From: adler@pulsar.wku.edu (Allen Adler) Newsgroups: sci.math Subject: Bees and 6-dim flag manifolds Date: 05 Dec 1997 23:59:11 -0600 On NPR this evening, they interviewed someone named Barbara Shipman (I am not sure of the spelling and can't find her name in the Combined Membership List of the AMS under any of the variants I tried). Apparently, she was considering projections of a 6 dimensional flag manifold (call it F) into 2 space and got pictures that reminded her of the dances that bees do to communicate with the hive about food. She also suggested that there might be some quantum mechanical reasons behind this. I am naturally skeptical about all of this, but I would like to read her work in order to arrive at an informed opinion. Can someone tell me how to get copies of the relevant articles? Allan Adler adler@pulsar.cs.wku.edu ============================================================================== From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: Bees and 6-dim flag manifolds Date: 9 Dec 1997 15:22:53 GMT In article <2gsos7ovv4.fsf@pulsar.cs.wku.edu>, Allen Adler wrote: > >On NPR this evening, they interviewed someone named >Barbara Shipman (I am not sure of the spelling and >can't find her name in the Combined Membership List >of the AMS under any of the variants I tried). Aha! A sleuthing challenge. I missed that broadcast, but National Public Radio's web site http://www.npr.org/programs/atc/rundowns/1997/Dec/atc.12.05.97 shows the topics from the Friday "All Things Considered", including [8.] [QUANTUM BEES] -- Robert talks to mathematician Barbara Shipman about her cross-disciplinary discovery. In mapping a six-dimensional figure onto two-dimensions, she recognized the pattern as that of the honeybee's ritual dance. To her, this implies that bees can sense the quantum world, since it is in that realm that six-dimensional geometry has real meaning. The bees use the dance to communicate to others in the hive the location and distance of a pollen source. (5:45) In the Math Reviews (& Current Math Publications) database, there are no articles by any B. Shipman. Thinking perhaps her work was too applied for MR, I tried Zentralblatt, and got one hit: 970.29479 Shipman, Barbara On the geometry of certain isospectral sets in the full Kostant-Toda lattice. (English) [J] Pac. J. Math. to appear (1996). [ISSN 0030-8730] We use momentum mappings on generalized flag manifolds and their momentum polytopes to study the geometry of the level sets of the 1-chop integrals of the full Kostant-Toda lattice in certain isospectral submanifolds of the phase space. We derive expressions for these integrals in terms of Pluecker coordinates on the flag manifolds in the case that all eigenvalues are zero and compare the geometry of the base locus of their level set varieties with the corresponding geometry for distinct eigenvalues. Finally, we illustrate and extend our results in the context of all the full $\text {sl} (3, \bbfC)$ and $\text {sl} (4, \bbfC)$ Kostant-Toda lattices. [ B.Shipman (Rochester) ] Keywords: momentum mappings; generalized flag manifolds; momentum polytopes; level sets; 1-chop integrals; Kostant-Toda lattice; isospectral submanifolds Classification: *58F07 Completely integrable dynamical systems (I don't understand why this wasn't in MR's database, since they have all of 1996's and most of 1997's PJM issues in their database; evidently PJM had some publication rescheduling after sending preview copies to Zbl for processing.) Very well, then, we visit www.math.rochester.edu, and there at the top we find the very NPR page I quoted above. Moreover, there is directory information placing her among the department's faculty. I can only imagine she would welcome inquiries about her work. I love a good romp through the literature. I found there were were 37 matches to Anywhere=(bees) (Well, OK, quite a few of them were papers by one "J. Bee Bednar".) For your reading pleasure may I direct your attention to, among others, 29 #524 Fejes Tóth, L. What the bees know and what they do not know. Bull. Amer. Math. Soc. 70 1964 468--481. (Reviewer: H. S. M. Cosxeter) 52.45 80a:92058 Wofsy, Carla Reproductive success for social hymenoptera. Theoret. Population Biol. 14 (1978), no. 3, 371--379. (Reviewer: Michael Orlove) 92A15 (92A20) 82a:92025 Yokoyama, Shozo; Nei, Masatoshi Population dynamics of sex-determining alleles in honey bees and self-incompatibility alleles in plants. Genetics 91 (1979), no. 3, 609--626. (Reviewer: Ivar Heuch) 92A10 (92A15) 87i:92058 Beli\'c, M. R.; \v Skarka, V.; Deneubourg, J.-L.; Lax, M. Mathematical model of honeycomb construction. J. Math. Biol. 24 (1986), no. 4, 437--449. 92A18 (92A06) 88m:92043 Omholt, Stig W. Relationships between worker longevity and the intracolonial population dynamics of the honeybee. J. Theoret. Biol. 130 (1988), no. 3, 275--284. 92A15 92j:90106 Peleg, B.; Shmida, A. Short-run stable matchings between bees and flowers. Games Econom. Behav. 4 (1992), no. 2, 232--251. 90D40 (90A30 92D40 92D50) 96d:73013 Nazarov, Seguei A. Junction problems of bee-on-ceiling type in the theory of anisotropic elasticity. C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 11, 1419--1424. (Reviewer: Alexander Belyaev) 73C02 (73B40 73K05) Coming up next: "The birds and the bees in mathematics!" dave