Yuri Tarnopolsky                                                                                                                      ESSAYS

22. On Errors

 errors. Graham Greene. QWERTY. Dvorak. Sigmund Freud. freudian slip. parapraxes. genetics. Confucius. topology. metrics

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Essay 22. On Errors

The Comedians by Graham Green is one of my most favorite books.

Three completely different men are packed as passengers into a narrow space of a cargo ship going to the Haiti of Papa Doc Duvalier: the saint, the rogue, and the narrator who is coming back to his tepid love affair with a woman who had once pulled him into the orbit of her marital desperation, as well as back to his stronger attraction in the form of a real estate possession.

The passengers are spilled out into the billiard pool of the Caribbean island “of fear and frustration” where they can hardly find any other "fellow white man, one of the slaver's race."  The human billiard balls collide with the rails of the table, as well as with each other, and fall into the pockets under violent blows of the cue.

The billiard ball is a flawed metaphor: it emphasizes individualism of humans and their compliance with external forces but obscures their ability to be pulled together and form bonds, as well as challenge the environment and each other. As objects capable of attraction, repulsion, and independence, humans are primary and unparalleled components of the world. Unparalleled—except by molecules.
Faithful to the chemistry of human nature, Graham Greene draws the lines of attraction between the balls.  The strength and sign of the bonds vary from suspicion to indifference to love. Greene avoids hate, although, unlike one of his fellow travelers, a provincial American preacher of vegetarianism who thinks "in terms of Mankind,  Justice, the Pursuit of Happiness," (the saint) he sees enough reasons for it in the world.

In the fine plot only an unbreakable marital bond and a broken one are clear from the start and they stay so to the end. Other bonds form, fall apart, and oscillate. Greene draws a dynamic sequence of  structures, including one real and one imaginary triangles, with a high art of taut storytelling, using understatement, echoing repetitions, and hints to weave his artistically calculated web. With a transparent symbolism, only the woman in the focus of the novel, who is always natural and does not play a part, is given the first name: Martha. The three comedians do not have them.

The narrator, skeptical up to cynicism, seems unable to have strong attraction to anything but his property, and yet he constantly and compassionately shares the entanglement with other people who are driven by more energetic impulses. The compressed space of action simply does not allow for any indifference. Driven by jealousy, he makes a tragic error that costs the likable rogue his life. In the end, he comes out of the game with no bonds left at all. For that matter, the saint and the rogue had made their errors, too.

It was not geometry, however, that fascinated me when I read The Comedians for the first time, soon after the book had been published and reached Russia. At that time I was entangled in a web of my own making. I saw in the book the drama of an accidental spark between a man and a woman that can irreversibly destroy the previous life. I was shocked by the discovery of  “a point of no return unremarked at the time” in my own life. Graham Greene insisted  that such points were part of human nature. I suddenly realized that my fate had the Olympian power over me, but the Olympus was, probably, some small bump in my brain.

Greene chose a quotation from Joseph Conrad as an epigraph to his later novel The Human Factor (1978), even more applicable to The Comedians: "I only know that he who forms a tie is lost. The germ of corruption has entered into his soul."

In the Soviet version of the Platonic Republic (see Essay 19 ) I believed in the stability of life based on work.  I learned, however, that the quiet order of things could be grossly violated locally, in a close contact with another human being,  within a narrow space, causing the catastrophic long range effects—the pattern well known to physicists studying crystal dislocations, (a beautiful chapter of physics) as well as statesmen, generals, and oncologists. I had formed a tie and was lost.

. The dislocation physics of solids is full of human symbolism. It says that perfect crystals should be very strong, but they do not exist. The weak imperfect crystals could be made stronger by making them even less perfect through additives and turning into alloys. The dislocation can be compared with the teeth of the zipper right under the moving slide.

Much later I was destined to learn the meaning of  "fear and frustration" coming from not personal but historical point of no return.

The Classic Greek tragedy was about impossibility to fight fate. The Western literature of the nineteenth century was about the rise and fall of an individual wrestling with the fate. The new wave  of the twentieth century, from modernists to Ayn Rand, annulled fate. Graham Greene, never with the crowd, equaled fate with accident, as any writer of page turners always did, but he encapsulated the character in a shell waiting to be cracked by an accident so that the hero could look inside himself and see that the cynicism was just a shell.

The ties with other people, whether attraction or repulsion, limit our personal freedom. The loss of ties, loyalty, and moral distinctions is what we pay for the anti-Platonic chaos of freedom. The ability to make such ties distinguishes us from billiard balls. Too much bonding—and we are simply parts of a mechanism, ball bearings, slaves, and tools. No ties—and we are atoms in the void. A very few very strong ties is my image of the home of a traveler and the anchor of his ship.

I read The Comedians countless number of times, always discovering new shades and details in his idealistic version of human chemistry. I was coming back to his other books, too.

I found another flash of geometry in Chapter 16 of Greene’s Travels with my Aunt .

It was getting chilly by this time, and I turned on the electric fire before opening the letter. I saw at once that it came from Miss Keene. She had bought herself a typewriter, but it was obvious that as yet she had not had much practice. Lines were unevenly placed, and her fingers had often gone astray to the wrong keys or missed a letter altogether. She had driven in, she wrote, to Koffiefontein—three hours by road—to a matinée of Gone with the Qind which had been revived at a cinema there. She wrote that Clark Fable was not as good as she remembered him. How typical it was of her gentleness, and perhaps even of her sense of defeat, that she had not troubled to correct her errors. Perhaps it would have seemed to her like disguising a fault. “Once a week,” she wrote, “my cousin drives into the bak. She's on very good terms with the manger, but he is not a real friend as you always were to my father and me. I miss very much St. John's Church and the vicar's sermons. The only church near here is Dutch Deformed, and I don't like it at all.” She had corrected Deformed. She may have thought that otherwise I might take it for an unkindness.
                   (Graham Greene, Travels with my Aunt)

The above excerpt also demonstrates Greene's style of placing the tip of an iceberg among the apparently meaningless verbal waves and giving us at least two snapshots of it ("...her gentleness" —  "...otherwise I might take it for unkindness"). One can draw a straight line between two points, distinguishing typical from accidental.  The line, however, is invisible in the text, not straight, and the reader has to be attentive. It goes sometimes through several pages, like a wormhole, with the points of entry and exit.

These Essays are also conspicuously interconnected by wormholes in the form of cross-references.

The errors made by Miss Keene needed the following corrections:



Graham Greene was a writer of fiction. The above errors could be completely fictitious. I have an evidence, however, that they were not.

This is the common typewriter layout known as QWERTY:


The typewriter keys Q and W, F and G, and D and R are neighbors and, therefore, can be mixed up easier than Q and D or F and P. It confirms that Graham Green was as realistic in this insignificant detail as he was in portraying human characters.

It turns out that there is an alternative layout called  Dvorak . Dvorak and its hopeless competition with QWERTY  has simulated a discussion of  philosophical magnitude, concerning some most important properties of our society.




Curiously, the properties of the space we live in predict our errors.

Whatever we do, the high probability of small deviations from the goal is a law of nature. This is why our most probable errors are concentrated in a small space: the neighborhood of the target (see Essay 16). In topology, the neighborhood of a point is a set of all other points close to it (actually, not so simple: "A neighborhood of a point or a set is an open set that contains it":  Topology glossary).

The proponents of Dvorak promise more comfort and less errors, which might be true because QWERTY is irrational. There is an opinion that the inventor of QWERTY put all the letters for the word TYPEWRITER in the upper row of letters simply for the convenience of the salesmen.

Concerning the social space, Plato promised a space with less errors by segregating the rulers from the masses. Hitler quite reasonably assumed that a larger Lebensraum would ease the stress of the Germans bumping into each other, but he overlooked, as Napoleon did,  the simple physics of a pressure drop in an expanding volume. In Russia, the largest country on earth, Stalin, in order to prevent both the bumping and pressure drop, designed the society as the crystal lattice of a marching column, but he, too, overlooked the physics of the melting solids,  as well of the brittle solids with dislocation defects).

Correcting my own typing, I constantly find that the closeness of the keys is a defining factor in making an error. In addition, because typing on the keyboard takes so little effort, I could occasionally depress two keys in the same row at once with one fonger (ha! that was an exemplary error!), for example: fd, kl, but not ok or ef.

Graham Greene’s characters are realistic because their words and actions make sense. The novel runs in a linear time cut into ahort (another typing error: should be “short”) pieces. Within the fragments, each couple of neighboring consecutive events is credibke (should be “credible”; well, enough to prove my point): they stick together.

A fiction writer takes realistic fragments of life and arranges them into credible sequences. The large sequences are combined into longer passages. The passages fit into chapters, and so the novel is crafted like a house. The difference between Graham Green and Stephen King is that the credibility of Greene covers also the joints between the larger blocks and goes up to the highest levels of the structural hierarchy, while the credibility of King ends at a much lower level where the fantastic events have no match in ordinary human experience.


Graham Green designed fictional stories that could happen because they did not contradict any known principles of nature, either physical or human. His characters and collisions could be played by real actors. King's books could be turned into movies only by using technical tricks falsifying the laws of nature and common sense.


Reality, which is a euphemism for Everything,  is like a computer keyboard: it has a topology. This mathematical term means approximately that there is a set of objects (points of a space) and for every two objects we can tell whether they are close neighbors or not, but not much more.


A topological space can be compared to a completely dark room where we have to move from point to point, groping around for objects and planning the next move. We may not know what is in the room, but we can conclude that the curtain is close to a window and the chairs are close to the table. Through a blind walk we can even find the exit to the light from the darkness.


In addition to topology, our natural metric space has distance between every two points. Metric space is a particular case of topological space.


Metric space is like the illuminated room. We can move straight from the window to the table because we can see distance, a not just closeness, between objects.


I have just loosely interpreted two mathematical terms, topology and metrics, by presenting their metaphors. We cannot learn mathematics or any other science through metaphors but we can understand them without going into details.

Biology has some topological flare, too. At the early stages of genetics, long before molecular biology and DNA sequencing, scientists could study the position of genes in a chromosome by groping around in the dark, without even knowing what either genes or chromosomes were. They studied the topology and derived the metrics from it in the same way Confucius built his moral scales (see Essay 13).

: Article Genetics in Encarta is a better source of information on this subject, mostly of historical significance, than the Web. The key words: chromosome, crossingover, recombination, Thomas Hunt Morgan.

To give a metaphor for the methods of formal genetics, it is the same as to reconstruct the keyboard layout by the statistical study of typing errors. By determinimg the most often misprints,  we can tell which keys are the closest: they are mixed up most often. In this way we can build a neighborhood of each key. Similar methods are used today in the computerized analysis of long biopolymers by comparing their fragments.

Another example is biological systematics where tiger and cat are very close while cat and fish are elements apart and cat and catnip are in different universes. In a different representation of the world, however, cat is pretty close to both fish and catnip but far removed from golf ball.

            A mathematician could say that systematics is a discrete space that has a tree topology.

Literary fiction helps us understand ourselves and the world, but we have to accept a share of misunderstanding. Nothing in the world, however, can spare us of errors.

Speaking about errors, to omit Sigmund Freud would be unspeakable.

In his Psychopathology of Everyday Life (1901), Freud analyses errors such as forgetting of names and foreign words, mistakes in speech, reading and writing, erroneous actions, and other faux pas known also as parapraxes and Freudian slips.  His main point was that we should not "ignore the realms of determinism in our mental life" (Chapter 12). Under his close scrutiny, the errors revealed deterministic influence of factors repressing the correct actions or enhancing the wrong ones.

Freud went against the tide of the contemporaneous experimental science by neglecting the statistical analysis of as many cases as one can collect and by burrowing, instead, into individual cases as deep as one can go. His novellas on individual errors read like detective stories. In some cases they are many pages long, for example, why the names of Botticelli and Boltraffio "intruded" on him instead of the correct name Signorelli (Chapter 1) or why the strange word Cardillac stuck in somebody's (his future translator's) memory (Chapter 12).  I was not convinced: it could be explained in a different way or not explained at all.  To find a single fitting explanation was certainly the worst way to look for determinism, but that was typical for Freud. If it looks like fiction and sounds like fiction, it probably is fiction.

Nevertheless, even if Freud stretched and twisted his explanatory apparatus, he opened an area where nobody had ever looked before except for fiction writers (and probably this is why he borrowed their methods): the area of the subconscious. He made it clear that the errors happened in a narrow space of associations, whether positive or negative. The actual errors were selected from the enormous space of all possible errors. The very volume of his observations seemed to "substatistically" prove that.

For example (Chapter 10) Freud found an error in one of his own books:

...Hannibal's father is called Hasdrubal. This error was particularly annoying to me, but it was most corroborative of my conception of such errors. Few readers of the book are better posted on the history of the Barkides than the author who wrote this error and overlooked it in three proofs. The name of Hannibal's father was Hamilcar Barkas; Hasdrubal was the name of  Hannibal's brother as well as that of his brother-in-law and predecessor in command.

As I dare to interpret this error, Hannibal and Hasdrubal are locked in the same dark narrow cell of our memory  with the address sign on the door looking like a classificator of a search engine (which is the best example of the tree topology):

        Ancient History > Carthage against Rome > story of Hannibal > Hannibal's family > names starting with Ha and ending with bal.

We may mistake one for the other in the dark. The error as fact is accidental because we are mostly right, but the content of error is partly deterministic. It would not occur to us to call Hannibal's father Sir Anthony Hopkins even though there is a link in a certain dimension of the tree space.

In a slightly larger cell of  

... >story of Hannibal> Hannibal's family>...

in the corner of  "names starting with Ha"  we may mistake Hasdrubal for Hannibal's father Hamilcar Barca. Whether it is the Ha that brings the three Barkides together, or simply their kinship, or, even simpler, their geometrical closeness on the pages of history textbooks,  is beyond proof in the particular case of Freud's own Freudian slip.

Similarly, Signorelli, Botticelli, and Boltraffio overlap by their -elli and Bo-.  

Through the relation between topology and partial order in mathematics, Graham Greene's novels, formal genetics, keyboard layout, Freudian slip, zipper, and Confucian ethics, I see the unity of Everything and its surprising wormhole (distant is in fact close) topology.

It is the patterns of the Everything that shoot the laser beams of similarity across the Universe of knowledge.

The cosmic beauty of the picture of the Everything prevents me from spoiling it by mulling over either the catastrophic blunders of my own life or the apocalyptic dangers of errors in the digital age.

Instead, I am reading The Comedians again. After many years I am still under the spell of Graham Greene's compassion.  


Perhaps the sexual life is the greatest test. If we can survive it with charity to those we love and with affection to those we have betrayed, we needn't to worry so much about the good and bad in us. But jealousy, distrust, cruelty, revenge, recrimination . . . then we fail. The wrong is that failure even if we are the victims and not the executioner.



P.S. (2016). On human molecules :  Hmolpedia (eoht.info), an A to Z Encyclopedia of Human Thermodynamics, Human Chemistry, and Human Physics, a unique, rich venture.


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