Tuesday, October 30, 2007

Riemann Riddles

Given a preference for surreals over the reals as arguments for the Riemann zeta function, one cannot help but wonder about the association of 2-branchings with the parity cubes in all dimensions. At the third level, for instance, there are 8 nodes on the tree correponding to (a) 8 vertices of a cube, or (b) a set of zeta values.

Does this set of zeta values combine to obey a Koide type relation, just like the primary 3 faces of the space generation cube? This sounds like an idea to generate endless hours of play, but that may have to wait until I am elsewhere! The good news is that I've found the best internet cafe in the city, which opens early and has good cheap coffee. And on the short walk from the bus station to work, there is a garden by the river where I can sit in the sun by a statue of Captain Scott, engraved with the words, "I do not regret this journey..."
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5 comments:

  1. DougOctober 30, 2007 12:44 PM

    Hi Kea,

    I have finally found the mathematician that I was looking for: Richard Ernest Bellman, USC-US in Mathematics, Electrical Engineering and Medicine with “621 papers, 41 books and 21 translations of books authored (or co-authored).

    biography
    http://www-groups.dcs.st-and.ac.uk/~history/Biographies/
    Bellman.html

    Dynamic programming or optimization
    http://en.wikipedia.org/wiki/
    Dynamic_programming
    or
    A Tutorial on Dynamic Programming, Michael A. Trick, Mini V, 1997
    http://mat.gsia.cmu.edu/classes/
    dynamic/dynamic.html

    Some ZETA papers include:
    1 - ‘Wigert’s approximate functional equation and the Riemann zeta-function’
    Duke Math. J. Volume 16, Number 4 (1949), 547-552.
    http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=
    Display&handle=euclid.dmj/
    1077475781

    2 - ‘On a Class of Functional Equations of Modular Type’
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 42, No. 9 (Sep. 15, 1956), pp. 626-629
    http://links.jstor.org/sici?
    sici=0027-8424(19560915)
    42%3A9%3C626%3AOACOFE%3E2.0.CO%3B2-8

    3 - and maybe [with Robert Kalaba] ‘On the Principle of Invariant Imbedding and Propagation Through Inhomogeneous Media’
    doi:10.1073/pnas.42.9.629. 1956;42;629-632
    http://www.pnas.org/cgi/
    reprint/42/9/629.pdf

    ReplyDelete
  2. AnonymousOctober 30, 2007 5:59 PM

    I also like surreal numbers, and some years ago wrote up a web page now at
    tony5m17h.net/surreal.html
    that has some material that might be relevant.

    Tony Smith

    ReplyDelete
  3. KeaOctober 31, 2007 9:06 AM

    Thanks for the links, Doug. Tony, I have a link to your page (once removed) in the post.

    ReplyDelete
  4. L. RiofrioOctober 31, 2007 12:21 PM

    Anyone who has endured a night in a cold shelter will empathise with Captain Scott. More scientists should take risks as Kea has.

    ReplyDelete
  5. CarlBrannenNovember 02, 2007 3:16 PM

    I've spent my share of nights in cold shelters, but I can't say I've ever spent a night in one so cold that I didn't regret it.

    ReplyDelete

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