## Archive for the ‘Life Story’ Category

i’ve been doing more shelving lately

even than usual… even unto moving

around actual shelves. whereupon,

strictly speaking, one is “decorating”

(rather than “shelving”, rightly so-

-called). but, then again. “all the

arts are one art”, as the saying goes

(or eventually will, if i get my way).

anyhow, here’s a shot about stuff about

the former “jugoslavia” (Југославија).

also some random furniture and whatnot.

you can see the mac whose built-in camera

took all three shots (in about the middle

of the mirror). here‘s a shot from

2010 with a different macbook & camera.

get away from me with your phony sympathy

i can see what you want in your eyes…

get away from me with your lies

(2009; now with much smarmy spam).

there is, indeed, one more fly

caught in the honey here than

in the entire collection of flies

i’ve ever caught in vinegar. also,

by one of those weird coincidences,

there’s a vinegar bottle right next

to the inverted honeybear. if the

lid had been airtight, all the goop

would’ve settled to the bottom with-

out making it quite so *damn* far… and

wasting a bunch of food and a little

time. and a fly, of course.

skynet wins; lifeforms lose.

so what. serves ’em right.

mostly.

meanwhile. i’m still trapped

in this stinking painful “body”

until the payoff. so what.

(more embarrassing whining

edited out here a few hours

after the original posting

of this piece)

seven times seven (e.g.)

7 principles (UU) the hymnal

7 days (_genesis_ & dylan) gods & traditions

7 seals (& churches; _revelation_) pointless lies

7 planets (& 7 “sisters” [“pleiades”]) science & mysticism

7 ages of man (_as_you_like_it [act 2, scene 7]) whining schoolboy; mere oblivion

7 deadly sins (dylan again [wiburys]; PALEGAS) i’m confident, you’re proud, he’s arrogant

7 colors (ROYGBIV & MRBGPYO) i have no idea what this means; leave me alone

too many is never enough

7 notes of the (major scale)

big theme: arts & sciences

(we UU’s are print junkies;

our strength & our weakness)

7 dwarves of _snow_white_ (who knows?)

(more self-pitying drivel cut here)

i’m planning on a campus trip monday

so look for me at bernie’s afterwards.

i might even stay for the monday medley.

anyhow, *i’ll* plan on banging around

a bit out on the smoker’s deck or what-

not.

i’m going to SPACE next week.

it’s columbus ohio, so the list

narrows down pretty quick:

the “arnold classic”, SPACE,

and, um, let’s see… there

*must* have been something

else…

“ameriflora”, maybe, in your

dreams. “miracle mile”, back

from the “miracle” days of

the long-gone late-great

thriving american working class

that shopped (until it dropped)

there. no. never mind.

the chief attraction of columbus

for *me* is that this is where

i *am* (moving around… or

even moving *stuff* around…

is *much* harder than they’d

have you believe…; & of course

the *next* best thing about

columbus is that *madeline*

lives here (and our happy home

*is* our happy home, much to

my surprise). and *staying*

here keeps me this way (happy).

it’s (1) cold (2) cruel

world (3) out there.

the (very existence of)

the billy ireland museum is,

enough to put columbus *somewhere* on

the comics “map”… and there’s already

a better list of local-and-quasi-nearby

talent at the “space” site… so let

me just give a shout-out to ray (!!) t

and “max ink” (still working as far as

i know); one more for glen brewer (even

though i think glen has quit the scene;

his _askari_hodari_ was, for me, very

much a local highlight).

everybody knows about _bone_;

it won’t escape my notice here

that the astonishing paul hornschemeier

lived here, too, when he was getting

started and i met him (and he drew

a cover for my zine gratis… eat

your hearts out). in fact, ghod

*bless* columbus. good night.

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…

today’s writing project.

i played guitar (and even talked a little)

in church today, too, so it’s been

a pretty productive day for a sunday.

(i suppose. now that i think about it,

monday morning deadlines have led me

to many a *highly* productive sunday

here at the grading table. and grading

is the actual *work*…)

********************************************

Let f(x) = x^3 + x + 57.

(Find all x s.t.

f(x)\equiv 0 (mod 125).

)

Since 125=5^3, we begin by working “mod 5”:

f(0) = 57 == 2

f(1) = 59 == 4

f(2) = 67 == 2

f(3) = 87 == 4

f(4) == f(-1) == 50 == 0 (mod 5).

So f has exactly one “mod-5 root”

(namely 4) and we consider

f'(4) = 3(4)^2 + 5 = 21 == 1 \not == 0 (mod 5).

This means that 4 is a *non-singular* root.

Hensel’s Lemma (HL)

now tells us that there is

exactly one root of f (mod 125).

But now, since

f(4) = 4^3 + 4 + 57 = 125,

we are done:

x=4

is the *only* solution to f(x)==0 (mod 125).

*************************************************

Let g(x) = x^3 + 10x^2 + x + 3.

(Find all x s.t.

g(x)\equiv 0 (mod 27).

)

Since 27=3^3, we begin by working “mod 3”:

g(0)==0

g(1)==0

g(2)==2 (mod 3).

Next, we’ll compute g'(x) = 3x^2 + 20x + 1

and evaluate it at each of our “mod 3” roots:

g'(0) =1 and g'(1) = 24 == 0 (mod 3).

The root at 1 is *singular*

(so “HL” isn’t helpful).

If “1” were lifted to a mod-9 root, x,

we would have x \in {1 +k*3} = {1, 4, 7}.

But

g(1) = 15 == 6,

g(4) = 231 == 1, and

g(7) = 843 == 6 (mod 9),

so there is *no* mod-9 root of f

satisfying x == 1 (mod 3)

(and so certainly no such mod-27 root).

The root at 0 is *non*-singular.

Since g'(0) = 1, its “mod-3 inverse” is

\bar{g'(0)} = 1.

“Plugging in” on “Hensel’s Formula”

(we have a_j = a_1 = a = 0;

our “f” is called “g”)

a_{j+1} = a_j – f(a_j)\bar{f'(a)}

(Display 2.6 of [NZM]) gives us

a_2 = 0 – 3(1) == -3 == 6 (mod 9).

Repeating the process,

a_3 = a_2 – g(a_2)\bar{g'(a)}

a_3 = 6 – 585(1)

a_3 = -579

a_3 = -(21*27 + 12).

a_3 == -12 == 15 (mod 27).

Our one-and-only solution

to f(x)==0 (mod 27) is x = 15.

(The result checks readily

[a calculator is helpful]:

f(15) = 5643 = 209*27 == 0 (mod 27).)

*************************************************

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”….

i’ve just signed up for the math circle institute.

so i’m rereading *out of the labyrinth*

(here’s jesse johnson’s review in the *notices*)

and looking around a little on the web.

two old blogpals i’ve never yet met

are also planning to be there; here are

relevant posts by sue van hattum and jd2718.

and another favorite blogger, ben blum-smith,

went back in ’09.

and, wow, kate nowak’s been there too.

and, double wow… i nearly forgot…

michael goldenberg (i’ve “known” him

longest of all… anybody remember mathedu?).

there’ve been math circles both here

in columbus and back home in bloomington.