As a diehard fan of Sherlock Holmes, I sometimes envy my (now former) SciAm co-blogger Maria Konnikova for figuring out to combine her love for Holmes with her field of psychology (cf. her bestselling book, Mastermind: How To Think Like Sherlock Holmes). So you can imagine my delight when Jen-Luc Piquant stumbled upon a short paper on the arxiv last week offering insight into the chosen title of a fictional scientific paper by one Professor James Moriarty -- Sherlock's arch-nemesis. The author, Alejandro Jenkins of Florida State University, sought to answer the burning question of why Moriarty titled his paper, "The Dynamics of an Asteroid," (singular) rather than using the plural form more common to modern usage.
Here's what Sherlock has to say about Moriarty in the 1914 short story, The Valley of Fear (actually set in 1888):
Is he not the celebrated author of The Dynamics of an Asteroid, a book which ascends to such rarefied heights of pure mathematics that it is said that there was no man in the scientific press capable of criticizing it?
No other information about this seminal work is provided in the Holmes canon -- it's the sort of detail designed to serve a narrative purpose, i.e., establishing the genius of the main villain as a worthy adversary -- but that hasn't stopped diehard fans with a geeky bent from attempting to flesh out the details.
Around the time the story is set, an American astronomer, Simon Newcomb, known for spiteful behavior, authored several books on the motions of planets in the solar system. And the Indian mathematician Srinivasa Ramanujan purportedly sent letters to his peers at the University of Cambridge in 1913 outlining his own work, only to find none could grasp it. (G.H. Hardy, at least, recognized the brilliance, but admitted the letters "defeated me completely; I had never seen anything the least like them before.") Both men may have served as inspirations for Conan Doyle when he was creating the character of Moriarty.
But that doesn't really address why "asteroid" is singular rather than plural in the title. Some have speculated that it might be a reference to Gauss's 1821 treatise on the dynamics of an asteroid (using a method still in use today). And Isaac Asimov wrote a short story in 1985, "The Ultimate Crime," that asserted Moriarty's treatise may have described a particular asteroid, a planetoid that scientists once thought may have "disintegrated into the current asteroid belt," according to Jenkins. Asimov believed that "the destruction of an entire world would have been a subject appealing to Moriarty's diseased genius."
Jenkins, though, thinks it may just be reflecting common scientific usage of the era. I emailed Jenkins to find out a little bit more of the backstory to his intriguing paper, and was not surprised to discover that he's a longtime Holmes fan, devouring all the canon as a child. His particular edition (Bantam) opened with an essay by Loren Estleman that, Jenkins says, "introduced me to the practice of writing about [the stories] as if they were accounts of real events."
But it was Lewis Carroll who proved to be the central inspiration for the paper -- Carroll, that is, and the 2011 Sherlock Holmes film Game of Shadows. I know, I know, it pales in comparison to the BBC reboot with Benedict Cumberbatch, but a key plot point in the film centers on using Moriarty's academic interests -- in this case, a book on horticulture -- to decode the villain's secret diary outlining all his nefarious plans for world domination.
Indeed, there is lots of incidental mathematics in the film, thanks to the efforts of two Oxford mathematicians, Alain Goriely and Derek Moulton, who consulted and shared their thought processes once the film was released. Moriarty's academic position was the result of another bit of work on the binomial theorem, written at just 21 (as detailed in "The Final Problem") -- the only other bit of Moriarty scholarship cited in the canon. So Goriely and Moulton decided that, "Given his obsession with the binomial theorem, we based the code we created for him on Pascal’s triangle. The code has three elements: a public key, a coded formula, and a cipher."
They also came up with a suitable topic for Moriarty to lecture about circa 1885, and latched onto The Dynamics of an Asteroid as a starting point. They drew upon the real-life work on the N-body problem by Henri Poincare and George Hill's 1878 solution to the restricted three-body problem (specifics can be found in the linked article), as well as the work of Paul Panleve on colliding bodies circa 1895. (The two men weren't especially impressed with the final film, but still conclude that Holmes "would have made a fine applied mathematician.")
But we digress. The film reminded Jenkins that Lewis Carroll had written an unusual parody, sending up academic politics at Oxford University, called "Dynamics of a Parti-cle." He'd also been perusing a few older British scientific texts to prepare tor teaching a course on analytical mechanics, and remembered that a treatise called Dynamics of a Particle, With Numerous Examples, was -- at the time in which Conan Doyle's story is set -- was pretty standard for introductory courses in classical mechanics. He concluded that Conan Doyle likely would have been aware of such texts, and thought this one might have been the inspiration for Moriarty's fictional masterpiece.
"It's not really so strange that [Moriarty] would have worked on asteroids because celestial mechanics has been the source of many major developments in pure math," said Jenkins, adding that there is also an interesting tie-in with the development of chaos theory. For his work on the N-body problem, Poincare won a special prize offered by King Oscar II, which led to Poincare authoring a series of three books on the subject (New Methods of Celestial Mechanics) published in 1892. But Poincare made an error in that first edition which -- as Goriely and Moulton point out in their article -- "led to the discovery of sensitivity to initial conditions and chaos in mathematics."
In fact, one of the first responses Jenkins received after posting his paper to the arxiv made this same point. That means that Moriarty was so brilliant that, had his treatise been real, he could have pioneered chaos theory 25 years before Poincare. "The orbit of an asteroid can become chaotic if it resonances with the orbit of a large nearby planet," Jenkins told me. "This is now the accepted explanation of the 'Kirkwood gaps' in the asteroid belt: in certain narrow bands, asteroid orbits become chaotic due to interaction with Jupiter, and they eventually collide with Mars and are removed from circulation."
Jenkins isn't the first academic to do a bit of literary sleuthing where Holmes and astronomy is concerned. Among the works he cites is a 1993 paper by Bradley Schaeffer detailing various astronomical connections in the Conan Doyle canon. He wasn't surprised about this. "Astronomy is the first science really," Jenkins said. "The fundamental idea of all science, that nature obeys regular laws that we can figure out by observation and reasoning, historically comes from astronomy. I think it's not so strange that detective stories, whose appeal is precisely showing reasoning bringing order back into a world threatened by crime, should have an affinity with astronomy and science fiction."
Of course, for all Holmes' purported intellectual sophistication, he famously expressed ignorance about the Copernican solar system -- you know, the one in which the earth orbits the sun rather than the other away around. It's a classic bit of Holmes lore, but there are other instances in other stories in the canon where Holmes reveals that he actually knows quite a bit about astronomy. "Perhaps he was just joking about not knowing anything about the solar system when he first met Watson," Jenkins muses. Or maybe it's just an embarrassing gap in the great detective's encyclopedic knowledge.
Asimov, Isaac. "The Ultimate Crime," More Tales of the Black Widowers. Garden City, NY: Doubleday, 1967, pp 166-80.
Goriely, Alain, and Moulton, Derek, E. (2012) "The Mathematics Behind Sherlock Holmes: A Game of Shadows," SIAM News, 45: 3.
Jenkins, Alejandro. (2013). "On the Title of Moriarty's Dynamics of an Asteroid," arxiv (preprint).
Schaeffer, B.E. (1993) "Sherlock Holmes and Some Astronomical Connections," Journal of the British Astronomical Association 103: 30-34.
Tait, P.G. and Steele, W.J. A Treatise on Dynamics of a Particle with Numerous Examples, 7th ed. London and New York: Macmillan, 1900.