… but we’re only going one way

there’s four directions on the map.
i’ve called ’em Up, Down, Equal, and Op
{U, D, E, O} more affectionately (or when
actually *writing things down*).
never mind why for now; these are just their
names. call ’em table & beermug if you like.

anyhow, the title of this display is “barycentrics”.
it owes this name to the great a.~f.~möbius
(he of the immensely famous non-orientable surface
[and the merely very-famous transformations of \Bbb{C};
also the not-quite-so-well-known (but still
essential!) inversion formula]); that guy…
and his concept of barycentric co-ordinates.
Photo on 6-18-20 at 9.26 PM 2

the drawing underlying all this mess was done
freehand by me a few years ago. the idea was
to be sure all 1+2+4+8 points of the tetrahedron
in question—P^3(\Bbb{F}_2)
if you must know—
were distinguishable one-from-another. you can
easily look up similar drawings in textbooks and
so on.

anyhow, here the face-centers (of the tetra) are labelled
Yellow, Blue, Red, and Mud (or {Y, B, R, M}—
you know the drill—); the vertices opposite
these points are the “secondaries”
Purple, Orange, Green, and Neuter.

the “four directions” (U, D, E, & O) then correspond
to the (opposite) color-pairs Y-P, B-O, R-G, & M-N.
i hope this is all completely obvious from the drawing.
because it’s very useful for the math.


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