Billiard curved space5/5/2023 Dietrich, "Form and Content in Cummings' 'Space being.Curved.'" Notes on Contemporary Literature 12 (Nov. Quasi-exact solution of the anharmonic oscillator in curved space-time with tensor. The circles are then connected by their common outer tangent lines of length L(see Figure 1) and the interior arcs are removed such that the boundary is C1smooth and convex and d p L2+ (R r)2. tive curvature (hyperbolic manifolds), provide a rich illustration of dynamical. Exact solution to Lippmann-Schwinger equation for a circular billiard. Classically, the billiard’s phase space is dened by the position and momentum variables of a point particle moving with constant speed in a straight line inside a compact domain Q 2 Rdexperiencing mirror-like reec- tions at the billiard boundary Q. Contrasted to what science presumes-to encompass the universe-technological achievement is ironically small, trivial, and destructive.įrom Richard F. The drivebelt billiard is constructed by two circles of radii rand R>rwith centers displaced by a distance d. The contrast points up the discrepancy between what Cummings understands the science of his day presumes-to explain the universe in a way that seems arrogantly to assign the role of creator to home sapiens-and what technology actually does with science-murder elephants to make billiard balls out of ivory (the "compassionate digit" ironically referred to is the "trigger finger"). Rational polygons are dense in the space of polygons. The recent progress in the study of polygonal billiards is mostly due to applications of the theory of at. This set-up is known as the Ehrenfest model, after the Russian mathematician Tatyana Ehrenfest and her husband Paul, who studied it to explain the behaviour of molecules in gases. study of the geodesic ow on negatively curved manifolds. Mathematically it is a class of hamiltonian systems with collisions defined by symplectic maps on the boundary of the phase space. The poem is structured around a contrast between two spherical images-the first that of Einstein's "curved universe," the second that of a billiard ball. Together with the Polish mathematician Krzysztof Fraczek she considered an infinite billiard table containing a lattice of rectangular obstacles. Hence whatever is the geometry of a wavefront emerging from the curved piece it will become convex and very at by the time it comes back to the. Cummings' "Space being.Curved" embodies a sarcastic and satirical protest against the way certain scientific theories appear to confine the spirit of humanity within a predictable and mechanical universe. A trajectory in such a billiard experiences visits to the convex piece separated by arbitrary long sequences of reections in at pieces, which do not aect the geometry of a wavefront at all.
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