Pynchon, Cohen, and the Crisis of Victorian Mathematics

Abstract

Reviewed by: Pynchon, Cohen, and the Crisis of Victorian Mathematics Thomas Dechand Daniel J. Cohen, Equations from God: Pure Mathematics and Victorian Faith. Baltimore: The Johns Hopkins UP, 2007. 242 pages. "They tell me you're kind of famous?" "Women at Göttingen form a somewhat beleaguered subset." She looked around. "And what is it you do here again?" "Drink beer, work on my sleep allowance, the usual." "I took you for a mathematician." "Well . . . maybe not your kind. . . ." "Yes? Come, don't be too clever." "All right, then." He squared his shoulders, brushed imaginary beer foam off his almost-matured mustache, and, expecting her to disappear just as quick as beer-foam, winced in apology. "I'm a sort of, hm . . . Vectorist?" Despite the shadow of an intent to flinch, she surprised him instead with a smile which, for all its resemblance to the smiles one gives the afflicted, was still able to turn Kit's extremities to stone. That is, it was some smile. "They teach vectors in America? I'm amazed." "Nothing like what they offer here." "Isn't England where you ought to be now?" as to a naughty child one expected to become, in a short while, naughtier. "Nothing but Quaternions over there." "Oh dear, not the Quarternion Wars again. That is so all rather fading into history now, not to mention folklore. . . . Why should any of you keep at it this way?" "They believe—the Quaternionists do—that Hamilton didn't so much [End Page 1180] figure the system out as receive it from somewhere beyond? Sort of like Mormons only different?" She couldn't tell how serious he was being, but after a decent interval she stepped closer. "Excuse me? It's a vectorial system, Mr. Traverse, it's something for engineers, to help the poor prats visualize what they obviously can't grasp as real maths."1 In his 2006 novel Against the Day, Thomas Pynchon exhumes a late nineteenth-century debate over the relative values of vector analysis (developed by Willard Gibbs and Oliver Heaviside) and quaternions ("discovered" by William Rowan Hamilton, and most fruitfully extended as a tool for physicists by Peter Tait) as competing mathematical notations used in mathematical physics.2 The dialogue above features two fictional protagonists: Kit Traverse, an American vectorist who trained at Yale under Gibbs, and Yashmeen Halfcourt, who is at Göttingen to work on Riemann's zeta-function. Associative but not commutative, a quaternion can be written in the form q = a + bi + cj + dk, where a, b, c, and d are real numbers and i, j, and k are vectors of magnitude √–1 along the x, y, and z axes. While relatively easy to work with, quaternions, unlike vectors, have proven notoriously difficult to think about. The non-commutativity of quaternions initially puzzled many mathematicians who found themselves unable to detect any physical analogies whatsoever. John Graves, described by one historian as "perhaps the mathematician best prepared for accepting" quaternions, wrote to Hamilton that there was "something in the system that gravels me. I have not yet any clear views as to the extent to which we are at liberty arbitrarily to create imaginaries, and endow them with supernatural properties."3 As Yashmeen's description of the debate as the 'Quaternion Wars' might suggest, the rhetoric used by both sides was particularly charged. Gibbs, in an 1888 letter to Thomas Craig, predicted that a "Kampf ums Dasein" was about to commence between the two sides. In one of the opening salvos of that struggle, Tait classed Gibbs as "one of the retarders of Quaternion progress" and labeled Gibbs's vector analysis "a sort of hermaphrodite monster." Such language is not commensurate with a debate merely over a choice of notation. As Gibbs himself recognized, something more important was thought to be at stake: "[Tait's] criticism relates particularly to notations, but I believe that there is a deeper question of notions underlying that of notations."4 Pynchon's novel provides a clue as to the meaning of the deeper question when Kit Traverse notes that Quaternionists believe "Hamilton didn't so much figure the system out as receive it...