### consideration like an angel came

**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!

September 24, 2011 at 1:23 pm

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.

September 24, 2011 at 2:16 pm

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.

September 24, 2011 at 2:23 pm

PS

some of the comments-thus-far

(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.