March 21, 2009

  • For Bach's Birthday:

    Counters in Rows

    "Music, mathematics, and chess are in vital respects dynamic acts of location. Symbolic counters are arranged in significant rows. Solutions, be they of a discord, of an algebraic equation, or of a positional impasse, are achieved by a regrouping, by a sequential reordering of individual units and unit-clusters (notes, integers, rooks or pawns)."

    -- George Steiner
       (See March 10, "Language Game.")


    For example:

    Model of the 21-point projective plane consisting of the 1- and 2- subsets of a 6-set

    Click to enlarge.

    Context:

    Notes on Finite Geometry
    (Section on 6-set structures)

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