none so blind

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
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
things t in A and
writing out their respective
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*?


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