Dynamics of a Hanging by Tony Pi

Tony Pi has a Ph.D. in Linguistics and currently works as an administrator at the Cinema Studies Institute at the University of Toronto. At the time of this writing, he is a finalist for the John W. Campbell Award for best new writer. His work has appeared in (or is forthcoming from) Abyss & Apex, On Spec, Intergalactic Medicine Show, and the anthologies Ages of Wonder, Cinema Spec, and Writers of the Future XXIII. He is currently working on a novel manuscript about the shapeshifters who first appeared in his story “Metamorphoses in Amber,” which was a finalist for the Prix Aurora Award.

Most people know Lewis Carroll (the pen name of Charles Lutwidge Dodgson) as the author of Alice’s Adventures in Wonderland. Dodgson became good friends with the family of one of his academic colleagues, the Liddells, and would often take their children along with him when he went rowing on the nearby rivers. During these expeditions he would make up fanciful tales to entertain the children, and one of the girls, Alice, was so enchanted that she begged Dodgson to write it all down. The enthusiastic reception for the manuscript by fantasy author George MacDonald and his children convinced Dodgson to pursue publication. Dodgson’s private life has been the subject of intense speculation, especially regarding his relationship with the Liddells. (Dodgson’s family apparently destroyed several pages of his diary, presumably to protect his reputation.) We know that he was tormented by feelings of guilt and shame, which apparently restrained him from following his father into the priesthood. It’s all very mysterious. One thing that’s beyond any doubt though is that Dodgson demonstrated brilliance in many different fields. Notably, he held a lectureship in mathematics, and wrote books on logic. It’s those abilities that he puts to good use in our next adventure.

 

DYNAMICS OF A HANGING
by Tony Pi

It was in the fall of 1891 that I received a telegram from the Reverend Charles Dodgson, inviting me to his residence in Guildford, Surrey. It was not for a medical consultation, but of vital importance to the present trial of the Moriarty gang: the mystery of Professor Moriarty’s cipher.

Reverend Dodgson was both an author of children’s books and a mathematician. My wife was fond of the Alice books under his nom-de-plume, Lewis Carroll, while Holmes once recommended me to read his Game of Logic to hone my analytical reasoning. It surprised me that Dodgson knew of the coded notebooks, as their existence had been suppressed. It was not five months ago that my friend Sherlock Holmes perished at Reichenbach Falls in his final confrontation with James Moriarty. Even in death, Holmes struck a fatal blow against Moriarty’s criminal confederates, leaving documents that thoroughly incriminated them. Inspector Patterson invited me to examine the materials recovered from one of Moriarty’s secret lairs: vials of opiates among blueprints and handwritten musical scores; purloined paintings beside burned account books; and most intriguing, notebooks written in Moriarty’s hand, the oldest of which had a page torn out.

Moriarty’s notebooks contained mathematical formulae interspersed with code. Mycroft Holmes speculated it was a Vigenère cipher, but even he couldn’t solve it. “Alas, both the Kasiski and Kerckhoffs methods failed,” said Mycroft. “If only we knew what the coded messages were about. Are they musings on mathematics, or something more sinister? Find the key, Watson, and we’ll glimpse Moriarty’s mind.”

I was intrigued by Dodgson’s message. Did he know the key, when even Mycroft Holmes failed? I immediately dispatched a telegram accepting his invitation.

Thus I found myself in Guildford, sipping tea with Charles Dodgson in his parlour. The Reverend, a thin man with uneven blue eyes and sloped shoulders, tilted his left ear towards me as we talked.

“My condolences, Doctor Watson, on the untimely passing of Mr. Holmes,” said he. “I fear I must bear some of the burden for his demise.”

“Oh? Did you know him?” I asked.

“I knew of Holmes at Oxford, though we never met. It was James Moriarty I knew, through our years at Christ Church debating mathematics and logic. Is there a volume from Moriarty’s effects, with a single coded page torn out?”

“Indeed!” I exclaimed. “How did you know?”

“Because I have that page.” Dodgson retrieved a copy of Through the Looking Glass from his collection. Tucked within was the coded page he spoke of, folded and yellowed with age. “Tenniel’s Jabberwock illustration always reminds me of Moriarty, hypnotic and serpentine.”

“How did you get this?”

“That, Doctor, is a twisted tale,” said he. “It began with the Order of Copernicus, and ended with the tragic murder of a young prodigy named Arthur Doyle.”

The Order of Copernicus is a fellowship of scholars, physicians, mathematicians and philosophers. The Copernicans often invite new members to enrich their symposia with fresh ideas and voices. Moriarty first introduced me to the Order years ago, after he completed his dissertation on the Binomial Theorem. I found their debates enthralling, and participated whenever I could.

In early summer, 1879, Moriarty and I were invited to Aston by a fellow Copernican, Doctor Reginald Hoare. Reginald introduced us to his young lodger, Arthur Doyle, a medical student who was working as a dispensing assistant taking house calls on Reginald’s behalf. I found him an engaging conversationalist and a sharp observer.

“What do you plan to do with your future, Arthur?” I asked.

“Surgery, sir,” said Arthur. “I’m very much inspired by Doctor Bell at the Edinburgh University. But I’d also like to become a writer like you, actually, and have written some stories for Reginald’s children. Edgar Allan Poe’s another inspiration, and I’m attempting a mystery now.”

“Poe! Now there was a true Copernican. I heard he was a great cryptographer,” I said.

Moriarty disagreed. “He indulged in substitution codes, barely worth the effort to solve, unlike Vigenère ciphers.”

Arthur asked what a Vigenère cipher was.

“It’s based on the Caesar cipher, which shifted letters by a chosen number of positions, looping back to the beginning of the alphabet if necessary,” I explained. “Shift the word JABBERWOCKY four positions to the right, you’d have NEFFIVSGOC. To solve the coded message, apply the shift in reverse.

“The Vigenère cipher uses a keyword where each letter in the alphabet represented a different shift. For example, if ALICE were my keyword, that would mean shifts of 0, 11, 8, 2, and 5. The keyword is repeated as needed, and so JABBERWOCKY becomes JLJDIRHWEOY.”

Moriarty nodded. “There are mathematical ways to solve a Vigenère code. Kasiski’s method determines the length of the keyword by measuring distances between repeating combinations, then uses frequency analysis to break the code. Kerckhoffs’ method focuses on solving the keyword itself.”

“Moriarty, didn’t you have a notebook at Christ Church where you jotted down your formulae?” I asked. “You used a cipher on the annotations. Was that Vigenère?”

Moriarty smiled. “It was, to ensure that the musings and errors of my youth were for my eyes alone. But I’m confident that my code cannot be broken by either the Kerckhoffs or Kasiski solutions. They assume the keyword would be short, and repeated. But if the keyword’s significantly long, like a piece of text, then a coded message would be virtually unbreakable.”

“Respectfully, Professor, the keyword may be impervious to analysis, but the codemaker is not,” said Arthur. “At medical school, Professor Bell taught us to observe the person as well as the disease in our diagnoses. By analyzing the man’s habits, experiences and indulgences, one can deduce the choice of text he uses for his code.”

“You presume to unriddle my cipher by mere observation?” asked Moriarty.

“If I had the chance to get to know you better, Professor, I daresay I could figure out your code,” said Arthur.

“I know a challenge when I hear one! Reginald, indulge me by releasing Arthur from his obligations on weekends. My university’s not far, and I will pay for travel and lodging. He may observe me in my element, while I in turn will mentor him and provide him with a sample of cipher to unriddle. If he succeeds by summer’s end, I will pay his tuition.”

Moriarty had obviously taken a liking to Arthur Doyle, perhaps eager to guide a young man into his genius.

Reginald heartily agreed. “If he doesn’t fall behind his duties here, why not?”

Arthur smiled. “It will be a pleasure learning from you, Professor.”

“Before I forget, gentlemen, Samuel Haughton left these for you on his last visit,” Reginald said, giving us each a copy of a treatise titled On Hanging. Reverend Haughton was a doctor and fellow Copernican from Dublin who dabbled in mathematics. “Haughton claims the mathematics of hanging can be useful in medicine. Humane versus inhumane hangings: depending on the criminal’s weight and the length of drop, it could mean the difference between a quick death from snapping his spinal cord, to a long death from strangulation.”

We argued awhile over the need for executions, with Moriarty maintaining ambivalence. When the topic somehow drifted onto the three-body problem in astronomy, which I had little interest in, Arthur and I excused ourselves so I could see his story manuscripts.

Arthur’s room was modest, and his desk cluttered with papers on medicine, scraps of writing, and sheet music. Among his medical books were works by Burton, Dickens, Leibniz, and of course, Poe. He moved a violin case off a chair so I could sit and read his stories. I found them well-written and engaging, and encouraged Arthur to continue writing.

Arthur retrieved a book bound in red Moroccan leather, gilt in silver: a copy of Alice’s Adventures in Wonderland. “Would you mind signing this, Reverend, for Herr Gleiwitz? I see him on my rounds, and feel sorry for the man. He’s down on his luck, raising his children on what little income he receives from giving German lessons. Perhaps your book will give his family some joy.”

I gladly signed the copy.

Arthur wrote to me at Oxford thereafter, telling me of his tutelage under Moriarty. At first, his letters were ebullient, saying that the Professor’s cunning rivaled that of Doctor Bell’s. Whereas Bell emphasized observation, Moriarty taught him anticipation. Predicting behaviour was as crucial as establishing history, he wrote, explaining Moriarty’s philosophy. The world was a chessboard and men were as predictable as game pieces.

But Arthur’s later letters were sombre, hinting at a rift between himself and Moriarty. Did Moriarty’s enthusiasm for his student turn to envy? Or did Arthur discover Moriarty’s dark dealings? In any event, it spelled death for him.

In late summer, both Moriarty and I accepted an invitation from a fellow Copernican in London. On our third night there, upon our return from the symphony, we learned by telegram that tragedy had struck: Arthur Doyle was found dead, hanged.

“Arthur had been concerned about matters in Aston, but refused to say more,” said Moriarty, stunned by the news. “I ought to have foreseen disaster.”

I consoled him. “How could you have known?”

“We owe it to the boy to investigate his death, Charles,” he insisted.

And so Moriarty and I returned to Aston, bearing our condolences to Reginald.

Reginald recounted the details of Arthur’s death. “Arthur had returned from house calls and retired to his room that evening as usual. The following morning, we were shocked to hear Arthur had been found in the bell tower at St. Mary’s, the church down the street. Inspector Ives took me there to identify Arthur’s body.”

“Cause of death?” asked Moriarty.

“All the signs pointed towards asphyxiation. Inspector Ives believes it was suicide,” said Reginald.

“Arthur would hardly take his own life,” said Moriarty. “Reginald, come with us and describe what you saw?”

Reluctantly, the good doctor accompanied us to St. Mary’s. The bell tower was several stories tall, with a ladder up to a trapdoor that led into the belfry. The bell’s rope dangled through a large opening in the belfry floor.

“The noose was tied to the bell’s gudgeon,” explained Reginald. “He was dangling six feet off the ground when we found him. He couldn’t have kicked away a support, or we’d have discovered one. He must have jumped from the bell chamber.”

“He could have pushed off the ladder,” observed Moriarty. “But the momentum might have swung his body into the wall opposite. Any bruising on his arms or legs?”

“No,” said Reginald.

“A dying man’s instinct is to claw at the noose, even if he intended to die. Did you find any scratch marks around his neck?” continued Moriarty.

“No.”

“But his hands weren’t bound?”

“Correct.”

“Then the evidence points towards a sudden drop from above,” said Moriarty. “Except that’s impossible.”

“Why?” asked Reginald, perplexed.

“Mathematics,” I explained, remembering Haughton’s treatise on hanging. “Given his weight, a rope that exceeded twelve feet would make the force of the drop so great that the noose wouldn’t simply snap his neck, it would cut clean through.”

Moriarty nodded. “Given the marks on his neck, where was the noose’s knot placed, Reginald?”

“Corner of his left jaw.”

“A knot placed there would throw the head back upon falling, resulting in a fracture or dislocation of the neck. He would have died of a snapped neck, not strangulated,” Moriarty concluded. “We’re faced with contradictory facts. Arthur couldn’t have jumped from that height without decapitation, but neither could he have hung himself in a manner consistent with asphyxiation.”

“A vorpal paradox indeed,” I agreed.

“That leaves but one conclusion: that Arthur Doyle was dead before someone strung him up,” said Moriarty.

“Perhaps he was strangled in his sleep? Marks from a garrote would have been hidden by the bruising of the noose,” I suggested.

“Perhaps. His room may yield more clues,” said Moriarty.

In Arthur’s room, Moriarty moved a familiar red, leather-bound book gilt in gold off the desk, and rifled through the young man’s papers.

“Here’s a draft of a paper he was writing for the British Medical Journal,” said Moriarty. “The Uses of Gelseminum As A Poison, by Arthur Conan Doyle. Arthur had been experimenting on himself with gelseminum, also known as jessamine, in the interest of medical research. We have our poison, gentlemen.”

“Poisoned! I thought his death was consistent with respiratory failure,” I said.

“Do you know what gelseminum does, Reginald?” asked Moriarty.

“It’s efficacious against spasmodic disorders, like epilepsy and hysteria, inhibiting nerve control and respitory functions,” replied Reginald. “A large enough dose would paralyze a man, even arrest his breathing and stop his heart! I naturally assumed it was strangulation by hanging, and never considered poison. You are as brilliant as Arthur said, Moriarty!”

Moriarty cracked a thin smile. “It takes only observation to tell truth from lie.”

“But who would kill him, and why?” I asked.

“I suspect if Reginald inventories his medicinal store, he’ll discover narcotics missing,” said Moriarty, with utter confidence. “Suppose Arthur was blackmailed into stealing the drugs. He might have threatened to go to the police, forcing his blackmailers to eliminate him quietly with an overdose of gelseminum, of which Arthur had in sufficient quantity to kill. To conceal their crime, they hoisted up his body in the bell tower to suggest suicide.”

Reginald paled. “Arthur, embroiled in such dreadful business?”

“Appearances can be deceiving,” said Moriarty. “Let us check the dispensary.” They left, but I stayed behind to say a prayer for the lad.

Moriarty’s analysis seemed plausible, but I didn’t believe it of Arthur. I observed two peculiarities. Arthur’s violin case was missing, and the book on the desk was a copy of Through the Looking Glass, not Alice’s Adventures in Wonderland. I had chosen the different gilt decorations for each myself. I flipped open the cover and found a forgery of my signature, but not a good one: my name was misspelled. It read: C.L. Dodgson (alias Lewis Carlool).

Why would Arthur go to the trouble of forging my signature, but spell it wrong? I came to the conclusion that Arthur left that clue for me alone. No one else would know I hadn’t signed Looking Glass.

Reginald checked his inventory and discovered that drugs were indeed missing. Further forensic examination of Arthur’s body confirmed he died of gelseminum poisoning, and the police started a search for Arthur’s killers. Moriarty returned to his college, but I stayed behind in Acton to investigate the lead of the forged autograph. I made some quiet inquiries and found Herr Gleiwitz, who welcomed me into his home.

“Mr. Doyle had been kind to us, God rest his soul,” said Herr Gleiwitz. “Once, when I couldn’t pay for the medicine, he gave me his watch and said I should sell it. I tried to give it back, but he wouldn’t have it. Several days ago, he gave my eldest a violin and made the boy promise to learn how to play.” He brought the instrument for my examination.

I could find no hidden compartments in the violin case, but I discovered a folded piece of paper inside the violin through its F-holes. It took several frustrating tries to get it out intact. It was a torn page written in code in Moriarty’s hand, and it must have been worth killing for. For the first time, I suspected that James Moriarty murdered Arthur Doyle in cold blood.

I was certain that Arthur had done what he promised: he had deduced Moriarty’s key by observation alone. But the younger Moriarty was proud, and would have taken great risks to protect his secrets. And so he orchestrated Arthur’s murder, with the perfect alibi—he was in London with me. He then hid his own involvement by playing detective to his own crime. What better way to throw the police off his scent?

I asked Herr Gleiwitz never to speak of my visit, and returned to Oxford. I worked in frenzy to solve the code, but to no avail. Finally, I decided to visit Moriarty, to observe him as Arthur had, look into his eyes, and hope to find a soul.

I called on Moriarty in late September, bringing pages for my next book, Curiosa Mathematica, Part Two, as pretext. Soon we were discussing math problems over tea in his den.

Moriarty’s taste in books was eclectic: art, algebra, music, astronomy. There were so many texts that could be his Vigenère key, it would have taken months just to check the coded page against the first few pages of each book!

Moriarty remained the confident and controlled gentleman he always was. But when I mentioned that he never did express his views on capital punishment, a sneer crept onto his face. “Death is the only punishment.” He smirked, then turned the topic to eighteenth-century painters. It was enough to convince me that he hid the heart of a villain.

Yet I had no evidence. If I went to the police with only an unsolved page of code, I too would have been marked for death. I resolved to engineer Moriarty’s fall in secret. So I wrote anonymous letters to key figures in his university town, hinting at shady dealings. The vile rumours spread, and soon Moriarty resigned his chair, retiring to London to become an army coach.

I thought the loss of the professorship would have taught him a lesson, but I was wrong. Instead, he built a veneer of self-effacement after his resignation, and became supremely cautious. I wonder what hand I had in his perfection as a criminal mastermind?

Reverend Dodgson stopped there, and I poured him another cup of tea. “Why didn’t Arthur tell someone? Or write a letter detailing what he discovered?” I asked.

“Moriarty would have silenced anyone who knew. Written declarations might have been found and destroyed. I suspect the forgery of my name was the only clue left intact,” said Dodgson.

“And still unsolved, I gather,” I said.

“You have it, Doctor Watson,” agreed Dodgson. “I was hoping we could solve the key together.”

I was about to suggest enlisting Mycroft’s aid, but young Arthur Doyle had meant the message for Dodgson, so it must draw upon the Reverend’s personal knowledge. Perhaps all he needed were my insights into the problem, as wrong as they might be, to help him arrive at the right answer.

“The misspelled name, Carlool. Was that the key word?” I asked.

“No. It has to be a long text, as Moriarty said, to foil simple decoding.”

“Could the code be based on Wonderland or Looking Glass?”

“Doubtful. Moriarty used the notebook while he was writing his dissertation, which was years before I wrote those books.”

What would Holmes say? He’d ask me how I’d send a message to a mathematician. With numbers, I’d reply.

And there was the answer. “The point of departure from your nom-de-plume comes after Car. It isn’t lool, but one-thousand and one!” I cried triumphantly.

Dodgson’s eyes widened. “I never thought of that.”

“Moriarty used Burton’s The Book of the Thousand Nights and a Night as his key, then,” I said, remembering Dodgson’s list of Arthur’s books.

“But that was published in 1885, years after Arthur’s death. He would only know of Burton’s travel writings,” argued Dodgson.

I thought about it further. “Poe write a story called The Thousand-and-Second Tale of Scheherazade? Not an exact match to one-thousand and one, and I’m certain it was published in 1845. Didn’t Arthur have a copy of Poe on his shelves?”

“Books? Wait, Arthur read Leibniz!” said Dodgson excitedly. “Gottfried Leibniz invented the binary number system. In binary, one-zero-zero-one is the number nine. Also, one-thousand-and-one is the product of three consecutive prime numbers: seven, eleven, and thirteen. They would be consecutive odd numbers but for the conspicuous absence of the number nine. Arthur hid that number twice in plain sight!”

“But how would nine be the key?” I asked.

We wrestled over the new question. My thoughts kept drifting back to Holmes. What would he consider next? He’d be fascinated by that violin, of course—

“The violin!” I cried. “It’s no accident that the note was hidden in it; it’s the missing clue. Moriarty loved music, didn’t he?”

“He did,” said Dodgson.

“If he wanted to remember a passage as a key, the lyrics of a song might be easiest to remember,” I suggested. “And there’s one symphony set to lyrics.”

“Beethoven’s Ninth, Ode to Joy!” he exclaimed. “Friedrich von Schiller’s poem set to music, in the original German. That’s why Moriarty was confident that a Kerckhoffs statistical analysis of his key would fail. Letter frequencies differ from language to language.”

We immediately set about deciphering the page using Ode to Joy as the key. It took many tries to determine how the key aligned to the code, but we barely noticed the passage of time. At last, Dodgson finished deciphering the entire page.

“What does it say?” I asked, breathless.

“It alludes to Moriarty’s triumphant murder of his mentor, someone who was as devilish as he was.” Dodgson handed me the coded page and its solution. “Alas, the name does not appear on this page, but the rest of the notebook should reveal who made Moriarty what he was, how he died, and why.”

“And perhaps other crimes, other accomplices,” I added. Now that we had the right key, we would learn at last about Moriarty and the trials that shaped him. “I’ll let Mycroft Holmes know. Thank you, Reverend.”

“No, thank you for restoring a man’s good name, Doctor Watson. Holmes would be proud,” said Dodgson. “At long last, we’ve put Arthur Doyle’s ghost to rest.”

[End]