Math Conundrum in Thomas Pynchon


Her idea of banter
Likely isn’t Cantor
Nor is she apt to murmur low Axioms of Zermelo,
She’s been kissed by geniuses, Amateur Frobeniuses
One by one in swank array, Bright as any Poincaré…

and so on in that vein.

It was when I came upon the word “automorphic”…Earth making its automorphic way round the sun again and yet again…periodic functions, and their generalized form, automorphic functions as a prelude to a scholarly discussion of time travel:

Time no longer ‘passes,’ with a linear velocity, but ‘returns,’ with an angular one. All is ruled by the Automorphic Dispensation. We are returned to ourselves eternally, or, if you like, timelessly.

You find an awful lot of hyperbolas in Against the Day. For example: the hyperbolic geometry in connection with automorphic functions; the “Automorphic Dispensation” which seems to be a “function… by which, almost as a by-product, ordinary Euclidean space is transformed to Lobachevskian”; and that “perfect hyper-hyperboloid” that “only Miles” Blundell, the one character to have comprehended the meaning of space-time, “can see in its entirety.” There are (hyperbolic) wave equations (and a whole family of Vibes) and the “noted Quaternionist V. Ganesh Rao of Calcutta University” who by rotating himself in an imaginary direction performs something “like reincarnation on a budget, without the element of karma to worry about.”

Or as the NewYorker puts it,

The readers will encounter many references to, and, frequently, extended disquisitions on, such matters as Hamilton’s Quaternions, Gibbsian vector analysis, Riemann spheres, Prandtl’s discovery of the boundary layer, the Hilbert Pólya Conjecture, the Minkowskian space-time track, and Zermelo’s Axiom of Choice. Inserting this stuff into novelistic situations produces passages like this one, describing a meeting of an outfit known as the Transnoctial Discussion Group.

“Time moves on but one axis,” advised Dr. Blope, “past to future—the only turnings possible being turns of a hundred and eighty degrees. In the Quaternions, a ninety-degree direction would correspond to an additional axiswhose unit is √-1. A turn through any other angle would require for its unit a complex number.”

“Yet mappings in which a linear axis becomes curvilinear—functions of a complex variable such as w=ez, where a straight line in the z-plane maps to a circle in the w-plane,” said Dr. Rao, “do suggest the possibility of linear time becoming circular, and so achieving eternal return as simply, or should I say complexly, as that.”. . . As if the hour itself in growing later had exposed some obscure fatality, the discussion moved to the subject of the luminiferous Æther, as to which exchanges of opinion—relying, like Quaternions, largely on faith—often failed to avoid a certain vehemence……..

Still coming to grips with this ?????????



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