### 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!

1. Calc IV? Is this school on trimesters? What’s covered?

I have yet to teach Calc III, which (at the cc’s I’ve taught in) is multi-variable calc. I’d like to teach it sometime in the next few years, so I’d be interested in thinking about the material.

2. we’re on quarters. it’s (the rest of)
multivariable stuff, mostly (intro to
vectors is in III). we did much the
same material in the 80’s at indiana
in a two five-semester-hour
“freshman calc” sequence followed
by a three-hour “calc III”.
IV existed but it wasn’t required
and i didn’t take it. i don’t even
properly know yet *what* i’m doing
this quarter… but some of it’ll be
stuff i never studied formally.
it’ll be fun. and sometimes
nerve-wracking.

3. PS
(for example, these remarks
on the fano-plane panel

are found, not in this blog at all
but in the lectures without words
posts in the blog next door.

so it’s even worse-organized than i thought.

• ## (Partial) Contents Page

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