## Archive for the ‘Uncategorized’ Category

### now… momentarily… with less spam

Blue Car, Blue Car (1998)
I finally got a learner’s permit
at age nineteen in Thousand Oaks,
where I’d been living like a hermit
on coffee, pot, and rum-and-cokes.
Now, back in school, a lack of patience
for classes during my vacations
had kept me out of Driver’s Ed.
But something had to give. I said,
“Of course I’d rather do things my way,
and walk, or thumb, or ride my bike.
But I can’t have things as I’d like.
This California’s one big highway!
It’s best to take things as they are.
I’d better learn to drive a car.”

And so my then-best-friend, Bob Shaffer,
agreed to bring me up to speed.
“I know a car that you could pay for.
I’ll teach you everything you need.”
“But what about repairs?” “Don’t panic!
This car was owned by a mechanic!
It’s in great shape! It runs just fine!
It sounded like that classic line:
“The only owner was some granny
who never drove”, but Bob was right.
I got the car that very night:
a sixty-three, push-button tranny,
Plymouth Valiant, not much rust.
It turned out worthy of my trust.

I made a hundred dollar payment
and owed another; then I’d bought
it. Breaking up the debt this way meant
I could pay with ease–I thought.
But then my boss at Howard Johnson’s–
whose every word was arrant nonsense–
said “Although it pains me, I
have got to let you go. Goodbye.”
(I thought I knew his secret reason:
I’d worked there for about a year,
and paid vacations cost them dear.
It’s always bellboy-shafting season.)
So even though I had enough
to make the payment, it was rough.

And so at last I started learning
how to drive. At least, I tried!
My second night, as I was turning
(way too fast and far too wid,
which should have been a minor error),
I saw a car and froze in terror,
making it a big mistake.
At last, too late, I hit the brake.
I’d caused a little fender-bender.
The other guy, whose car I’d hit
was more than fair, I must admit.
A small amount of legal tender
I called and got it from my dad.

The testing had me really worried
and, in fact, I failed it. Twice.
But then I got a guy who hurried
once around the block. How nice!
To earn the necessary rating
depended less on skill than waiting.
(I might have known from back in school
that grades are like that as a rule.)
I drove my Valiant to Laguna
to show my dad the famous dent.
He thought his money quite well spent;
he only wished I’d done it sooner.
He always hoped I’d leave the stage
of wayward youth and come of age.

But that’s another, longer, story
and not the one I came to tell.
I’m sticking to the task before me.
I think you’ll find it’s just as well.
Enough to say that now that twenty
years have passed, I’ve grown up plenty–
but still today, without a doubt,
I need a lot of bailing out.
Returning to my car: it never
once broke down, though there was once
I thought it had but like a dunce
I hadn’t checked the gas tank. Clever!
They’ll never make a fool-proof tool
as long as there’s a perfect fool.

Once I had the driving habit
I gave the car up as a loss.
I had a chance–and chose to grab it–
to move to Vegas with my boss.
It didn’t take a lot of thinking;
we’d sleep till noon, and then start drinking,
and work as little as we could
at cleaning carpets. Life was good.
But I was broke, as was my pattern,
and owed my landlord two months rent.
He got the car and off I went.
From then until I bought my Saturn–
that is, till fifteen years had passed–
that Valiant was my first and last.

At thirty-five, I got a fairly
well-paid job. But I lived far
enough away that I could barely
get around without a car.
I’ve never liked to deal with dealing–
a root canal is more appealing–
and so, I chose the one brand name
that cheated everyone the same
and wouldn’t make me drive a bargain
to drive a new car off their lot:
in short, a Saturn. Still, I got
a song-and-dance and empty jargon
completely freezes over, dealers sell.

I had a girlfriend, Betsy Baxter,
in Bloomington (my old home town).
I e-mailed, phoned (but never faxed) her,
and every weekend, drove around
five hundred miles in any weather
so we could have some fun together.
I married her, she finished school,
and then I learned I’d been a fool
for thinking that our love was thriving.
when she decided we’d been wrong.
As long as it was mostly driving
back and forth from state to state
our marriage really worked out great.

Of course my car was bought on credit:
the price tag was eleven grand.
In sixty months, I’d finally get it
free and clear—or so I planned.
My enemies contrived to spoil it;
my whole career went down the toilet
(it might have lasted longer, but
I wouldn’t keep my big mouth shut).
I lived six months on unemployment
and credit cards whose interest rates
would ruin even William Gates.
Then, after all the fun enjoyment—
no job in sight—the bills came due.
So I went bankrupt. Wouldn’t you?

My two divorces, uncontested,
For this, though, common sense suggested
the banks would go for all I had.
My wife, the former Shauna Kearney,
referred me to a good attorney
who looked at my accounts with me
and, taking out a hefty fee,
said, “Well, this car’s worth too much money.
Depreciation’s cut the cost,
but not enough. And so, you’ve lost
because you’ve saved. It’s funny
but that’s the way things sometimes are.
You’ll keep the rest; they’ll get the car.”

### this belongs in the other blog

somehow the password i’ve used there
for years… though not quite as long
as i’ve used the same one here…
is *no longer in effect*.

this is not my fault.

i suppose i’ll try to fix it up.
somehow nobody’s munged my e-mail
recently.

on the other hand, why fucking bother.

### his bright materials

seven signs in seven positions.
PALEGAS and MRBGPYO (aka ROYGBIV)
and days-of-the-week and ages-of-
-man and whatnot… the trivium &
in various interesting ways.
the seven principles of UU will
eventually be invoked if this
is ever (again) the basis of a
sermon by me. “window crayons”
on cardboard box; 2015.

### she wears an iron vest

{1, 2, 3, 4, 5, 6, 7} (“barred” inside
the “big circles”… as they ought to
be throughout) are here identified with
{
001,
010,
011,
100,
101,
110,
111
}
in the usual way (“binary arithmetic”).

these objects — triples of zeros-and-ones —
can of be considered as (so-called) 3-vectors:
{
(0,0,1),
(0,1,0),
(0,1,1),
(1,0,0),
(1,0,1),
(1,1,0),
(1,1,1)
}.

these can be pictured… exercise (or you could
look it up… warning: the earlier drawing
uses a different assignment of the colors)…
as the “nonzero” vertices of a cube.

by considering this set, together with (0,0,0),
one forms a (so-called) finite abelian group.
renaming objects (again), this group—call it (G,+)—
can conveniently be displayed as
G = {
(E,E,E),
(E,E,O),
(E,O,E),
(E,O,O),
(O,E,E),
(O,E,O),
(O,O,E),
(O,O,O)
}.
the group’s operation, here called “+” (i’d’ve
defined by “add E-for-even and O-for-odd in the usual
way, three times (once for each “column”)” (or “add
component-wise, mod two”).

thus (E,O,E) + (O,O,E) = (E,E,E), etc.

(G,+) now has the structure of a ${\Bbb Z}_2^3$
three copies of the “parity group” ${\Bbb Z}_2$.
this happens to be the simplest example of a 3-dimensional
vector space. the simplest projective plane,
S = (P, L), is then
(1) a set of seven Points
P = {(0,0,1),…,(1,1,1)}
(or P = {[1],[2],..,[7]}—
easier to type, but harder to
compute with), together with
(2) a set of seven Lines
L={
{[1],[2],[3]},
{[1],[4],[5]},
{[1],[6],[7]},
{[2],[4],[6]},
{[2],[5],[7]},
{[3],[4],[7]},
{[3],[5],[6]}
}.

one now places “colors” on the (nonzero)
“corners of the cube”— or, equivalently,
on the “points of S”— in such a way that
the “blends”, the “blurs”, and the “ideal”
all “line up”… which is to say, “occur
as triples-in-L”.

to each of the “lines” of S
one has
{
{[0],[1],[2],[3]},

{[0],[3],[5],[6]}
}:
the (7) “planes through the origin”
in (Z_2)^3… the front, side, and bottom,
for example, and four others harder to
describe without the handwaving; the
“bottom”, for example has z=0 (in the
usual (x,y,z) interpretation of an
ordered-triple. each of these planes
is a subgroup of ( (Z_2)^3, +)
[or a (vector) subspace].
now back to the 2-D versions.)

our diagram today has
M-R-B-G-P-Y-O (in this order:
mud, red, blue, green,
purple, yellow, orange)
identified with
[1]-[5]-[7]-[4]-[2]-[3]-[6].

this ordering is one of the (168) ways
to cause the “lines of rainbow space”
(blends, blurs, and ideal) to coincide
with the algebraically-defined “lines
of S”.

each of the dots-and-sticks
(at each colored-circle
“point” of today’s selfie)
gives a *graphical* representation—
a “figure”, let’s say—
of a Line. so at lower-right, (the
Green point), we have [4]= (O,E,E),
associated to the set
{Mud, Yellow, Purple}—
one of the “blurs”—,
and also to
{[1],[3],[2]}… i.e., to
{
(E,E,O),
(E,O,O),
(E,O,E)
}; each triple {[A],[U],[X]}
(in any order) satisfies
[A]+[U]=[X], i.e., for
A=(a,b,c),
U=(u,v,w),
X=(x,y,z),
one has a+u=x, b+v=y, and c+w=z
(all “mod two” of course; recall
that we are “adding” Evens and Odds).

one now checks—over and over—
that the drawing at hand “satisfies
pro-planarity”. in terms of colors-and-figures,
this means that the blends-blurs-and-ideals
coincide with the 7 “shapes” of the figure.
in vectorspace terms, with the planes-
-through-0 (of (Z_2)^3). in the
“fano plane” (w’edia),
S=(P,L) of “abstract” Points and Lines,
with lines. so on.

the rest is commentary. for a while.
eventually you want to get to know more
about those 168 ways, for example.

### square one

$\sum_{i=1}^\infty (1/2)^i = 1$, “without words”.

### i probably won’t be able to find it here either: random comment crosspost

I have briefly mentioned that the alternative to explicit instruction may be described as ‘constructivist’ teaching. I don’t want to become bogged-down in this – I am aware that constructivism is actually [a] theory of learning and not of teaching and I have no problem with it in this regard; we link new knowledge to old etc. If it is true then, no matter how we teach, our students will learn constructively. However, some educationalists clearly do see implications for how we should teach.

i don’t want to become bogged-down in this either.
and yet i have been, deeply, many times, for years.
not so much these days. i just, you know, despair
of anything useful being said or done and check out.

all educational philosophies are useless in practice
until particular special cases are to be discussed
in carefully constructed contexts… so all we readers
ever seem to get is atrocity stories and suchlike
ill-disguised partisan politics.

“carefully constructed contexts” would include, for
example, a lot more attention than i’m usually able
to find about who the heck “we” are supposed to be.
this annoying pronoun is used as if it’ll mean all things
to all people. but it usually means nothing to me.

(in the passage at hand, i take “we teachers”
readily enough, so this isn’t a good example of
what bothers me… but hints at it. in electoral
politics, “we” can mean we-voters, we-americans,
we-patriots… and, often enough, two or three meanings
must be inferred to make any sense out certain
passages at all.)

angels dance on pinheads and owen leaves the room.﻿

### an invitation to vlorbik’s library

i pulled my (dover edition of) cantor’s epoch-making
contributions to the founding of the theory of transfinite numbers
yesterday to show tony from church;
he’d noticed my (prominently displayed)
copy of god created the integers
(hawking’s anthology of great math by math greats)
and mentioned “infinity” a few times in
my hearing, so it seemed like a natural.
and maybe it is… anyway, one does *not*
need a lot of high-tech “advanced math” to
read cantor’s stuff… and be just as mystified,
most likely, as most of the mathematicians
of cantor’s time (and many long after).

but i *should* have broken out the fourth dimension (w’edia),
by rudy rucker (w’edia).
tony’s *also* mentioned “the fourth dimension”
(as a concept) and *this* thing is bound to be
a whole lot more accessible than cantor.

i don’t know this particular rucker book at all well…
but i used his infinity and the mind in a class
long ago and’ve read some of his stories and whatnot.
rucker’s one of math’s best “popular” writers ever,
with a “transreal” SF-like vibe all his own.

i’d post more but my mouse is acting up again. damn it.

• ## (Partial) Contents Page

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