Iwakan

Heart Growing Fonder, Anyone?

2012-01-10T10:57:00.000-08:00

Sorry for the long absence, but I had basically no internet access for the last month. Although, from the looks of the comments, nobody really noticed. Well, back to the mathzzz.

Mammon, You Been on My Mind

2011-11-29T12:14:00.000-08:00

Here you go, an unfinished product, but a product nonetheless. Forgive the eye rhymes and whatnot; it's just a goofy little song that resulted from posts/comments. Also, I'm not sure if "My" should be capitalized or not:

Never met a man named

Nebuchadnezzar

I guess he was

One of a kind

I ain’t sayin’

It can’t happen never

That Mammon, you

Been on my mind

Maybe Judas’s little sister

Or a long lost cousin

Needed a new heart

And a little more time

Thirty pieces of silver

For a simple operation

Or maybe, Mammon, you

Been on my mind

I can’t be the only one

To think the golden calf,

And I ain’t sayin

It’s a sign

Looks like a chargin’ bull

By little more than half

But Mammon, you

Been on my mind

The joke is really just a reference to a Bob Dylan song, "Mama You Been On My Mind." I figured it was obscure enough that nobody would get it. I was busy writing better songs, so this one is kind of a throwaway. It's good to write throwaway stuff sometimes, I figure, especially if it gives me practice in different keys. This one's written in F, which is not so difficult to play in, but sort of hard to sing in. I recently wrote a (better, in my opinion) song in D (!!!), which means two sharps for anyone who doesn't know. More sharps is generally more difficult, but D is a sort of particularly strange key for me because I don't have a D harmonica, and playing the blues in D, besides maybe being kind of weird historically, would require a more functional G harmonica than the one I have, which is held together only partially by a liquefied rubber band.

In terms of lyrics, choosing a structure where the last line is always the same or just a slight variant on the same line is a convenient way of churning out a song but makes it difficult to fit in what you want to fit in. The third verse demonstrates that, I think, since there's no natural way to phrase it that doesn't require the other lines to end in something like "calf" or "bull" and almost nothing rhymes with the former, while the latter seems only to rhyme with three+ syllable words, like "syllable," which make for awkward lines. Anyway, I challenge you to do better, since I think it's pretty clear how to structure a verse.

Excellent

2011-11-19T12:49:00.000-08:00

Olbermann owns Bloomberg. Hilarious, Keith. Too bad it's on a channel nobody has.

Songwriting Potential

2011-11-08T16:35:00.001-08:00

I can't have been the first one to notice how reminiscent of this this guy is. Feel free to build your songwriting career as the poet of OWS on this observation.

Well

2011-10-29T04:35:00.001-07:00

Don't that just beat all. Literally.

Wow

2011-10-28T05:14:00.001-07:00

The best headline I've seen about it: "You can't spell 'Cardiac' without 'Card'"

Motte

2011-10-12T20:20:00.000-07:00

What the what? On a night when Carp can't locate pitches, this guy steps in and does that? Not just him, yes, but that's just electric pitching.

Sports Writing

2011-10-06T09:29:00.000-07:00

There's a blog I read regularly which has a few posters and covers politics, sports, literature, all sorts of stuff. Today there is a lengthy piece detailing the Red Sox's late season collapse, and I thought people who like quality sports writing would enjoy it. That's all.

Lekach

2011-10-03T08:24:00.000-07:00

Since nobody seems to like my lengthy, math-heavy posts, I'll make a short, non-math post. It was recently Rosh Hashanah, so to celebrate, I made this Lekach, a Jewish honey cake. I found the recipe online. It's got raisins and walnuts in it and is pretty good. Think more like zucchini bread than actual cake. My non-practicing Jewish housemate made matzoh ball soup, which for him is really more like chicken noodle soup with matzoh balls added because that's way better than just chicken broth with doughballs. Regardless, it was pretty good. L'chaim!

Continuing the Discussion

2011-09-06T09:11:00.000-07:00

There's an old saw in mathematics that a mathematician is a machine for turning coffee into theorems. There's a newer saw that then says a comathematician is a machine for turning cotheorems into ffee, but that's a bit of a category theory joke. So, I've posted a picture of my new coffee cup for reference into how much of a functor I am lately. Anyway, I thought Pops raised some interesting points in the comments to my second to last (is "penultimate" appropriate here?) post, and for lengthy discussion, the blog post format seems more apt. I had been using this cup to hold change, by the way, but I decided it would be more convenient just to drink two of these instead of five normal cups, and it amuses me.

First, abelian groups. Or maybe Abelian groups. I'm not sure if that should be capitalized, as it's a common noun if we compare it to similar terms, such as simple group or finite group, but it's named after Niels Henrik Abel, who was quite proper. Regardless, I'll catch you up on what that means. A group is a set with a well-behaved "multiplication," that is a set G, and a function m: G x G -> G, that is associative, and the set is equipped with an identity and inverses. Generally, we drop the m notation and just write it like multiplication, so that all we require is that for all a,b,c in G, we have

a(bc) = (ab)c

an element e in G such that

ae = ea = a

and an element a^(-1) such that

aa^(1) = a^(-1)a =e.

You'll recognize this as being pretty normal, since all the sets of numbers you've ever worked with should meet these conditions for addition, and if you remove 0, they'll work for multiplication, too. Square matrices of a given size provide another convenient example for both operations, as long as you restrict to invertible matrices in the multiplicative case. If you don't know what that means, it just means matrices that meet that last condition. Certain sets of functions also provide common examples, but I won't go into too much detail.

The matrix example is nice because if you've ever done multiplication with them, you'll notice that AB = BA is generally not true, so we have an example of a non-abelian group. Abelian groups are groups where the multiplication does commute, so they are especially nice. Real numbers, rationals, integers, and anything you can come up with built around those will probably be abelian.

A group is called finite if, unsurprisingly, the underlying set G is finite. A nice example would be integers modulo an integer, where the "multiplication" is given by addition. To make that concrete, take all the integers (positive and negative) and divide by a fixed integer, say 4, but stop at the remainder step. You'll notice that you can only get 0,1,2, or 3. Now, choose two integers and add them, and then take their remainder when divided by 4. You'll notice that you get the same result whether you took the remainders first and then added or if you added first and then took the remainder, as long as you interpret adding remainders 2 + 3 = 5 to mean the remainder of 5, which is 1, etc. So it makes sense to add remainders, and you get a nice operation that maybe you never thought of before. You get weird looking relations like 2 + 2 = 0 and 3 + 3 = 2, but that's group theory for you.

The point I was making about finite abelian groups is that even though there are an infinite number of them (in fact the class of finite abelian groups is a proper class, not a set, unless you mod out by isomorphism), they are easily classified. Every finite abelian group it turns out is just a direct sum of this type of group, where the remainder is taken after division by a prime power. A direct sum just means an n-tuple in this case. It seems to me that chemical reactions should behave in a similar way, that more complicated molecules could be thought of as sums of simpler molecules, so that we should always be able to do arithmetic in higher molecule spaces using arithmetic in lower molecule spaces, if that makes any sense. Maybe not, though.

Now, on to the story that amuses me. As I mentioned in the comments, a lot of my students seem incapable of thinking, or at least content to go on avoiding it for as long as possible, so they just shotgun a bunch of terminology every time they come to a question they don't immediately understand. I like to use this to amuse myself and see if I can get them to write unnecessary things that they otherwise would never include in an answer. So, for example, one time we had a lab that focused on a non-parametric test, a permutation test. This type of test basically works on data that is in two groups, and we want to see if permuting which group each datum is in affects anything. If not, then we can attribute any differences we see in the groups to the randomness of the sampling. So, it requires a computer to generate random permutations of data, which is something computers are notoriously bad at doing. In fact, they are incapable of doing anything random by the deterministic nature of their operation, so programmers get around this by making the computer take strange inputs like the number of milliseconds we're at, and running them through bizarre functions that should produce seemingly random outputs. Of course, it's not random, so numbers generated in this fashion are called pseudo-random. None of this knowledge is necessary to explain how the test works because you could do it manually by generating random permutations yourself, but unless you have a few years to kill, I wouldn't suggest it. So, I decided to talk all about pseudo-random numbers, and lo and behold, students' lab reports contained all sorts of usage of the terms "pseudo-random" and "deterministic," which made me chuckle. Keep up the good work, bio department!

Mirepoix

2011-09-05T18:10:00.000-07:00

Happy labor day to all. I was sitting around doing very little, wondering what to make tonight, when I noticed I had the requisite onions, carrots, and celery to make mirepoix, though I couldn't remember the name and had to do some Wikipedia-ing to find it. Regardless, Google didn't fail me in finding an easy recipe which used it. So, I present the fruits, or rather, meat and vegetables, of my labor:

How is it? Pretty good, but not mind blowing, as I expected. I like it, and I have to hand it to the French for coming up with mirepoix, which seems like it would be a good base for many a delicious dish, but I also understand why we order out for Chinese food instead of French. That is, when you order food, you are hungry now and don't want to wait for food to simmer for two hours. Also, bay leaves? A grand conspiracy if I have ever seen one. At best some iota of flavor only after waiting hours. I confess I didn't have the thyme (haha) to do this recipe right, but I imagine that that didn't really change the outcome. On the whole, though, I was pleased with the outcome and would vote a solid would make again if I have the time. I accompanied the meal with Shock Top instead of the recommended sauvignon blanc, but that's thanks to the archaic alcohol laws here in Pennsylvania, which make it possible to buy wine only at liquor stores, of which there aren't any within walking distance. Also, despite Andy's best efforts, all red wine just tastes like weird grape juice to me, and all white wine just tastes like, well, slightly different juice. Shock Top is a kind of meh (we said "meh," M-E-H) Belgian-style witbier (wheat beer) with some orange in it. It's alright, but I can only drink about two before it starts to act strangely in my stomach. On the plus side, it's brewed in good ol' St. Louis. Alright, that's it

Generalized Abstract Nonsense

2011-08-28T10:42:00.000-07:00

When people find out that I'm a graduate student in math, they usually react by asking something like, "what research is there in math?" which sort of baffles me. In my view, it's easy to see that not only is there a bunch of stuff left to be learned, but that unlike in other fields, there will always be more stuff to be learned. If anything, it's fields like biology and chemistry that should induce these sorts of questions because those seem like very finite systems, where we're just trying to figure out how a relatively limited number of objects act and interact. At times it seems crazy that we don't know yet how any reaction would work. Math truly is infinite in the sense that there is no limit to the objects under study, so it's a bizarre concept to me that people think there's nothing left to do.

I guess it's because most people take math classes that make it seem like a bunch of methods and never think beyond that. The other day, a guy asked me if I was taking things like "Calculus VI." I had to keep myself from laughing, but I guess it's reasonable if you just keep your head down and are taught:

-how to solve one step equations
-how to solve two step equations
-how to solve quadratic equations
-how to solve trigonometric equations
-how to row reduce a matrix
-how to find a limit
-how to differentiate
-how to find a Riemann sum
-how to integrate
-how to find a gradient
-how to integrate multiple variables

Note that none of those things make it clear where problems come from or even what the objects you are dealing with are, so it seems like there is just a finite set of stuff to solve and it's been done by other people and this is how you do it. It's such a strange mindset, though.

Anyway, other math people sometimes like to ask what I do and by this point that almost makes me laugh, too, because I know that almost nobody will understand the answer, or at least not have the patience to understand it. If you do research in any field, you are probably familiar with the phenomenon that is hyper-specialization. We tend to look at people in a field as having a sort of homogeneous area of knowledge, and it's probably true to an extent, but when you're in a field, it seems so heterogeneous and disparate that you would never have any chance of knowing what the guy down the hall actually does beyond being able to specify a general subfield.

It's funny because grad students don't know anything (and I include myself here) but we're starting to specialize and so we learn that these things are important and these other things can be ignored, but our friend is learning just the opposite. I have a friend whose office is right near mine who studies compositions. I actually had to look up whether it was compositions or partitions the other day because I had a sum that looked like it was over compositions of an integer and I wanted to know if that was the right term. For reference, she deals with ways of adding integers to get a certain integer. For example (2,1, 1) and (3,1) are compositions [I think, I don't deal with these objects and have little interest in them] of 4. She deals specifically with random compositions and the distributions of things related to them. I don't really know, and though she is good at what she does, I can't ever bring myself to read what she writes because it looks like what I like to call "the wrong kind of math," which is just page after page of algebraic manipulation of sums and occasionally "Big Oh"-notation, which is generally just a sign that I won't enjoy it.

She won't even ask what it is I do because it makes no sense to her.

Another friend likes graph theory and wants to do research with that, though it's hard because almost nobody does that here. He's asked me a few times how categories or diagrams work because they're objects he's never dealt with and I've tried to explain it in terms of directed graphs, to limited success. Any other approach is like Chinese to him, but I think he gets some of it.

So what do I do? I am supposed to be working on a theory of curved A-infinity algebras that parallels non-curved A-infinity algebras, which I guess are pretty well understood and are rather important to string theory, though the physical systems they model are beyond my knowledge (this is another peculiar phenomenon of mathematical research). Of course, this is just words to almost everybody. It doesn't help that it is a rather abstract algebraic setting and most of the grad students I know hate abstract algebra to a certain extent.

I've often thought of people, at least up through the undergraduate level, who self-identify as "math people" as being in two camps, the ones who liked algebra but not geometry in high school and the ones who liked geometry. Nobody likes trigonometry, by the way. In my view, people in the first camp don't actually like math; they like being told how to do things and then doing them. Unlike in things like literature where it is evident that some thought will be necessary because "there is no right or wrong answer," it's not clear that some math classes (algebra, as taught in high schools) just require application of techniques to many similar problems, and some require a higher level of deductive reasoning (geometry, as taught in high schools). Almost needless to say, "real" math people tend to look down on "fake" math people.

Recently, though, I've come to think of it more like a spectrum, as those liberal arts people are so eager to append to human sexuality, or like some other, more complicated object (it almost irks me to use the word spectrum like this, since it has two specific uses in math that aren't like what "spectrum" probably makes you think of, but that's math for you). There are some people who like having some rules to work with, and some people like to have more rules, and some people like to have less. Some people want more tools, and others like to get by with as few as they need. To make it more concrete, I'll make it more abstract. Some people hate abstract algebra because they don't like not being able to commute variables, or not being able to say if a product is 0, then one of the factors is, too. Some people are comfortable with real numbers and are content to deal with the analytic properties and whatnot and others only like the integers and the concept of modding out or gluing spaces together frightens and confuses them.

Anyway, my point is that in order to understand what I'm learning about, you have to be ok with the concept of an algebra, and then with the concept of a graded algebra, and then a differential graded (dg-) algebra, etc. Some people don't like this concept even if they are ok with vector spaces, which is really basically what they are, minus the grading, maybe. So if I explain it, I always have to explain it starting there. So, to make a long story short, an A-infinity algebra is a graded algebra which has a bunch of "higher multiplications," which are really linear maps from the tensor powers of the algebra back to the algebra, which satisfy a certain equation stated in terms of a sum of all the possible ways of mapping from the n-th tensor power to the algebra. What it really means is that the higher multiplications are "associative up to homotopy." This means that while you maybe can't group any way you want and get the same answer, you'll get the same answer up to homotopy, which is a concept I don't even want to explain. Needless to say, this concept scares a lot of math people.

An A-infinity algebra A, by the equations it must have a linear map of degree 1 b_1:A -> A that squares to 0, so it is naturally a dg-algebra. To be curved, the algebra just needs an extra map that takes the 0-th tensor power of A back to A. The 0-th power is understood to be the underlying field. Anyway, this means that all the defining equations can now include this map, so the sums are different, and this means that in general b_1 won't square to 0, so it's no longer a dg-algebra in the natural way. This messes up all sorts of category theory type conclusions that were true in the non-curved case, and so it needs to be investigated, I guess by me. I guess also that that's enough for now, so later!

New Hat

2011-08-14T18:50:00.000-07:00

If right wing ideologues are going to destroy this country, the only reasonable response seems to be pushing further left. Go carryin' pictures of chairman me, and you ain't gonna make it with anyone, anyhow.

The hat is a souvenir from a Chinese girl in my department who just got back last week. I gave her a ludicrously jingoistic USA hat in return.

In Response to a Math Question

2011-06-20T22:08:00.000-07:00

I got a comment a few posts back about Graham's number and whether it larger than a googolplex of towers or some such thing. Let me first say sorry for not replying to that; I thought I had, but apparently just thought about it for a little and forgot to write anything up. The answer is I have no idea. I don't even know where you would begin trying to prove something like that. If you read the wikipedia link about Graham's number, then you actually know more about it than I do, since I didn't finish reading it originally and then forgot all about it until now.

If you don't feel like reading about what it is, suffice it to say that it is a positive integer that was given as an upper bound to a problem in Ramsey theory, which is a branch of graph theory. I don't really know much about it, but it seems like an interesting branch of mathematics, albeit one that I don't think about much. As for how large it is, I think only the word unfathomably suffices to describe it. Something like there aren't enough particles in the universe to save it in digital form.

In order to keep this post slightly less low-content, I'll mention that what amazes me is that even though numbers like Graham's number are basically impossible to get a handle on, in math we routinely deal with things that are much, much larger than that. For as large as it is, it's still a finite number (which is the same as a finite ordinal [sort of]!), and we deal with sets that are infinite all the time.

I think we sort of lose track of how big infinite is because we think of sets like the natural numbers, which are infinite, but we think of them in forms like

{1,2, ...}

which sort of hides the fact that there are huge things in there and it's almost easy to forget that.

Now, to blow your mind a little bit, which are there more of, non-negative integers, or non-negative even numbers? Intuitively, there are more non-negative integers since all even non-negative integers are non-negative integers. But consider the function f(n) = 2n. It turns each non-negative integer into an even non-negative integer, and it does it in such a way that we don't repeat anything and every even non-negative integer gets hit. So there must be the same number of them.

So it's natural to think that maybe there are only finite and infinite things, and in the literal sense that is true: something is either finite or NOT finite, but in a sense it isn't true. There are lots of infinities. For example, consider the real numbers. If you don't know what that is, suffice it to say consider the set of all sequences you can make of 0's and 1's. Now, if that set is the same size as the positive integers (or non-negative integers, or just integers, or even rational numbers), then we can count them, and we can make a new sequence by starting with the first sequence and setting the first entry of the new sequence to be the opposite of whatever the first sequence is. That is, if the first sequence has a 0 in the first place, choose a 1, and if it had a 1, choose a 0. Then move on to the second sequence and do the same thing with the second entry of the new sequence.

If you keep doing this for each sequence, you'll get a new sequence that differs from every sequence in one place, so can't be an element of the original set of sequences, but is clearly just made of 0's and 1's, so must be an element of the original set. So, there's a contradiction and you must have a bigger set than the natural numbers. In math terms, we say that the real numbers form an uncountable set.

Can we get even bigger? Yeah, just consider the set of all subsets of the real numbers. Then consider the set of all subsets of that set, and so on and so forth. Cantor proved that you always get a bigger set by doing this, so that there is no largest set. It gets even crazier than that, but I guess that's enough food for thought.

Hey Look What I Made

2011-06-19T08:17:00.001-07:00

It's noodle salad. It's the first time I made this kind of noodle salad, which uses Italian dressing and not mayonnaise. So that's pretty good. My buddy Phill had a cookout yesterday so that is what I made and people liked it. Not much else happening.

Take a Load Off, Fannie

2011-06-08T20:13:00.000-07:00

I realize I haven't posted in weeks, but I've been busy. Fortunately, that should all be done now and I get to go down, Miss Moses and wait on the judgment day. Won't you stay and keep Anna Lee company? So, maybe there will be a content post soon. Looking forward to weddings and Illinois.

Planet Waves

2011-05-08T12:29:00.000-07:00

It looks like I will have to follow through on my threats of pointlessly reviewing semi-obscure Dylan songs because the comments have been Slow Train Coming (it sounds like slow in coming; expect more terrible puns if I don't get satisfactory comments).

So, I've decided to write a brief review of Dylan's 1974 album, Planet Waves. It will be brief partially because there isn't that much to say about it. It's nice sounding because he's got The Band backing him up again and their version of "roots rock" is always pleasant and interesting, with them switching instruments and having multiple moving parts all at once, but lyrically there isn't much there. Most of the songs feel like they were written on a lark and they don't really address anything deep or have the layered meanings and references of John Wesley Harding. Anyway, here is my track by track review:

"On a Night Like This" - A strong opener because the band knows how to use accordion and have fun with a lighthearted song.

"Going Going Gone" - Sort of nondescript. The best line is probably "all that's gold isn't meant to shine," which is hardly up to his usual standards.

"Tough Mama" - Another upbeat number that The Band gets to have fun with. There's a little bit more imagery here. In a way it reminds me of his earlier song "Love Minus Zero/No Limit" in that it's a step up from most love songs which are bland and not descriptive. You would think if you were so in love with somebody to write a song, you would have plenty of reasons to enumerate, but usually all you get is blah about nice hair or eyes or something. Dylan steps it up here by painting you a picture of his "Tough Mama," though it doesn't come off as genuine as the earlier work. He gets bonus points for this line, though : "Today on the countryside it was a-hotter than a crotch."

"Hazel" - He's played this one in concert, so I have a live version, I think from The Band's Last Waltz concert, but other than them having played it together, I can't think of why he chose this song over any of his others. It's just a typical love song to "Hazel," who never really comes off as a real person to me. There's some nice piano driving the song, though, so that's fun.

"Something There is About You" - More fun stuff going on in the background from the Band, and this time it's under something at least fairly interesting. I don't know what's with the strange structure of the title, but something there is about it that I like. Also sort of notable for a mention of Dylan's childhood in Minnesota, which he never really talks about, "rainy days on the Great Lakes, walking the hills of old Duluth." :)

"Forever Young" - I'm sure everyone has heard this song. Most people are fans of the first version that appears on this album (the next track is another arrangement of the same song), but I like the second one better. Lyrically, it's a decent track and maybe the album's strongest, but I can't see it actually working as a lullaby, which is supposedly the intention. If you're going to write an ineffective lullaby, you might as well have the Band go crazy behind you, I figure.

"Dirge" - "I hate myself for loving you" and whatnot. It's pretty good, and more Dylan imagery. "Doom Machine," "just a painted face on a trip down Suicide Road," etc.

"You Angel You" - a song with "dummy lyrics," in Bob's own words. It's catchy, at least.

"Never Say Goodbye" - this song and its bass line keep getting stuck in my head, so there's that.

"Wedding Song" - Closing the album on a down note seems kind of odd, but it's not as if he didn't do that with "Highway 61 Revisited," "Blonde on Blonde," and "Desire." On the other hand, those albums were far less bouncy, so it's kind of odd. This closing track is ok, but not nearly up to the closing tracks of those albums. Meh

Alright, well that's it. Maybe the next post will be a bunch of nonsense about model categories.

Can You Guess Who?

2011-05-04T20:36:00.000-07:00

Can you guess who I saw tonight? The answer is Salman Rushdie. This wasn't like that episode where Kramer thought he saw Rushdie but it was just some dude named Salbas. He came here to talk about writing and novels and crap. He was kind of hilarious and almost made me want to read one of his books. Too bad I'm busy doing a bunch of math. But it's alright.

Comment!!!

2011-04-18T21:24:00.001-07:00

Comment away or I will start reviewing obscure Dylan songs!!!

Ain't No Good

2011-04-12T19:34:00.000-07:00

Every other Wednesday there is a seminar that lasts about an hour at most by a grad student in our department. The only people that come are other grad students because faculty have better things to do than listen to us talk about research or often just definitions of stuff that they probably know better/don't work with, and who else would come to a talk about math?

Anyway, I haven't given a talk and don't really plan on it, at least not any time soon, despite the girl who is in charge of it asking me multiple times to present just to avoid some of the less...enjoyable...people from talking more than once. I've only recently actually considered doing it at all since I've produced exactly sin(0) work until now, and the idea of presenting old problems or just introducing people to some area they aren't familiar with seems somehow more pointless than category theory (get it, because we generally want to move away from thinking of objects like sets, etc. by what "points" they contain and move towards thinking about the maps between such objects...?). But this quarter I am taking an independent study with a professor, pending official approval from the department head and whatnot on a form I had to fill out (for the question about how my grade would be evaluated, he said to write "by professor." haha).

Forgive my abuse of punctuation.

Anyway, it isn't research, at least not yet, but it's sort of close in a way, and may get there if I can master the small object argument (don't ask), so it seems more worthy of presenting. The main allure of it, though, is that if I talk about what I am doing to any other student, literally no one knows what I am talking about. Here's an example:

If a functor from a model category to a category with a class of weak equivalences that is closed under the 2-of-3 axiom takes trivial cofibrations between cofibrant objects to weak equivalences, then it preserves all weak equivalences between cofibrant objects.

That's called Ken Brown's Lemma, apparently. The wonderful thing about it is that it simultaneously says so much and so little. So, I may tell her that I'll do it, but I have to consider it more and make a bit more progress first. Also, I'm always wary of her invitations; she'll pull out your feathers for her brand new hat, and when she's done that, she'll feed you to her cat.

I've Been Listening To This Song Obsessively Lately

2011-04-07T23:22:00.000-07:00

In keeping with my obsession with Dylan and his seeming obsession with adverbs, I thought I'd title this post something like the above. I keep listening to "Buckets of Rain" over and over again. It's the closing track to "Blood on the Tracks," for those of you less versed in Dylan's repertoire, and one of Eric's favorites, if I recall correctly. There's something quiet and brilliant about it, like the sermon of a broken-hearted Minnesotan Buddha. Here's a gem:

I been meek
And hard like an oak
I seen pretty people disappear like smoke
Friends will arrive, friends will disappear
If you want me, honey baby
I’ll be here

Cool.

New Quarter

2011-03-27T15:05:00.000-07:00

I've got a shiny new quarter! We are on the quarter system, so this is kind of a pun.

So, what is on tap for the next few months? Class #1 is Complex Analysis, which is not just normal analysis but harder, but specifically analysis (think calculus) in the field of complex numbers. I don't know why but it seems like complex numbers are a thing that everybody who's had at least Algebra II should know about, but nobody seems to know by name. They're just numbers of the form a + bi, where a and b are real, and i is the familiar square root of -1. There are bunches of ways to think about them, but usually people think about the real numbers as being a line and the complex numbers being a plane where the real numbers are one axis and the imaginary numbers are the other axis. Other times people think of the complex numbers, with a "point at infinity" attached, as a sphere. Then the real numbers would form a great circle on the sphere, as would the imaginary numbers, or any other line, for that matter. The most important thing, though, is that this is the last of my "required" courses.

Class #2 is part two of Applied Functional Analysis, which I am taking just to fill out my credits and because the first quarter was almost laughably easy, so I'm assuming we'll continue on in that fashion for the next ten weeks.

Class #3, which I haven't gotten officially recognized as a class yet, but only because I haven't talked to the secretary over break, is a reading class with the professor who taught my Topology I & II courses over fall and winter terms. He asked me if I would want to finish (the relevant parts of) the book we had been using and then read some stuff about model categories and other nonsense, probably because I was the only one who liked all this abstract nonsense and diagram chasing and wasn't busy doing research about numbers in boxes or some such. So, I'm keeping busy reading and re-reading stuff until I can't think any more.

As far as teaching goes, I was expecting to be doing a recitation section or two for what I call "math for dummies," but the first years don't have any teaching experience yet, so they got all those, which means I am relegated to the tutoring center for nine hours/week. Until now, the most I've had in there is six hours/week, so I am trying to get my hours scheduled to days that aren't before large exams. Those are the worst days because all these people who have never gone to class and can't do basic algebra come in and ask you to basically teach them everything in a few hours, and it is frowned on to just tell them that that is stupid and they are stupid and should just drop their class because they will assuredly fail, even if it is true.

I should specify: there are a few types of students who come for help.

1. Students who come in periodically for help with specific problems/concepts that they don't understand - Most of these students are good and nice to work with because you can't do problems for them and then let them do similar problems, or just guide them through the problems step by step, or sometimes just casually watch over them as they work. Usually these students come from one of the many calculus classes or linear algebra, which is understandable, since linear is the first time that most people have to think abstractly at all, and sometimes calculus problems just involve seeing some clever transformation that isn't obvious the first time, but also sometimes they come from lower classes, trying to figure out when to apply what formula.

2. Hopeless students - These students are usually continuing education students or sometimes low-level people trying (often for the 2nd or 3rd time) to get the math requirements for their major done. These students are a huge pain to work with because while they try, they will never succeed, and you can't just dismiss them, because at least they are trying and aren't putting it off till the last minute. I don't know whether it speaks to the absolutely horrendous state of math education K-12 in the U.S., or if there is just a segment of the population that is completely incapable of reasoning or the use of symbols to further that reasoning. One of the biggest hurdles is people that, as I mentioned earlier, can't do even basic algebra. I really think that if you graduated high school without the ability to do everything in a typical Algebra I (I am talking h.s. or junior high level) class without any real thought or effort, you are basically on the same level as someone who is still sounding words out when they read and your school completely failed you.

The reason I can't figure out whether it is the fault of the educational system or of just some people is that people seem to lack a fundamental understanding of what they're doing, rather than the specifics of how to do it. For example, you are probably familiar with the quadratic formula, and most people that come in have at least that formula drilled into their heads. But if I give you the equation of a parabola and tell you to find x-intercepts, would you know to use that formula? People don't make the connection between an equation and a graph, that the graph is a set of points with coordinates (x,y) that satisfy a given equation. They don't seem to even understand what that means, i.e., that an equation is a statement which is either true or not. They can't distinguish between an equation and an expression, and instead just memorize how to solve equations and are baffled by what an equation, or any mathematical expression, for that matter, is saying. I don't know whether this is something that most people can be taught or if it is just something you have to work out for yourself.

3. Awful students - These are the previously mentioned students who don't care enough to do anything but care about getting passing grades. Another thing they love to do is try to make you do their take home quizzes/homework for them. Some of them realize that we won't just do their problems for them, but will do similar problems, so they "cleverly" copy their problems to another sheet of paper and then ask us to do those problems. I don't know why people think this will work. It is insultingly dumb and really annoying.

So that does it for my rant, and since this is already a basically impenetrable wall of text, I'll just end the update here.

Not Much Happening

2011-03-06T13:51:00.000-08:00

As the title would leave you to believe, there's not much happening. The term is almost over, which is nice because I won't have to deal with all the work that teaching (teaching assisting?) Data Analysis entails. It's not a horrible class or anything, but the grading takes forever since it's all explanations, not math. I often have to read through paragraph+ length answers despite the fact that all the questions can be answered properly in AT MOST two sentences. The problem is that the class is for bio major seniors who have spent the last four years learning to regurgitate terminology mindlessly, and who have taken to heart the lesson that the less you know, the more you should write. So, there are all these practically novella length completely wrong answers, which I have to read through. The kids that are good at it have started to learn how to be concise and right answers are generally easy to grade, anyway, because I can just comb through them for the right combination of words, but wrong answers take forever because I have to try to figure out what they are thinking (which is usually nothing) in order to give partial credit, and then I have to write something about how they are wrong or what they should have said.

They just had an exam this last week, which means the grading was even worse because I have to be more careful and the length of their answers has been stepped up War and Peace levels. One girl, who is almost surely the worst student of all time, actually wrote a whole page of nonsense that didn't even answer the question, and then a request for at least partial credit for addressing something tangential to what was asked. I wrote "this does not approach an answer" and gave her 0 points for that. They lose points with me for wasting my time with stuff like that. Other things I have written on exams include "don't write me a novel," "answer the question," "do this [with an arrow pointing to the directions]," and "baffling." That last one actually made some other TAs laugh. They are generally sympathetic, but not sympathetic enough to help grade.

Most of the classes have many sections, taught by a few instructors/TAs, and there are usually one or two TAs who just grade, which means when the low level classes have an exam, there's an all day grading session in the common area/break room/whatever it is called where the mailboxes and coffee are. I have been part of a couple for a class last spring, and it's almost nice because it's social and there is pizza. Of course, the social aspect can be not so great if you don't like the people you are working with, but sometimes I get jealous, since when I am grading exams, it is just me and the one professor who teaches the class in our separate offices for nine hours at a time and there is no pizza :(

On the learning side of things, there's not much happening, either. I have three courses this term, as I am trying to finish up all my course requirements this year, which means three courses per term. They're not bad, though.

One of them is applied functional analysis, which is probably the easiest course I have had here. It's like baby analysis, definitely a step down in difficulty from the analysis course I had here last year, which was intended to be preparation for the qualifier, so it was fairly rigorous. This course is for people who have already had analysis, but the book we use is for someone who never has, so a lot of the exercises are nothing new if you have a solid grasp of things like vector spaces and metric spaces. Since this post is already rambling and fairly low-content, I guess I will explain.

A vector space is just a set of vectors that meets certain basic algebraic conditions. This may sound daunting, but it isn't. It just means that you can add and subtract vectors and stay in the space, as well as multiply them by scalars (which basically just means real numbers or complex (!) numbers). The addition and multiplication have to behave nicely, too. They have to be associative and commutative and whatnot.

A metric space is just a set that has a distance function on it. I think I've talked about them before, and it's not super hard to figure out what is meant by a distance function, anyway. It just needs to tell you the distance between two points in a way that a distance does. For example, d(x,y) = |x - y| is a metric for any Euclidean space [n-tuples of numbers].

In this class, we are specifically interested in normed vector spaces, which is basically a vector space that is also a metric space, and the metric behaves like an absolute value, and even more specifically in inner product spaces, which are normed spaces where the norm (absolute value) comes from something that acts like a dot product, if that means anything to you. So, it's not highly interesting from my point of view, but it's alright.

My second course is abstract algebra, which is concerned with abstract algebraic (duh!) spaces, such as rings and groups and whatnot. I had a class in it in undergrad, and I haven't picked up a whole lot here, but it's nice to get the review and to learn Sylow's theorems, which are super useful.

My third class is my most interesting, so I arbitrarily numbered it third. It's algebraic topology, which I can only define in an abstruse way. Topology is generally the study of topological invariants, and algebraic topology is just a branch where these invariants are algebraic structures like groups. There's more to it than that, but I can't really explain everything. It's the field of study that primarily lead to category theory, which is probably the most abstract form of math. It's also very difficult to understand in my experience. A category in the mathematical sense is just a collection (not even just sets!!!) of objects with morphisms, which are basically just arrows between the objects that you can compose if the head of one points to the tail of the other. This makes everything basically into a category, and they can usually be thought of in tons of different ways if you just change what you want to be the morphisms, and ultimately you sort of don't care about the objects at all. It's very bizarre. Here's an example:

A group is an algebraic concept. It's just a set where there's a "multiplication," which is associative [ (ab)c = a(bc) ], and there's an identity element ,e, which acts like a 1. That is, ea = ae = a, and every element has an inverse, which basically means you can divide. Anyway, we can think of a group as a category with only one object, which is the group itself, and all the morphisms are multiplication by one of the elements of the group, so that all the arrows in the category point from the only object back to itself, so it's a very simple category.

For a totally different example, you can think of the collection of all sets being the objects of a category, and the morphisms just being functions from one set to the other. Since if f:X -> Y and g:Y -> Z, then we can compose the functions like g(f(x)), this makes sense as a category. Technically, we also need identity morphisms, but for each set X, the function i(x) = x suits works fine. So, this is a gigantic category. In fact, it is so big that the objects don't form a set at all, but rather a proper class. IT'S CRAZY.

Risk-y Business

2011-02-27T12:50:00.000-08:00

In case anyone was wondering, I tried to let that dude down easy, and he hasn't replied, so I assume he's feeling a little (-_-;)

Anyway, my students have an exam on Tuesday, and most of them had their last lab on Wednesday, so they generally wouldn't be getting the graded labs back until after the exam, but since some kids asked me for them, and since I am such an excellent TA, I came in today (Sunday) just to grade them. It's not particularly long or anything, but I will make sure they know how I slaved and slaved for their benefit, of course.

Grading took at most an hour, since I already had one of the two sections graded and since I am very lenient and tend to grade people that I know work together just once and replicate the grade across the group. So I had a bunch of time left over, and the math grad organization recently came into possession of a bunch of board games for the purposes of a board game night, which I didn't go to in order to play board games in Virginia, but I have the combination to the locker in which they are stored, so I decided to simulate some world conquest in my office. As secretary (maybe???) of the organization, I have a lot of pull as to what we do with our money (note: I took the job because there is no work and I am not even required to go to meetings), so I insisted we get Risk. There was plenty of money, so this was no issue. The president (my officemate) picked out the original version of Risk, as per the advice of the department board game aficionado. So here is what is different:

Not much.

There aren't III or V pieces, just oblong pieces that represent X's. The I's are in this version just wooden cubes. Interestingly, there's no brown, but there is pink. I am guessing that they realized that guys do not like to play with pink things in general. I assume that most people who enjoy Risk are men, as well as nerds. I also couldn't find in the instructions, which seem to be pared down for the re-release, how many armies each side starts with, but fortunately I remembered. If there are six players, each gets 20 armies, and for each fewer player, each side gets 5 more, by the way. If you only have two players, there's some sort of dummy third player, but I'm not clear on how that works because who plays Risk with two players?

I think a big part of the fun is the unofficial diplomacy that occurs when you actually have 3 or more (ideally at least 4) people playing that know how to play and don't get all butthurt when you inevitably break your alliance by smashing through their continent's defense. Some more unorganized thoughts about the game:

It's interesting how taking Australia first almost always ends not just in disaster, but in a particular kind of disaster. Almost every time I play, there ends up being a color that is almost forced to try to take Asia because there simply aren't enough continents for everyone to take a safer one at the beginning, and somebody has to get stuck with a bad position, including a couple territories in northern Asia. That guy basically has to try to take over all the undefended territories in a way that lets him maximize the armies along the border, which means for slow playing. Trying to take Asia in one fell swoop at the beginning is essentially suicide, so you get this weird thing where there's one guy with Australia whose goal is basically to get out of Asia, but has no choice but to go through Asia, and one guy who is stuck with most of Asia but no army bonus because he doesn't have Siam/India/Middle East, which is the Australian's path to expansion. But, because he's always taking these little undefended countries, the Asian guy gets to collect a lot of cards, which means he'll eventually get a set, and it tends to be at a time after the Australian guy has his continent but doesn't want to expand north because it would be trying to take Asia from the guy who has been trying to take it all game. What usually happens is that the guy with the set smashes through the border because the set will by that point outweigh the continent bonus, and likely will just take over Australia in a single turn. Maybe it is only due to using the usual rules for sets, which highly favors taking territories because the set values quickly outweigh everything else. I'm not sure what happens if you use the rules where sets only increase in value by 1 each time, but I do sometimes play that way, and it seems like a similar thing happens, in that I don't think I've ever played a game where the color that take Australia first wins.

Since I usually have to play by myself, I have to make sure to preserve features of the game that come from different people playing, and I try not to bias it towards any color or anything by making one guy do stupid things, but of course that isn't perfect. I always have a soft spot for the color that ends up being what I want to term the "roving empire," or maybe the huns of the game. Usually everyone's best strategy at the beginning of the game is to take a continent that that are set up to take, but as I mentioned, if you play with six players, there really aren't enough continents for this to work, so one player will inevitably end up losing this bid. This player never, in my experience, wins, but he's (pardon my androcentric pronouns, but generally all sides are me) also generally isn't really knocked out until later because eliminating another player requires a lot of armies, which nobody will have early in the game. So, he's just this guy who inhabits a non-claimed continent but can't take it from a more powerful player, meaning that his best chances lie in trying to survive long enough to get cards and hopefully establish himself again once the superpowers start fighting over the Bering Strait or something. In effect, he becomes this wandering army, trying to take weak territories, but not really holding onto them because the cards matter more than any individual territory if the continent is impossible to get. I think it's natural to root for this guy and much more fun to play than the guy who has to take the other strategy for a guy who lost his continent bid, which is to sit like a rock, collecting armies and hoping that somebody gets messed up. Probably just counting out armies is annoying.

Some places in the game inevitably get contested more than others, particularly ones that are on the boundary of two continents, and it's funny that for every one that mirrors some historically conflicted area, such as the whole Mediterranean sea, which reminds me of Rome vs. Carthage, or Greece and Turkey, or the middle east, or even 30 Years War-esque battles for Europe, there is an oddball, like Iceland vs. Greenland, two places which have probably never had a historic war, or North Africa vs. Brazil, which seems almost laughable if you look at an actual globe.

As much as I love Risk, the end game isn't very fun, and I usually just give up because I know how it's going to end and counting out 50+ armies for a set becomes tedious. I think the +1 rules are better for sets in general and probably should have started playing that way today but didn't, so I got stuck counting out too many armies, which is especially tedious without III's and V's.

Alright, well, that's probably enough for now.

Gaydar

2011-02-25T13:14:00.000-08:00

So, I went with my friend who happens to be gay to a meeting for a grad students' gay rights thing because he didn't want to go alone and because there was a free happy hour after the meeting. The meeting was alright except there was a Chinese kid and an Indian kid, neither of whom understood the icebreaker of saying which muppet you would be. I chose one of the two old dudes, by the way. The happy hour was fun and saved me having to make my own dinner. Maybe I should have specified that I am not gay, though, because some dude sent me an email, which I got this morning, asking me out. Oh, dear. (~_~;)

Takoyaki party!

2011-02-04T14:34:00.001-08:00

Since it's been almost a week since my last post, and since the trickle of comments has dried up on that one, I've decided to post some more pictures of my trip. One day, Mie's older sister, who has two kids, invited us over to make takoyaki. Before that, we passed the time playing sugoroku, which is a generic name for a type of boardgame that generally just involves rolling a die or spinning a spinner, etc. to decide how many pieces to move. So, like Candy Land, except without the candy theme. This particular game was all about ojisan gyaggu, old puns and jokes that older men tend to say. An ojisan is an uncle, but it's also the term for any older guy who isn't old enough to be an ojiisan, a grandpa. So, you would play like normal, and on certain squares, had to say one of these gags, which are very corny and dumb, so of course I love them. The little girl in the picture is Misato, Mie's cute-as-a-button niece, whom we often call Mi-chan. Her younger brother was with his dad, so it was just the three of us and Mie's sister (not in the picture), Kaori. I don't remember who won, actually.

Here's us making the takoyaki. Tako means octopus, and yaki comes from yaku, which means to fry or burn or bake or whatever. The character is 焼く, if you are interested. The character for octopus is 鮹　or 蛸, but neither is used very much. Anyway, as you can probably guess, takoyaki is cooked octopus. Specifically, it is little balls of dough with octopus (sometimes other things like shrimp, too) that are cooked in this special maker thing that looks like a hot plate. It has little half-sphere indentations, and you fill those up most of the way with batter, and then add the stuff that goes inside. You have to turn the balls to make them cook evenly and get a nice shape to them, which requires a bit of skill.

Misato is quite the little cook, so hers were probably the best. Apparently, I don't turn them fast enough, so mine get cooked more thoroughly, but I think it's better that way. We divided the hot-plate into territories for which we were each responsible for one, except Misato, who was in charge of her mother's territory, too. Despite that, she still had time to intervene in mine because from her and Mie's point of view I ran my territory rather like a third-world country. Regardless, they were delicious!

Misato and her mom gave us these matching hats for Christmas, which turned out to be pretty convenient because it was easier to find each other on the ski slopes with them on. But, that's a post for another time!

Belated Pictures of Sand

2011-01-30T13:18:00.000-08:00

I got pictures of my winter trip to glorious Nippon a while back, but I haven't gotten around to posting them yet, obviously, since it's one of those big projects, at least as blog posts go. So, I'll try to get them up with some sort of commentary about what we were doing, but it won't end up in chronological or logical or morphological or any other kind of -logical order because I've no doubt forgotten details in the time since and organizing stuff isn't really my forte.

Here we are celebrating our ascent to the top of the Tottori Sand Dunes. When I heard about the sand dunes, I figured it was just going to be like a long beach, but it turns out that the dunes are quite sizable and climbing up them is rather like hiking up a hillside except that the hillside is made of sand and thus more easily deformable under your feet. Forgive me for the topological terminology but I've been computing fundamental groups lately.

Perhaps this picture will give you an idea of how large the dunes really are. We hiked up to the top of the biggest dune we could see, which seemed to be the thing to do. It was cold and clear that day, so we were wearing winter clothing, which seems sort of odd against the backdrop of sand and sea.
My outfit, incidentally, was almost 100% Japanese made. The pants, jacket, and neckwarmer were all gifts from Mie, who apparently has a different idea than most westerners of what looks good on me. The shoes I bought last year in Japan, and the hat was a gift from Mie's niece, who should show up in a later post.

We weren't alone on the trip. Mie's friend accompanied us there. She lives in Tottori (the city, which is on the opposite end of the prefecture from Yonago, where we stayed), so she acted sort of as a tour guide. Her name escapes me at the moment because most of Mie's friends have names that end with -ko, which is very typical for Japanese girl names, but makes remembering them an exercise in frustration.

After tromping around on the dunes for a while, we decided to take a ride on a camel. But there was no real reason to do that, and it was cheaper just to sit on the camel and get our picture taken, so we opted for that. Also, I think we were sort of cold and tired at the time, so it was more practical. When we were sitting on the camel, it started making some weird noises, so the dude there had to calm it down, or at least we thought so. Mie's friend told us after that it was really just pooping and he was probably trying to get us not to notice.

Anyway, after that we headed back and I bought some pear-flavored soft serve because I had never had it before. Pears are a specialty of Tottori prefecture, so we never had it in Shimane. It was really good, even better than green tea ice cream, which is what I would normally get if I were eating ice cream in Japan.

Finally, here's another picture of me. I ran down to the ocean while Mie and her friend stayed up at the top. I suspect they didn't want to climb back up the hillside since it was rather a lot of work. Can you tell which one is me?

I was originally planning on posting more here, but there are too many pictures and I don't feel like spending the next two hours crafting a blog post, so it will have to wait. Until then, it's time for more category theory!

Eric

2011-01-06T06:43:00.000-08:00

I should have posted something earlier, but I didn't. I don't know what else there is to say about Eric, but here is a fitting song from an album we both liked. Maybe it's a little obvious, especially given the first lines of the song. It's weird because neither of us had this music during college and we both came upon it afterwords, so it's just another one of those things that we only got to share indirectly.

I was in Japan when Eric died, which was sort of worse. Japan was a thing we both got to experience for a while, but never together and I had hoped we would get to some day. He loved talking about what he did when he was studying in Tokyo and I think it was some of his best times. He loved going to Coco Ichibanya Curry, so I went there with Mie as a sort of tribute to him. I never really understood why he liked it so much, since it's kind of just a chain restaurant and curry is such an easy thing to make. So I had level 4 hotness curry because I think that's what he recommended. It was pretty good. Later I walked around looking for a vending machine that sold Boss coffee because he liked to talk about that, too. Well, I guess that is my tribute to Eric.

He was a friend of mine.

Sorry I couldn't find the Bob version.

Title

2010-12-27T21:27:00.000-08:00

Since new posts push old posts down (I believe this would be FILO), comments accompanying old posts get sort of lost in the shuffle and I can't be sure if people read the responses I leave to comments there, so just to clear up some Japanese, I'll make this post.

The title of my blog is Iwakan, in Chinese characters, 違和感, which translates roughly to "feeling out of place." For some pointless but fun (for me) analysis of the word, we break it down into its roots, which for Chinese-root words (漢語) conveniently means by character, since each character roughly represents a single concept, as well as a (possible multiple) reading. I've written the Chinese reading* in parenthesis, just so you can see how the following borrowed readings (音読み) change them a little.

違 - (wéi) i - This character is also read chiga-u, which even people who only know a little Japanese would recognize from Chigaimasu!, meaning wrong or different. My dictionary tells me that you could also use the character 異,　(yì) i, for the first character. This has a similar meaning of foreign or different, but is much less common. The only words I can think of that use it are 異人　ijin, meaning "foreigner" or "barbarian" and kotonaru, which isn't very common, but means "to differ."

和 - (hé) wa - This character is important in Japan because it is an old name for Japan, one that dates back to some ancient Chinese tome, but also because it means harmony, which is a central principle here. Social harmony is very important.

感 - (gân) kan - This one is simply feeling. It doesn't have a Japanese reading, at least not one that I've ever heard of being used, but interestingly enough, it is used as a suru-verb, meaning that you can attach the verb suru, to do to the end of it to make it into the verb "to feel," but it is so common that over time this has changed into the easier to say kanjiru, which then conjugates as one would expect a Japanese verb to do.

Now, the word in the URL (I don't remember what this part of a URL is called) is fukakai, written in Chinese characters as 不可解, meaning "incomprehensible." Again, let's break down this word.

不 - (bù) fu - Not. Of the famous "bu yao!"

可 - (kê) ka - Possible.

解 - (jiê)kai - Explain, understand, solve.

So, if you put it all together, you get "not possibly understood," or "incomprehensible."

I thought the names were fitting.

*making the upside-down circonflex is more hassle then it is worth, so you get stuck with thinking that the town I'm implying is up-down, when it's really more like down-up.

More Math

2010-12-26T17:01:00.000-08:00

I said I would get around to another short post, so I'll do that. There should be a Christmas post coming, but I don't have pictures yet, so it wouldn't be as good as it could be.

Anyway, while reading about Bayesian inference on Wikipedia, I came across the Raven paradox, also known as Hempel's paradox. You can just read on there about how it works, or you can read my explanation which will be basically the same thing. So, here goes.

Consider the statement "all ravens are black." As a logical statement, this is the same as "if x is a raven, then x is black." Like all logical statements, it is logically equivalent to its contrapositive, which is "if x is not black, then x is not a raven." If you don't deal with logical statements like that, you should probably think about why statements and their contrapositives are logically equivalent.

Now, if we use the scientific (inductive) method, we can support or disprove this statement (or its contrapositive) with evidence. For example, if we see a raven that is black, we support our statement, and if we see a raven that isn't black, we have disproven the statement. Of course, since the statement and its contrapositive are equivalent, support one is the same as supporting the other and disproving one is the same as disproving the other.

So, what if we see a green apple. It is green, and since an apple is not a raven, it supports the contrapositive "if x is not black, then it is not a raven." So, this observation supports the original statement. But what happens if we start with the (obviously false) statement "if x is a raven, then x is white"? The contrapositive here is "if x is not white, then x is not a raven." Seeing the green apple again supports this contrapositive, so this observation simultaneously supports the (obviously contradictory) statements "all ravens are black" and "all ravens are white."

Weird.

Bayesian at the Moon

2010-12-16T16:19:00.000-08:00

I bet you were expecting more Japanese nonsense, but nah. Today I will talk about something that even mathematicians find boring: statistics.

A friend in the math department was presenting her work to some non-math people a while back, which is of course death for trying to say anything meaningful because an invitation to do so always comes with the caveat of "no math." Anyway, her research is on random compositions. A composition is basically just a set of integers that sum to a given integer, I think ordered from biggest part to smallest or something. I'm not an expert on that stuff, but it's sort of irrelevant because isn't it obvious that this has nothing to do with terrorism? I only ask because someone apparently asked if her work could be applied to something about terrorism. Seriously. It's funny that there's this supposed order of intellectuals looking down on each other that goes something like

mathematicians > physicists > chemists > biologists > psychologists > sociologists > fruity humanities type people

because we really try not to look down on people, but then they go and ask questions like that. Incidentally, if anyone has any additions or revisions to that ordering, let me know in the comments. I'm curious.

So I'm almost don't expositioning (expositing? exposing?). Somebody else asked a more relevant question, as to whether she had considered using Bayesian techniques or something like that. Not knowing what Bayesian really means, she didn't know what to say other than she hadn't used them, and since I am apparently the go to guy for statistics (???) she asked me about it later. All I could tell her was what I knew about Bayesian stats, which is this; in Bayesian statistics, you treat population parameters themselves as random variables. I read some more about it, but that's still my basic understanding of it.

You see, there are two approaches to statistics, frequentist (which is what I teach, sort of) and Bayesian (which is not what I teach). We'll see which makes more sense to you by looking at a problem.

Let's say that there's a population that we're measuring something from, and let's say that there's a distribution to that measurement, which I won't make any assumptions about the shape of, or anything, other than that it has finite mean and variance (this is not really much of an assumption, but if I feel like it, I may talk about a distribution that doesn't have these). Let's call that mean M. Normally, we would use the Greek letter mu, but I can't do that on here. Now, to a frequentist, this mean is just a fixed number that is inherent to the population, and we don't know it. If we want to know it, well, we're out of luck, but we can make a good guess at it.

The way that statisticians guess is by taking a random sample and using an appropriate test statistic or estimator built from that random sample. To estimate the population mean, you can imagine that a good estimator is the sample mean. That is, take n measurements from the population, add them up, and divide by n. Let's call that value m. In fact, m is what's called an unbiased estimator because its expected value is the desired value, M.

You can see now what I meant by M not being random, but m being random. M is fixed, to a frequentist, and so doesn't have probabilities associated with it, but m, being built out of a RANDOM sample, has probabilities. It doesn't have just one value, but a range of them, hopefully with those near the actual value of M having higher probabilities. Using m, then we can estimate M by building a confidence interval around it, which depending on our confidence level will probably contain M, though we can't say where. This is what they mean on the news when they say that some proportion is something plus or minus a margin of error. That's a confidence interval.

Alternately, if we wanted to see whether the M for our population is the same as some given mean, like a national average, or an accepted value of some sort, we can perform a hypothesis test. This is slightly harder to understand, but I think highlights a frequentist way of thinking. What you do here is come up with a null hypothesis that always looks like

H_0: M = (given value)

and assume that null hypothesis is true. Now there's a giant theorem, called the Central Limit Theorem, which states that under certain conditions, such as independent observations and large enough sample size, sample means (which are random, remember!) have a normal distribution centered at M, the population mean, and standard deviation (sigma)/(n^.5), where sigma represents the population standard deviation. The exact value there isn't what's important. What matters is that if we assume that our population mean is a given value, we can find the probability of getting a sample mean like ours (m) [nearly] exactly.

Put in common sense terms, if M is actually 0, and we take sample means from the population, most of them will be near 0, but not actually zero. Occasionally, we would get a strange sample, but not that often, so if we get a mean that is "far" from 0, we know that our assumption of the null hypothesis must be wrong. (Statisticians supposedly think that rare events do happen, just not to them). What a hypothesis does is quantify how strange test statistics are by putting them in terms of conditional probabilities.

Now, what do Bayesian statisticians do? Sort of the opposite. They say that a population parameter is a random variable and look at the conditional probability that a hypothesis is true given some evidence. They calculate

P(H|E) = P(E|H)P(H)/P(E) = P(E|H)P(H)/[P(E|H)P(H) + P(E|~H)P(~H)]

which should strike you as weird for a couple reasons. Firstly, we are looking for the probability of a hypothesis being true, such as the hypothesis that the earth orbits the sun. It doesn't make sense because it is intuitively not a random thing. It's just something we don't know whether is true or not, at least to me. Secondly, to do that calculation we have to know P(H), which is the probability that the hypothesis is true. That is, we have to assume a distribution for the truth of H going in. Generally, this is something sort of intuitive, like given two options about which we know nothing, there is a 50% chance of either being true.

Maybe this makes more sense to you, if you are scientifically minded. It's like the scientific method in that you go in thinking that a hypothesis is either true or not, with some probabilities assigned, and you do an experiment, and the results of the experiment either makes it seem more or less likely that the hypothesis is indeed true. Anyway, it's sort of interesting, right?

Since I have a bunch of time, I'll mention one distribution that doesn't meet that finite mean and variance condition from before.

Hopefully that picture loaded. I made it for a homework assignment a while ago using the Mac's built in and extremely handing graphing utility. The red curve is a normal (also called Gaussian) distribution, which is extremely useful, but has finite mean and variance and is only there for comparison. The black curve is a Cauchy distribution, which doesn't have finite mean or variance. Notice that the "tails" on the Gaussian distribution go to zero very quickly, and that those on the Cauchy distribution don't go to zero quite as fast. That is, it has "fat tails." This is an actual term in probability. Fat tailed girls make the world go 'round.

The explanation I've heard for a Cauchy distribution is this. Imagine that you set a flashlight up so that it is pointed down a given distance from the ground, and allow it to rotate freely 180 degrees in such a way that the angle from the vertical line from the flashlight to the ground and the ray of light coming from the light is uniformly distributed. What that just means is that the distribution for the angle is just a box; that is the probability is equal all throughout the 180 degrees and zero elsewhere. What is the distribution of the distance (technically displacement) from the inital position of the light to where the light strikes the ground?

You can see that the probability of the light being perfectly parallel to the ground is 0 (since there are an uncountably infinite number of possible angles), but that there is a considerable probability of the angle being near that, so that the displacement is huge. This is what results in the fat tails. The pdf is given by

f(x) = 1/[pi(1+x^2)]

which math nerds can tell you integrates to 1, so it is a legitimate pdf.

What happens when you try to find the mean, though? To do so, you need to integrate

xf(x) = x/[pi(1+x^2)] ~ 1/x

which doesn't integrate. That is, the integral diverges. In other words, even though 1/x -> 0 as x gets big, it doesn't get small enough fast enough. So, a Cauchy distribution doesn't have a finite mean. For variance, you would need to integrate x^2f(x), which you can imagine diverges even faster, so it doesn't have a finite variance, either. Or any well-defined moments for that matter. Booyeah

日本語の投稿

2010-12-15T15:40:00.000-08:00

日本にいるけん、投稿は日本語での方がいいでしょ？今日、第二故郷帰りをしようと思ってたが、昨晩美絵ちゃんのお母さんが晩ご飯に誘ってくれたから、行かないと思う。好きな奥出雲町は米子市から列車で何時間かかるから、行って、帰ればあそこにいる時間が短いし。美絵ちゃんと飲み会に行くから、明日も無理だそうで、来週にしようかと思ってる。

兎に角、雪が降ってる。近くのコンビニにも行きたくない。顔が凍る感じだ！だけど、ホット•レモンが美味しそう！どうしよう？？？

日本に着いてからの食べたものリスト：

すき家の牛丼
味噌汁
大好きな納豆ごはん
五目飯（なんじゃらご飯だがニュアンス分からない）
カレーライス（ビーフの、もちろん）
たこ焼き　（凧じゃなくて、鮹だ）
インスタント焼きそば
鍋
ポテト•サラダ

美味しそうだけん！

Natto

2010-12-14T15:43:00.000-08:00

I don't have anything new to post, so I'll post an old picture of an old favorite, something I can't get in America, even in Philly's Chinatown, which otherwise is full of great stuff, not all of it Chinese, including Pho restaurants, Japanese candy and general Korean weirdness. The food I have missed more than any other is probably natto, which most people think is disgusting, but I just ate another bowl of today.
It's just fermented beans, basically, and it smells sort of awful, but it tastes really good, at least to me, and is apparently awesome for you. I think in the picture, it has shouyu (soy sauce) and karashi (mustard), which is my favorite combination of things to eat it with, but I have been eating it with daikon oroshi (ground up daikon [I think we use the word daikon, right?]) {grouping symbols}, which is also good.

Speaking of grouping symbols, did you know that there is such a thing as a Lie bracket. It looks just like a bracket, but it is named after Lie. Here is an example:

[Y,L]

You would think that this is a closed interval containing the endpoints Y and L, but maybe it is an binary operator, defined in some crazy way with a sum of partial derivatives, at least if we are talking about a finite-dimensional vector space.

Math is crazy like that; you always think you know a bunch, and then it turns out you don't know anything.

Winter Trip

2010-12-13T19:23:00.000-08:00

Well, I've made it to Japan and am currently messing around in Yonago. There's not much going on, but the trip should involve an "illumination cruise" in Osaka, a trip to the Tottori sand dunes, and playing the role of Santa Claus himself. There's not much to add, but it's going great.

Well, it's Another Saturday Night

2010-11-06T19:11:00.000-07:00

...and I ain't got nobody
I got no money because I ain't got paid
Oh, how I wish I had something to do
But sit here and grade

Halloween

2010-10-30T01:02:00.000-07:00

It's a little late, but happy birthday, John (not Lennon). Also, to everyone else, Happy Halloween. It's that magical time of year where college students get so drunk that they pass out and don't wake up and then their friends pull the fire alarm so everyone has to leave the building at 2am to stand in the cold wind. Then when the poor girl gets to walk embarrassed to the ambulance, people take out their anger at her for having the audacity to not wake up when she's had to much to drink by yelling at her. Oh, college.

Happy Birthday, John

2010-10-09T22:01:00.001-07:00

I guess I am a little late, but Google told me that today (yesterday now) is (was) John Lennon's birthday, so I might as well put up a little post. A very little post. He wasn't really even my favorite Beatle, but he was pretty darn good, you have to admit. So the question on everyone's mind must be what is my favorite song of his. Maybe it's weird, but it's "Oh, Yoko." He's usually so angry or depressed, but when he's talking about Yoko he's just so happy, and it's so upbeat and simple that I can't help liking it. Maybe it's because I've got my own little Yoko. On a sort of related note, her name is actually 洋子, which should be transliterated Youko or Yooko, because it has a long vowel, so when he sings, "Oh, Yo-o-ko," it is actually the right pronunciation.

Do you have a favorite Lennon song?

2010-09-28T05:27:00.001-07:00

Classes have begun, and as such, I have less time to put up stupid posts that nobody reads. Anyway, I am taking a topology course, which so far has been nothing new, but this professor doesn't seem to get that this is a grad course and he shouldn't be giving us two assignments/week, especially when it mostly amounts to busy work, since it's stuff we've seen before, but I think maybe he just underestimated how many people have heard of closure operators, or really topology in general (it uses an undergrad book). I am also taking a prob/stat class, which is also pretty boring and elementary thus far, and it is notable basically only because I don't want to buy the book because it has nothing new for me (or really most people), but I need the problems out of it, so I need to MacGyver a solution somehow. I am also taking an ODE class. For those of you who don't know what ODE stands for, it means Awkward Russian guy talking for three straight hours and there not being a projector, which he did not anticipate, leading him to have to hold up papers with figures on them. So-so.

I know I am complaining about things, but this is probably the last time I will do it, and that's what blogs are for, anyway. The worst part is that there is one guy who is in all my classes and constantly complains to me about how the classes are too easy and that "graduate students shouldn't be allowed to take these classes because they are too easy." Maybe a direct quote. I realize I am complaining about the same thing, sort of, but I don't really mind them being too easy. I am more annoyed by having to do homework, but it's not like it takes a huge amount of time. I'm more more annoyed by students (and professors!) who think classes are beneath them. Students, if it is too easy for you, don't take it! You'll be here for years, and there will be more challenging stuff later. I'm taking classes just to get the credits, at least mostly. Professors, don't fall all over yourself trying to prove that you know more about the subject than we do. If we didn't accept that as a first principle, we wouldn't sign up for your class! Also, don't dismiss legitimate questions about what your arbitrary notation means (not my question, even), especially when you don't define it, and when you choose to use non-standard symbols!

Anyway, that is the report from the front lines. All quiet on the western front.

Break Updated

2010-09-07T11:22:00.000-07:00

I've added a couple new things I've watched.

As if working about 10 hours a week over the summer wasn't leisurely enough, I'm now officially on break for a couple of weeks, so I have plenty of time to use my roommate's netflix account to watch tons of movies, as well as waste time on the internet. So, I've been catching up on some movies that aren't exactly new releases but that I felt like I should see, sort of.

Aliens - I am just finishing this and it is awesome. It's incredible how much more real it looks (because of the use of actual sets and props and actors) than Avatar, and how much better James Cameron used to be.

The Insider - This is kind of awesome, as well. It's sort of a different role for Al Pacino, but he still gets to yell a lot, which he is very well suited to.

The Rock - Good and dumb fun. Reminds me a lot of ConAir, but somehow not as good for not having ridiculous villain characters.

Spy Game - Robert Redford and Brad Pitt. Current and future heartthrobs team up to make a cool movie about spies. Good stuff.

The IT Crowd - not a movie, but a British TV show I had heard something about. It's kind of funny, not amazing or anything, but very British.

Wall Street - I liked this movie, though it seemed rather hamfisted in its morality. I'm guessing it just hasn't aged well, but seeing Martin Sheen play Charlie Sheen's dad is actually pretty cool. There's not really much to it, just a sort of simple morality play, but not a bad one by any means.

Raising Arizona - The first real Coen Brothers' movie. It is good, I think. I was exhausted for some reason when we were watching it, so I fell asleep for the second half, but I'll go back and finish it. I am a big fan of these guys' movies, though, so if you don't like them (The Big Lebowski, O Brother, Where Art Though, No Country for Old Men,...) you probably won't like this one, either.

Moon - This is an excellently composed science fiction movie, not huge in scope or even particularly innovative. Anyone with experience at all with SF or just mystery-type plots in general should be able to see what's coming about a parsec away (haha), but that doesn't mean it's not a good watch.

The Office (UK) - I'm a big fan of the US version of The Office, and consider it far and away better than the original version, but I hadn't seen the last few episodes or the Christmas special that acts as an epilogue to the series, although it is actually about the length of a whole season (or series, if you prefer the Brit term). They are both good shows, and they really do complement each other. There's an excellent essay comparing the two versions that is linked to in the Wikipedia article, which I won't bother looking up. I agree with the author that the British version is much darker and that Michael Scott is much more likable than David Brent, but that both versions bring something to the show. I completely disagree that Dwight is unbearable, however, and feel he is much MUCH funnier than his British equivalent, Garreth. Anyway, see the series, read the article, enjoy.

Batman: Mystery of the Batwoman (or something like that) - I can't resist DC animated stuff. This is basically a movie follow up to Batman: The New Adventures, which itself was a follow up series to The Adventures of Batman and Robin, or Batman: The Animated series, whichever title you prefer. It's quality, as everything from the Timmverse is, but I have a preference for the earlier style, as opposed to the simpler more "cartoonish" style of TNBA, but that's just me. The story is ok, but definitely not as good as some other ones. It was annoying to me that they sort of brought up Batgirl and then just forgot about her. Also, Robin didn't do anything but fly the Batwing, which seems particularly out of character, but I suppose it is to give more screen time to the titular character. Ah, well.

Let the Right One In - This is a Norwegian (I think) vampire movie about a junior high (again, I think) boy and his new friend who turns out to be a vampire. It's generally thought of as a horror movie, but it works much better as just a drama with a vampire. It's surprisingly sweet and understated despite people getting bitten to death by a 12 year old. Very good, but obviously not for everyone. Probably unnecessary word of warning: lots of extremely pale people.

McDonald's Breakfast - Not a movie, but always satisfies. Their coffee is so good since they started pretending to be a low rent Starbucks in the morning. This is supposedly an intentional move on their part to capitalize on the recession and people not being able to afford $5 coffee any more. I stopped getting sugar in my coffee a long while back now, and I told the girl behind the counter I was "on a diet," to which she mentioned that I was, indeed, also ordering a McGriddle. Haha, but I can't help it; the McGriddle is probably one of the most brilliant fast food items ever created, even if it has been overshadowed by that sodium bomb known as the Double Down.

Also, this site has a wonderful series of articles mocking and destroying the stupid arguments made by the tea parties, and I feel people should read it just because it puts into words so succinctly what is wrong with these people.

Since I've already established this blog as left-wing extremist by the measuring stick of a seemingly increasingly conservative (not coincidentally, also increasingly stupid and inching steadily towards collapse) society, here is another link for you about income disparity. Enjoy.

Zorgus Borgus

2010-08-30T09:11:00.000-07:00

I just got bit by the love bat...

and it's driving me mad!!!

Short Review

2010-08-20T21:59:00.000-07:00

Since nobody else appears to be updating, I guess I will have to take the wheel. I saw Inception recently, and I have to say it pretty much lives up to the (ridiculous) hype. It's pretty exciting and the multiple layers keep you interested. The rules are all explained without delving into the mechanics of shared dreaming, which would have been a nightmare (ha ha) to sit through. Instead, we get walked through the rules nicely as the story progresses, just enough to let us understand and not enough to bore us. Good acting and all that. Despite what you may have heard, the story isn't confusing at all; it's very straightforward and easy to follow as long as you can keep track of dreams within dreams (there are only three levels, so it's not like you'll forget what is going on). The ambiguous ending is well done even if it is obvious; if you know the premise of the movie, in fact, you can probably guess the ending without seeing it. Anyway, check it out if you somehow haven't by now.

Also, if you aren't watching the new episodes of Futurama, then you are missing out. They're even better now than before they went off the air.

Tragedy!

2010-08-13T14:33:00.000-07:00

Cathy is ending! What will the world do without her?

The teeth of great lions are broken; the lion perishes for lack of prey, and the cubs of the lioness are scattered!

Please take Funky Winkerbean instead!

Camden Yards

2010-08-09T17:01:00.000-07:00

It's been a bit since my last update, so how about a short one. Over the weekend, I went down with two of my roommates to Baltimore, where we met up with Eric to take in an Orioles vs. White Sox game. Camden Yards, or rather, Oriole Park at Camden Yards, is a nice ball park, pretty large and very clean. It also has nice views of the city, if you are facing away from the field, with no walls to obscure your view, at least at the upper levels. I should have some pictures, but I have not received them as of now. Anyway, the White Sox, who are in a division race, beat the O's, who are only in a race in the purely mathematical sense of it is theoretically possible that they win something like 90% of their remaining games and all other teams in their division do horribly from here on out. So, Eric was happy with that. Baltimore fans seem pleasant, knowing that their team is pretty bad, and didn't mind sitting with a St. Louis fan, a White Sox fan, a Phillies fan, and a Yankees (boo!) fan. Afterwards, we enjoyed some Chicago style pizza near the park. I know that's weird. Next stop, NY, NY!

Cheesesteak

2010-08-04T08:59:00.000-07:00

I finally had a Cheesesteak from the legendary Pat's. I don't have a picture of the "wiz wit" that I ate because I took it on my phone and I don't know how to transfer the pictures. Anyway, it was awesome, but if you go, be sure to follow their ordering instructions. They have them posted on a sign. You need to have your money ready when you order or they will start yelling at you. I can read, but apparently some people can't, so I got to witness that first hand. The reason for their strictness is the absurdly long lines they have, and thus the need to rush everyone through. Anyway, it was awesome, and I suggest it to anybody who loves great (but terrible for you) food. Maybe Geno's next time...

I Lament the Coming of 3D

2010-07-03T07:41:00.000-07:00

Let me just say that Toy Story 3 is awesome, much cooler than Amtrak, which doesn't run sufficient numbers of trains over the July 4 weekend for me to get down to Virginia. I saw Toy Story 3 a little while back and I was very pleased, movie magic and all that. It provided a nice bit of closure to a trilogy that was good through and through, and had some of the best laughs of the series. An instant classic, yada yada.

I had to see it in 3D, however, which annoyed me right off the bat, since 3D tickets are more expensive, and movie tickets in general are too expensive, since you can't know going in if the movie is even going to be worth watching. There are hints, of course. If it is directed by M. Night whatshisface or stars Gerard Butler, you are probably better off saving your money. But that was not the case, and the movie turned out to be worth the price of admission, or at least what the price of admission would have been if it weren't in 3D and the theater didn't change management to some jerks who don't give student discounts when they think they can get more money out of you (any time they are playing anything you would want to see).

But my main quibble is that 3D doesn't work for me, at least not very well, and a lot of the time, just makes it look like things on screen are surrounded by halos of light or that there are two of them. When it does work, it doesn't really add anything to the movie as such, besides sometimes a headache. So, long story short, I wish 3D would die, but it probably won't because people have always appreciated flashy crap more than a good story, and we all know which of those thing Hollywood is better at churning out, anyway.

In closing, a joke from one of my roommates:

What's the difference between a teabag and England?

A teabag stays in the cup longer. Ha ha, take that, English people.

World Cup Update

2010-06-28T06:11:00.000-07:00

I actually watched a game. It is still uninteresting, but at least when you are watching at a bar with a bunch of other people cheering for the same team, some of whom are dressed like Uncle Sam, etc., there is a good atmosphere. I guess I will just "root for" glorious Nippon now, although they will probably also lose.

World Cup

2010-06-11T04:08:00.000-07:00

I guess the world cup is starting (has started?), so I will post my thoughts on that. Here they are:

It is boring.

I don't get why soccer fans are so insecure about their sport. Yes, Americans don't like it. It's not that we don't understand it, at least not in any cases I've ever seen. We just don't like it. We have other sports that are just more interesting. We have seen it and fail to see why you would get so excited about 88 minutes of low-speed passing and maybe two minutes of anything meaningful.

Only soccer fans don't get this. I like hockey and of course was crazy excited about the Stanley Cup this year. I watched almost every game the Flyers played and it was awesome, but I get that some people don't like it. I don't try to get other people to like it; I am satisfied with watching it. Soccer fans always try to convince you that just because nations are competing with nations now instead of teams within a nation, that the game has somehow become less mind-numbing. It hasn't. That's it.

Make It So

2010-05-30T08:05:00.000-07:00

How awesome is Patrick Stewart?

Graphs and Donuts

2010-05-24T20:15:00.001-07:00

I think I wrote a couple posts ago that I would post something about some stuff that I am fooling around with in a mental sense, so I will do that.

I came across a book about Topological Graph theory and since that sounded good and weird and like I wouldn't need to find a bunch of inequalities to do it, I started reading it, and came upon a problem involving planar graphs. A little explanation, though not anything rigorous:

First you have to know what a graph is. It is essentially a set of points connected by line segments. The points are called vertices, and the segments are called edges. Technically, graphs are sets which contain two sets, an edge set and a vertex set, where the vertex set is basically single numbers (generally integers), and edges are pairs of numbers, where both of the integers in the pair appear in the vertex set. But for our purposes, they are just dots with lines connecting them.

For most purposes, simple graphs will suffice, which are graphs where only one edge can appear between any two vertices, and no edge can connect a vertex to itself. If you are inclined to chemistry, you can think of them as molecule diagrams where no double bonds are allowed, but any number of bonds can be made between atoms. Actually, there is an interesting problem in graph theory of counting isomers of carbon chains of arbitrary length, but I digress.

The next thing you have to understand is what is meant by planar graphs. A planar graph is a graph that can be drawn in the plane without any edges intersecting. The analyst in my office would complain about that definition, but my tensor professor would love it because he insists that "R^2 is not a plane; a plane is a plane. R^2 is a set of pairs of numbers. What is a plane? I can't tell you, but I know what it is." That isn't an exact quote, but it is close. He also says things like, "There's no such thing as integration by parts. There is only the product rule." (^_^)

I will now give examples, like a good textbook:

This graph is K4 (the 4 is supposed to be a subscript, but blogs...). That is shorthand for the complete graph on four vertices, meaning that it has every edge that can exist on four vertices. Exercise: how many edges does Kn (the complete graph on n vertices) have?

Is K4 planar? One is tempted to say "no," since those two edges in the box intersect, and that's a no-no according to our definition. However, what if we draw it like this:

Now we have the same graph drawn in the plane, with no edges intersecting, so the answer above should actually be "yes." Technically, these graphs are not the same, they are only "isomorphic," but all that means is that if you treat graphs as they should be treated, as sets, and make a renaming function (i.e., an isomorphism) between the sets, all the relationships are preserved.

A better question is what graphs are (not) planar? A dude named Kuratowski essentially answered that question all at once and very neatly. He said (and proved) that all the non-planar graphs contain a copy of K5 or K3,3 (the bipartite graph on 3 and 3 vertices; a picture will follow). Technically, they just have to contain a subdivision of one of these two graphs. That is, if you take one of those graphs and add vertices on already established edges, you also can't draw that on the plane, but the important point is that we can tell, in a certain sense, very easily if a graph can be drawn in the plane.

K5

K3,3

The second one is called the complete bipartite graph because it has two subsets of vertices {1,2,3} and {4,5,6} that have no edges inside them, but all the other edges are there.

So, how do we know that things are planar/not planar? To show that something is planar, it's easy enough to just draw it in the plane, though in practice this could be staggeringly difficult for large graphs. To show something is non-planar, you can't just show one non-planar representation; you have to show that no planar representation is possible. Here's a bare-bones proof that K5 is non-planar, using the concept that that previous planar representation of K4 is "unique" up to bending, stretching and renaming, none of which affects planarity.

Now try putting the fifth vertex in any of the regions we've created and see if you can draw an edge to all the other vertices. So K5 isn't planar! I'll leave a proof of K3,3 up to you, but it can be done in much the same way.

Now, a mind that likes puzzles might wonder what is so special about the plane? What about other shapes, like a ball? Well, that question has been asked, but not totally answered. From now on I'm going to call "shapes" "surfaces" because that is the actual term. I'm not going to give you a real definition of a surface, but it essentially boils down to adding loops and crosscaps to the sphere.

The first part of the question is are there "planar" graphs and "non-planar" graphs for other surfaces, and the first answer is yes. In fact, some dude showed that for any surfaces, there is a finite set like {K5, K3,3} that generates all the non-embeddable graphs. However, except for the sphere, nobody knows what they are, so that is what I am messing with, but it is pretty complex. Let's consider the sphere:

There's our good buddy K4 drawn on the surface of a sphere. It shouldn't come as a surprise that anything we can embed on a plane we can embed on a sphere, since a sphere is what's called "locally Euclidean;" it looks like a plane as long as you only look in a little disk. But is that drawing still unique, as it was in the plane?

Oh, ho, ho! What if we wrap the last edge around the back? Well, it turns out that that doesn't change anything at all, because wrapping around the back is the same as stretching back and back and back. So, well, the sphere isn't too interesting. It's the same as a plane, but we like to use a sphere to judge from because it's what's called "compact." Don't worry about that much.

So what's the next simplest thing? A doughnut, or donut to normal people. Mathematicians of course call it a torus because we are contrarians by nature. Let's try drawing K4 again:

Try and draw the fifth vertex and you'll run into the same problem as before. But does this mean that K5 is non-embeddable on the torus? You should know by now that that isn't the case. What if we start by drawing the box in more natural ways?

Now try to draw that fifth vertex and you'll find that not only can you draw K5, but you can draw it in more than one way! So a donut has a little more freedom than a ball.

So, I'm not really sure which graphs can and can't be embedded yet, but I've managed to embed K5 but not K6 on the torus, as well as K3,4. I don't know if I embedded K4,4 yet, as I have tons of scrap paper with drawings on them now. Anyway, that's what I've been up to.

2010-05-24T11:36:00.001-07:00

Now that Lost has supposedly ended (I did not watch it, but it's all over the internet), I'm expecting a bevy of posts from the Losties soon, but maybe not. It seems the consensus is that the finale was lame and didn't answer any interesting questions (again, I don't know which those are).

For my part, I just watched Superman: Doomsday, which was pretty good. In a way, it is disappointing because it's just a little story. When DC killed Superman, it was a big deal (like even non-comic nerds bought those issues). Then there is a long saga of four dudes claiming to be Superman taking over and us finding out who they all are, and eventually it segues into Hal Jordan, the Green Lantern, becoming Parallax and all this junk. Anyway, it's a huge deal, not just for Metropolis, but for people in general. In this movie, we don't get to see anything but Metropolis, and that is almost distracting, since I couldn't help thinking that when a somewhat evil Superman shows up and starts laying down the law, it seems unlikely to me that somebody like Batman would just let it happen and not try to Kryptonite the guy. There are just so many things that could happen, but we get a little story about Lex Luthor and then Superman just unceremoniously comes back to life and we get a battle Royale, which would be way more entertaining if it was with Captain Marvel or something. Ah, just limitations on movies.

Anyway, there's not much going on here. It's just muggy and gross. That's it for me.

Half-Post 350?

2010-05-20T04:55:00.000-07:00

350 isn't an important number, is it? I don't know; I'm not too good with numbers. Maybe that's why lately I've been fascinated with embeddings of graphs on surfaces. Maybe I will post about that when I have time to draw some pictures.

In other news, I think Holiday picked up a hit the other day, even if we lost. At least the Reds lost, too.

Lol-iday

2010-05-07T12:10:00.000-07:00

Matt Holliday needs to learn to hit a pitch. I went to two of those games and he was awful. Pujols was barely better. If we can't be Kendrick, then there is something wrong with the club. Hopefully we can pick up a few wins against the Buccos.

Also, can we not pick up a shortstop who bats above .200?

野球

2010-05-02T15:34:00.000-07:00

On Friday I went with a couple dudes to watch the Mets absolutely destroy the Phillies. Too bad, but I can't say I care that much. At least it's not the Yankees doing the winning. It was pretty crazy, though, since the Mets are the Phillies biggest rivals and this was their first meeting of the season. The stadium was packed and the parking lots (all the stadiums are right next to each other, so the parking lots can all be used at once) were full of people tailgating. So, that was cool. Alright, that's it.

Hi Emily!

2010-04-14T18:19:00.000-07:00

I know you probably don't read this blog, but if you do read it, I just want you to know that I am writing you a letter; I've just got no ideas.

Too Many Mornings

2010-03-25T12:15:00.000-07:00

In an effort to balance out that last post, I'll talk about something that is probably of marginally more interest to people but still sort of galvanizing: Bob Dylan.

He's famous among his fans or rock fans or music fans or something for recording many (at times very) different versions of his songs, and I've had one of those songs that keeps popping up in his repertoire over the decades stuck in my head, so I thought I'd use that as an example. Here's the original, from The Times They Are A-Changin' (1964). It's got a nice simple melancholy to it, which is pretty much how most of the album feels. It's probably only his second best acoustic album, after The Freewheelin' Bob Dylan, but still leagues better than Another Side, which is pretty weak in my opinion. This is probably one of the best tracks from the album, which says something for an album that contains THE LONESOME DEATH OF HATTIE CARROLL - a favorite track of IWU roommates.

Folk fans everywhere were saddened when Dylan abandoned this sound and started hanging out with the guys who would become The Band, but he didn't forget this number and mixed it up to fit their "thin, wild mercury" sound. You have to fast forward a bit to get to the song. I would have thought this would have been an easier version to find, since it is on The Bootleg Series, Vol. 4, but I guess not.

After the whole electric thing, he went back to recording acoustic stuff, famously making a short but sweet country album called Nashville Skyline, a favorite of Dan's if I recall correctly. While recording for that album, I believe, he ran into Johnny Cash, and they recorded duets of some of each of their songs as well as some others. This is one of them. It's got a very simple Johnny Cash sound to it, with Dylan using his country crooner voice. Not my favorite, but not terrible.

Just a few years later, we get a collaboration with another famous Dylan friend, George Harrison. I believe this was recorded around the time of New Morning, but I'm not sure. I kind of like it, but I've got a soft spot for that album. Overall it's not that good a version and seems highly out of character for the lyrics, but it's worth a listen, at least.

A few years later we get to painted face, cowboy hat wearing, going a bit crazy Rolling Thunder Revue Dylan, which is one of my favorite eras. This version is from Hard Rain, a live album much maligned for being listless and not as good as the first half of his tour with the RTR. I think that is part of the charm of it; the RTR was a big, energetic last push by Bob before he seems to have lost it all for a decade or so, and here we get to see Dylan rough around the edges, basically yelling into mic, breathing new life into the song.

Quite a far cry from this. Leather pants?

Alright, well, that's about it. You can dig up some more versions of it on YouTube if you want.

I Review a Movie I Have Not Seen

2010-03-24T14:16:00.000-07:00

The Blind Side is terrible. My roommates are in love with it. I was so bored within the first fifteen minutes of it that I gave up and went to surf the internet instead. How did this movie succeed? It seems like it's just some sort of Hallmark Channel movie of the week. Does it make white people feel good about themselves, thinking that in the same situation they would do the same thing when they no doubt wouldn't? I don't get it.

Hidden Post

2010-03-22T21:47:00.001-07:00

I had a new post, but it was rather lengthy, and due to extenuating circumstances, it didn't get done until after my last couple short posts. So, I put it up today, but I guess blogger puts things in order by when you start them, not when you finish them, so you'll have to scroll down if you want to get to it. WARNING: LOTS OF MATH.

Finally Done

2010-03-20T17:20:00.000-07:00

To slow this blog's descent into nothingness, I thought I'd post an announcement that I finally finished my responsibilities for this quarter with a few hours of grading exams. It's very frustrating having to deal with people who lie to your face about turning things in that they didn't and people who cheat just cleverly enough not to get caught, and even worse, people who do both. Ah, well, good luck getting into med school with a C in what's basically a high school math course.

The weather was fantastic today, so after spending hours in a gray windowless office, I took the opportunity to read the internet and promptly fall asleep. Maybe I'll come up with something to put up to match Dan's bizarre short story-like post. Recombobulation indeed.

Update: Since apparently Sarah is in Milwaukee, she should be careful:

No Posts

2010-03-02T23:15:00.000-08:00

I know I haven't posted anything in forever. I am working on that, but it is nearing the end of the quarter so it is unlikely I will have adequate time to type a bunch of stuff up because I am busy typing up other stuff when I do finally manage to figure it out. Also, grading. I just finished a marathon session of it and that was only half of the problems on half the exams. Fortunately I am only responsible for half the problems. Peace!!!!!!!

New Post

2010-02-26T10:34:00.001-08:00

I'd had this update sitting on my hard drive for a few weeks, incomplete, before today, but I just got around to finishing it because of being sick and finals and whatnot keeping me out of the blogosphere. Now I'm on break, so "enjoy."

I've talked about topologies before, so if you are interested in reading my ramblings but don't know what it is, you can find it in some old post. Or you can just use Wikipedia like a normal person.

Anyway, many useful topologies are defined by a function called a metric, which just measures distance between two points. A metric d is defined as having three properties:

1) d(x,y) >= 0 and d(x,y) = 0 iff x = y (if we relax this last condition, it is a pseudo-metric

2) d(x,y) = d(y,x)

3) d(x,z) <= d(x,y) + d(y,z)

You can see that distance in the normal sense meets all of these conditions. In fact, property 3) is called the triangle inequality and you have to use it all the time in analysis.

The way that a metric induces a topology is pretty straightforward. You just define an "open ball" as the set of all points less than some distance from a point, which you can call the center of the ball. Picturing this in the Euclidean 3-space, known to non math nerds as just 3 dimensions in the usual sense, means spheres of some radius, not including any points on the surface. From here, you just say that a set is open if every point in the set has an open ball containing it which is entirely contained in the set. In Euclidean space, this again translates into anything that is missing its boundary. I'm not going to define boundary for you, although it is a rigorously defined thing in general topology, but it should be clear in Euclidean space what that means. For example, in Euclidean 1-space, heretofore known as the real line, the boundary of the interval [a,b) is {a,b}. So, this set is not open, since it contains some of its boundary. More rigorously, open balls in 1-space just mean open intervals, so if you try to put an open ball around a, it will contain things to the left of a, which can't be in the original interval. Then that set can't be open. It's not closed, either, but I won't get into that.

You'll note that the way we defined this topology does indeed give us a topology:

1) The empty set has no points, so it vacuously meets the condition to be open. Obviously, any open ball of a point will be contained in the entire space, so the entire space is also open.

2) If a point is in a union of open sets, it's in one of them, so it's got one of these open balls, which as a subset of one of the sets, is a subset of the union, so a union of open sets is open.

3) If you intersect two open sets and choose a point in their intersection, then there is an open ball centered at that point corresponding to each of the two sets. Just choose the minimum of those two radii and you've got yourself the open ball you wanted.

Anyway, I was just dragging my feet on undergrad stuff until now. It's time to step it up to measure theory, but not really. I'm just going to glide over all the annoying parts of trying to set up integration the Lebesgue way because it doesn't matter for what I want to get to.

Intuitively, how "big" is the interval [0,1]? It should have length 1-0 = 1, right? How about the interval (a,b)? If you said b-a, you know how to generalize, but aren't Stieltjes (which just means you are normal). Anyway, how about the interval (a,b]? It should still be b-a, right? All we added was one point, and that point should be infinitely small in a certain geometric sense.

Now, how about a union of intervals, like, say, [0,1] U [2,3]? It should just be 2, to my mind since it's just two (disjoint) intervals of length 1. And how about [a,b]U[c,d], assuming c>b; that is those intervals are disjoint? If you said b-a+d-c, congrats. So I think we're clear on how to "measure" intervals, and I'll let you work out for yourself how to do it if you want to union a countable number of intervals.

But, how do you measure something that's weird looking? For example, how big is the set of integers? Well, it should work out to be 0, since if you think about it, they don't really take up any space on the line. They're just like inch marks on an infinitely long ruler. To cut to the chase, the way that Lebesgue thought to do this was to put intervals (which we know how to measure) around sets, and call the measure of the set the infimum of the intervals we can put around it. The infimum of an ordered set is just its greatest lower bound for my intro analysis students out there. So, revisiting the integers question above with this new definition of measure makes it obvious because we can certainly cover the integers with a bunch of very small intervals, arbitrarily small, in fact. That's a sort of baby analysis problem for you, so I won't bother working out all the details without TeX handy.

Alright, so I jumped around a bit, going from metrics to measures, which seem from the names like they should be the same thing, but aren't. Now I'm going to tell you how to induce a metric from a measure, which as you recall, we used to induce a topology. Stick with me through all this terminology.

Some of the properties of a measure make it very attractive as a candidate to induce a topology not on say, the real line itself, but rather on the set of its subsets, called its power set, since a measure measures sets, not points. How would we do that? Intuitively, sets are close together if they overlap quite a bit and far apart if they don't. Less intuitively but still pretty clear, what we are really concerned with there is the parts of sets that DON'T overlap. For example, [0,2] and [1,3] have as their intersection [1,2], but so do [-100,2] and [1, 100] but this second set of measures seems more far apart than the first one. So what we want to measure is the symmetric difference of two sets, (A/B)U(B/A).

This seems to work out nicely, as (A/A)U(A/A) is empty, so it has measure 0. Furthermore, using the symmetric difference makes our would-be metric symmetric. You can check the triangle inequality for yourself, but you'll note that there is a little problem with our definition.

What is the "distance" between [0,1]U{2} and [0,1]? These are not the same sets (not the same points in a metric way of thinking), but their symmetric difference is {2}, which has measure zero, so according to our "metric" these points (sets to a measure way of thinking) are the same. That's a peculiarity.

So what do we do? What mathematicians always do in this kind of situation. Mod out.

What I mean is, these sets aren't equal, but the "metric" tells us that they are, so let's just say that they are and work from there. More precisely, let's define an equivalence relation R by saying that two sets are equivalent if their symmetric difference is 0. Now we have a new space, the set of equivalence classes mod R of [measurable]* sets of real numbers. Using the our "metric" based on the symmetric difference of two sets now gives an actual metric. So the question is, what are open sets in our induced topology? What are closed sets? Compact? Etc., Etc.

Have fun with that for a while, I'm on break.

*I say measurable because it turns out that not all sets are measurable (in the Lebesgue sense). What kind of sets aren't measurable? I don't know, but I can tell you what kind of sets are: Borel sets. These are the kind of sets that you get by performing countable set operations (unions, intersections, complements) on intervals. So, you are going to have to work hard to find a set that isn't measurable, but they are out there. In fact, because there are non-measurable sets in Euclidean 3-space, you can take apart the surface of a sphere and rotate the parts around without stretching them or anything and reassemble them into two spheres of the same size as the original sphere. I know this makes no sense, but it's called the Banach-Tarski paradox and it's one of the coolest results out there.

Converge Slow, Homie

2010-02-12T12:22:00.000-08:00

Since a string of digits recently asked me to mention something about math on here, I'll bring up a problem I am working on that should be easier than it is.

Hopefully, we are all familiar with convergence in the numerical sense, but if not, I'll try to hand-wave at it so that even an eighth grader can understand it. I've been told a good teacher can explain anything so that an eighth grader can understand it. It seems like an arbitrary line to me, but maybe a good enough one. Perhaps that is when people start displaying abstract thinking ability.

So, we can start with a sequence. A sequence is just a special kind of function, and for our purposes, we'll stick to sequences of real numbers. As to what a real number is, it's just about any kind of number you can think of that doesn't involve i somewhere. So whole numbers, 0, fractions, even irrational stuff, like 2^(1/2) or pi.

That said, a sequence is just a function of natural numbers, so something like

1, 2, 4, 9, 16, ... you can see how this sequence "goes to infinity," in that it just keeps getting bigger (I am purposefully being vague about this concept). On the other hand, the sequence s(n) = 1/n, that is

1, 1/2, 1/3, 1/4, ... doesn't keep getting bigger; it keeps getting smaller. However, it doesn't "go to negative infinity." In fact it demonstrates the central idea of calculus, which is convergence. In particular, it is said to converge to 0, or that the limit as n approaches infinity of s(n) is 0. What do I mean by that? I mean that we can think of this sequence as approximating 0, as if I didn't know what 0 was, but I was guessing at it, and each time I guessed, my guess got closer. The sequence is said to converge to a number if it approximates that number to any error. More formally,

A sequence s(n) is said to converge to a number L if and only if for all E > 0, there exists an index N such that if n > N, |s(n) -L| < E.

If you think about it, it just says that the sequence gets as close to L as we would like and stays at least that close; that we can approximate L infinitely well with a big enough term of s(n).

A proof of convergence usually goes like this: Given E > 0 (we actually use epsilon, usually)

|s(n) - L |

(bunch of algebra with inequalities)

< E for n such and such

That is, we usually set E and find an expression for N in terms of E that suffices. In the simple case above, you just set N = 1/E and you're good.

Sometimes it isn't so easy, and that is what I'm dealing with at the moment. The sequence I'm looking at is

S(n) = 1, 1/2, (1/2)(3/4), (1/2)(3/4)(5/6), ...

And so on. The denominators are just the product of the even numbers and the numerators are the product of the odds, always smaller. Each factor is less than 1, so each term is smaller than the last term, but that's not enough to show that it converges to 0. One idea might be a comparison test.

That is, if I can show that for any positive integer k, there's a positive integer N such that S(N) < 1/k, I can just compare it with the previous limit problem and say the limits must be the same. [It is easy enough to show that a sequence of positive numbers cannot converge to a negative number, so the new sequence must be "squeezed" between the old 1/n sequence and 0.]

Just working out some terms of the sequence explicitly, I've found that the limit must be less than .15, and I'm convinced that it is actually 0; that I can somehow show it is squeezed down by 1/n if we look far enough along the sequence. The problem is that this convergence is very slow. You'll note that each subsequent factor is bigger than the last, in fact, the last factor converges to 1. However, they still are less than one, so they make each term decrease, just by less and less. It is rather annoying and making it hard for me to find the right expression or technique.

Anyway, it is just part of a somewhat bigger problem related to a theorem of Tauber.

Snow Day 2: Bad Sequel Joke

2010-02-11T07:29:00.000-08:00

I always see things with the number 2 appended to them, and then ":Electric Boogaloo" as a joke. I can't think of any specific times, but it seems like this is a hip joke to make, and every time it comes up I know it is going to happen and that annoys me. I suppose it is awesome to make fun of terrible movies from the 80's, but aren't we past that by this point? Can't we move on to making fun of terrible movies from the 90's?

Regardless, it is yet another snow day here in the city of brotherly love, which is hilarious to me because who cancels college classes, especially two days in a row? But, whatever, it has extended my weekend Wednesday - Monday, I think. I have to check if it is a holiday on Monday or not, but I never have specific work on Fridays and that pleases me in the greatest. I think I can manage a 2 day workweek. Alright, peace out!

Snow Day

2010-02-10T11:10:00.000-08:00

Philly got hit pretty hard with a snowstorm, so today's classes were preemptively canceled, which is nice because it gives me more time to type up my homework and to generally laze about. As I'm not really doing anything, I don't really have that much to add at the moment. Just this:

The wind, it was howlin', and the snow was outrageous
We chopped through the night, and we chopped through the dawn
When he died, I was hopin' that it wasn't contagious
But I made up my mind and I had to go on

Know what that's from?

Some Movies

2010-01-29T07:46:00.000-08:00

Greetings internet. I have not posted in a bit because nothing really happens that is of interest. I did watch a few movies lately, though, so I will share my thoughts on them.

Avatar - If you are alive you have probably heard that the special effects are amazing but the story is not very good. I just want to reiterate that the story is essentially just cliches linked together and I was falling asleep after about the first twenty minutes. None of the characters is interesting in the slightest (don't let reviewers fool you into thinking otherwise about the typical hardass scientist played by Ripley herself), the premise is the kind of ludicrous tripe that gives science fiction a bad name, and even the supposedly vibrant world that Cameron has imagined is fairly dull. Making things glow does not amount to imagination, and it's actually really stupid because there's no reason whatsoever for all these organisms to evolve neon lights. I'd also like to say that the already obvious allegory for Native Americans is pounded into your head over and over again and is actually insulting. Io9 had a good article about how it is a white guilt fantasy. Anyway, I'm done complaining about this movie. Except that the 3D glasses hurt my head. Now I'm done.

The Hurt Locker - The critics really hyped this, and they are right. It is awesome. It's surprisingly funny in a very dark way. Anyway, you should see it.

Sherlock Holmes - Pretty dang good. Robert Downey, Jr. plays himself or Iron Man in old timey clothes, but who doesn't like that? Jude Law actually manages to seem like he's having fun for once instead of being so upset about having to act. The story is fun, with enough mystery to keep you interested between absurd fight scenes. I'm looking forward to a sequel, anyway.

Alright, that's it, go home.

Japan Trip

2010-01-12T15:58:00.000-08:00

I had previously posted that I would post later about my trip to Japan, but I haven't felt like doing that lately. It was a lot of fun, but I don't know how interesting it would be to anyone else. I don't have any pictures to go along with it because I didn't have a camera. But here are some things I did.

-Visited my 第に故郷 or second hometown. It was pretty nice to see some people again and surprise the folks at the BOE. I spent basically a whole day at a kindergarten that asked me to come as soon as they heard I was there, playing with little kids.

-Spent about a day and a half playing with the nephews/niece of the friend of Mie, who was also visiting Japan with her American husband. The friend was. Mie isn't married. I guess that was confusing, and I guess I also rock with little kids. We built a snowman even though there was only about an inch of snow on the ground. Japanese snowmen are made of only two snowballs instead of three.

-Visited Osaka castle, which was sort of funny in that I'd been there twice and neither of the Japanese people in our group had ever been there. It's a pretty decent castle with a museum in time.

-Ate some awesome okonomiyaki in Osaka.

-Ate some Osaka style ikayaki, which is cooked (grilled?) squid. I don't know if it's actually Osaka style, or if that's a thing, but that's what it said, and it was different from normal ikayaki.

-Ate kitakyuushuu style ramen in Fukuoka at a place called Ramen Stadium.

-Ate yakiramen, a Hakata specialty, from a street vendor in Fukuoka, in the same night.

-Stayed in an awesome ryokan with an onsen for a couple days.

-Nomihoudai!

-All around awesomeness.

That's about it for now.

Baby Got Back

2010-01-03T22:45:00.001-08:00

I just got back from Japan and I already miss it, especially the Mie part of it. More updates when it isn't like two in the morning.

Short Update

2009-12-20T09:36:00.000-08:00

Just getting ready for my trip. Should be a good one. I have The Wedding Singer on in the background and it's still pretty good. Adam Sandler movies are so inconsistent. Half of them are pretty great and half of them are terrible.

In reading other blog posts, I realize I should probably mention that we did get some snow here. It snowed pretty much all day yesterday, so there's probably about a foot. I don't know for sure, but it was kind of a lot for somebody with no boots. I spent all day yesterday inside trying to avoid the cold and that worked out, but I needed to get some stuff today so I had no choice but to brave it in sneakers.

No pictures or videos of dogs running around in snow, though.

Planes, Trains, and Automobiles

2009-12-18T19:00:00.000-08:00

Possibly the greatest movie ever and if aliens ever land and try to figure out what humans were all about before President Palin blew us all to smithereens, this is the one video they need to pick up.

L&0S20

2009-12-18T12:40:00.000-08:00

I just finished catching up on Law & Order season 20, and even though nobody who reads this blog cares, I'm going to talk some more about it. The season isn't over yet, but it has been shaping up nicely. It was satisfying to see the drug cartel's ex-DA mouthpiece get convicted, as well as ICEBURNED by Connie on the stand. Jason Jones's continuing role as a right-wing blowhard talking head is of course hilarious on a meta level. Lupo and Bernard keep on being awesome.

Of course the big storyline is the lieutenant having cancer and having Ernie Hudson (yes, Winston!) as a boyfriend. I'm guessing she'll be leaving the show by the end of the season, either dying or just retiring. Apparently she is the longest running character on the show, which is kind of cool. Actually the medical examiner appeared first, Wikipedia tells me, but has appeared fewer times.

This Lt. is clearly a lot better than Cragen (thumbs down) and has only gotten better as the series has progressed. It was nice to see Curtis return, if only for a few minutes, looking REALLY old and mentioning Lenny (!!!). It makes me wonder if Green will ever return. L & O fans will recall that he just left the force after his return to his gambling addiction, and Jesse L. Martin hasn't died, so a return at some point, even if it is only for an episode or something, is certainly possible. As he is one of my favorite detectives, that would be a real treat. The more pressing question is who will replace Lt. Van Buren if she does in fact leave the show. My guess would be a new character, as it seems unlikely that they would promote one of the detectives that we all know and love, especially since neither of the current detectives are particularly experienced, with only a couple seasons between them. Of course there is the possibility of bringing back a previous detective to replace her, but I have my doubts. Here is a slapdash list:

1. Green - Unlikely due to the circumstances of his departure, plus it's not like the actor probably needs this fairly small role.

2. Fontana - I'm pretty sure he's retired and again I doubt Farina would want a role like that.

3. Cassidy - In the words of Wayne, yeah, right...

4. Falco - Nobody liked him in the first place.

5. Cragen - I guess he could move back from SVU, but I'm pretty sure he was disgraced and all. I would root against this possibility, anyway. SVU just keeps getting worse from what I can tell and drags all its characters down with it.

6. Logan - He left CI and I doubt he'd come back, but who knows? They seem to love his character even though he's sort of bland and was always overshadowed in my mind by Briscoe.

7. New Guy/Gal - I see this as most likely. They should probably get a new woman, or this show will start failing the Bechdel test, although I suppose it failed that test for most of its run.

That's about all I have for now.

L&0S19

2009-12-17T12:04:00.000-08:00

As I mentioned in a previous post, one of the things that rocks about time off is time to catch up on tv shows I may have missed. I just finished season 19 of Law & Order, which deals on and off with McCoy's run for DA and the almost comically corrupt governor trying to make deals with him, helping out his opponent, and eventually resigning after his ridiculous scandals catch up with him. It is artfully done all season and I have to hand it to the writers of the show. They may lack some subtlety, but the way they managed to string that story out in bits across the whole season is pretty great.

Lupo and Bernard are quickly becoming my favorite detective pair. It is hard to say that they're better than Brisco and Green, but they're up there. They have great chemistry despite them both being smart mouths. I'm kind of glad that they didn't do too much with Lupo and Rubirosa or a possible romance between Cutter and Rubirosa. She's fantastic and is now either my #1 or #2 favorite ADA. Cutter's alright, what with his ridiculous legal theories that somehow work out, but I have to say they are being very generous with the convictions given the evidence that he uses all the time. Also it kind of annoys me that he was promoted over Rubirosa, who, as I mentioned, is great, and has a very fun name to say, to boot. Alright, that's it. On to season 20 or maybe some zombie movies.

Watching TV

2009-12-11T12:30:00.000-08:00

One of the good things about break is watching tv. Usually it is terrible, actually, but I just happened upon a rerun of the Monk finale, which I hadn't seen. I have to say that it seems like a cheap way to end the show to suddenly introduce his wife's daughter, and the false suspense of will he survive the poison and all that. Also lame that the killer wasn't a major character, at least, it wasn't anybody that I knew from what little I had watched of the show. The ending song, however, is pretty good. It seems kind of weird in that only one character is actually leaving. When shows end, I think it is customary for the characters to go their separate ways and then their nostalgia makes sense. In this one, though, only the viewers are really aware that it is an ending, so why would the characters get weird? Whatever, I just wanted to find that song.

Star Trek

2009-12-11T11:48:00.000-08:00

I wrote that I would get back to talking about Star Trek, so I'll put together a few disorganized thoughts here.

The cast was pretty good all around, and it was pretty cool how they managed to find people who looked something like their respective predecessors. New Spock in particular looked similar. New Sulu is the wrong ethnicity, I guess, but Old Sulu came to our school and talked about how the name Sulu was chosen to represent Asia without being a particular national name, so that's no thing.

Sulu got to swordfight and that was awesome. We never got enough of that. New Chekov was amusing, from not being able to say v's to running down to the transporter room yelling "I can do that!"New Kirk was pretty much exactly what a young Kirk should be, punching people, getting into trouble and in general being ridiculous.

McCoy was my favorite character, so I was glad that the new guy did a good job and they wrote what little he was in pretty much perfectly in keeping with the character. It was nice how they explained without explaining really why his nickname is Bones.

New Spock was alright, but I didn't like the fact that he is with New Uhura. It really doesn't make any sense, but both of them were good. Old Spock was nice, but where is old Kirk, the SHAT, when you need him?

The only one I wasn't a fan of was Scotty. He was supposed to be a comic character, I guess, but he and that little alien dude with him were just kind of annoying. The villain was also kind of so-so and I kept thinking of him as the Hulk the whole time.

The story was alright overall, even if it involved flying spaceships through black holes into alternate universes.

Captain Pike - good reference, as was the brain worm thing, which I took to be an homage to Star Trek II. Anyway, I guess that's enough.

Done For a While

2009-12-10T17:33:00.000-08:00

Exams are finally done. That is a little one for the gents!

More to Come

2009-12-09T06:21:00.000-08:00

I saw the new Star Trek movie, finally. More to come on that later, though. I'm busing trying to finish a take home exam in the next two days.

Small Event

2009-12-04T21:04:00.000-08:00

Michael Cera came to campus to promote his new movie, and they actually showed a screening of it. At least I think they did. I went to see him talk for a few minutes, but apparently they don't know how to run DVDs here and kept messing it up, so I got bored and left to go to a holiday reception just for the purpose of getting free food, which worked out pretty well. Ah, well, almost done for the quarter...

The Big Nap

2009-11-25T10:22:00.000-08:00

If you are reading The Big Sleep, don't stop reading it for a bit and then pick up reading it again. It's confusing enough even if you don't forget which character is which. DO read it, though, because it is awesome.

Don't Drag Me to Hell

2009-11-23T22:00:00.000-08:00

This is why I don't watch good horror movies. Good ones freak me out, and Drag Me to Hell is definitely one of those, even if it has the Mac guy in it. If you do like them, definitely check this one out.

2009-11-19T08:58:00.000-08:00

Nothin' much is happenin'. Just lookin' forward to Thanksgivin'. Never had one in Virginny.

November

2009-11-10T07:34:00.000-08:00

Is anybody writing a novel for novel writing month? Anybody growing a mustache for Movember? I've got no plans right yet, but we'll see.

Updates

2009-11-04T20:03:00.001-08:00

I realize that I haven't updated as much here, but grad school is way less interesting than Japan, so I think that makes sense. But that last one took quite a bit of effort and no comments. ???

Fright Fest

2009-11-01T05:39:00.000-08:00

Happy November, everybody. I hope your Halloween was as cool as mine was. I went to Fright Fest at Six Flags (Great America?) in New Jersey somewhere. It was pretty great.

Having been to the Six Flags in/near St. Louis a bunch, I had to compare. This one is very nice and I think bigger than St. Louis's, which means more roller coasters. There are some bad sides, though. As you increase the size of the park, I guess you increase the number of people disproportionately or something, because some of the wait times are just ridiculous. We got a "Flash Pass," which lets you reserve a ride an hour in advance, basically, and when you get there, you get to use a different entrance which cuts your wait time down to maybe a couple minutes. It is basically the only way to go in a park where some of the roller coasters have wait times of 2+ hours. So I will talk about the coasters and hopefully other fans will like that.

Kingda Ka - This is their newest one, and it's insanely popular. It is really only one hill, but it is supposedly the highest hill in the world at 456 feet or so. They don't pull you up with a chain or anything like that; they basically use a slingshot at the beginning to rocket you to insane eye-watering speeds. Even then, I guess it fails some times so that the train just rolls back down (safely) to be launched again. The other insane thing about this is the wait time. The average wait-time I think is 150 minutes. I can't imagine it on a summer day, which would be even worse. That is for a ride of about 10 seconds. It is ridiculous. Also, it breaks down all the time. Even with the flash pass, we waited about two hours because it broke down three times. Everyone else was raving about it, but I think it's kind of "meh." It's just one up and down, even if it is very high and fast.

Batman - Very similar to the Batman in St. Louis, so pretty good, but I'm not going to go into more detail, assuming you have ridden that one.

Superman - We didn't ride this till last, when it was dark and raining, but I think that may have helped it. It is sort of gimmicky in that you get in the chair and then it tilts so that you are facing the ground, and the coaster simulates flying. It does sort of make you feel like superman, although fundamentally it's not that good a coaster. There is a part where you are in a loop, facing the sky that is pretty cool. The only other issue is that the restraints are in front of your chest and feet, but not anywhere else, so it is sort of an awkward position. Not bad, though.

Bizarro - Bonus points go to this one for continuing the DC theme with one of the cooler Superman villains, who are on the whole very lame. I guess it used to be called Medusa, but Bizarro is way better. The play strange music/people talking at you the whole time, which is nice, but I couldn't tell what is going on. I like the DC theme and when it is made to feel like the coaster is part of something going on (Superman flying, Batman swinging around) in the DC universe, but I didn't get what Bizarro was doing. Still good. The coaster itself is like inverted Batman, but had some very good loops and whatnot.

Skull Mountain - This was like the little kids' roller coaster that we did on a laugh. It's all inside a building, so it's dark, and there are blacklit skulls and pumpkins and whatnot. It's actually not bad, but maybe I just like rollercoasters where you can't see every drop, etc.

Nitro - Good Lord this one is fast. It's a traditional one that goes insanely high and insanely fast. It was weird for me because there's no belt or anything, just a single lap thing connected to a bar. I don't know why that feels so freaky, but it does. Anyway, lots of fun, especially when it is misty and you can't see very far ahead. Also, the first hill is a crazy steep drop, so if you are in the front, it looks like you are just falling straight down.

El Toro - Very nice wooden coaster. It's very fast, I think one of the biggest, smoothest wooden ones around. We rode it in the rain and it was stinging our faces, but it was still probably my favorite. All of them were pretty great, though.

I think that's it. I'm still waiting on a Green Lantern-themed space coaster.

Yankees Fans

2009-10-30T05:59:00.001-07:00

I don't get Yankees fans. It's like watching Star Wars and actually rooting for the empire.

Lack of an Update

2009-10-28T19:08:00.001-07:00

I suppose I should update, but there's not much to say. It's almost Halloween, I guess. That's pretty neat. It doesn't really smell like fall in the city so you kind of lose touch with that kind of thing. Penn's campus has trees, at least.

2009-10-21T20:53:00.001-07:00

Phillies just won. People are going crazy outside. You can hear them from the 14th floor.

SNL

2009-10-17T21:47:00.000-07:00

I haven't watched SNL in years, but since I don't have much else to do except linear algebra homework, I figured I might as well check in and see how it's doing. I have to say that it's pretty alright and that I would probably enjoy it quite a bit if I were still fourteen years old. There are still completely unoriginal talk show skits, but even the best generations of SNL casts did those, so I can hardly count those against this batch.

My only real complaint is Kristin Wiig. She's so painfully unfunny that she managed to be overshadowed by the straight man in a sketch where she was pretty much the whole joke. She seems to be from the Molly Shannon school of weird voice = funny, right guys? I continue to be mystified by critics' love for her since she seems entirely devoid of talent.

On the plus side, Shakira's performances are so horrendous that that they are funny.

Edit: I forgot to mention that either these Bud wheat beer commercials are way off the mark or I am old beyond my years. They are terrible and make me want to drink this new beer less, which is saying quite a bit.

Happy Birthday to Me

2009-10-16T05:13:00.000-07:00

Happy Birthday to me. Internet identity thieves don't steal this information about me.

Sort of unrelated things that I'd like to post about. I spent 9-5 yesterday grading an exam with the professor of the class. Today I will probably grade some labs. Hooray.

But, when I got back, my roommates and I had taco night and they also bought an ice cream cake, all of which was great. Thanks also to ma for the gifts.

Two days ago, though, was huge. Guess who came to campus? I will tell you since I can't hear your guesses, anyway. George Takei. That's right, Mr. Sulu! He is also on Heroes, I guess. A Japanese person told me I spoke better than he did, though, which is hilarious.

Regardless, he is awesome and it is crazy to see and hear him in person. That voice! He was mostly there talking about the gay marriage thing, but also about his time spent in internment camps as a kid and of course a bit about Star Trek. There was a too-short period for questions, where a few people asked about Obama, etc., but the highlight was a hugely nerdy dude asking about Star Trek who even mentioned a specific episode ("Mirror, Mirror") in his question.

Live long and prosper!

Columbus Day

2009-10-12T11:33:00.000-07:00

No work today because we are honoring Christopher Columbus, a guy who is famous for having the wrong answer to a problem that was solved over a millenium before he was born, and neglecting to convert units NASA style, so that he ended up nowhere near where he was going. Upon arrival, he decided that the peaceful and friendly people "ought to make good and skilled servants" and that he could "conquer the whole of them with 50 men." He instead ended up just killing the lot of them. And for what it's worth, he also probably brought syphilis from the New World, killing a few million more folks in good time. Happy Columbus Day!

Edit: I forgot to mention that Monday was coincidentally a Japanese holiday, taiiku no hi, which a friend reminded me about in an email. It's sports and health day, roughly.

The Very Hungry Caterpillar

2009-10-08T09:33:00.001-07:00

I was clicking around on a break from homework and found this article about The Very Hungry Caterpillar, and it took me back to reading this book to little Japanese kids so many times that I could recite it from cover to cover. Good times. I can also attest that one of those 47 languages it's been translated into is Japanese. Anyway, it's Thursday, so I've got four strawberries to eat...

Legendary SVU Episode

2009-10-06T10:36:00.000-07:00

This is it! This is the one where the computer guy is on the edge and disobeying orders and whatnot. Hilarious!

Grading

2009-10-02T18:05:00.001-07:00

Is incredibly boring. Ninja Warrior is great, however.

Back to the Monday

2009-09-28T19:44:00.000-07:00

Today was Monday. I didn't really do much, but I guess that is kind of par for the course. A lot of people here seem to not come in to work unless they have something specific to do at the office. I go in to study a bit, but I had office hours today, which meant I had to be there to do very little since very few people come in this early in the year, so I studied then. I don't know.

One thing I did do was play some Back to the Future for the NES, which is just as terrible as I remember it. It is such a grating game for a few reasons, which I think I will talk about for lack of anything else to say.

A lot of NES games suffer from horrible controls, which render them basically unplayable, and therefore forgettable. You try them once and give up. Back to the Future actually controls just like it is supposed to, so you are constantly under the illusion that you can succeed when you really can't, leading to much frustration.

The problems result from a few enemies/stages. The first is the bees. Why does it have to be bees? You are attacked numerous times each level by bees that are unfairly allowed to essentially home in on you, which is really unfair in what is basically a forced scrolling shooter because you can't move in a reasonable way while they can.

The next problem is the non-running stages. When I played the game almost every day on the actual NES, I managed to get past the first special stage through sheer devotion, but since then I've never been able to get past it. The perspective switches to a sideways shooter where you throw something at bullies who run at you. It looks like you are throwing sandwiches, but I can't tell. The problem is that there's no real visual indication which "slot" the enemies are in, so you sort of have to get very used to slight visual differences just to hit them, and the requirement for success is so absurdly high that only the most dedicated players will beat the stage, and it is only about 1/4 of the way through the game.

I'm not even going to bother mentioning that none of the game makes sense or has anything to do with Back to the Future in anything but the most tenuous sense. Try it on virtualnes.com if you want to see what I am talking about.

Weekend

2009-09-27T10:44:00.000-07:00

Eric came up this weekend from D.C. and we had some fun. I don't have pictures of anything, sadly, so I'll just make a short, incomplete list.

-Saw some sort of festival in chinatown.

-Ate Peking duck.

-Drank birch beer, which is like root beer.

-Ate a cheesesteak, with Whiz, of course.

-Various general fun things.

Ambiguous Pronoun Reference

2009-09-23T16:46:00.001-07:00

One of the drawbacks of being part of a culture instead of just on its fringes is that you are constantly exposed to it, which can become grating very quickly. What I mean is that I think the words "if you like it then you shoulda put a ring on it" will never find their way out of my brain. I keep imagining what that could mean out of the intended (but not specified) context. What kind of rings would need to exist to obey this rule in every case? How does one put a ring on abstract concepts?

Monday

2009-09-21T10:01:00.000-07:00

I have my first official office hours today. Other than that there's not much going on. There are some welcome events which I think are aimed at undergrads but I might try to get some free food out of one later. Alright, that's it.

Hairpiece

2009-09-17T17:24:00.001-07:00

Can someone please point me to something with Kristen Wiig in which she is funny? I have only seen a few things featuring her, and she is always the weakest part. I just saw an imitation of Madonna she did and it was painfully unfunny. I have seen her in a few things that were funny, but not the parts that she did. Her main skill seems to be saying/doing something awkward and staring at the camera or otherwise holding up what we'd like to see from happening. Yet, she is being heralded as the new Tina Fey. What am I missing?

Orientation Day 4

2009-09-17T13:14:00.000-07:00

Today was by far the most useful, and also gave me not only a free lunch, but the opportunity at another free lunch later. Today we finally got put into our departments and did some practice teaching, which I think I did pretty well at. I also found out a bit more about the class I am TA'ing for. My hotel card key stopped working today, but they did something to it and it started working again. I guess they are designed to stop working after so long, but I don't know. Seems weird to me.

Orientation Day 3

2009-09-16T10:15:00.000-07:00

Today is basically a day off. Apparently it is commuter orientation day, so there are a bunch of local noobs running around, I guess. I had to go in to campus to talk to financial aid about why they sent a letter outlining a different package to me. It turns out that everything is cool, it's just that some stuff is run through the department or doesn't count as financial aid so much as a salary, so once they figured out what it all meant, nothing really had to be done. Other than that, I spent some time reading about eigenvectors and listening to some new freshmen (I guess) talk about the health care reform "debate." Now I'm back enjoying the wonderful hospitality of the microtel. There is a bed-like thing right under/beside the window. I am not sure if it is actually a bed, but it seems designed for people to lie on it. I'm not clear why this is included unless these rooms can be used by three people cramming in here. It is a mystery!

Update: I may be TA'ing for an upper-level stats class now? That could be bad as I only took stats one time, four years ago, and it was both my weakest and least favorite math class. We shall see, I guess.

Orientation Day 2

2009-09-15T14:21:00.000-07:00

My, or rather Microtel's, alarm clock didn't go off today, so I didn't wake up till 8:50, as I'm still on central standard time. There was a free breakfast today for TA orientation 8:30-9:00, but obviously that is optional. The real stuff didn't start until 9:00, and even that was only introduction. The real talks started at 9:35, but since the earliest train I could take in was at 9:17 and takes about 12 minutes to get to the station nearest to campus, I was a couple minutes late, still.

I came in a little after they had started talking about being prepared to teach classes, etc., which doesn't really matter too much to me since A)I have three years of experience as a TA B)I'm not actually teaching a class C)I have actually taught a ton of classes for the last two years, albeit to little kids and mostly in Japanese and D)teaching isn't really that complex, anyway.

Anyway, I craftily got myself a nametag off the table, wrote my name on it, and turned it in with everyone else at the end, so I was there for the purposes of attendance. The talks (classes?) weren't terrible but were fairly general. There was a chemistry professor who now runs some sort of office dealing with student retention, and she actually talked about trends that are somewhat interesting. Other than that, it was mostly stuff that should be common sense, like being prepared and explaining things in different ways.

We got done around noon, and since nobody contacted me from the math department about there being anything else, I just walked around, even around the math building, which was mostly empty, until I got bored and I was close enough to the train station that it was convenient to take the next train back to the hotel.

I'd like to do some math or at least some teaching, and I'd also like it if the university would figure out what financial aid they offered and I accepted, instead of sending letters home about me being approved for loans I never asked for. Anyway, tomorrow is a day off (why is it scheduled like this?), so I will probably go talk to them then.

Orientation Day 1

2009-09-15T10:34:00.001-07:00

I am writing this on day two of orientation for convenience, but I will split it up into two posts unless I just give up after one day.

All the info I had about orientation was wrong, probably from the wrong year, but I don't know for sure. I wandered around campus trying to figure out where to go and what to do for a while, then I went back to the hotel to get some documents which it turned out were (A) wrong and (B) unnecessary. I got an ID card, which only took a couple minutes. Then I just wandered into the building that had a bunch of people in it. You would think there would be signs all over telling you where to go, but no such luck. Also, other people on campus seemed to not know where to go.

Anyway, I got registered for the thing. I wasn't late, but I was one of the last people to arrive, I think, and so the few people that talked to me probably think I am stupid or something. The only bad part is that I think some organization was giving out bags because a lot of people had them, but I couldn't find it, so I think they probably ran out or left.

After a while there were some talks that basically amounted to "be professional and proactive," but took a few hours. Nobody ever accused academics of efficiency. They weren't terrible, but they also weren't particularly interesting. I met a dude from China. There seem to be a lot of new Chinese students, so maybe I should have studied Mandarin, or maybe Cantonese. I don't know where in China they are from, I was just reading their nametags, except for this one guy I already mentioned.

After all was said and done, there was a picnic-like thing for the new students, so I got some free food and Yuengling beer, which is at least a third-tier beer as I see it, so I was happy. Also one of the dudes working gave me an extra can toward the end of the night and he seemed cool. I hung out with some public health students and an electrical engineer and they seemed pretty alright. Fascinating day...

Microtel

2009-09-13T14:08:00.000-07:00

I'm in a microtel, a small hotel whose name is derived from microphone and Rotel, the name of a Japanese electronics company based in the UK. Look it up.

Actually it isn't that small and it's ok, so I put up a couple pictures for your viewing pleasure. The part that sucks is that I have to live here for a week and commute into the city even though my apartment is basically on campus because they won't let me move in for basically no reason at all.

Iwakan

Heart Growing Fonder, Anyone?

Mammon, You Been on My Mind

Excellent

Songwriting Potential

Well

Wow

Motte

Sports Writing

Lekach

Continuing the Discussion

Mirepoix

Generalized Abstract Nonsense

New Hat

In Response to a Math Question

Hey Look What I Made

Take a Load Off, Fannie

Planet Waves

Can You Guess Who?

Comment!!!

Ain't No Good

I've Been Listening To This Song Obsessively Lately

New Quarter

Not Much Happening

Risk-y Business

Gaydar

Takoyaki party!

Belated Pictures of Sand

Eric

Title

More Math

Bayesian at the Moon

日本語の投稿

Natto

Winter Trip

Well, it's Another Saturday Night

Halloween

Happy Birthday, John

Break *Updated*

Zorgus Borgus

Short Review

Tragedy!

Camden Yards

Cheesesteak

I Lament the Coming of 3D

World Cup Update

World Cup

Make It So

Graphs and Donuts

Half-Post 350?

Lol-iday

野球

Hi Emily!

Too Many Mornings

I Review a Movie I Have Not Seen

Hidden Post

Finally Done

No Posts

New Post

Converge Slow, Homie

Snow Day 2: Bad Sequel Joke

Snow Day

Some Movies

Japan Trip

Baby Got Back

Short Update

Planes, Trains, and Automobiles

L&0S20

L&0S19

Watching TV

Star Trek

Done For a While

More to Come

Small Event

The Big Nap

Don't Drag Me to Hell

November

Updates

Fright Fest

Yankees Fans

Break Updated