Shred of Evidence

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 key to Professor Moriarty’s cipher.

I knew of Reverend Dodgson as 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 for lack of useful content. It was not five months ago that my friend Sherlock Holmes perished at Reichenbach Falls in his final confrontation with James Moriarty. But even in death, Holmes struck a fatal blow against Moriarty’s criminal confederates, leaving documents that thoroughly incriminated them. Out of respect for my work with Holmes, Inspector Patterson invited me to examine the materials recovered from one of Moriarty’s secret lairs. There were implements of crime inventoried with ill-gained bounty: vials of opiates among blueprints and handwritten musical scores; rolled-up canvasses of paintings beside shredded and burned account books. Most intriguing was the set of notebooks written in Moriarty’s hand, the oldest of which had a page torn out.

The notebooks were mathematical formulae interspersed with code. I failed to solve the code even after reading Holmes’ monologue on the subject; upon consultation with Mycroft, he speculated that it was likely a Vignere cipher. “While Kasiski published a mathematical solution for that code in ‘61, it is impractical for keys of significant length, which this is. While I will attempt a statistical analysis, the chance of success is low. It may be easier to solve if we knew the type of information worth concealing. Are they musings on mathematics, or something more sinister? Find the key, Watson, and we’ll glimpse Moriarty’s mind,” said Mycroft.

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.

* * *

And so it happened that the next afternoon, I found myself at ‘The Chestnuts’ on Castle Hill 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 passing of Mr. Holmes,” said he. “He was taken from us too soon. I fear I must bear some of the burden for his demise.”"I find it curious that you would blame yourself,” said I. “Did you know Holmes?”

“I knew of Holmes at Oxford, though we never met. It was James Moriarty I knew better, through our years at Christ Church debating mathematics and logic. Even then, he had been secretive, and wrote his notes in code. Is there a volume from Moriarty’s effects, with a single page torn out?”

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

“Because I came into possession of that page,” said he. He stood, and retrieved a copy of Through the Looking Glass from his collection. Tucked between a page and an illustration of the Jabberwock was the sheet he spoke of, folded and yellowed with age. “This Tenniel plate of the Jabberwock always reminds of James, hypnotic and serpentine.”

I confirmed that the page was in the same hand as the puzzling notebook, and likewise encoded.

“How did you get this?” I asked.

“That, Doctor Watson, 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.”

* * *

“What is the Order of Copernicus?” I asked.”A fellowship of scholars, physicians, mathematicians and philosophers,” explained Dodgson. “Like Nicolaus Copernicus, who had been doctor, church canon, mathematician, and astronomer in his lifetime, so too were we men with diverse talents. James first introduced me to the Order years ago, shortly after the completion of his dissertation on the Binomial Theorem. It’s the practice of the Copernicans for each host to invite one new member, to enrich the meetings with new ideas and voices. I found the intellectual debates enthralling, and was pleased to have found like minds. I joined the Order, and continued to participate in the symposia whenever I could.”On one such occasion, early summer 1879, I was invited to Aston, near Birmingham, by Doctor Reginald Hoare. Reginald was a stout and jovial man who had been in the Order for years. He introduced us to his lodger, Arthur Doyle, a pleasant young man whose naive looks belied a keen and mischievous intellect. Arthur was studying medicine at Edinburgh University, and was working for Reginald as a dispensing assistant taking house calls for him. I found Arthur an engaging conversationalist, as well as a sharp observer. James insinuated himself into our conversation, and we were soon joined by Reverend Samuel Haughton, a doctor from Trinity College, Dublin, and Joseph Lockyer, an astronomer from South Kensington, London.

” ‘What do you plan to do with your future, Arthur?’ asked Samuel.

” ‘Surgery, sir,’ said Arthur. ‘I’m very much inspired by Doctor Bell, at the medical school.’

“Samuel nodded. ‘A bold choice, difficult but with its own rewards. But I asked about your future, not your career. Don’t neglect your other intellectual pursuits! That is the aim of every Copernican: excel in all your gifts. I myself continue my interest in mathematics, for example. Take this treatise of mine, On Hanging.’ He produced three copies of the manuscript, and distributed them to James, Arthur, and I. ‘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, before I brought the conversation back to the topic of Arthur’s interests.

” ‘I’d like to become a writer, actually. I’ve written some stories for Reginald’s children, like you. Edgar Allan Poe is another inspiration, and I’m attempting a mystery now.’

” ‘Poe!’ cried Joseph. ‘Now there was a Copernican candidate. I heard he was a great cryptographer.’

” ‘I wonder,’ said Moriarty. ‘His vaunted skill seems so much misdirection than genuine genius. He indulged in substitution codes, barely worth the effort to solve. What so-called gems of cryptology belonged to Aeneas Tacticus.’ Reginald asked who that was. ‘A Greek military strategist who lived in fourth century B.C.,’ continued Moriarty. ‘Aside from describing various cryptography methods, he was the inventor of ancient telegraphy. He noted that water clocks measured the passage of time by water levels. Imagine that two such clepsydrae were prepared with identical coded messages, each associated with specific water levels. Then, by the use of two beacon signals, one to start the flow of water and one to stop, two generals could communicate over great distances.’

“The mathematicians among us began debating the death of the Vignere code, given that the general solutions developed by Kasiski and Kerckhoff. Politely, Reginald asked again for an explanation of the Vignere code. ‘The Vignere code is based on the Caesar cipher, invented by Julius Caesar,’ I explained. ‘Caesar’s cipher shifted letters by a chosen number of positions. For example, if the word JABBERWOCKY were shifted four positions to the right, you would get the word NEFFIVSGOC, where the shift of Y four positions right would loop back to the beginning of the alphabet, and continue the count. To solve the coded message, you needed to know the length of the shift and apply it in reverse.

” ‘For the Vignere code, instead of a single shift, a keyword was used where each letter in the alphabet represented a shift. For example, if I took the phrase ALICE as my keyword, that would mean shifts of 0, 11, 8, 2, and 5. If needed, the keyword is repeated, and so JABBERWOCKY becomes JLJDIRHWEOY.

” ‘Kasiski found a way to determine the length of the keyword by measuring distances between repeating combinations, then used frequency analysis to break the code. Kerckhoff’s method focused on solving the keyword itself.’ This discussion of codes reminded me of an early habit of Moriarty’s at Christ Church. ‘James, didn’t you have a notebook where you jotted down your formulae? You used a cipher on the annotations. Was that Vignere?’

“For the briefest moment, James cast a dark look toward me, as though I had revealed to the world a closely guarded secret. Then, he smiled. ‘It was; I was reluctant to share the musings and errors of my youth with eyes other than my own. But I am confident that my code cannot be broken so easily, even with the Kerckhoff and Kasiski solutions.’

” ‘How so?’ asked Arthur.

” ‘A fundamental flaw in their methodology is the assumption that the keyword would be of short length, and repeated. What if the keyword is significantly long, like a piece of published text? Then, a coded message would be virtually unbreakable,’ explained James.

” ‘Respectfully, Professor Moriarty, I beg to differ,’ said Arthur. ‘While the keyword may be impervious to analysis, the codemaker is not. The same as in medicine: Professor Bell taught us to observe the person as well as the disease, to make the correct diagnosis. Thus, I contend that 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 James.

” ‘We’ve only just met, Professor. However, if I had the chance to get to know you better, I dare say I could figure out your code.’

” ‘I know a challenge when I hear one! Reginald, if you could indulge my curiosity in this young man’s abilities, by releasing him from his obligations on weekends this summer? My university’s not far from Aston, and I will pay for his travel and lodging. He will have a chance to 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 for his tuition. Assuming Arthur’s interested, of course.’

“James had obviously taken a liking to Arthur Doyle, perhaps eager to guide a young man into his genius. Of course, at the time, I had no inkling of Moriarty’s criminal bent, and thought it as a kind gesture. Reginald thought the same, and heartily agreed. ‘If he promises not to fall behind his duties here during the week, I don’t see why not. Arthur?’

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

* * *

I poured Reverend Dodgson another cup of tea. “Did Moriarty turn Doyle onto the path of corruption?” I asked.”Corruption? No. Doyle’s heart was pure. But if I hadn’t mentioned James’ code, perhaps Arthur Doyle might still be alive,” said Dodgson wistfully. “I had a chance to speak to him in private, later that evening. James and Joseph began discussing Mozart, before my stray comment about Twinkle Twinkle Little Bat somehow turned the conversation to the three body problem in astronomy. While they argued dynamics, Arthur asked if I could come up to his room to take a look at his manuscripts. I agreed.”His room was modest, and his desk cluttered with papers on medicine, scraps of writing, and sheet music for violin. Arthur was well-read: his bookshelf held not only medical books, but books by Emile Gaboriau, Sir Richard Burton, Charles Dickens, Gottfried Leibnitz, and of course, Edgar Allan Poe.

“He showed me some of his stories, and moved his violin case off a chair so I could sit and read. He had great potential: his stories were well-written and engaging. I encouraged him to continue writing, and to bring me more of his work in the future.

“Arthur went to his bookshelf and retrieved a book bound in red Moroccan leather, gilt in silver. I recognized it as a copy of Alice’s Adventures in Wonderland. ‘Would you mind signing this, Reverend? It’s for Herr Gleiwitz’s children. He used to be a renowned Arabic and Sanskrit scholar, but now he’s down on his luck, raising his three children on what little income he receives from giving German lessons. I see him and his family on my rounds, and feel sorry for the man. Perhaps your book will give his family some joy.’ Gladly, I signed the copy, then said farewell and retired for the evening.

“Arthur wrote to me at Oxford thereafter, telling me of his tutelage under Professor Moriarty. At first, his letters were ebullient, saying that James’ 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. I myself toyed with that notion in Through the Looking Glass, of course.

“Arthur continued to observe James as part of their contest. But his letters later that summer seemed more sombre, and he hinted at a rift between himself and Moriarty. As he never stated the reason explicitly, I can only speculate as to the true cause. Did James’ enthusiasm for his student turn to envy, like Daedalus envied his nephew for outshining him? Or did Arthur discover James’ dark dealings? In any event, it spelled death for him.”

* * *

It was chilling to hear someone lay another death at Moriarty’s feet. “How did Doyle die?” I asked.”Ah.” Reverend Dodgson sighed. “Therein lies a vorpal paradox.”I was puzzled by his choice of terms. “That’s your word for a beheading, isn’t it?”

“Yes. I’ll explain why in a moment, but first I must describe the circumstances under which we learned of Arthur’s death,” said he. “In late summer, both James and I accepted an invitation from Joseph Lockyer to visit him in London for a few days. On the third night, when we returned from an exquisite performance of Beethoven’s Pastoral Symphony at the Royal Philharmonic Society, there was a telegram waiting for Joseph from Reginald Hoare. Tragedy had struck: Arthur Doyle was found dead, hanged.

“We were shocked. Such a promising young man, dead at twenty! The circumstances of his death seemed unusual: did he commit suicide by hanging? Therein lay a mystery.

” ‘Did he seem different to you, on his last visit?’ I asked James.

” ‘He was concerned about matters in Aston,’ he answered. ‘I detected some reluctance to discuss the problem, so I didn’t press him. But I have a suspicion that it involved shady dealings. I feel at fault; I ought to have foreseen disaster.’

” ‘Don’t blame yourself, James,’ I consoled him. ‘How could you have known?’

“He shook his head. ‘We owe it to the boy to investigate the circumstances of his death, Charles. We must go to Aston.’

“And so it was that James and I returned to Reginald’s house the next day, promising to convey Joseph’s condolences. When we arrived, we discovered a bleary-eyed Reginald, trying to console his wife and children. After we spoke our sympathies, Reginald took us aside, and let us know the details of Arthur’s death.

” ‘It must have happened after we had gone to sleep. Arthur had returned from house calls earlier that evening, and retired to his room without a word. We found out early the next morning, when Inspector Ives came to our door, that Arthur’s body had been found in the bell tower at St. Mary’s, the church just down the street. Ives asked me to come to the scene, to identify Arthur and the means of his death. It was horrible, simply horrible, to see him hanging lifeless at the end of that rope!’

“James consoled him. ‘What was the cause of death?’

” ‘In my opinion, death by asphyxiation. His body showed all the signs of it.’

” ‘Do you think it was suicide?’ asked James.

” ‘Inspector Ives thinks so,’ admitted Reginald. ‘But why?’

” ‘We shouldn’t jump to conclusions, until we’ve examined all the evidence,’ James replied. ‘Arthur simply did not seem the sort of man who would take his own life. Reginald, would you mind coming with us to St. Mary’s, and describe what you saw?’

” ‘Reluctantly, the good doctor took us to the church, and showed us where Arthur was found. The bell tower was several stories tall, and a perpendicular ladder climbed up to a trapdoor that led into the belfry. There was an opening in the belfry floor, and the bell’s rope dangled through. ‘The noose was tied to the bell’s gudgeon,’ explained Reginald. ‘He must have climbed into the bell chamber, and jumped from there.’

“James and I looked at each other, skeptical. ‘Are you certain he jumped?’ I asked. ‘The mathematics say otherwise.’

” ‘He was dangling six feet off the ground when we found him. He couldn’t have kicked away a support. We didn’t find anything.’

” ‘He could have pushed off the ladder,’ observed James. ‘But in doing so, the momentum might have swung his body into the wall opposite. Was there any bruising on his arms or legs?’

” ‘No. I considered that, but there weren’t any.’

” ‘If his hands were free, 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 James.

” ‘No. But you’re right, his hands were free.’

” ‘And his neck wasn’t broken?’

” ‘No.’

” ‘Then the evidence seems to point towards a sudden drop from above,’ said James. ‘Except for the fact that such a drop is also impossible.’ I nodded in agreement.

” ‘Why?’ asked Reginald, perplexed.

” ‘Because a drop from that height would sever his head,’ I explained, having read 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, and it would cut clean through.’

“James agreed with me, but not to be outdone, he asked Reginald another question. ‘Would you say, given the marks around his neck, where the knot was placed on the noose?’

” ‘Why, it would be consistent with the corner of the left jaw.’

” ‘Another enigma!’ proclaimed James. ‘A knot placed in that position would throw the head back upon falling, it would more likely result in a fracture or dislocation of the neck. He would have died of a snapped neck, not strangulated. We are faced with several contradictory facts. He could not have jumped without decapitation, but neither could he have hung himself in a manner consistent with asphyxiation. He did not struggle, but there was no reason not to. That leaves one conclusion: that Arthur Doyle was dead before someone strung him up.’

* * *

I was confused. “If he didn’t die of hanging, how did he die?” I asked the Reverend.”Asphyxiation, as the doctor said.”

“Strangled, then, in his sleep?” Marks from a garrote would have been hidden by the bruising of the noose.

“It was more devious than that, Doctor Watson. We would find the answer back in Arthur’s room. James insisted on going back there to see if we could discover clues. I noted that Arthur’s things seemed in disarray, and mentioned it to the others. James went over to the desk, moved aside a familiar red, leather-bound book gilt in gold, and rifled through the pages. He put aside a few sheets, then nodded to himself. ‘A theory reveals itself. Reginald, you need to tell Inspector Ives that Arthur was poisoned, before his murderers tried to conceal their heinous act by making it seem like suicide.’

” ‘Poisoned! But his death was consistent with respiratory failure,’ said Reginald.

“James showed us the pages he had singled out. ‘Here is a draft of a paper he was writing for the British Medical Journal. The Uses of Gelseminum As A Poison, by Arthur Conan Doyle. It seems Arthur had been experimenting on himself with gelseminum, also known as jessamine, in the interest of medical research. Are you familiar with the substance, Reginald?’

” ‘Why, gelseminum is efficacious against spasmodic disorders, like epilepsy and hysteria. It inhibits nerve control, and respiratory functions. But a large enough dose would paralyze a man, even arrest his breathing and stop his heart.’ Reginald wiped his brow with a handkerchief. ‘How could I have overlooked it? I naturally assumed it was strangulation by hanging, and didn’t pay attention to the other signs that would point to poison! Astounding, James, you are as brilliant as Arthur said!’

“James cracked a thin smile. ‘The hanging was a distraction. A criminal mind conceives of plausible lies and hides the truth therein. It takes only observation to tell true from false.’

” ‘But why?’ I asked. ‘Who would poison him?’

” ‘I suspect if Reginald inventories his medicinal store, he will discover narcotics missing, like morphine. Perhaps Arthur became the target of blackmail, forced to give over the drugs. He might have threatened to go to the police, and his blackmailers decided to silence him. Or, his shady dealings went wrong, and death was the price. Whatever the circumstances were, his killers gave him an overdose of gelseminum, of which Arthur had in sufficient quantity to kill. Then, to cover up their crime, they took his body and hoisted him up in the bell tower. That is why his neck wasn’t broken.’

“Reginald paled. ‘Thank you, James. I shall have to check the dispensary. I would never have suspected Arthur to be embroiled in such dreadful business! ‘

” ‘Appearances can be deceiving,’ agreed Moriarty. ‘Come, we’ll bring our hypothesis to the Inspector.’

“I stayed behind a moment, to say a prayer for Arthur. James’ analysis seemed like the only plausible scenario, but I did not believe Arthur was the kind of man who would commit crimes, unless he had no alternative. I looked around the room one last time, and two peculiarities struck me. Firstly, his violin case was missing, but his sheet music was still there. I checked under his bed and in the closet, but there was no sign of it. Secondly, 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 book myself. I flipped open the front 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 Doyle go to the trouble of forging your signature, but spell it wrong?” I asked, puzzled.”I asked myself the same question, and came to the only conclusion: Arthur Doyle left that clue for me alone. No one else would likely have known that Looking Glass wasn’t the book I autographed. A dread feeling came over me, and I felt compelled to keep this secret from both Hoare and Moriarty. I left the book where it was, and went back downstairs.”With Moriarty’s helpful deductions, Reginald checked his inventory, and discovered that drugs were indeed missing from the dispensary. Arthur’s death was re-examined, and forensic evidence found that he did indeed die of gelseminum poisoning, not strangulation. Inspector Ives thanked Moriarty for his consultation, and informed us that they were now searching for suspects based on the new information.

“After Arthur’s funeral, Moriarty returned to his college, while I stayed on for another day in Aston. There was more to Arthur’s murder, of that I was certain. I had a lead to investigate before I returned to Oxford: the forged autograph. Arthur likely gave the original signed book to Herr Gleiwitz. I made some quiet inquiries and was directed to Gleiwitz’s home.

“Gleiwitz was a gaunt man with a florid face; he welcomed me into his home after I said I was a friend of Arthur’s. ‘Mr. Doyle had always been kind and generous to us. Why, once, when I couldn’t pay for the expensive medicine, he gave me his watch and chain and said I should sell it. I tried to give it back to him but he wouldn’t have it, saying I needed it more than he did. God rest his soul. He came here several days ago, and gave your book to the children, who are delighted with it. He also gave my eldest the violin, and made the boy promise to learn how to play.’

“That was one enigma solved. ‘Do you have the violin and its case? Might I see them?’

“He nodded and brought them to me. I looked for hidden compartments in the case, but couldn’t find any. Then, I examined the violin. Looking inside the F-holes, I saw a folded piece of paper hidden inside. It took several frustrating tries to get it out intact. To my surprise, it was this torn page.” Dodgson smoothed out the sheet in front of us. It was a jumble of letters. “I knew where it came from, and whose hand it was. Arthur had stolen it from Moriarty. Whatever was encoded on that page must have been worth killing for. For the first time, I suspected that that my dear friend, Professor James Moriarty, murdered Arthur Doyle in cold blood.”

* * *

“That’s diabolical!” I cried. “To execute someone, conceal it as a suicide, then mock the police for missing murder?”"Moriarty was flaunting his superiority,” said Dodgson. “The younger Moriarty was proud, and took far more risks than the modesty of his later years. He had the perfect alibi: he was in London at a public concert when Arthur was killed. I suspect he played maestro to his agents, planning the murder to the last detail, and directing his executioners to play out the moves. Then, he hid his own involvement by playing detective to his own crime. What better way to throw the police off his scent?”But all I had were speculations. What could I bring to the police, an unsolved page of code? I knew the only way to prove that James engineered Arthur’s death was to figure out the cipher. I was certain that Arthur had done what he promised: he deduced Moriarty’s key by observation alone. Furthermore, he gave me a clue in the forged signature.”

“Why didn’t he tell someone? Or write a letter detailing what he discovered?”

“Perhaps he knew Moriarty would kill anyone who knew. Or, threats were made to his adopted family. I don’t know. As for written declarations, anything obvious would have been found and destroyed by his killers. I suspect the forgery clue was the only clue left intact.

“I asked Herr Gleiwitz never to speak of my visit to anyone, and made him understand the potential risk to his family. I returned to Oxford the next day, and worked in frenzy to solve the code. But I didn’t know where to begin. Finally, I decided that I needed to visit James Moriarty: to observe him as Arthur had, and to look into his eyes and hope to find a soul.

“And so I visited James at his home, one afternoon in late September. I brought with me some pages for my next book, Curiosa Mathematica, Part Two, as a pretext. He welcomed me in, and soon we were discussing math problems over tea in his den. James offered me snuff from his musical snuffbox, but I refused. Instead, I let my gaze wander around his room. It wasn’t the first time I had been there, but this time, I was seeing everything with new eyes. Anything and everything could be a vital clue that Arthur Doyle noticed.

“James’ taste in books was eclectic: from books on astronomy and paintings to texts on calculus and algebra, from a collection of poems by Samuel Taylor Coleridge to Whitaker’s Almanac. Indeed, there were so many possible texts that could have served as his key, that it would have taken months just to check the coded page against the first few pages of each book!

“While we talked, I wondered how this man I had known so long could have a secret worth killing for. Indeed, he remained the confident and controlled gentleman he always was. But there came a brief instant, when I mentioned that he never did express his views on capital punishment, that a sneer crept onto his face. ‘Death is the only true punishment,’ he said. He smirked, then turned the topic to eighteenth century painters.

“It was the second time in all the years I had known him, that his facade cracked. It was enough to convince me that he hid the heart of a villain.”

* * *

“Yet you had no evidence, without the key,” I said.”You have it. I knew I had to reveal his evil to the world, but without concrete evidence, I could not go to the police. Neither could I let James know that I came into possession of that coded page, or else I too would have been marked for death. I needed a way to strike a blow against him, without him knowing that it was I who engineered his fall.”So I wrote anonymous letters to key figures in his university town, hinting at shady dealings that involved Moriarty. The rumours spread, and my guesses must have come close to the truth. Moriarty soon resigned his chair, and retired 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 from the mathematical chair. It might have been my tampering that made James Moriarty supremely cautious and more devious. I wonder what hand I had in his perfection as a criminal mastermind? If only I had solved the key sooner!”

“How did you discover the key?” I asked.

“The misspelled name, Carlool, ultimately led me to the key.”

“Was that the keyword?”

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

“Could the code have been based on Wonderland or Looking Glass?” I asked.

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

“Why Carlool, then?”

“The point of departure comes after Car. I agonized over what Arthur intended for weeks. Finally, I realized I had to think like him. How would you send a message to a mathematician? Use numbers, of course.”

It dawned on me what he meant. “It isn’t lool, but one-thousand and one!” I cried triumphantly. “Then Moriarty used Burton’s The Book of the Thousand Nights and a Night as his key!”

“Which was published in 1885, years after Arthur’s death. Arthur only knew of Burton’s travel writings. But I did try early translations of The Arabian Nights Entertainment by Jonathan Scott, Edward Montague, Henry Torrens, and even Edward Lane. None of them worked, and the sheer size of the book made it impossible to use as a key.”

I thought about it more. “Didn’t Poe write a story called “The Thousand-and-Second Tale of Scheherazade”? Not an exact match to one-thousand-and-one, but it’s much shorter, and I’m certain it was published in 1845.”

“Another good attempt, Doctor Watson. Indeed, I spent quite some time trying parts of that story against the code, with no success.”

“What an impenetrable mystery,” I complained. “Perhaps there was no key at all.”

“That had been my impression, after months of fruitless hypotheses. I had to be satisfied with the end of James’ career at university. I had not thought about the coded page again, until I heard about James’ death in May. I set upon solving the code anew, with new resolve to clear Arthur’s name. I looked again at what I knew about the case, about Moriarty and Doyle. Finally, I realized what clue I had overlooked. Arthur hid the key, twice in plain sight.”

“Twice?”

“First, Leibnitz’s work amongst Arthur’s books. In addition to co-inventing calculus, Gottfried Leibnitz was also the inventor of the binary number system, in a paper entitled Essay d’une nouvelle science des nombres. In binary, one-zero-zero-one is the number nine. Second, 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.”

“But how is nine the key?”

“James Moriarty was at essence a music lover. If he wanted to remember a passage as a key, the lyrics of a song might be easiest to remember. And there is one symphony set to lyrics. Beethoven’s Ninth.”

“Ode to Joy!” I exclaimed.

“Right. Friedrich von Schiller’s poem set to music, in the original German. I believe that was why Moriarty was confident that a Kerckhoff statistical analysis of his key would fail. Letter frequencies differ from language to language. Knowing the key, I was able to decipher the page.”

“What does it say?” I asked, curious.

“It alludes to Moriarty’s triumphant murder of his mentor, someone who was as devilish as he was. Alas, the name did not appear on the stolen page. Now that you have the key, it will be of use to you to decipher his earlier codes. I suspect you will discover the identity of the man who made Moriarty who he was, the way he died, and why.”

I nodded. There would be much to learn about Moriarty and the trials that shaped him. “I shall let Mycroft Holmes know your discovery. Thank you, Reverend.”

“No, thank you,” said the Reverend. “At last, I’ve put Arthur Doyle’s ghost to rest.”