Tuesday, 1 November 2016

D-r Tchékhov: A Textbook Case . . . Prof. Yanychev’s Three-Cornered Duel

I have mentioned on a number of occasions the existence of the manuscript, A Textbook Case, putatively by Chekhov, which fell into the possession of my father at the end of WWII, and whose pages relate the misadventures of the morphine-dependent D-r Anton Tchékhov, aged 28 years, when investigating the mysterious duelling death of an aristocratic cadet in a remote snowbound northern garrison.  
        Evidently, my father believed the ms to be the long-lost novel to which Chekhov referred in a letter to Pleshcheev on 9 Feb. 1888; understood by scholars to be a fugitive work in progress but never found: ‘Ah, if you knew what a plot I have in my noddle! What marvellous women! What funerals . . . !’

        Well, a funeral there was, for this extract from the ms – An Unwreathed Burial – may be read here . . . 
        . . .  but, before a funeral there must be a death, and that passage from the ms has yet to be seen by a wider readership. So here it is, with an expanded exegesis on my father’s part to explain D-r Tchékhov’ allusion to The Three-Cornered Duel Problem posed by Professor Grigoriy Yevseyevich Yanychev (1804-1867), mathematician and leading 19th Century proponent of probability theory (his gifted young protégé was the distinguished algebraist, A. A. Markov the elder).
        Note: the idiosyncratic orthography throughout is my father’s.

A Textbook Case

In the dead of winter, for a Muscovite medico-anthropologist to stumble across a tableau mort frozen rigid in an attitude of heroic redundancy was to bow to an unwelcome knowledge that the catalogue of diseases inhabiting the General’s ill-favoured region was apparently not complete.
  “Make way!” shouted the komendant. “Field-surgeon forward!”
   Under the doctor’s generalship the party advanced.
   “A textbook case,” mused the General. “A perfect diagramma for a duel imprinted on the snow.”
  The undertaker crew halted a sazhen from the corpse.
   Again was uttered another dreadful dissyllable.  “Umer!” Anton heard an ensign exclaim. “Dead!” O! Nicolai Chudotvórets! Wonder Worker! Saint of God!”
  Anton thought of the morgue under the Moscow Medical Faculty building. 
  “Alas,” he reflected, “what is terrible is not the corpses, but the fact that I am no longer terrified of them.”
  “We must live by the quick and not with the dead.”  The General answered the unspoken thought.
  “First we’ll review the stricken field. A posthumous procès-verbal may well be required to satisfy our masters. That job falls to you,” the General ordained. 
  “HQ’s going to have me strung up for this, but,” and he gripped Anton’s shoulders compellingly, “while a noose is still running there’s still time to pray.”
  He broke away with a bitter laugh.
  “There’s the barriere.” He pointed to an odd shaped piece of wood stuck in the snow.
  “Take note. Cannoneer Kulikov’s shin-guard for a starting post.”
  In the moonlight the impressed footsteps were quite clear. The old frontier scout essayed a rapid reconstruction of the victim’s last moments, intent upon unriddling the monomachian rituals performed by insulter and insulted, by slayer and slain. 
  This was not the first time the General had smelled powder. 
  “Eight paces. Trod by the Offender. The Challenger proposes distance so, naturally, the Prince faces the butts – to be sure he gains the advantage of a co-ordinate. It assists the eye to draw a bead on a marker. Then it’s . . .  ‘Stations, Gentlemen, Attend!’ The Prince would have conceded to Pomidorchik. So Kulikov steps forward. ‘Aim! Fire!’  The Offender fires first.  The Aggressor has to make himself as small as possible – remember Mychetzky?* – by standing sideways, right hand on his chest, presenting the most difficult target. Dammit! Then what?  This problem is worse than Professor Yanychev’s Three-Cornered Duel!”
   There was a muffled report as the General blew his nose and resumed.
  “According to the Duello honour code, the rôles would then reverse, and the Prince would’ve returned fire whilst Kulikov stood his ground. Unless it was a lucky first shot I can’t believe Kulikov’s marksmanship could strike a mortal blow from that distance. He’d never handled a rod until today. Look! Five steps to the barriere, his pace is unbroken, he doesn’t pause to fire, just keeps walking in the return direction!  There’s the puzzle!” 
  Reluctantly, the General’s eyes swept the combat area until his gaze rested on the dark enigma that broke the surface of the field.
  Khvatit! Dovol'no! No more! Enough!” groaned the General. “Proceed, mon cher docteur, let our post-mortem begin.” 
        Anton braced himself, eyes half-shut, resisting full immersion in his drug-induced repose. He knew with certainty, as he struggled to withstand the narcotic’s serpentine embrace, that chance was beckoning him to draw near to witness one of the last and purest fountainheads of the empire’s accursed sentimental morbidity, frozen forever at its furthermost source ; that providence suffered him – and he alone – to be present in such close attendance at the pallida Mors of panslavonic Wertherism; to witness the fleurettes and gasconnades of an age of literary flâneurs wither in the Russian snows; to certify once and for all their extinction in all their tragic pathos.
       A doctor, as everyone should know, enjoys being at a duel. 

For the General’s recollections of duels between the cadet Mychetzky and his classmate Nezlobin, see Winter Rules and Le Diable Boiteux at :

[ End of extract. ]  

Lèse-majesté – Yanychev’s Three-Cornered Duel.

Following the death of Aleksandr Pouschkin in a duel (January, 1837) fought with his wife Natalya’s admirer, Baron D’Anthès, the brilliant young mathematician, Grigoriy Yevseyevich Yanychev devised the satirical problem of the three-cornered duel, incorporating Aleksandr Pouschkin [A], the Baron [B] and, a second anonymous lover, the Count [C ]. This squib was considered by the Tsarist Court to have defamed the aristocracy and, in consequence, Yanychev was banished as a poselenets to Archangel (an exile-settler status for transgressors who did not fall into the harsher category of katorzhnik or convict).

Pistols for Three

“It is highly probable,” said Natalya to her lover, “that in a three-cornered duel only one of my three admirers will survive. Therefore, my dear Baron, so you alone may live, I beseech you to miss with your first shot.”
(1) Natalya began by assuming that the Baron was acquainted with the relative proficiency of his rivals.  This is how she calculated that B would be the sole surviver, and not A, her husband or C, her rejected lover : 
(a) If B kills A, it is C’s turn to fire.  There is a 3/4 chance that he will  kill B.  If he misses, the Baron has a second shot. There is a 2/3 chance that he will now kill the Count and secure the love of Natalya. 
(b) If B misses Aleksandr, C will fire at A next. (This is certain, because if C fires at B and kills him, he will next be killed in turn ; while if C fires at B and misses him, A will equally kill C next, as the more dangerous of his opponents.) 
     (i) If C misses A, Aleksandr will kill C.  Now the Baron, with his second shot, has a 2/3 chance of being the sole survivor.
     (ii) If C kills A.  B again has a 2/3 chance of being the sole survivor.
 Summarising these chances, the Baron’s chances of being sole survivor
 are :      ⅔   •  ¼   •   ⅔  (a)
     plus  ⅓   •  ¼   •   ⅔  (b)  (i)
     plus  ⅓   •  ¾   •   ⅔  (b)  (ii)
               i.e. are ⅓ in all. 
(2) Natalya, of course, also calculated the Baron’s chances of survival were he so foolish as to fire first at the Count.
     (a) If the Baron kills the Count, he is forthwith killed by Aleksandr.
     (b) If the Baron misses the Count, the Count fires (as before) at                         Aleksandr.  The Baron’s chances are now as in (i) (b) above :                         i.e. 2/9 in all.
(3) A secret smile then plays on Natalya lips as the logical conclusion finally dawns on her. Suppose the Baron makes sure of missing!  Now, since the Count will next (as before) fire at Alexandr first, the Baron’s chances of survival become 2/3.  Hence, Natalya’s message to Baron D’Anthès was to make sure of missing her husband with his first shot.

Precursor of The Three-Cornered Duel.

Incidentally, Yanychev claimed, in his defence to spare his banishment, that this puzzle was inspired not by Pouschkin but by a Three-Cornered Duel fought between a midshipmen, a boatswain and a purser's steward, described by an English seafarer. It is indeed a fact that such a duel was published in 1836, a year before Pouschkin’s death. [An extract follows.]

       “You have grossly insulted this gentleman,” said Mr Biggs, in continuation; and notwithstanding all your talk of equality, you are afraid to give him satisfaction—you shelter yourself under your quarter-deck.”
       Mr Biggs," replied our hero, who was now very wroth, I shall go on shore directly we arrive at Malta. Let you and this fellow put on plain clothes, and I will meet you both—and then I'll show you whether I am afraid to give satisfaction.”
       One at a time, said the boatswain. 
       “No, sir, not one at a time, but both at the same time — I will fight both, or none. If you are my superior officer, you must descend, replied Jack, with an ironical sneer, "to meet me, or I will not descend to meet that fellow, whom I believe to have been little better than a pickpocket.
       This accidental hit of Jack’s made the purser's steward turn pale as a sheet, and then equally red. He raved and foamed amazingly, although he could not meet Jack’s indignant look, who then turned round again.
       Now, Mr Biggs, is this to be understood, or do you shelter yourself under your forecastle?
       I'm no dodger, replied the boatswain, and we will settle the affair at Malta. . . . 
       . . . Mr Biggs having declared that he would fight, of course had to look out for a second, and he fixed upon Mr Tallboys, the gunner, and requested him to be his friend. Mr Tallboys, who had been latterly very much annoyed by Jack’s victories over him in the science of navigation, and therefore felt ill-will towards him, consented; but he was very much puzzled how to arrange that three were to fight at the same time, for he had no idea of there being two duels; so he went to his cabin and commenced reading. Jack, on the other hand, dared not say a word to Jolliffe on the subject; indeed there was no one in the ship to whom he could confide but Gascoigne: he therefore went to him, and although Gascoigne thought it was excessively ‘infra dig’ of Jack to meet even the boatswain, as the challenge had been given there was no retracting: he therefore consented, like all midshipmen, anticipating fun, and quite thoughtless of the consequences.

“Equal angles subtended by equal sides.”

The second day after they had been anchored in Valette Harbour, the boatswain and gunner, Jack and Gascoigne, obtained permission to go on shore. Mr Easthupp, the purser’s steward, dressed in his best blue coat, with brass buttons and velvet collar, the very one in which he had been taken up when he had been vowing and protesting that he was a gentleman, at the very time that his hand was abstracting a pocket-book, went up on the quarter-deck, and requested the same indulgence, but Mr Sawbridge refused, as he required him to return staves and hoops at the cooperage. Mesty also, much to his mortification, was not to be spared. This was awkward, but it was got over by proposing that the meeting should take place behind the cooperage at a certain hour, on which Mr Easthupp might slip out, and borrow a portion of the time appropriated to his duty, to heal the breach in his wounded honour. So the parties all went on shore, and put up at one of the small inns to make the necessary arrangements.
       Mr Tallboys then addressed Mr Gascoigne, taking him apart while the boatswain amused himself with a glass of grog, and our hero sat outside teasing a monkey.
       Mr Gascoigne,” said the gunner, I have been very much puzzled how this duel should be fought, but I have at last found it out. You see that there are three parties to fight; had there been two or four there would have been no difficulty, as the right line or square might guide us in that instance; but we must arrange it upon the triangle in this.”
       Gascoigne stared; he could not imagine what was coming.
       Are you aware, Mr Gascoigne, of the properties of an equilateral triangle?”
       Yes,” replied the midshipman, that it has three equal sides — but what the devil has that to do with the duel?”
       Everything, Mr Gascoigne,” replied the gunner; it has resolved the great difficulty: indeed, the duel between three can only be fought upon that principle. You observe," said the gunner, taking a piece of chalk out of his pocket, and making a triangle on the table, "in this figure we have three points, each equidistant from each other: and we have three combatants—so that, placing one at each point, it is all fair play for the three: Mr Easy, for instance, stands here, the boatswain here, and the purser’s steward at the third corner. Now, if the distance is fairly measured, it will be all right.”
       But then,” replied Gascoigne, delighted at the idea; how are they to fire?” 
       It certainly is not of much consequence,” replied the gunner, but still, as sailors, it appears to me that they should fire with the sun; that is, Mr Easy fires at Mr Biggs, Mr Biggs fires at Mr Easthupp, and Mr Easthupp fires at Mr Easy; so that you perceive that each party has his shot at one, and at the same time receives the fire of another.”
       Gascoigne was in ecstasies at the novelty of the proceeding, the more so as he perceived that Easy obtained every advantage by the arrangement.
       "Upon my word, Mr Tallboys, I give you great credit; you have a profound mathematical head, and I am delighted with your arrangement. Of course, in these affairs, the principals are bound to comply with the arrangements of the seconds, and I shall insist upon Mr Easy consenting to your excellent and scientific proposal.”
       Gascoigne went out, and pulling Jack away from the monkey, told him what the gunner had proposed, at which Jack laughed heartily.
       The gunner also explained it to the boatswain, who did not very well comprehend, but replied—
       I dare say it’s all right—shot for shot, and d—n all favours.” The parties then repaired to the spot with two pairs of ship’s pistols, which Mr Tallboys had smuggled on shore; and, as soon as they were on the ground, the gunner called Mr Easthupp out of the cooperage. In the meantime, Gascoigne had been measuring an equilateral triangle of twelve paces—and marked it out. Mr Tallboys, on his return with the purser’s steward, went over the ground, and finding that it was equal angles subtended by equal sides,” declared that it was all right. Easy took his station, the boatswain was put into his, and Mr Easthupp, who was quite in a mystery, was led by the gunner to the third position.
       But, Mr Tallboys,” said the purser's steward, I don’t understand this. Mr Easy will first fight Mr Biggs, will he not?”
       No," replied the gunner, this is a duel of three. You will fire at Mr Easy, Mr Easy will fire at Mr Biggs, and Mr Biggs will fire at you. It is all arranged, Mr Easthupp.”
       But,” said Mr Easthupp, I do not understand it. Why is Mr Biggs to fire at me? I have no quarrel with Mr Biggs.”
       Because Mr Easy fires at Mr Biggs, and Mr Biggs must have his shot as well.”
       If you have ever been in the company of gentlemen, Mr Easthupp," observed Gascoigne, you must know something about duelling.”
       Yes, yes, I've kept the best company, Mr Gascoigne, and I can give a gentleman satisfaction; but —
       Then, sir, if that is the case, you must know that your honour is in the hands of your second, and that no gentleman appeals.
       Yes, yes, I know that, Mr Gascoigne; but still I’ve no quarrel with Mr Biggs, and therefore, Mr Biggs, of course you will not aim at me.
       Why you don’t think that I am going to be fired at for nothing, replied the boatswain; “no, no, I'll have my shot anyhow.
       But at your friend, Mr Biggs?
       All the same, I shall fire at somebody; shot for shot, and hit the luckiest.

[Please forgive the lengthy extracts but I have followed the Oulipoian principle of the footnotes being of substantially greater depth than the cited text.)


For other excerpts from Tchékhov’s as-yet-unpublished crime novel, D-r Tchékhov, Detektiv, see:

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