## Archive for October, 2016

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

satisfied him–not too bad!

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

about the warranty. Till Hell

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.

We hadn’t lived together long

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,

had, legally, been not too bad.

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.”

the left-hand photo shows

a nine-point plane: an “ordinary

two-dimensional plane” over the

field with three elements (and its

label is, therefore, ).

such a plane is ordinarily co-ordinatized as

(0,2) (1,2) (2,2)

(0,1) (1,1) (2,1)

(0,0) (1,0) (2,0):

the set of (x,y) such that

x & y are both elements of

the set {0, 1, 2}.

one could convey the same information more

concisely as

02 12 22

01 11 21

00 10 20.

it’s useful for our purpose here, however,

to consider our plane as belonging to a

*three*-dimensional space… (x, y, z)-

-space, let’s say… and as having a

*non-zero* “third” (*i.e.*, “z”)-co-ordinate.

thus, in the photo, our plane is represented by

021 121 221

011 111 211

001 101 201.

the colors come into play in displaying the

solution-sets for various (linear) equations.

the reader can easily verify that the Green

equation—x=2— is “true” for the points of

the vertical line at the right… *i.e.*, for

{ (2,0), (2,1), (2,2) } (old-school), *i.e.* for

{ 201, 211, 221} (“our” version).

likewise “y=x” (the Red equation) gives us

{(0,0), (1,1) (2,2)}… *i.e.*,the “Red line”

{001, 111, 221}.

now for some high-theory. by Algebra I, one has

a well-developed theory of Lines (in the co-ordinate

Plane). the usual approach there is to use the

(so-called) Slopes. the (allegedly intuitive) notion

of “rise over run” allows one to calculate—for any

*nonvertical* line—a number called the Slope (of that

line). vertical lines are said to have “undefined”

slopes. one might also say that they have an “infinite”

slope… though this invites confusion and is usually

best left unmentioned.

y = Mx + B

x = K

are then our “generic” *equations of a line*.

any particular choice of numbers M & B will

correspond to the a set of solutions lying

along a (nonvertical) line having the slope

of M (an passing through (0,B)… the so-

-called “y-intercept” of the line); each vertical

line (likewise) is represented by some particular

choice of K.

now. having different “forms” for vertical and for

nonvertical lines can be devilishly inconvenient,

so, also in algebra I, one sometimes instead uses

the “general form” for an equation of a line in the plane:

Ax + By = K

(with A & B not both zero).

likewise (but typically *not* in algebra-i)

Ax + By + Cz = K

(with A, B, & C not all zero)

is the equation of a *plane* in *three*-dimensions.

thus far i’ve been as precise as i know how.

but now i’m going to start waving my hands around

and making leaps-of-faith all over the place.

in the second photo, four new “points” have been

added into our framework (namely

{010, 120, 110, 100}—the “line at infinity”).

the upshot… without the details… of this move is

that one now has an algebraic theory of “Lines” in a

“Plane” containing precisely our 13 “Points”. more-

over, this theory is “structurally” very similar to

“ordinary” linear theory. in particular, we dealing

with solutions to

Ax + By + Cz = 0—

the “K=0” case of the “general form” for (the 3D case

of the “ordinary” theory).

the Green equation—which must now be written without

its “constant term” (x = 2 is “the K=2 case” of x = K)—

becomes x – 2z = 0;

similarly, rather than (the three-point “line”

of ) “y = 1” (concentric black-and-

-white circles), the (“homogeneous”—for us, right now,

this can be taken as meaning “having no constant term”)

equation is “y – z = 0” (and, again, we pick up a “new”

point at 100).

when the smoke clears… which won’t be here and now…

we’ll have a *very nice* geometry. just as in “ordinary”

space, two distinct points determine a unique line.

but… *unlike* “ordinary” space, it’s also true that

(*any*) two lines determine a unique point.

the same “trick”—homogeneous co-ordinates in finite

fields—converts any plane having p^2 as its number

of points to a *projective* plane having

p^2 + p^1 + p^0

as its number of points. thus there are PP’s having

7, 13, 31 = 5^2 + 5 +1, 57 = 7^2 + 7 + 1, ….

as their number-of-points. there are also some others.

but the margin is too small.