Vlorbik's Diner

son of owen's cooking show

perhaps *this* will refresh your memory

Posted by vlorbik on November 23, 2010

pages 4 & 5 of MEdZ #0.9.


One Response to “perhaps *this* will refresh your memory”

  1. vlorbik said

    the seven points in the center represent
    the seven “directions” from 000 on a cube.

    [to wit {001, 010, 011, 100, 101, 110, 111}
    (binary 1 to 7; one calls 001, 010, and 100
    “unit vectors” (in the x, y, and z direction
    respectively… or not… but such things
    are good to know…).]

    the bigger circles around (& in one case,
    amongst) the seven-in-the-center “plane”…
    are associated with the *lines* of
    P = P_2 ({Z}_2).

    These lines are then treated as the *points*…
    think of the circles… of the “dual” space P^*
    (“pee-star”). then there’s a
    structure preserving map
    (called, i suppose, “star”) from P to P^*:
    a mapping P—-}P^* that not only takes
    points of P (dots, say) to points of P^*
    (circles), but simultaneously takes the
    lines of P to the lines of P^*.

    the appropriate arithmetic is modulo 2;
    in the two bottom lines i’ve given examples
    of “why” the points 111 and 100 do and do not
    (respectively) lie on the line [110]:
    the “dot product”
    [xyz]abc := xa +yb + zc (mod 2)
    produces 0 (it *is* on the line)
    or 1 (it’s *not*).

    the mod-2 addition table is given;
    just remember everything is in
    “remainders on division by two”.
    (think “even” and “odd”, rather,
    i suppose, for most people…)

    this drawing was something of a breakthrough
    for me. it was soon followed by

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