Academic journal article Mosaic (Winnipeg)

Sherlock Holmes and Game Theory

Academic journal article Mosaic (Winnipeg)

Sherlock Holmes and Game Theory

Article excerpt

Before turning to those mortal and mental aspects of the matter which present the greatest difficulties, let the inquirer begin by mastering more elementary problems.

--Arthur Conan Doyle, A Study in Scarlet

Although mathematical interpretations of rationality appeal to the analysis of detective fiction, literary critics have seldom used mathematics to interrogate narratives in which logical deductions solve crimes or elucidate mysteries. While "the specificity of narrative models lies in depicting experiential content, if only by virtue of depicting agents in pursuit of humanly recognizable goals," explains Peter Swirski, the elements of logic in mathematical models "are valued precisely to the extent they can be voided of subjectivity." Literary critics have offered "scarcely any commentary to date about the analogies between mathematics and narrative fiction" because they are "intimidated by such manifest differences" (50).

The prolegomena that follows addresses Swirski's concern by applying the elementary principles of Hungarian-born mathematician John von Neumann's game theory to a selection of Sherlock Holmes tales from the canon of Arthur Conan Doyle. Attendant philosophical contentions then help to broaden this application to a context that considers lateral thinking and rational irrationality as valuable interpretive supplements to the necessarily strict delimitations imposed by game-theoretic rules. This overall treatment supports the positive side of Ian Ousby's judgment concerning the Holmes oeuvre: Doyle's stories do experience a general decline in standard following World War I, but a game-theoretic reading of Holmes's adventures supports the case that this deterioration "is neither total nor entirely uniform" (170). Hence, as Ousby concedes but fails to contemplate in detail, Doyle's inventiveness occasionally shapes Holmes's later adventures, with Holmes evolving into a thought-provoking portrayal of human cognition.

As his autobiography testifies, Doyle first studied mathematics at Stonyhurst, the Jesuit college he attended between 1868 and 1875, where he underwent "the usual public-school routine of Euclid, algebra and the classics." In Doyle's opinion, the Jesuits "calculated to leave a lasting abhorrence of these subjects" (Memories 10) on their pupils, but in his case failed; rather, as Doyle recounts in Through the Magic Door, he resolved to gain "a broad idea" of the sciences and "understand their relations to each other" (249). Membership of the Society of Authors, a formal group of writers confederated in 1884, rewarded Doyle's determination through his acquaintanceship with Henry Ernest Dudeney. Dudeney's mathematical conundrums for various journals, including the Strand Magazine and Tit-Bits, were somewhat of a novelty. "Puzzles in periodicals were uncommon at that time in England," notes Angela Newing. "Lewis Carroll had a few mathematical puzzles printed as a series in 'The Monthly Packet' from 1880, but that was a magazine for young people" (297).

At one level, the cases undertaken by Doyle's "elementary" detective are akin to Dudeney's conundrums, because they require clear thinking and sustained logic to solve, but at their core, Holmes's mysteries often amount to the logical puzzles of interpersonal relations known as "coordination problems." In these dilemmas, states William Poundstone, "one must make a choice knowing that others are making choices too, and the outcome of the conflict will be determined in some prescribed way by all the choices made" (6). Not only are coordination problems independent of participant class and social status, but they also respond to demographics in which individual actions affect numerous people to a previously unimagined extent as the population of a region markedly increases. Doyle's oeuvre, especially his collection of Holmes stories, which date from 1887 to 1927, responds to the demand from this evolving dynamic. …

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