Archive for the ‘Rambles’ Category

here’s a pdf of marta flanagan’s
we are unitarian universalists flier.

i picked up a hardcopy version on sunday;
one of those 8{1\over2}\by11 folded-twice-
-the-short-way jobs you see in flier-racks
in all manner of waiting-room-like venues,
with three, what i’ll call, “panels”
on each side of a standard sheet:
the front “panel” has white letters
on a red background and the rest have
red letters on a white background;
the only non-typographical graphic
elements being three UU “chalice” icons.

sez “WELCOME” under the chalice on the front,
tipped at a jaunty 45^{\degrees} angle like the
“banner” and “foldover” cover-elements you see on
magazines. anyhow. i can get behind most of this
stuff. mostly without much embarrassment.

in this context.

i mean, well, look: *any* statement beginning
“we” immediately calls for… or, anyway, usually
brings forth in me… the question “who is this
‘we’, you’re talking about, there, anyhow?”, but
in this case “we” more-or-less obviously means,
“we UU’s”; score one for the flier.

“we believe”? well, one has longsince learned that
people hardly ever say interesting things about
their belief systems on cue. you’ll learn more
about their inner lives by asking ’em about what
they love. but they’ll lie about that, too, usually.
ask ’em what they *don’t* like and you can get some
pretty good accuracy pretty quick sometimes, though.

anyhow. (where was i?) the flier gets a pass here
again, for the same reason: i found this in the
front room of a church, for heck sake. people
actually do show up in this building wanting
to know exactly this, “what we believe”. some
of ’em are shy to actually *ask*… i know *i*
would be, and i’ve more than hinted at one of
the reasons… so we do very well, in my opinion,
to offer suchlike fliers in plain sight.

but “we believe people should”
is something of a deal-breaker.

i’d rather not believe people “should” do *anything*.
whenever i find out one of ’em thinks *i* should do
anything, that’s usually trouble for me and i don’t
like it. golden rule; game over.

i don’t say they *shouldn’t* spend their lives thinking
about better and better ways to push people around;
that would be hypocritical. but i damn well *wish*
they’d, you know, consider in the bowels of christ
that throwing-first-stones might be, i don’t know,
deeply fucking *wrong*. so, you know, just for me,
just for today, i’m not giving anything like full
assent to any “belief” with a “should” in it (until
more context is given; “if you want to learn any
advanced math, you should think about how equations
work” doesn’t give me much trouble, for example).

back to the document at hand.
“we believe people should be encouraged to think
for themselves.”
(but, i guess evidently, by using *our* courage
to do so.)

i’ve offered such encouragement *many* (many!)
times in my working life (and a little in
“real” life, too, i suppose). heck, i’ll
even urge anybody thinking they’d like to
try teaching to do the same.

the generous error.

strange loops indeed.

Advertisements

letting
{\Bbb N}_1 = \{1\},{\Bbb N}_2 = \{1,2\},
{\Bbb N}_3 = \{1,2,3\} \ldots
(i.e., {\Bbb N}_k = \{i\}_{i=1}^k… en-sub-kay stands
for the set of positive integers from
one to kay, in other words)…
and immediately turning right around
and redefining {1, 2, 3, … k} as
“N_k” instead, without all the fancy
type…

last monday’s bogart so far
was a ramble on stirling numbers (of the second
and first kind, SN2K & SN1K) and how it was
to read about ’em in KPB (kenneth p.~bogart’s
_introductory_combinatorics_… or should i
just say “op cit.”?). the notations i’ve just
introduced are mine not bogart’s; this will
persist as i imagine.

now i’ve read that section some more and
its pages are littered with my pencil notes.
for instance,
x^n = \sum_{j=0}^n S(n,j)(x)_j,
copied out verbatim for the sheer joy
of it, and
* [ (k)_n counts one-to-one F^n’s]
* [ k^n (counts functions)]
* [ S(n,k)k! counts “onto”
functions N_n —->> N_k]
,
written out on p.~50 (where the “falling
factorial” function (k)_n = k!/(k-n)!
is defined) because it seems to me
as clear a summary of what for me
is the heart of the matter as i can
produce at this time: this is what
SN2K’s are *for*, in the context of
some very familiar material (one has
delivered manymany lectures
bearing on “one to one” and “onto”
functions [and even quite a few
devoted to those topics specifically]…
but typically in a context where
“infinitely many” such functions
will be imagined to “exist”… which
makes “counting” the functions sort
of beside the point).

we could go so far as to *define*
stirling numbers of the second kind by
SN2K(n,k) := #{ f | f: N_n —>> N_k}/k!
.
“count the onto functions and divide by
the permutations of the range”… this
of course give the number of *partitions*
of N_n into k “classes” (regardless of
order “within a given class”).
not that i think this would be a good idea.

okay. like i said on monday, a good section
of KPB (2.3 “partitions and stirling numbers”).
i’ve read over all 18 exercises & even set some up.
heck, some could even be considered “done”.
but really i came to ramble about sections 3.1
and 3.2. or so i thought. but *really* i came
to avoid marking up some pages. and i’ve done
about enough of that. for now.

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-
-*beam*.

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
eliminate-the-negative-ism creates
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”
[celcius-to-farenheit]? *estimate
your basal body tempature in the
scale least familiar to you [show
a calculation].)

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,
simply by
carrying out arithmetic on
(“simplifying”)
things t in A and
writing out their respective
(“simplified”)
results t’
(and leaving other things in A
unaffected… the “=” signs in
this case)
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
as possible.

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,
for ages?

and *why*?

a (pretty commonplace) math-ed
BC nurtured by me at various times:
“never memorize what can instead
be calculated out from first
principles.”

(particular examples:

*the quadratic formula
i’ve elaborated somewhere
in here.

*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…]

*many others

)

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.

bullshit commitments

BC’s are a certain species
of what are (annoyingly)
called “rationalizations”:
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
(merely) “rationalization”
(and “bad”)?

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.)

anyway.
—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-
-sciences playground.

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,
now-and-forever, once-and-for-all,
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.
*really* quitting.

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
forget it!]).

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
better.

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
to beginners”….

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*?)
was that
“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*.

(first post since the name change.)

things’re going fine all around…
other than some computer-interface
hoo-hah snafu-ing the grade entry…
and it’s about time for the first test.

which the lecturers grade for themselves
according to the usual department practice.
so there’ll be maybe a little better chance
of me actually *posting* something around here.

meanwhile, let me go ahead and report for today
that for quite a while now i’ve actually been
*reading mathbooks* pretty avidly again.

recently it’s been one of my favorite
work-avoidance tricks.

reminding me of nothing so much as myself
in grad school when i’d spend hours in the
math/physics/computo-stuff library (in swain
hall west) avoiding the actual sit-down-and-*try*-
-something work that horrifies almost all beginners.

browsing around in the stacks at IU…
i didn’t neglect the *main* library
or that of the education school…
certainly wasn’t a *waste of time*.
i was one of the best-read amongst
a bunch of *very* smart people and
learned a lot of “math culture” stuff
most grad students never find time for.

because they’re, you know, actually *working*.

certainly it’s a relief to look over well-
-reasoned (& sometimes even well-written!)
work after… or during… a marathon session
of correcting basic-mistakes-stubbornly-
-clung-to created by students who should
have long since known much better. (it all
starts with the “=” sign… but [for now]
i’ve ranted enough on that matter in earlier
posts.)

and now that i’m mostly working with my *own*
books… almost entirely gotten on the cheap,
i assure you… “free” and “dover” are the
biggest categories here… i feel (more) free
to *write in ’em* (as i should’ve been doing
much more of all along [in *pencil* of course!]).

making my avoidance-technique that much more like
the actual work, you see.

heck, even *crossword puzzles* (usually
a big enough part of any go-to-campus-&-back
day since i almost invariably work ’em on
the bus) have a certain reading-and-writing
… and even *problem-solving*… feel to ’em.

so i’m spending a *lot* of time in some
mathy-or-anyhow-*kind*-of-mathy state.
immersed in the world of symbols-and-syntax
(or of concepts-and-code if you prefer…
i’ve got a million of ’em…).

and i *like* it like that. the trick is
to avoid, not facing-down-unfamiliar-symbols
or even grading, but, you know, those messy
“real world” encounters with other beings.

some math users… famously the great pascal…
have even reported an anesthetic effect
(he used analytic geometry against toothache).

the *dreams* you get from a math OD, though?
usually not so good in my opinion. usually
it’s too much like real life: not “one
damn thing after another” but the *same*
damn thing, over and over.

anyhow. past bedtime now. wish me luck.

this is the limit

so i’m grading linear algebra like i usually do.

where we need to speak… or anyway, to read
and write… frequently about *column vectors*.

much the usual thing (for example) in defining
a linear transformation (called F, say)
on “real three-space” (so F: R^3 —> R^3)
is to *consider R^3 as the space of real-valued
column 3-vectors* and then to supply a matrix
(called [F], say; [F] will be a 3-by-3
matrix in this context) such that
F([a, b, c]^T) = [F][a, b, c]^T.

the “caret-T” here denotes “transpose”…
the idea is that one has something like
[a, b, c]^T=
[
a
b
c
]
;
in laypersons’ language, the transpose
symbol ^T tells us to turn our old rows
into the new columns (which simultaneously
turns our old columns into the new rows).

in the language of the widely-used
TI-* calculator line, one has
[a, b, c]^T = [[a][b][c]]…
and this is starting to look
better and better to me right
in here.

but what one really seems to *want*
here is a quick-and-dirty notation
for expressing (what we will still
continue to *speak* of as)
column-vectors, as rows.

and i’ve noticed student papers using
< x, y, z > = [x, y, z]^T.
this looks like a real useful convention
to me and i’ve adopted it for my own use
until further notice.

angle-bracketed vectors have been useful
to me before. mostly, i think, in the context
of “sequences & series” typically dealt with
in about calc 2 or 3.

LANGLE x_0, x_1, x_2, … RANGLE
(i.e., < x_0, x_1, x_2, … >
… “angle brackets” are special characters
in HTML and so i prefer to avoid ’em)…
in either notation…
represents sequence of objects
LANGLE x_n RANGLE
(which is of course *not* the same
as the *set* R={ x_n } = {x_0, x_1, x_2, …}
[the set of values taken by the function
f(n) = x_n
on the natural numbers NATS:={0, 1, 2, …}]).

this usage actually *extends* a usage,
ideally introduced and maintained earlier
in a given presentation (class or text or
who knows maybe someday even both at once)
using angle-brackets for (finite-dimensional)
*vectors*.

LANGLE 3, 4 RANGLE
now represents the vector that, ideally,
we would represent in some other part of
our presentation as [3,4]^T…
a *column vector*.

i remark here that meanwhile
(3,4)
represents a so-called “point”
in “the x-y plane”… an entirely different
(though closely related) object.

we pause here and take a deep breath.

i’ve pointed at two distinctions:
sequences-as-opposed-to-sets and
vectors-as-opposed-to-points.

many textbooks… and many instructors…
are *very sloppy* about keeping these
(and many other suchlike) distinctions clear.

the *notations* used in *distinguishing*
the distinct situations in each case were
“delimiters”: pairs of opening-and-closing
symbols used to mark off pieces of code
meant to be handled as single objects.

delimiting conventions are vital even in
ordinary literacy (“you see? he” sa)i(d.
and i claim they’re all the more so in maths
(since we get fewer and weaker “context clues”
when the code gets munged [as in the example]).

and students’ll just leave ’em out altogether
if they think… or god help me, know… they
can get away with it. failing that, choose
randomly (itt…oghm,k…).

failing that, “well, you *know*
what i *meant* was”…

too late, too late. here endeth the sermon.

in our next episode of “who stole my infrastructure?”:
the dot product. when they came for the opening-apostrophe,
i pleaded and begged. when they came for the
sign-of-intersection i raved incoherently.
never had a chance, no hope, no hope. doom doom doom.
can somebody pick up the torch, here?
i don’t think i can go on much longer.

vlorbik on punctuation for the twenty-twelve.
more clarity!

written as a comment to
sue v.’s
are (k-12) math textbooks getting worse?
(with particular reference to its link to
annie keegan’s
afraid of your child’s math textbook?
you should be.
)

google trimmed the top off in the preview.
they’ve rejected me for going on too long before
so i tried editing it into two comments. but
then i kept getting the “doesn’t match the
prove-you’re-not-a-robot-gizmo” message regardless
of how careful i was. to hell with it.
i’m never playing *that* game again…

thanks for alerting me to
annie keegan’s piece.
math texts have mostly
been worse-than-useless
for some time but the
deterioration continues…
and somehow the process
continues to fascinate me.
good to have another “inside”
source.

the elsevier boycott is a whole
different can of worms… *this*
giant might just get brought down
by the faculty. the motherlode
is this astonishingly-well-researched
journal publishing reform page.

one has about as much hope of fixing
the textbook industry in the large
as of shutting down the war machine
or getting USA on single-payer health…
it would require a *radical* reform
of our entire system of goverment-
-by-global-capital (and probably
wouldn’t be pleasant… cf the french
and russian revolutions and their
subsequent reigns of terror…).

so i’ve given up hope for it
(that’s what’s so strange about
the fact that the rotting corpse
of textbook math-ed *does*
continue to fascinate me…).
still, *some* radical change
is likely and that right early
(i just don’t *hope* for it).

any survivors of the whole ordeal
that for some reason want to create
some math textbooks would do well
to dig up some shaum’s outlines
and dover books and whatnot:
much cheaper and much more useful
than contemporary USA eyecandy-
-weighing-a-metric-ton doorstops.
they’re available even now to faculty having
the power actually to *choose* their texts…