turning coffee-stains into theorems
the pink point is “on its own polar”
(in the “polarity of P^2(F_4)” shown here)
& so the Big pink Circle “includes” one
of the little pink circles.
the other colored points of the display
*don’t* have this property… one sees
instead that the Orange Circle “includes”
a blue circle, & the Blue “includes” an
orange. note that the “maps” of 21-space
found in the Orange and Blue Circles
correspond to the *positions taken*
by the orange and blue circles
(respectively): the blue circles
“go across the top and then take the
rightmost point”—the Orange ‘position’,
if you will—and the oranges “go up the
right-hand-side and then take the very middle”
(i.e., the Blue position).
similarly the “turquoise” & “lime”
points (let’s say) are found
respectively on the lime & turquoise
before you recycle anything
scribble all over it and make copies.
so nothing goes to waste.