## Archive for the ‘Life Story’ Category

here’s the seasonal doo-dads again,

updated. more stuff. also the bob

dylan section has been relocated;

visible but unrecognizable from here

are some CDs & cassettes, a bunch of

books, and an LP-sleeve with cover

art from several early albums. bob

is god around here. other artists

have (smaller, lesser) such sections

back in the audio-files room (where

most of this stuff was hitherto).

all this just to the right of the

mirror. there’s a foreign-language

section in there too.

self portrait with comix stuff & art

supplies. happy days, everybody!

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).)

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