one stack of paper yet to grade

slight change in format

to (a) the finite Points
(of P_2; these are
lines-of-finite-slope
in F^3) and (b) the
“Line at infinity”
consisting of the
*vertical* F^3 lines,
we have now added
(c) the “Point at infinity”
(in the lower-right-hand
corner of the diagram).
voila.

here it is again obfuscated by graphics

note the “pac-man topology” effect.
the three finite Points (clusters of
nine dots *above* the dotted line)
running down the middle column
*all* depict “lines of slope one”
but this is only obvious when one
has become used to “wrapping
around” at opposite edges.

note how the dots in the middle Point
proceed “up and to the right”.
now look at the Point below this one.
starting at the left-hand edge, we
again see the up-and-right move
but then “vanish off the top of the
screen” to “reappear at the bottom”
(like pac-man or many another
video icon… likewise, when a point
“vanishes off the right edge”,
it “reappears” at the left…).
from an algebraic point of view,
all this is a consequence of
“working mod 3”.

the zero slopes along the left edge
and the “infinite” (vertical) slopes
along the bottom are of course
much easier to make out.

just remember [2]+[2]=[1] and we’re all set

pp. 2 & 3 of the newly-minted .

the (linear) equations above the line
will turn out to correspond to “finite points”
of the projective space of the title;
the algebraically-alert will easily confirm
that these are the lines (in )
having “finite slopes”. the x = A
lines can then be thought of as
having *infinite* slope (and represented,
just as in R^2 [ordinary real 2-space],
by *vertical* lines). here come the
next couple pages.

(the icon by my finger, for now,
indicates only that these three
latest points “have something
in common”… a hint of things
to come.)

origin of species

MEdZ 0.9.1 pp. 2, 3.

there’s no place like home… there’s no place like home…

the camera on madeline’s computer still works.

“now here’s something you’ll *really* like”… “that trick *never* works”

i’m actually kind of reluctant to post this;
it’s probably the best idea i’ve had since
i started making up lectures without words
and now it’ll be easy to steal. you saw it
here first.

the Big triangle is made up of seven Little triangles.
each Little has seven Points. moreover the Points
of each Little (considered as subobjects of their Little)
are arranged in the same pattern
as the Littles themselves are (considered
as subobjects of Big).

pick any Little and call it L1.
there are three dark points in L1.
find the three Littles that correspond
to these three Points.

(for example, let L1 be the lower-left Little;
the three Littles i refer to now run along
the right side of Big [just as the dark Points
run along the right side of L1]).

the three Littles in question are then
precisely those in which the Point…
P1, say… that corresponds to L1
(considered as a subobject of Big)
is dark. i’ll be here all week.

(it’s better with the handwaving.)

perhaps *this* will refresh your memory

pages 4 & 5 of MEdZ #0.9.

stop me if you’ve heard this

pages from MEdZ #0.8…
the “K_4 — K_n remix”
issue. this provides a
wordless introduction
to the standard-binary-
-into-‘MEdZ-notation’
algorithm (and its inverse).

everybody gets this pretty quick
that tries in my experience so
it’s a lot of fun to talk about.
which is what the “lectures
without words” series is *for*
in some sense. anyhow,
i’ve been having a blast
thrusting these on people
and then banging out whatever
little mini-lectures i can get ’em
to sit still for.

this is some of the simplest stuff there is.
in my pedagogy it’s *obvious* that you’ll
appeal again and again to the simplest
things so you might as well get used to
at least a few of ’em.

today i learn that the “i” of “the _i_ching_”
can mean “simple” as well as “change”.
now “ching” means something like “scripture”
(my source actually said “sutra”;
another way to say it would be
“classic text”). so on this model
the “sixty-four ways”… 000000
up to 111111… are “simple scripture”.

anyhow, an *introduction* to
simple scripture…
there are actually 4096 “readings”
possible for th’ _i_ching_, not just
64… and they’re not all equally
likely… so things get complicated
pretty quick (as you can generally
expect math problems to do).
just thought you should know.

the robot and the guy are doing battle.

Photo 96

zines made on madeline’s printer/scanner. all i can do with this box so far *is* make copies. still it’s a milestone. while you’re up get me a grant.