## Archive for the ‘joyce’s milkmaid’ Category

i’ve typeface-ized the “formula” stuff

but the point here is the english.

tonight i encountered the passage

Since there are (p-1)/2 quadratic residues & 1^2, 2^2, …, [(p-1)/2)]^2 are all the residues, we need to show that the quadratic residues modulo p are all distinct…

and, after much wailing and gnashing

of teeth, decided that the best spin

i could put on it would be

to *omit* the first “the*

and to replace the second “the”

with “these”:

Since there are (p-1)/2 quadratic residues & 1^2, 2^2, …, [(p-1)/2)]^2 are all residues, we need to show that these quadratic residues modulo p are all distinct…

(which “works” in its context

as the original passage certainly

does *not*).

they should give medals for this kind

of copyediting. this is *hard work*.

not that it does anyone any *good*,

mind you…

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*?