## Archive for September, 2011

my sidebars appear at the bottom of the page

under the posts. i’ve seen this before and been

able to tweak the code until it looked right.

to me. how it looked to other people?

none of my business evidently. anyhow,

after laying off for a long time and

flirting with coming back, a sign that

this *isn’t* (at *all*) how i want to

spend my time. it sure was fun when it

was easy.

my latest… i thought i was quarterly

when i issued it but maybe i’m semi-annual…

looks like this.

1876

2345

in the upper left are the “covers”:

these become the front and back

of the zine in folded form.

i discussed the title a few hours ago

(along with some other stuff).

suffice it to say here that our

subject is *self-dual spaces*.

*under* the title (in folded form;

above it here) are two

representations of the *simplest*

example: duality in P^2(F_2).

the space P^2(F_2) is itself

displayed (without a duality)

on p.5 (the lower right of the

photo) in the usual “triangle” way.

the colors are used to show

how these two objects…

*and* a certain subobject

of the space on pp. 7 & 8

(the 21-point P^2(F_4))…

can be considered “the same”.

the lower left (pp. 2 & 3)

are the desargues configuration.

i’ve discussed it recently

(here, for example)

and’m starting to hurry.

finally then (for now),

the cube-and-cross sections

bits are much the most vivid

visual motivator i’ve found

for the concept of “projectivity”.

the colors are surprisingly

helpful here. i’ll try to convince

you later. company coming. bye.

**introductory ramble**

i’ve been passing around the “spring 2011”

issue of MEdZ pretty freely and’ve posted

quite a bit *about* it.

but it isn’t very well-organized.

so in hopes of finding a curious reader

hoping to learn about the pictures in the zine

(MEdZ S’11 is in pictures-only “lecures

without words” format… an 8-page

micro-zine “unstaplebook” made by copying

all 8 images [including the front & back

covers of course] onto a single standard sheet

and cut-and-folded into tiny-booklet form;

this is the first issue in color and very much

my personal favorite [of the moment]), i decided

to poke around in the ol’ Archive for the ‘Graphics’ Category

(and so on) and write out some connecting remarks.

**prehistory of MEdZ S ’11**

the title is .

i pronounce this “ess is isomorphic

to the dual of ess” if i read it

symbol-for-symbol; one might also

read it (more freely) as

“S is a *self-dual* space”.

in some sense, this zine is about

spaces isomorphic to their own duals.

whatever that might mean.

in Some Finite Projective Spaces (01/07/11)

are several lectures-without-words shots

from earlier zines. including this one:

.

this was something of a breakthrough drawing for me.

(*Self-duality of the Fano Plane*, one might call it

[were it not a lecture-without-words].)

somehow i’d finally stumbled on a “visual” representation

for duality. this inspired a great deal of graphical

fiddling around by me. the same algebraic tricks

used in constructing the 7-point-to-7-line duality

for fano space could *also* be used on any n-point “space”

having n = 1 + q + q^2,

where “q” is some power-of-a-prime.

fano space is the case q = 2. so i did q=3 and q=5

(and the results are in the post i’ve linked to above)

and published ’em. by february 1, i’d developed

a much cleaner-looking graphical presentation

for these (projecive-planes-of-small-order).

but the next real “breakthrough” ideas

came with the case of q=4. in this early draft

i went a little bit “deliberately weird looking”.

a later version of *Self-duality of the Projective
Plane Over the Field of Four Elements*

became the last display of the (black-and-white)

edition of Spring 2011 and i announced it

on april 17.

but now i have to backtrack. i haven’t done any of the math.

okay. enough for today.

PS. fall quarter finds me doing two sections

of Calc !V at big-state-u. i met the lecturer

wednesday and met my students thursday. whee!