushions on the couches have been bored into or ripped open. The very books in the library have been taken down one by one; each page has been turned, and even the bindings have been tested. The prefect is in despair; for the letter is a compromising one, and its possession by the minister may lead to serious political results.

Dupin listens, says very little, and soon the prefect goes away. A month later he once more visits Dupin, and again expresses his despair. The letter has not yet been found. An enormous reward has been privately offered for it. The prefect would himself willingly give fifty thousand francs to any one who should recover it. Then Dupin, who has been puffing at his pipe, tosses a cheque-book to the prefect and says:

"You may as well fill me up a cheque for the amount mentioned. When you have signed it I will hand you the letter."

The prefect gasps and stares, then makes out a cheque for fifty thousand francs and gives it to Dupin. Thereupon Dupin quietly unlocks a writing-desk, takes out the missing letter, and hands it over to the thunderstruck official.

This is an extremely interesting and dramatic story. Merely as regards incident, it is absolutely perfect. Then when Dupin comes to explain how  he got possession of the letter where the police had failed, his explanation is a beautiful blending of mathematics and psychology. To be sure, it seems  at first sight to be a criticism of mathematics, yet it is just the sort of criticism which a transcendental, mathematician would bestow upon a mathematician of the ordinary type. We have here in reality, a  suggestion of mathematical imagination applied to a psychological problem. Dupin has read the mind both of the prefect of police and of the minister, and he reasons from thought to action with the close logic of the advanced mathematician. By so doing he has been able to arrive at a solution which the professional detectives absolutely failed to hit upon.

Again, there is the story of The Gold Bug, in which the discovery of a hidden treasure depends upon the deciphering of a cryptogram composed of numbers. Cryptography was a subject in which Poe always took an extraordinary interest. When he was connected with a Philadelphia periodical, he issued a sort of challenge, declaring that he could read anything that might be sent to him written in cipher. Im consequence many cryptograms reached him from all parts of the country, some of them concocted hy persons-whe-did not observe the conditions of the challenge, but either used foreign languages or blended several alphabets in the same cipher -of even ran words and sentences together without any indicated intervals. Yet Poe solved all of these intricate puzzles, except one which was meaningless, being made up of a jargon based upon characters used at random.

Afterwards, Poe wrote a series of papers on Secret Writing, which appeared in the pages of Graham's Magazine. In these papers he analysed the methods by which cryptograms could be deciphered, and he did so with an obvious zest in that sort of mathematical trick-work. In all this we see the mathematician at play. The story of The Gold Bug is written around a cryptogram just as his poem, The Raven, was built up around the single word "Nevermore."

Another famous tale, The Mystery of Marie Roget, affords a still more extraordinary instance of Poe's logical and mathematical skill. As every one is aware, a young girl named Mary Cecilia Rogers, well known in New York, was found murdered in Hoboken. The police were unable to discover any clue to the mystery of her death. The problem baffled all investigation. Then, Poe, merely from putting together the facts that had been reported in the newspapers, composed a story in which, laying the scene in Paris and substituting French names and places for the real ones, he unravelled the tangled skein of evidence and explained just how and why the murder had been done.

His flawless, relentless reasoning is remarkable, and the story itself ends with a paragraph which is essentially mathematical, referring directly to the calculus of probabilities. It also contains the following very striking sentence:

"This is one of those anomalous propositions which, seemingly appealing to thought altogether apart from the mathematical, is yet one which only the mathematician can fully understand."

This sentence may well be applied to the working of Poe's mind in all of his most famous stories. His mathematical exactitude was confirmed in regard to the Mary Rogers case when, long afterward, the confession of two persons proved that Poe's deductions had been absolutely correct.

The same intense mathematical reasoning was brought to bear when Dickens began to put forth in serial form the novel, Barnaby Rudge. Before many numbers had appeared, Poe published an exposition of the entire plot of the story, and he did it so accurately that Dickens was aghast. "Are you the devil?" he asked of Poe. Here again was a mental feat, not obviously mathematical, yet one which only a mathematician's mind could successfully accomplish.

Poe's great popularity in France is largely due to the scientific lucidity of his thought; for the French are a mathematical people, ruthlessly logical, and with a love for what is definite and precise. Their instinct for the dramatic accounts for the toleration of his stilted rhetoric, which at times offends the taste of the Anglo-Saxon reader. Perhaps the fact that Poe rants in some of his stories is due to hereditary influences, for both his father and his mother were actors. Take, for example, these sentences from his greatly overpraised Fall of the House of Usher:

"And now—to-night—Ethelred—ha! ha!—the breaking of the hermit's door, and the death-cry of the dragon, and the clangour of the shield! Say, rather, the rending of her coffin, and the grating of the iron hinges of her prison, and her struggles within the coppered archway of the vault! Oh, whither shall I fly? Will she not be here anon?"

This is surely Ercles' vein. It will not do to say in Poe's defence that this sort of overwrought declamation was characteristic of the style in which men wrote at the time when Poe composed the story. He himself by no means lapses very often into verbal hysteria. In the best of his tales he writes with the same naturalness that we expect to-day of even second-rate authors. The real defect of Poe is not to be discovered in his occasional bombast. It is a defect that is far less superficial and far more profound; and it deserves not only mention, but concrete illustration.

The mathematical quality of Poe's mind gave singular effectiveness to his fiction. His imagination was a constructive one. It worked in harmony with his reasoning faculties, and he proceeded bit by bit to build up an almost flawless literary structure. Dr. Charles Sears Baldwin has very well said of Poe:

"When he talked of literary art, he talked habitually in terms of construction. When he worked, at least he planned an ingeniously suspended solution of incidents; for he was always pleased with mere solution."

It is true that because of his invention, his constructiveness, and his correlation of details, Poe is one of the great masters of the short story. But I should be unwilling to say with Dr. Baldwin that "from his brain was born the short story as a complete, finished, and self-sufficing whole." This seems to imply that Poe originated the short story in its perfection. It is difficult to understand how a professor of English literature or, for that matter, of any literature whatever, could make so extraordinary an assertion. What does Dr. Baldwin think, for example, of Balzac's short stories, such as El Verdugo, La Grande Breteche, and Le Colonel Chabat —not to mention others? Every one of these is superior to Poe's, while still representing "the grotesque and the arabesque." Or, if Dr. Baldwin pleads that Balzac was a contemporary of Poe, what could be more nearly perfect than Sir Walter Scott's horror-story called The Tapestried Chamber—wonderful in its simplicity, yet so powerful in its effect that, after reading it, men of the strongest nerves are unwilling to go to bed immediately or to be left alone in the dark? But retrace our steps still further to the Decameron of Boccaccio, or still further to the Milesian Tales which are interwoven by Apuleius in his Metamorphoses. The story of the commercial traveller in the first book, and that of the robber in the fourth book, are "complete, finished, and self-sufficing." And how about the tales in Herodotus, that superb story-teller? The narrative of Rhampsinitus and the Robber has invention, directness, and suspense as its chief qualities. And we may continue our researches and look at some of the short stories in the Bible, of which, for example, the story of Joseph and his brethren, of Samson, of Esther, and of Job, have always been fascinating to men and women and children, and they show that the true genesis of the short story antedates Christianity as it probably antedates any written records which the world possesses. It would surely have been odd if men had been obliged to wait until the year 1830 for a short story that was "complete, finished, and self-sufficing"! Yet my principal reason for dissenting from Dr. Baldwin's dictum is found in the very limitations which were imposed upon Edgar Allan Poe by the mathematical bias of his mind.

A truly mathematical mind dwells, as it were, in a sort of vacuum. It conceives order, harmony, proportion, form—that is to say, every sort of abstraction. It does not often, however, possess sympathy and an understanding of the emotions in their wider range. This truth is admirably and rather pathetically exemplified in Poe. He can construct a plot and compress it within small compass. He can work out its solution with marvellous ingenuity. He can excite wonder, curiosity, and terror. But the one thing that he can not do is to create character.

In this respect, his short stories are just as defective as the short stories which the Greeks composed three centuries before Christ. His personages are dummies. What they do is extremely interesting; what they are and what they feel, no one knows or cares. Thus, M. Dupin is a thinking-machine, an embodiment of reason, impassive, impersonal; but he does not live for us as a man, since he is not a man.

Compare him, for example, with Sherlock Holmes as drawn by Sir Arthur Conan Doyle. Conan Doyle has not so original a genius as Poe had; yet, none the less, he has some qualities which make his best work more pleasing and far closer to the universal understanding. The proof of this is found in the fact that the name of Sherlock Holmes is known all over the civilised world; while if you mention M. Dupin to the man of average intelligence, it is long odds that he will not remember and recognise it.

Let me illustrate this sharp distinction by examining a famous short story of Poe's, and by comparing it with a short story of Conan Doyle's which was clearly suggested by the other.

The Cask of Amontillado is one of the shortest and also one of the best known of Poe's fictions. It is supposed to be narrated by an Italian who has suffered insults at the hand of a professed friend, Fortunato. He plans revenge; and at the time of the carnival he asks Fortunato's advice about the merits of some Amontillado wine. Fortunato is a connoisseur of wine, and willingly consents to go down into the vaults where the great cask is supposed to be. His enemy really conducts him into the catacombs, through heaps of bones—a slimy, gloomy, terrifying place, beneath the river's bed, and reeking with the moisture which has oozed down through the walls. Fortunato enters a sort of niche, only to find that his progress is arrested by solid rock. In an instant his enemy has shackled him to the wall, and almost at once begins, with stone and mortar, to close up the entrance to the niche and to make of it a tomb where Fortunato must perish in the dark. The story is told most vividly; and at the end one hears the shrieks of the victim and the tinkle of the bells that he wore upon his carnival attire. The sound ceases; the vault is closed; and vengeance is achieved.

Now, this narrative is made to thrill us with a sort of nameless horror; yet the defect in its art lies in the fact that our sympathies go out entirely to Fortunato, and we regard the man who seeks revenge in this dreadful way as far worse than an ordinary murderer. Poe has not made us feel the justice of the act. He merely speaks quite casually of "the thousand injuries of Fortunato" without giving any clue to what they were. Hence the effect of the story is impaired by our natural human sympathies, which the author has taken no account.

Compare now Conan Doyle's story called The New Catacomb, the plot of which is directly borrowed from a German student in Rome, who has deeply loved It is told by one Julius Berger, an English girl and has hoped to marry her. A dissolute Englishman, however, has wronged her, and has cynically told his friends of what he deems a gay adventure. The girl's honour is lost, and she disappears in order to hide her shame. The Englishman does not know that she had first loved Julius; and in talking with him, he makes a jest of the whole affair.

Here the art of Conan Doyle is higher than the art of Poe. He has appealed to our humanity, and has aroused in us a lively indignation, so that we are prepared for the terrible revenge which Julius takes. The German student has discovered a catacomb of which no one else has learned the secret; and he invites the Englishman to accompany him through its mazes to the central chamber. When there, Julius, who knows every turn of the catacomb, suddenly extinguishes the light, retreats backward into the appalling darkness, and in a voice which echoes strangely through the hollow vaults, tells the reason why he has done this deed. The story ends with an impressive awfulness which is not inferior to that attained by Poe, and which affects us far more, because we feel that justice has been done, and that innocence has been avenged.

Herein, briefly, lies the difference between the short story, as Poe wrote it, and the further development of the short story which is not inferior in invention and constructiveness, while it is otherwise superior, because in it the cold-blooded impersonality of the mathematician has been replaced by a warmth of feeling which belongs to men and women who have hearts as well as heads, and in whom the whole gamut of emotion can be stirred by the hand of a master who knows how to make an instantaneous appeal.

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