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This essay reanalyzes the game theory interpretation by John von Neumann and Oskar Morgenstern of Arthur Conan Doyle's "The Final Problem." The usefulness of this interdisciplinary hermeneutic is then supplemented by lateral and philosophical thinking as prompted by subsequent tales involving Doyle's detective.
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;...