nobody writes to the kernel

anyhow. this notion of “literal truth”
appears to be doing a great deal of damage.
begin ramble.

wellknown principles.
the map is not the territory.
the tao we speak of is not the tao.
constants aren’t; variables don’t.

much ado about equations.
*here*’s something well known:
there’s a great deal of mystery
even about the *sign of equality*.

every teacher of algebra will soon encounter
a cluster of phenomena usually summarized
by remarking on a tendency to use
“=” when one means ““:
5X = 15 = X = 3, for example.

what can we learn from this?
because we’ve mostly learned nothing or worse
and it’s sort of troubling.

the student *does not mean*
by “=” what the teacher *wants* them to mean;
moreover… the part nobody wants
to talk about… the student doesn’t
*want* to mean what the teacher wants them to.

resistance on this is fierce.
*not* every algebra teacher knows this or cares.
most of them “get” algebra all right
but they sure as hell don’t “get”
the whole teaching-as-opposed-to-training
vibe; they’ll just mark it wrong
and say try again harder or
explain it in exactly the same way
that’s failed for the student
in front of them since first fucking grade.

or, as i usually did, one could try talking about
what the *student* thinks is going on.
this is where the resistance comes in of course.
usually i’ve found it prudent… on learning
that sure enough the student thinks they’ve
*had* this conversation before and that
it’s experienced as *punishment* and so
they don’t *want* to do it… to change
the subject pretty soon.

“just write the new equation
*under* the old one and the issue
won’t arise. also it’ll be easier
to read anyway. don’t spare the paper!”

there’s a slightly more advanced form
of this situation where the student
*has* understood what i’ll here call
the distinction between a so-called
“algebraic expression” like 3X or 15
and a “proposition” like “3X = 15″…
but maybe not quite. so you’ll see
inappropriate ‘s
scattered throughout. typically
these are “good” students…
able to carry out calculations from
“prerequisite” courses with
much less guidance than the
“not so good” students making up
the big undifferentiated middle.
since such students, in the situations
i’m here reliving (at, let it be said,
a certain cost to my own peace of mind),
will actually have a better notion
than their less-well-prepared near-peers
of what the sticking point that they’re
*really* working on, is, i’ve found it
prudent simply to mention something like
“you’ve done well to notice that
these *implications* here aren’t
*equations*. but look… *this*
isn’t really quite right *either*!
now, nobody’s going to ‘take points
off’ over this issue in your class
i bet… but you’d do well to keep
*thinking about it*. now, about
that equation we were looking at…”
(usually. but by heaven sometimes
i’ve just damned-the-torpedoes right in
and done the philosophy of math
with ’em and for all i know some of
’em even learned something.)

because *their attention* is
the coin of the realm around here
and i’m damned if i’ll waste it
trying to sell them something.

okay. everybody already knows this
or doesn’t care so this is rather
a poor start to this ramble maybe.

math phobia? why?
well, dammit, because the student
*rightly percieves* that
the mathy point-of-view
demands that its user
*abandon*… or anyhow,
momentarily *reject*
certain habits of mind.
habits that, while clearly seen
not to “work” in certain situations,
are nonetheless the only
habits that the student *has*
for dealing with (what appear
to have been) similar situations
and “pick up your bed and walk”
just ain’t getting it.

you’ve got to get a job, mr. thomas.
what, and give up show business?

“mathematics is characterised
by its intolerance of nonsense”
as i remarked in the one
and only presentation i ever made
on math ed. and i still believe this.

but most of life is too horrible
to contemplate *without*
plenty of nonsense…
that’s why they invented
helpless laughter, for example.
also religion. also politics.

so it’s no damn wonder
math is so repellant;
the amazing thing is that
it can be done at all.

it’s as if, say, a truefaith mathhead
were to, say, try to become a member
of some math-and-computer-science department.
at a small liberal arts college
in central ohio, say. hypothetically.
and were to discover that the only
*truly essential* piece of work,
for purposes of… what to call it?…
“service to the department”
(or “career moves” or “fitting in”
or “going along to get along” or
some such “dumb things i gotta do” work)
in, say, a given week were to produce
some documents describing the policies
of the department in language appropriate
to the regime-of-the-hour.
suppose moreover that the appropriate
language include a “definition” of,
oh, i don’t know, “learning”.
and that what is expected, nay required,
is actually about the furthest thing
in the world from a “definition”
in mathematics or even in ordinary life.
one doesn’t even attempt in suchlike
documents to pretend that these
“definition”s will have anything to do
with the usage of the word in question
in *any other context*… they serve
(pretty precisely) only to show that
the body that created them has learned
certain contemporary codewords
and to make certain psuedoclaims
about how-we-do-things-here
without actually leaving oneself open
to actually having said anything
with a precise meaning (that,
after all, could then be shown
to have been a *lie*).

“mission statement”. to part fools
and their god-damn money, what the hell
do you think? this is a *business*,
buddy. what the fuck to we need
with a fucking *mission statement*?
oops, sorry.

suppose such a truefaith math-head
weren’t such an imbecile as he
no doubt appears to the world at large
and *does* sort of get that
the work of an academic department
isn’t *merely* to spread the true faith.

we’re paid by the folks with the money
and it’s in our interest to convince them
that we’re willing to do things their way.
stuff like that. such a hypothetical
truefaith math-head might… something
like the even-hypotheticaller mathphobe…
feel that, okay, i can see that there’s
this *point of view* that i ain’t got;
i can see that it’s *paid off* for
some collection of people i’ve encountered;
i can even see that some of what
one does to *acquire* this point of view
is *abandon* certain notions.

like “words should be used to
describe thoughts as clearly as
one can find a way to do it”.
that’ll have to go real quick.
also “clothes should be cheap
and comfortable; they shouldn’t
require much care”. also,
“a lie to the face is a god-damn insult
and shouldn’t be taken lying down.”
stuff like that.

well such a truefaith mathhead might choose
to despair of ever accomplishing *anything*
in an environment that requires you to leave
all your favorite stuff at the door and makes
no guarantee that you’ll *get* anything out
of it at all.

well, this guy never really wanted
to be an assistant professor anyhow, did he.
just wanted to talk to undergrads
about math problems. should’ve gotten
that out his system in grad school;
there’s real work to be done. fair enough.

i read some story somewhere about
a beginner’s ballet class.
they’ve learned the five positions
and whatnot and are about to learn
the big-girl move of standing “on toe”.
well, the narrator was impressed
at watching the faces fall:
it *really fucking hurts*.
this is the fantasy-reality interface.
one isn’t going to *be* a ballerina;
evidently ballerinas have a
*much higher threshold* for pain
than, say, this-particular-girl
has or can even think about wanting.
dealbreaker.

it happens all the time.
there doesn’t have to be any
mysterious fucking phobia
about it either. one has
estimated the benefits and costs,
badly. new information,
a revised estimate, bingo.
not even unreasonable necessarily.

now it’s also true that people in pain
make really poor long-term decisions:
pain focuses the attention on the *moment*.

the *body* doesn’t remember that it
can “get used to anything”; anyhow
if we can’t make the down payment,
maybe it doesn’t matter what the
terms are going to be month-to-month.

some of the girls decide it’s worth it.
and the world doesn’t actually *need*
a whole hell of a lot of ballerinas anyhow.
hence no “ballet phobia”.

trying to get a “real job”.
out of the question;
unqualified on sight.

getting from here to a place where
i *wouldn’t* be unqualified.
bound to fucking hurt.
maybe even more than this.
no very good idea
what it would be worth to me
should i somehow achieve it.

teachers can’t help with stuff like this.
all they can do is say “worth it, worth it, worth it”:
*i’ve* got to actually do the exercises.
and they’re *bound* to say “worth it, worth it, worth it”;
it’s their god-damn job. the fact that it was worth it
*to them* should barely count as information at all.
everybody knows this. a hell of a racket really.