so when i came back to work today
after being laid off all summer,
i just logged right in on the first try.
and into a better environment for working
in wordpress, too (than what we’ve got at home…
even when i use the 17″…)
it’s quite a large grading load:
advanced calc, vector analysis, and lots
of good old linear algebra. (i’ve also
committed to a writing project in intro
to calc… so it’s busybusybusy for me
for quite some time to come.)
now, where’s that doggone *textbook*?
… around here somewhere…
so. a poor workman blames his tools
and i’m about to get right back to it.
recap: i’m just as guilty as anyone else.
when there’s stuff i think i’d *like* to know…
but that i *don’t* know… there are probably
for example: (1) maybe i *don’t* want to know
(“does she *really* love me as much as
she says?”, e.g.).
or this: (2) the possibility of consequences
too horrible to accept (“is this guy just
another macho windbag or is he actually
tough enough to *hurt* me?”, let’s say).
or it’s just (3) flat-out too much trouble
(“what’s my credit rating and who’s
looking?… and who should i believe?”)….
and one could of course go on.
but in our context. and, again, i’m just
as guilty as the next guy.
i might “want” to know…
without having to admit
that i’ve been *wrong*.
wanting what can never be: life on one’s own terms.
including, in this case, an apology from the universe-
-at-large for having pretended for so long that one
hadn’t long since *really* known the true heart
of the matter. (stubborn universe. oughta know better.)
well, it’s pretty pathetic stuff, heaven knows.
but like i say, i’m just as guilty as the others
(that i’ve been working with right in here) seem
pretty consistently to be. give or take.
your milage may vary.
so, now. damn it.
when you hate and fear mathematics.
what then are we to do?
well, *avoid* the SOB if you get a chance, obviously.
i hate and fear fighting with fists and have done
fairly well so far running away from every chance…
too well to learn anything *about* that subject
in any realistic way.
but that’s what *you* should do.
what then are *we* to do… when, in some strange
power’s employ… “you” and “i” have agreed to
work together on clarifying some of your ideas
well, with any luck, *i* will be sensitive to
some the emotional baggage that typically goes
with *your* position. in dealing with some
intricate system of rewards-and-punishments,
you will have come up again and again against
some authoritative force telling you “you need
more math” (to acheive such-and-such a goal).
and, with any luck…
*you* won’t take it for granted that i’m just
another con artist out to get over on you
by pretending that making-it-look-easy
does anybody any service.
this is not fucking gym class.
maybe i’m willing to try to understand your point
of view; maybe i’d really like to help you get
closer to *your own goals*.
so, now. why? why? why?
why, *for the love of god*, will you look away
the second the words “do the same thing to both sides
of the equation” escape my mouth?
why, when i make it a point to get your attention
back to the work on the page and say it again,
will you *openly complain* that i appear to be
changing the subject (from “what’s my next move
in this particular problem” to “how does one
actually go about *solving* problems like ours”).
why, when i fucking *beg* you to take me seriously
(this *one* fucking time) and get over your infantile
insistence that *you* know better than every teacher
of the subject worth taking seriously (alive or dead),
must you have some fucking *problem* with that?
because, sure, *i’m* an emotional basket case.
but *i* passed this fucking class easily and
have gone on to learn *much* more about it,
whereas *you* are going to fail it badly
(and deserve to) because you don’t want to
consider that an expert’s opinion *might*
sometimes be more valuable than the ill-
-formed fantasies of some bare-beginner.
(your smug self-righteousness won’t weigh
much on the exam, most likely…)
go ahead, *hold* me in contempt.
you’ve paid for the privilege.
but, geez. this trying to *understand*
why you do it has me just about worn out.
so, you know what?
just *humor* me.
“do the *same* thing to *both* sides of the equtation.”
do the same thing to both sides of the equation
*on my authority* if it makes you feel any better.
(and *remain* a true-thinking math-is-nonsense
“normal” person… *blame me* if you have to…
“i’m not *really* pretending to be a math-head;
my teacher just *makes* me do it [like *all* teachers]
just to prove he can push me around”)…
i haven’t got the strength even to talk
about this any more.
because the *right* answer to “what do i do next?”,
after you’ve taken some perfectly good code
and munged it up by changing only *one* side
of an equation, is, and can’t ever *not* be,
“fix up this equation so it’s right”.
and if… never *mind* your reasons…
you’re not *having* it? well, it’s just
another one of those (many, many) problems
whose *solution* is “owen leaves the room”.
now at least part of the point of me going on
about *my own* “bullshit commitments” (BC’s)
will have been that i’m about to start looking
at somebody *else’s*.
and i am. so why make a fuss?
well, i get pretty tired of hearing (pretty
quick!) about the beam in my own eye, the minute
i bring up certain motes in the eyes even
of far-off strangers.
yeah, okay… i get it. your own
particular eye-motes look more like
those of the position i appear to be
attacking than they do like my eye-
the thing is, i’m willing to consider
my eye-beam at great length, and *have*
done (many times), but just now for some
reason i’m trying to get at something
about this little *mote* here in this
*hypothetical* guy’s eye, okay?
without getting all personal about it?
for just a few more minutes, here?
and it sometimes gets to feel like
a climate where to find *anything*
wrong with *anything* (about the way
things are done) is to invoke some
“well, a lot of people feel differently”
conversation-stopper (or, more generously,
topic-changing device… one should
*use* this trick if it should appear
helpful in getting out of learning
people’s opinions about, famously,
religion and politic [and, more
generally, any such all-noise-
-no-signal discussions as seem to
arise so naturally on those topics]).
so i’ve got bullshit commitments for sure;
many of ‘em much deeper-rooted and more
destructive than the math-ed stuff i kicked
around upthread. so there *that* is.
meanwhile, one has observed shocking
pathologies amongst certain populations
of math students.
“212- 32 = 180 / 9 = 20 * 5 = 100″ (string A)
now, in “string A”, we have a calculation
showing that 212-degrees on the farenheit
scale represents the same temperature as 100
degrees on the centigrade scale. the
author of string A has successfully
computed the results using “subtract 32,
divide (the result) by 9, and multiply
(the latest result) by 5″.
and this is a good thing to be able to do.
praiseworthy, even. i’m reasonably sure
i myelf will have been praised for learning
how to do this… *and* for audibly practicing
it, and by one or both of my parents at that.
(whose praise i valued far more than that of
any mere teacher.) good work all around.
(exercises: *how do you “go backward”
your basal body tempature in the
scale least familiar to you [show
but in math *class*… in “advanced” maths,
in “formal” maths… we *won’t* be able
to accept string A as good code. Not for
the farenheit-to-celcius conversion.
It *is*, if not “good”, at least *clear*
code for a pair of lies and a truth:
180 = 20 = 100 = 100 (A’).
A’ is obtained from A, after all,
carrying out arithmetic on
things t in A and
writing out their respective
(and leaving other things in A
unaffected… the “=” signs in
to produce A’.
A and A’ “have the same meaning”
(because we’ve “just done the math”).
or we’re sunk.
we are *replacing* things
with things equal to themselves.
one of our oldest-established tricks:
a cornerstone of the algebraic method.
if we’re to make this trick work at all,
though, we’ll have to be *very* finicky
about *saying* things are equal (and
writing “=”) only when (we believe)
they *really are* equal (and so, can
be safe in making such substitutions).
clear classroom work… or math-*book*
work… good *home*work, for heck’s sake!…
then calls “the equality meaning of the
equals sign” to be maintained as consistently
but this is *not* what many of the
lifelong users of runon-sentence-bad-habit
gibberish like string A
believe they signed up in a math class
to find out. and find it out they *will* not.
so they’ll go on putting
a number equal to a set
a point equal to a space
a vector equal to a number
a 2\by2 matrix equal to a 2\by4 matrix
and… here is thunder on the horizon…
getting away with it.
but one should’ve had the wakeup call
at least, say, two semesters ago.
one is required to have had four
quarters of calc for this thing!
how do you *study* advanced mathematics
without finding out what *every* mathematician
means by “=” (most of the time)—and has done,
a (pretty commonplace) math-ed
BC nurtured by me at various times:
“never memorize what can instead
be calculated out from first
*the quadratic formula
i’ve elaborated somewhere
*values of trig functions
[for "basic" angles (i.e.,
\pi times 0, 1/6, 1/4, 1/3, & 1/2)];
i now (mildly) urge beginners to develop
a routine of *charting* these
values for the “sin” function
when faced with several exercises
calling for trig calculations.
the other charts are easily
devloped as needed from there.
but heck, i’d've just done better
myself to admit that sin(\pi/6) = 1/2
is a *darn useful thing to know*
even without drawing some big ol’
equalateral triangle in my mind’s
eye every time just to “see” it.
*various “infinite series”
like e^x = 1 + 1/[1!]x + 1/[2!]x^2 + 1/[3!]x^3…
[one is utterly puzzled at some point
about how integrating-the-recipocal
can have such easy-&-useful tricks
associated to it; too many unfamiliar
notations (or unfamiliar properties
of [somewhat] *familiar* notations)
are floating around. one is waiting
for the “aha” when “differentiates
to itself” will be able to work itself
out *vividly*… anyhow, it’s nice
a nice simple *target* set up for
certain suchlike gropings-in-the-dark…]
but, of course, “figuring out from first
principles” is *hugely important* and
widely under-rated in the imagination
of our typical students… so, just
rephrase it as “*seldom* memorize…”
and you’ve got a *winning attitute*
rather than a BC.
it’s that *totalizing* thing: “never”.
again: “accentuate the positive”
is a winning attitude (dammit).
but “eliminate the negative” is
a bullshit commitment
(as is “don’t mess with mister
in-between”, i suppose).
it’s just no use *talking* with a
hardened hear-no, see-no, speak-no
evilist. or anybody else that already
knows the answer before the question
arises. be it jesus or allah or
more teachers or younger teachers
or more training (or less) or acceptance is
the answer to all my problems today.
BC’s are a certain species
of what are (annoyingly)
excuses to avoid looking
at something we… umm… fear?
no, let’s not bring *that* into
it… something we *aren’t
willing* to look at (just now).
i find “rationalization” (as
a folk-technical term) annoying
because it invites confusion:
*who* (after all) will be able
to draw a clear line between
what is (really) “rational”
(and “good”) from what is
not me, not if i can help it.
at long last, this kind of thing
will finally emerge as some sucker-
-bait snipe-hunt philosophical
fool’s errand: figuring out
what the *other* guy “should”
do (when i’m seldom even at all
close to certain what i “should”
do myself [and will sometimes
prefer to avoid the question
altogether... and sometimes
be ready even to do violence
*to* avoid it]).
and then, in some horrible moment
of weakness, forgeting that the
whole point of any ethics-rightly-
-so-called is “love your neighbor”,
we, i, “one”,… the subject…
forgeting all *true* ethics,
the subject will look around for
an excuse *not* to do the right thing.
(or, maybe more precisely, for an excuse
not *to have done* the right thing.
bullshit commitments have ways of nearly
erasing time and space.)
—how do you feel?
—never mind that, how do i look?
for now, let that stand as our model.
or, let’s say, take a guy like me.
and endow that guy with a cultural scene
to rival any great city’s in any era…
athens, alexandria, bagdhad, vienna…
at any time. let it all seem to fall down
from heaven like a gentle spring rain
until that guy-like-me never sees any
need to go out and pay any serious attention
to the whole nature-red-in-tooth-and-claw
thing until it’s far too late.
there will always be more fun people
to mess around with in the arts-and-
now, that right there, as far as i can
tell, is pretty close to the *opposite*
of a bullshit commitment…
or maybe i’m just not willing to look
that far ahead…
but let’s say (and examples exist) that
in one such case some poor damn fool decides
one day that *whatever* these so-called
musicians are doing with their shape-notes,
it can only *really* be,
some sort of spiritual *trap* designed
by some unrighteous force to get us to
*fake it better* instead of *really feeling
it* (and that’s why the world’s allegedly-
-best singers, for instance, can deliver
pitch-perfect performances without moving
untrained listeners in the least, whereas
that raw-talent kid can break your heart
in two notes and everybody feels it but
the obvious posers).
“technique is the enemy of sincerity”, then.
(rephrasing… summarizing… what have you.)
another, better, model of a “bullshit commitment”.
tired. quitting for now.
new readers are showing up in my email
as having signed on for my “feed”.
if this isn’t some twisted form of spam,
i’m proud to learn of it. probably if
it’s at all real, it’s a “twitter” thing.
i somehow along the line signed up to get
links to my posts appear there automagically.
i’d've quit that account months ago if
it’d been easy; i can’t work it at all
anymore. google’s in many ways worse.
the net’s getting away from me faster
and faster. with no willingness
on either side to change our ways.
what the heck. the kids are alright.
so be it, of course. *really* tired.
dad was a magician.
by the time i knew him, he was also
a life-of-the-party singer-&-piano-player;
also an outstanding classroom lecturer.
so quite the performer all-around.
but he’d been a magician early on.
and he must’ve studied hard back there
in radio days, cause he was *real* good.
(he’d even made a little money at it.)
close-up card magic
seems to’ve been a specialty; any-
how, that’s the stuff he showed me
(& my brother & sister, natch).
he’d rattle off the patter just right
and get you all involved in the story
as he showed the cards, and we’d cut
the deck when so instructed and never
see a single false move… but he was
sure *making* ‘em: one of our favorites
involved palming cards, dealing seconds,
several “passes” of the cards (bottom
stack to top stack: a very basic move
in card magic), and a few other such
tricks, all with you looking right at
his hands practically the whole time.
and then, right where you *don’t* expect ‘em,
ace, ace, ace, ace. wow!
but then we’d, as it were, go backstage.
and he’d show me how the behind-the-scene
card manipulations worked. and he’d always
tell me beforehand that a real pro
“never tells the secret”
(or some such language; i can’t claim
perfect accuracy here… sooner or later,
you forget *everything* [and don't you
so. of course i was very pleased to’ve been
let in on the secrets and even studied up
on ‘em a little now and then as if to prove it.
my best move was a back-palm “vanish”;
my “pass” always left much to be desired.
i worked with a “stacked deck” a little
until i could do a few decent stacked-deck
“tricks”. stuff like that.
but my (younger) brother nathan took it
much more seriously and was already
a pro performer in teen years.
most, maybe all, of his magic gigs
were at kids’ parties (where the actual
paying clients were parents, of course).
i saw many a “dress rehearsal” of his act
but never saw him working with the kids.
and *me*, he’d “tell the secret”;
how to work the rings, the “dove bag”,
the thumb tip, the scarves…
but you can be darn good and sure
he didn’t show the *kids* how to
“do the magic”.
because it just *ain’t magic* once
its audience understands it. and because,
like i said, he was already a pro…
and that’s just not the way a pro does it.
now, there was this whole episode
of _house_ wherein a magician patient
carries on a series of discussions
with the scientist main character;
the patient says “it’s better *not*
to know” and the doctor says “it’s
better to know”.
i cite this story to prove, as it were,
that this “real magicians don’t tell”
business is fairly well-known.
now, i’ve always leaned pretty strongly
in the direction of better-to-know.
i don’t like *being* fooled
and i don’t like having somebody think
*i’ve* fooled *them*. (actually *having*
fooled them is another story of course…
but of this i know but little.)
but, as i slowly began to learn, it’s
not just *magic* where “never show
anyone how it’s done” is a crucial
part of the art.
no, it’s show-don’t-tell in fiction,
it’s faking-’em-out in sports,
it’s the “poker face” in cards.
and on and on it goes.
it’s life itself: “never let anyone
outside the family know what you’re
thinking” (as don corleone has it).
and a lifelong ideal of “radical honesty”…
something along the lines of “say what
you mean as clearly as you can whenever
you feel safe doing it”, an ideal i’ve
espoused many times and for a *long* time…
well, it’s probably been much more of
a weakness than a strength.
not that i intend to change on this account.
(i’m heck-yes proud to be able to report
that my last wife told my current girlfriend,
about nine years ago: “he’s not husband
material… but he won’t lie to you”.
i seem to have done at least *one* thing right.)
just something, like i say, that i feel
myself slowly coming to *understand* a little
according to the “saint francis prayer”
(here’s last sunday’s ramble),
i’d do much better to try and understand
the other guy instead of buttonholing
the poor bastard for some endless
greybeard-loon rambling by me, always
hoping to have *been understood* at last.
and maybe if i didn’t go around radiating
self-doubt in every direction, it would
become somewhat easier to get a *job*.
so on, so forth.
now let us turn our attention to the question
of “introducing standard mathematical notations
when i was back there in philosophy 100,
there was a person there (earl, if i
remember correctly, conee… something
like that). young guy, probably a
grad student as i understand now,
shaved cueball-bald. anyhow…
this guy was trying on the socratic
style, kicking ideas around circle-
-fashion (while leading us to some
predetermined answer). and it was
reasonably fun, too (as these things
go, for me).
and the semester-kickoff question was,
“what is knowlege?”
and the answer… after a bunch of
give-and-take (along with some take-
-while-pretending-to-give or what
have you)… that we arrived at
(having been led to it… “is this
really *enough* so far? have we
considered such-and-such *example*?)
“knowlege is justified true belief”.
now ain’t that just like a philosopher:
you give ‘em *one* question and they
give you back three *more* questions
and pretend to’ve given an *answer*!
because i’ll be hornswoggled if it
doesn’t feel like it oughta be easier
to *know* a thing than to, for pity sake,
*justify* it somehow! i’m looking
into *understanding* something and
you give me back, what? *ethics*?
and what about “belief”? geez!
who the heck even *thinks* they know
what somebody else even *means* when they
claim to *believe* something?
“is this the way to the kitchen?”
“i *believe* so…”
okay, i get it… but if you really
*believed* it, you’d just say “yep,
right down that way” (or something
like that…the issue of anyone
having reason to *doubt* it
never having crossed your mind).
by saying you *believe* it, you mean
you *don’t* know it… not for sure.
this my-best-guess-as-of-now interpretation
isn’t at all rare, so i hope readers
will recognize it from their own lives.
but then, in some other *context*,
“what i believe” will turn out to mean
something like “what my people are taught to
say and what i’m prepared to say in order
to go on standing with my people”.
both very different from the way we might “believe”
an object we’re looking at *is* as it *appears*
and will be there if we reach for it
(or what have you; for me this looks like
a pretty typical example of what i take to
be the most natural “default” idea about
what “belief” means in my dialect).
and maybe *the* basic philosophical move
is “draw a distinction”.
but sooner or later, you’re going to have
to *fix some terms* so you can see eye-to-eye
and do some honest-to-boole *reasoning*.