## Archive for September, 2011

### blog broken

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.

### unfolded and taped to piece of cardboard

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.

### consideration like an angel came

introductory ramble
i’ve been passing around the “spring 2011”
issue of MEdZ pretty freely and’ve posted
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
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 $S \cong S^*$.
i pronounce this “ess is isomorphic
to the dual of ess” if i read it
symbol-for-symbol; one might also
“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!

• ## (Partial) Contents Page

Vlorbik On Math Ed ('07—'09)
(a good place to start!)