In Canto Three of his poem John Shade (the poet in VN’s novel Pale Fire, 1962) mentions empires of rhyme and Indies of calculus:
But who can teach the thoughts we should roll-call
When morning finds us marching to the wall
Under the stage direction of some goon
Political, some uniformed baboon?
We'll think of matters only known to us -
Empires of rhyme, Indies of calculus;
Listen to distant cocks crow, and discern
Upon the rough gray wall a rare wall fern;
And while our royal hands are being tied,
Taunt our inferiors, cheerfully deride
The dedicated imbeciles, and spit
Into their eyes just for the fun of it. (ll. 597-608)
In his essay Sobre los clásicos (On the Classics) included in Other Inquisitions (1952) J. L. Borges points out that, in Latin, "calculus" means a small stone and that the Pythagoreans used such stones before the invention of numbers:
Few disciplines could be of greater interest than etymology; this is owing to the unforeseeable transformation, over the long course of time, of a word's original meaning.
Given such transformations, which may border on the paradoxical, a word's origin is of little or no value in the clarification of a concept. Knowing that, in Latin, "calculus" means a small stone, and that the Pythagoreans used such stones before the invention of numbers, does not allow us to master the mysteries of algebra. To learn that a "hypocrite" is an actor and a "person" a mask is hardly a valuable tool for the study of ethics. Similarly, to understand our current designation of a "classic," it is of no utility that this adjective comes from the Latin classis, a fleet, which later would assume the meaning of order. (Let us recall in passing the analogous information contained in the term "ship-shape.")
In J. L. Borges's story El Hombre el en Umbral ("The Man on the Threshold," 1952) the action takes place in India (in Punjab). According to Kinbote (Shade’s mad commentator who imagines that he is Charles the Beloved, the last self-exiled king of Zembla), after line 274 of Shade’s poem there is a false start in the draft:
I like my name: Shade, Ombre, almost 'man'
In Spanish... (note to Line 275)
The Spanish word for “man” is hombre. Borges's story El Hombre en el Umbral begins as follows:
Bioy Casares trajo de Londres un curioso puñal de hoja triangular y empuñadora en forma de H; nuestro amigo Christopher Dewey, del Consejo Británico, dijo que tales armas eran de uso común en el Indostaní. Ese dictamen lo alentó a mencionar que había trabajado en aquel país, entre las dos guerras (Ultra Auroram et Gangen, recuerdo que dijo en latín, equivocando un verso de Juvenal). De las historias que esa noche contó, me atrevo a reconstruir la que sigue. Mi texto será fiel: líbreme Alá de la tentación de añadir breves rasgos circunstanciales o de agravar, con interpolaciones de Kipling, el cariz exótico del relato. Este, por lo demás, tiene un antiguo y simple sabor que sería una lástima perder, acaso el de las Mil y una Noches.
Bioy Casares brought back with him from London to Buenos Aires a strange dagger with a triangular blade and a hilt in the shape of an H; a friend of ours, Christopher Dewey of the British Council, told us that such weapons were commonly used in India. This statement prompted him to mention that he had held a job in that country between the two wars. (“Ultra Auroram et Gangen,” I recall his saying in Latin, misquoting a line from Juvenal.) Of the stories he entertained us with that night, I venture to set down the one that follows. My account will be faithful; may Allah deliver me from the temptation of adding any circumstantial details or of weighing down with interpolations from Kipling the tale’s Oriental character. It should be remarked that the story has a certain ancient simplicity that it would be a pity to lose—something perhaps straight out of the Arabian Nights.
"The Indies of calculus" and "almost 'man'" make one think of Chetvert' loshadi ("Quarter of a Horse"), the first story in Gleb Uspenski's book Zhivye tsifry ("The Live Numbers," 1888). The author of Vlast' zemli ("The Power of Land," 1882), Gleb Uspenski (1843-1902) suffered from mental illness and spent the last years of his life in a madhouse. According to the critic Mirski, Uspenski believed that he was split in two men - one of them, Gleb, was the embodiment of all that was good in him, and another, Ivanovich (Gleb Uspenski's patronymic), was the embodiment of all that was bad in him. One cannot help remembering R. L. Stevenson's novella Strange Case of Dr. Jekyll and Mr. Hyde (1886). In his essay The Double included in The Book of Imaginary Beings (1957) J. L. Borges mentions R. L. Stevenson's ballad ‘Ticonderoga:’
Suggested or stimulated by reflections in mirrors and in water and by twins, the idea of the Double is common to many countries. It is likely that sentences such as A friend is another self by Pythagoras or the Platonic Know thyself were inspired by it. In Germany this Double is called Doppelgänger, which means ’double walker’. In Scotland there is the fetch, which comes to fetch a man to bring him to his death; there is also the Scottish word wraith for an apparition thought to be seen by a person in his exact image just before death. To meet oneself is, therefore, ominous. The tragic ballad ‘Ticonderoga’ by Robert Louis Stevenson tells of a legend on this theme. There is also the strange picture by Rossetti (‘How They Met Themselves’) in which two lovers come upon themselves in the dusky gloom of a wood. We may also cite examples from Hawthorne (‘Howe’s Masquerade’), Dostoyevsky, Alfred de Musset, James (‘The Jolly Corner’), Kleist, Chesterton (‘The Mirror of Madmen’), and Hearn (Some Chinese Ghosts).
The ancient Egyptians believed that the Double, the ka, was a man’s exact counterpart, having his same walk and his same dress. Not only men, but gods and beasts, stones and trees, chairs and knives had their ka, which was invisible except to certain priests who could see the Doubles of the gods and were granted by them a knowledge of things past and things to come.
To the Jews the appearance of one’s Double was not an omen of imminent death. On the contrary, it was proof of having attained prophetic powers. This is how it is explained by Gershom Scholem. A legend recorded in the Talmud tells the story of a man who, in search of God, met himself.
In the story ‘William Wilson’ by Poe, the Double is the hero’s conscience. He kills it and dies. In a similar way, Dorian Gray in Wilde’s novel stabs his portrait and meets his death. In Yeats’s poems the Double is our other side, our opposite, the one who complements us, the one we are not nor will ever become.
Plutarch writes that the Greeks gave the name other self to a king’s ambassador.
Shade's murderer, Gradus is Kinbote's double. Shade’s poem is almost finished when the author is killed by Gradus. Kinbote believes that, to be completed, Shade’s poem needs but one line (Line 1000, identical to Line 1: “I was the shadow of the waxwing slain”). But it seems that, like some sonnets, Shade's poem also needs a coda (Line 1001: “By its own double in the windowpane”). In his story El Hombre en el Umbral J. L. Borges mentions Mil i una Noches ("A Thousand and One Nights"), a collection of fairy tales also known as the Arabian Nights.
Gleb Uspenski is the author of Garshin's obituary. In March 1888 Vsevolod Garshin (the author of Nadezhda Nikolaevna, 1885) committed suicide by throwing himself down the stairwell. An American scholar of Russian descent, Professor Vsevolod Botkin went mad and became the poet Shade, his commentator Kinbote and his murderer Gradus after the tragic death of his daughter Nadezhda (Hazel Shade's "real" name). Nadezhda means in Russian "hope." There is a hope that, when Kinbote completes his work on Shade’s poem and commits suicide (on Oct. 19, 1959, the anniversary of Pushkin’s Lyceum), Botkin, like Count Vorontsov (a target of Pushkin's epigrams, "half-milord, half-merchant, etc."), will be full again.