Archive for the ‘“categories” is broken’ Category

an awesome work of scholarship.
by a great musician and lay leader.
but not my real subject.

(bait-and switch.) .  
(the editor hates plain-text and wants me 
to learn about "block"s.  not today.  
dates & titles; formatting not my fault.)

1/19/14 m.l. king.  
6/13/14 gospel exegesis.  
10/19/14 uu &uuce.  
5/24/15 number mysticism.  
11/15/15 schools & churches.  
1/24/16 arts & sciences.  
3/13/16  self-publishing. 
6/12/16 how to be interesting.  
3/3/19 vonnegut, uu, & me.  
3/24/19 library lore. 
5/5/19 maps of the world.  
7/7/19 philosophy & nonsense.  
8/18/19 the art of teaching.  
11/3/19 notes from the hymnal.  
12/18/19 uu & me.  
11/12/20 2020 vision.  
2/16/20 chinese philosophy.  
3/15/20  confucius, lao tzu, & me.  

Photo on 9-21-15 at 6.33 PM

P^2({\Bbb F}_5), i’d’ve called it today.
i drew this thing over twenty years ago as a page
in a geometry test. the coloring-in is much more

anyhow, two triangles perspective from a point
are perspective from a line. you could look it up.

Photo on 4-28-15 at 1.21 PM

i’ve given the equations of the (seven)
planes-in-ordinary-(x, y, z)-space
that pass through the various
“color triples” of rainbow space—
the blends, the blurs, and the ideal.

(upon putting the “primaries” [*not* one
of our triples] {R, Y, B} onto the vertices
(100, 010, and 001) of a cube
[namely, the “unit cube” I^3=
\{ (x,y,z) | 0 \le x,y,z \le 1 \}
if you wanna get all *technical*…].)

somewhat awkwardly, *one* of our planes
(up in the upper right somewhere) does
*not* pass through (0,0,0)
(or 000 as it’s also called here).

what gives?

mod 2 arithmetic, is what.
the equations in the display “work”
in good old-fashioned {\Bbb R}^3
or E^3(R) [euclidean 3-space]—
but to get the 7-point-space
— P^2 (F_2) [projective 2-space
over the 2-element field]… if
you wanna get all *technical*…—
we have to “work mod 2”.

and, believe it or not, 0 = 2
on this model. (so we pick up
(0, 0, 0) as a solution to
“x+y+z = 2”
[which it now becomes more
convenient to write as
“x + y + z = 0 (mod 2)”

and that’s essentially it.

this “dualization” i’ve been
going on about for years, now?
here it is.
the set-of-seven *equations*
or their planes in three-space,
or their color-triples,
or their color-triples-plus-000,
or the “lines” of P^2(F_2)…
these are all ways of saying
the same thing…
can *also* be given a 7-point
“fano space” structure.

and has been (in some sense),
here on the page, via the [X:Y:Z] notation.

(note that the set-of-seven *points*
already *has* such a structure
[i.e., any two distinct points
determine a unique 3-point line]).

(details suppressed with great effort…
part of the point here is that we 
*don’t* need the [“linear algebra”]
formalism [usually learned, oddly
enough, in “calculus” classes (if at
all)]—“dot products” and so on—
to achieve our dualization: we
can just *draw* the doggone thing
and check directly that our structure

thank you and good day.