topology has been joy-rioted

whats panarchy like these days?

everyone's week sucks. equivalently, it wasn't anyone's week. time for another week now.

the insane effectiveness of the BLOCK button from high school.

OH AND THE WARN BUTTON

aim was my favorite computer game.


god and then it turned so dark, with allow lists.

+it turns out i was making too big a deal out of things!!!!! i love when that happens
-i can't find my ipod.

i don't usually do these, but this one is fun.

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* Grab the nearest book.
* Open the book to page 56.
* Find the fifth sentence.
* Post the text of the sentence in your journal along with these instructions if you want to.
* Don't dig for your favorite book, the cool book, or the intellectual one: pick the CLOSEST.

in my case, it's kind of lame: jean-pierre serre's local fields was the nearest book, and the sentence is

Decompose the rational function 1/f(T) into a sum of "simple elements" a_k/(T-x_k), and determine the a_k by the usual procedure.

1. one small remaining slice of fake meat quesadilla that jon and jamie cooked last night ( i slept over bc i had to get up early to potentially sub for nick cotton's class)

2. three relatively small pasta shells stuffed with spinach and cheese and mushrooms and covered with marinara sauce

3. a lot of blueberry kugel

4. two servings of yogurt, with granola and blueberries

5. two pieces of sour dough bread with artichoke spread

6. a can of corn chowder

the point is that i should stop, but i don't want to.

sunset rubdown concert was good. i am really into twitter now and only post here occasionally as a result, it seems. these things ebb and flow though, i have noticed. i'll be back. word.

i have been incapable of moving myself for like two hours by accident.

it is like god wanted me to solve differential equations and has been punishing me ever since for calling him out on how much they suck. so i'm TAing the course. i have been grading diff eq homework since fall of 2003.

that's ok. it's dull, but it's easy and takes so little time relative to other things.
i'm fantastically hungry and think i'll head to baltimore.

everyone should get a twitter. it's like facebook status without the facebook.

outside the coop, which is not known for its john-mayerishness there was a john-mayerish guitar player. he wasn't untalented as a guitarist or a singer, but his sensitive vocals were pretty grating. anyway, as i munched on a delicious burrito, he started playing a few tunes he had written. then he said something along the lines of "this next one's not by me folks. it's a tune from jump little children called 'mexico.'"

omfjump. it's so improbable, i thought i was dreaming. JLC is from charleston, but theyre-- they were-- pretty centrally rooted in NC, having met at the school of the arts (where my mother taught english, and where her friend's daughter dated the lead singer jay clifford). i saw them many times late in high school. chris garrett had a crappy autographed JLC poster which i earned from him for some reason, which i hung in my room at panarchy (the penthouse) and which garrett jones was like "Who is this band?" in response to visualizing. the only point of the poster was that i vaguely knew that it was cool to be into bands that were a. local b. unfamiliar to everyone, though i didnt have the foggiest clue how much work that would be.

"mexico" is not a bad song. i heard the premiere of it by JLC themselves, once, at the Carrboro arts center! this guitarist played it well, and arguably sang it better than jlc themselves, but it's not a good song for a one man band because it features an accordion, which he didn't have.

god it's like flesh is the theme of the day. everyone is all flesh flesh flesh flesh flesh

i lost my phone

i am existing in a moment of terror regarding russell's paradox.

if i stay in grad school, i will probably not get to be a professor at a decent school. on the other hand, if i drop out of grad school, i will definitely not get to be a professor at a decent school.

guys. i think i have found my career. i should take algebra quals. i'm serious. i'm teaching the algebra qual review session tomorrow, and we're going over an old qual, so i sat down and did it today. what a complete joy it was. it is the only area of human communication where i've ever felt fluent.



I will give an example that someone who's never done math before can enjoy (I hope).

A GROUP is collection called G, consisting of elements and an operation called *, such that
1. there's some element called 1 where for any x in G, 1*x = x and x*1 = x
2. * is associative; that is, (x*y)*z = x*(y*z)
3. each element g in G has an inverse, h, where gh = 1 and hg = 1.

Examples:

1. take G to be the set of nonzero real numbers and take * to be ordinary multiplication. It's associative, the element "1" is the element that we always call 1, and the inverse of a real number x is just its reciprocal. (You have to throw zero out because it doesn't have an inverse)

2. The "trivial" group is the set {1} where * is defined the only way possible: 1*1 = 1.

3. The group Z2 has two elements called 1 and x. Let's define * (it turns out there's only one way to define it). Axiom 1 says that 1*1 = 1, 1*x = x, and x*1 = x. So we're left to try to find x*x. Well, axiom 3 says x needs an inverse, and 1 isn't x's inverse since x*1 isn't 1. So x must be its own inverse, since there's nothing left to work with. That forces x*x to be 1.

4. This one's related to the symmetries of an equilateral triangle. G is the group of the following "words": {1, r, rr, s, rs, rrs} where the multiplication rule is: to multiply two words together, first write them next to each other in order, then erase any rrr you see, any ss you see, and turn any sr you see into rrs. (the empty word is 1). Examples of the multiplication:

rs * rs = rsrs = r(sr)s = rrrss = (rrr)(ss) = 1 (so this proves that rs is its own inverse)
rs*rrs = r(sr)rs = r(rrs)rs = (rrr)(sr)s = ()(rrs)s = rr(ss) = rr

(it's not obvious why * satisfies rule 2 above-- trust me)


What's interesting about this example is that it proves that a group does NOT have to satisfy the commutative axiom a*b = b*a. For example, r*s = rs, but s*r = rrs.

5. The integers form a group, but only if you interpret * as meaning + and 1 as meaning 0. The integers don't form a group when * means "times" because integers greater than one don't have inverses.


RIDICULOUSLY FASCINATING ALGEBRA PROBLEM: Let G be a group and suppose that G consists of a PRIME NUMBER of elements. Prove that G DOES have to satisfy the commutative law.

That one's probably too tough to solve from just the definition of a group, but this next one is do-able.

RIDICULOUSLY ENJOYABLE ALGEBRA PROBLEM: Let G be a group and suppose there are exactly 4 elements in G: 1, x, y, and z. prove that G satisfies the commutative law. (hint: make a 4 by 4 multiplication table for G and use logic to fill it in).

on a saturday night and are easily prone to nostalgic hysteria (WOMB DISEASE):

1. google street view your old haunts

older readers may remember my revelation of september 2005 that a position is something that one posits. it came to me during a hurricane in an airport. i was taking anti-anxiety medication.
FALSE
think about it
a supposition isn't something that you supposit
the opposition isn't the set of folks that opposit
a proposition isn't something that you proposit

and so on. a position, of course, is a manner in which one poses. a quick google confirms that "posit" was first used in english several centuries after "position."

i worked all day and didnt finish till 10:30 with no interruptions and it was wonderful

i lost my pants at pantsarchy
it turns out that perl and respectability are intertwined but non-intimately
i am getting distracted by programming when i should be studying. but soon i'll get distracted by studying when i should be programming, so i'm not worried.

suddenly 2-adic numbers seem more rustic than rustiality proper?

j'ai brisé quelques coeurs