LaTex Happiness

Whoa. Thanks to Lee (and the folks at watchmath.com), I can now put stuff like this

$\int_{a}^{b}f(x)dx$

on my blog. Aren't you glad? (Note that if you view this in an RSS reader it likely won't come up right. Sorry!)

Today's Accomplishments

Life is hard around here lately. School kind of ate me, and I'm waiting to see if I will agree with its digestion. (I'm not sure which outcome to prefer, frankly.) I'm not technically "behind" at anything right now, but I still feel I'm being crushed. At any rate, here are my accomplishments for today:

• Wrote up the last lecture of analysis notes. (I rewrite, with additions/modifications/clarifications, the notes from each analysis lecture. This is critical to my understanding and ability to reference the material later. Lately I was several lectures behing, but I am now caught up.)
• Talked to Ed about a couple of things I didn't understand from the analysis notes. We were able to resolve them together.
• Looked extensively at the two problems on this week's analysis homework. I solved (I think) the first problem, which I typed up in LaTex. The second problem was less tractable but I identified some of the difficulties I have with it, and thought about those for a while.
• Typed up the Logic homework problems. I haven't started working on this homework yet, and I think we haven't covered almost anything that is on the homework (due 11 days from now), but at least the problems are typed up, so I can modify this document when I'm ready to start working. Also, by typing up the problems, I now have a much clearer idea of what the homework entails. ("Entails," ha ha ha.) These homeworks have typically been 15-20 pages of dense handwriting on college-ruled paper, so I've decided to experiment with typing this one up instead of killing my hand. (My right middle finger has developed a chronic bruisey ache when I write by hand for more than an hour or so at a time.)
  
• Tested the draft lecture notes I wrote for the 10-minute mini-lecture on completing the square that I might have to deliver on Wednesday (but probably won't deliver until the next week). My first draft took 12 minutes to deliver, which is pretty good, so I revised it downward. The second draft took 14 minutes. Oops. I have done a third draft but I didn't have the heart to deliver this (complete with writing on the board, of course) to an empty room for the third time, so that will have to wait.
• Brought my Probability book home from school so I can finish up the homework due Wednesday (which was posted to our course website yesterday, when I did about 3/4 of it when I saw that it had shown up).
  

Despite the above, it hasn't felt like a very productive day. I can't tell what is or is not productive. I'm pretty sure I didn't work anywhere near 8 hours, which is a standard work day. My program doesn't seem, so far, to require that amount of work. Yet the amount of work that it does require feels like it might be beyond me. And yet, I'm basically crushing (with enormous effort) my classes so far, and, as I said earlier, I don't think I'm actually behind on anything. So I don't know what to think. I feel like a person driving a car that has lost control of steering and brakes but who happens to be going down a straight freeway with no traffic...for the moment.

At least this isn't as bad as Tuesday night, when, as I stayed up until 4AM to finish my logic homework, I kept thinking about how grad school was pitting the intolerable (finishing the homework) against the unthinkable (not finishing it).

Fiasco Week

The past couple of weeks, before this one, have been pretty easy. I knew that they were going to be pretty easy because I didn't have any logic homework due until this week and nothing big was happening in my pedagogy class, leaving only the normal weekly analysis and probability homework. And the first of these two weeks, I worked hard to make sure I was doing enough not to make this week hellacious. But last week I didn't do very well, and in fact I am not sure I accomplished anything at all Thursday through Saturday aside from attending classes.

This morning, our third mammoth logic homework was due. It had 10 problems. We usually have two weeks for these homeworks, but our professor was out of the country for a week, so we had three weeks for this. Last night I had finished the 8th problem by 8:30, so I had two more problems to do.

I finished (mostly) at 4:19 AM. And...ugh. That is just way too late to be up doing homework. Part of the reason it took so long is that sometime after 8:30 I just really broke down. I had a bad headache, I felt hopeless about the derivations that I had to do, and I just...I don't know. A friend from our program invited me over to her house, and I went, and working with her was great, but didn't prevent me from falling apart.

I skipped logic class this morning (got Ed to turn in my homework for me) and slept in until 12:30, then barely made it to my probability class on time at 2. (Thank goodness I had finished my probability homework, also due today, some days earlier.)

Tomorrow I have analysis homework due. We get this homework once a week and it's always one problem. Sometimes the problem is fairly tractable and other times it fills me with despair, but so far I have always gotten them done on time, correctly, for full credit, so that's promising. This is my little mountain to climb each week, and doing them, and doing them well, fills me with a lot of joy every time.

I am almost always either completely finished by Monday or I basically know what I'm doing and just need to clean up the execution a tiny bit during the week. But even though this one is due tomorrow, I still don't know how to do it. I did work on it a little bit (read: four pages worth of notes' worth of work) on Saturday, but I didn't get anywhere with it. I do have things I can try next, so I don't feel hopeless quite yet, but I'm not in a great position.

Another thing I do every week is neatly rewrite my analysis class notes, filling in the missing details and making sure that I understand them. I'm three lectures behind on doing that (there are two lectures each week), so that's not great either.

I think one thing that I need to do is regularize my sleep schedule. I have morning classes M/W/F but only afternoon classes T/Th so it's always very tempting to sleep in on those days, especially if I've stayed up late the night before working on something, but really in any case. But I don't think that's doing any favors for my productivity overall, because it means there are more days on which I feel disoriented due to getting up at a strange time.

I am also thinking of giving up caffeine (for the umpteenth time). It's getting to the point where I feel mentally dull all day until I have my tea, and that's not good, and last night's headache may have been caffeine-imbalance-related as well.

Now it's time for me to go tackle the analysis homework for real. What's unfortunate is that I am much more willing to work on something that isn't due yet than on something that is due soon. I don't like the feeling that I have to figure this out in the next, say, eight hours in order to have a legitimate shot of being able to turn in something decent tomorrow, and it makes me not want to look at it at all (or, you know, not yet).

Looking forward, next week should be a bit easier. We don't have a new logic homework yet, possibly because we have a (small) paper due in 2.5 weeks, and the only big thing I need to do other than next week's analysis is prepare and be ready to deliver a 10-minute mini-lecture on a college algebra/pre-calc topic for my pedagogy class. That means I'd better work hard on that paper next week.

The Axiom of Choice

You can't get too far in analysis without running into the Axiom of Choice (AC), which is an easy idea to explain but deceptively tricky to grasp, I think. (Analysis, for those who aren't aware, is basically the study of functions - it is what calculus is called when it gets theoretical.) I've wanted to write about AC for a while.

What the Axiom of Choice says is that if you have an infinite collection of nonempty sets, it is possible to choose an item from each set. So if you had, for instance, an infinite set of sock drawers, you could choose a sock from each drawer.

There are two "choice" types of situations where you don't need AC. If you have a finite number of sets, no matter how many, then you don't need AC. You can use the principle of mathematical induction instead. That is, you can say, basically, OK, I can choose something from the first bin because, duh, it's not empty. Then, if I've chosen something from some number of bins up to this point, I can always choose something from the next bin, because again, it's not empty. But even though this works for any finite number of bins (even one billion bins), it doesn't cover an infinite number of bins.

You also don't need AC if you have a specific method of choosing from the sets (bins). For instance, if you have an infinite collection of pairs of shoes, you could say, "From each pair, choose the left shoe." That's basically creating a function from the pairs to the chosen objects, which is what we want. (AC says there is such a function whether we can define it explicitly or not.) People often contrast shoes with socks to explain this difference, because shoes have a right and left and so there is an explicit function for choosing, but socks are undifferentiated.

Of course, AC is usually used with sets of numbers, not sets of socks, because there are not actually an infinite number of socks even in the entire universe, as best I'm aware.

Now, if we were talking about sets of natural numbers (subsets, that is, of {1, 2, 3, ...}) we could just say, "Always choose the smallest one." Every set of natural numbers has a smallest element. This property is called being "well-ordered."

The real numbers, though, in their normal order, don't have this property. There isn't a smallest one of all, and there are a lot of sets of them, even bounded sets, that don't have a least element. For instance, "Every real number larger than 2" doesn't have a least element. (2 isn't in the set, so that's not it, and no matter how close you to get to 2, even if you pick, say, 2.000000001, there is always a smaller one still in there, say 2.0000000000000000000001.)

The Axiom of Choice is equivalent to saying that the real numbers are well-ordered. It's not true in their normal order, but AC says that there is some order you could put them in such that every subset of them would have a least element. (It's sort of a crazy idea - don't try it at home. AC doesn't provide such an order, it just claims that it exists. In fact, if we could define the order, we wouldn't need AC at all!)

To see the equivalence, let's say you had an infinite collection of sets of numbers, and you wanted to choose a number from each set. If you have well-ordering then you can use the rule "always choose the smallest number."

Similarly, if we have Choice, and we want to well-order the reals, we can first choose one to be the lowest one, then choose another one to be the next lowest, and so on ad infinitum.

So why this is interesting? First, AC is an Axiom. That means you can't prove (or disprove) it from anything else in the normal theories we use about numbers. It's just an assertion from the heavens. And while most axioms that you commonly encounter (such as that two points determine a unique line, or that a*b = b*a) are what we might call "obvious," AC is...well, is it obvious to you?

In fact, its use is rather contested.

If you don't use AC, then you can't prove a lot of the important theorems of calculus. And that's not just a matter of theoretical concern - we use calculus all the time to solve all sorts of problems, and it demonstrably works. Calculus is important, and it would be nice to think that it has a sound theoretical basis and isn't just a bunch of malarkey that works by chance, or for reasons beyond human comprehension.

On the other hand, if you do use AC, then you get some crazy results like the Banach-Tarski paradox. Those guys proved that, using AC, you can cut a sphere into a finite number of pieces and then reassemble the pieces into two spheres the same size as the original, which is more or less obviously not true. (The way the cuts are done is not something we can actually replicate, even though it is a small number of cuts, so this isn't an empirical question.)


So, there you have it: the Axiom of Choice.

An Idea

I never write stories or even try to write novels, but I was thinking about this today. It would be funny if you had a story involving a person (like an agent) time-traveling back to Nazi Germany to complete some mission, and the mission was put into peril when they had to wait for a late train. Imagine the annoyance at learning that the canonical one good thing about life under fascism was not true.

(Come to think of it, that is sort of how I feel when Republicans are not fiscally conservative.*)

(*No comparison of Republicans to fascists is intended or should be inferred.)

The Working-Procrastination Continuum

My work habits have definitely changed a little bit since I started grad school, shifting towards the better end of what I see as a continuum between working and procrastinating that goes something like this:

Flow: You're working and not even thinking about not working. You might not notice that you're getting hungry or stiff, and when it's time to stop, you wish you could go on. If you do take a break, you spend it wanting to get back to work.

Work is Work: You're working pretty steadily, but it's rough going. You take breaks when you can, and think a lot about how much longer you have to go, or how much more you need to do.

Pretending to Work: You're sort of doing some work, but you stop every few minutes to check email or play solitaire or stare into space. You're trying to get settled down and do some work, but not much is being accomplished.

Trying to Get to Work: You have a definite plan to start working, but you're trying to pry yourself out of bed/away from the TV/off the Internet. There might be a couple of things you need to do first, like clean off your desk or get a glass of water, but you're not quite doing those things yet. But you will soon - honest!

Procrastinating: There's something you could, maybe should, be working on, but you figure you can work on it later, maybe tomorrow, maybe next week. You definitely plan to do it, there's no doubt about that, but not right now.

Pretending to Procrastinate: You claim that you're going to do something, but if you look into yourself, there is no plan at all for getting it done. You might be in a sort of passive rebellion against doing it. There is no time that it could occur to you to work on it that you would actually then go and actually work on it. It is not possible that the conditions under which you would do the work could occur. Some change in attitude (perhaps partly unconscious) would be required in order for it to happen.

Refusal/Blowing Off: You consciously have no intention of doing a particular thing, though you realize that in some sense you should. Perhaps you've given up because there is no longer enough time to get it done before it's due, and it won't be accepted late, or maybe you've just decided it's not a priority for you.

I used to spend the bulk of my working hours in the range from "Pretending to procrastinate" to "Pretending to work" range. I find that, now that I'm in school, I'm never (so far) pretending to procrastinate, and most of my work times are in the "Trying to get to work" to "Flow" range. It's hard to distinguish between procrastinating and just not working right now in my current life, since I always have work that I could be doing, and yet I don't need to work 12 or 16 hours a day either. But cutting out that "pretending to procrastinate" stage is a big deal for me, and spending more time in the various working stages is great.

I still spend a vast amount of time in the "trying to work to work" and "pretending to work" phases. I'm not sure how to get better at that.

A Knock at the Door

Around 4:15 this morning, I was dreaming of something with the feel of fractions, or nested intervals, or cups of varying sizes. Suddenly, something happened whose translation into the world of my dream was alarming, necessitating some sort of action. A couple of minutes later it happened again, and I put words to it: someone was knocking on the door.

I bolted upright, eyes open, heart racing. What did this sign mean? Surely it required a response, but what kind? "Someone's knocking on the door. What is - why?!" I asked out loud to Ed, who was still asleep. I patted my bedside lamp to turn it on.

Once I figured out what door-knocking means in our world, I crept to the door and peeped through the fish-eye lens set therein. I saw, I thought, two women in their early 20s.

Should I open the door? I should not, I thought. My door has (I verified) no chain or little bar to allow it to be opened partway. Perhaps these women were the harmless front of some attack. Why were they knocking at such a late hour? I crept back to my room.

I am sure they saw that I had turned on a light. They knocked again, louder, and again a minute later. They were knocking quite violently. Did they need help? Had they been attacked, raped, left abandoned at my complex? Did they hope for me to call the police, a taxi, their mom? Was I prolonging their plight by ignoring them? Were they our downstairs neighbors, dealing with a water leak?

Ed sat up in bed, dazed, Frankensteinian in his sleeping mask and earplugs. He thought it was morning. What was happening?

"Someone is knocking on the door," I said. "I don't know what to do. I think I'm going to call the police."

Yes, someone is knocking on our door, and they won't stop, I imagined saying. I don't know who they are or what they want, but they won't go away. Maybe they're in some kind of trouble.

"Unless you want to answer it," I said. I told him what I had seen of the knockers. He crept to the door and back. He hadn't seen anyone and thought they had given up - he heard them knocking next door.

Holding my phone, and knowing they were no longer at our door, I opened our door and stepped partly out onto the walkway. A woman stood alone outside of the next door down. She saw me but said nothing.

"Did you need something?" I asked.

"Yeah," she said casually. "My friend lives here." She was pointing at the door. "Do you know Jared?"

"No," I said.

"At all?"

"No," I said.

She was silent.

I went back in and to bed. It took me a while to fall asleep again.

Library Excitement

Today I went to the math & science library at school to get some books I had identified as possibly useful for the 1000-word paper I need to write about a 19th century logician. I visited that library when I was here in April, but hadn't been since school started.

The main library here seems very nice and spacious, but the science library is byzantine, cramped, low-ceilinged, and noticeably fluorescently-lit. (Of course, everything on campus is fluorescently lit, but it's not usually objectionable.) However, there were multiple shelves of books about logic and logicians and I wanted to collect them all! It was very exciting.

Also, since I am a doctoral student, my books are not due until the end of the freakin' semester, which kind of blew my mind. Overall I am pretty psyched about the library situation, thus further proving, were it necessary, that I am a nerd.

Indian Cookery

I've heard many times that vegetarian Indian food can be very easy and cheap to make. I happen to love Indian food, and would be really excited to be able to make it, especially easily and cheaply. (I mean, what's not to like?) So this weekend, I googled around to try to find some easy recipes for daal (lentils) and aloo saag (potatoes & spinach). I read several of these recipes, and then suddenly they all kind of gelled together and I realized I didn't need a recipe. Or at least it felt that way.

So I got some things at the grocery store (Walmart, actually; I can't bring myself to pay grocery store prices these days) and tonight I made my food, roughly as follows:

Daal
1 lb. lentils
1/2 large white onion, diced fine
1/2 clove garlic, chopped
1 can tomato paste (the usual small size)
vegetable broth (about 4 cups, from a box)
butter
peanut oil
spices including chili powder, cinnamon, cumin, cardamom pods, cloves, etc.

I put butter and olive oil in the pan, cooked the onions and garlic at high heat, then put in the spices and stirred everything around in the spice paste until it seemed like going any longer would burn things. Then I put in the broth and tomato paste, and the lentils. I just cooked those forever (they took way longer than I expected!), adding more water as necessary, until they were done

Aloo Saag
4 small red potatoes, cut into bite-size pieces
1 large bag of frozen cut leaf spinach
1/2 large white onion, diced
1/2 clove of garlic, chopped
butter
peanut oil
spices including garam masala (2T), chili powder, and crushed red pepper
salt

I again started with butter and oil, and cooked the onion and garlic in that, and then added the spices, making a paste. I pre-boiled the potatoes (before starting with the skillet part, of course), let them air dry pretty well, then tossed them into the hot skillet with the spice paste. That mixture was a little bit dry, so I kept adding little bits of water to keep everything going. Once I thought the potatoes might have a nice crisp on them (they didn't, really, but whatever), I put in the frozen spinach and a bit more water, and just let that cook down, and then I salted the whole thing.

The lentils tasted amazing all along, but the potatoes & spinach scared me because they smelled extremely much like pumpkin pie, and I didn't want to taste it. I don't usually like it when savory foods go in too much of a sweet direction. But when I did finally taste a potato, my GOD! They were fantastic! Now maybe you just can't screw up potatoes, but the spinach in there was wonderful and...wow, it was just a great dish.

For dinner I had everything, with some brown rice under the lentils. It was really amazingly good, satisfying. I'm afraid of how much leftovers I have (a really enormous amount), despite the fact that Ed also dined on my stuff. The lentils were were well spiced, but very mild (of course), and the aloo saag actually succeeded at being slightly spicy. It wasn't Indian food like you'd have in a restaurant, and it probably would have been more Indian-tasting if I'd put in some cream, but it was recognizably Indian in its general flavor profile. So I have to agree with others: vegetarian Indian food is easy and cheap to make.

My Life

Before I moved here and started grad school, I felt that I had no idea what this life would be like. I know just what it's like to go to an office job every day, and I think the tenor of that life is similar across different jobs. But being in school full time - especially doing nothing but school, as I'm doing now - is a different thing. What would it be like not having as much income? A more variable schedule? A choice of where to work most of the time?

Well, I know what it's like now, I guess. In some ways, it's surprising how much I feel the same, like the same person as I was before. I know that couldn't surprise anyone else about me - of course I'm the same Tam! - but it feels surprising inside somehow.

One observation is that my current life feels much simpler than my old life. Every day, M-F, I walk to school, do stuff, and then walk back home. I almost never drive anywhere during the week, and on the weekends I usually only make one or two trips, for groceries and maybe to go eat somewhere or something. As a result, I don't see as many different things as I used to. My world has contracted a bit physically.

5 times a week, usually at lunch, I eat at a dining hall here, usually the same one. The food is different every day, but the experience is very similar. I used to eat out almost every weekday for lunch, at all different places, so this is another simplification. I go to this place and I eat whatever they have there. The rest of my meals I eat at home, and they are also not greatly varied.

At work, I used to interact (for work purposes) with a bunch of different people, and my assignments were varied, numerous, and overlapping. I'm doing more work now than I was then, yet it is given by fewer people and is less varied while at the same time also being far less routine. And everything has very clear deadlines, which wasn't the case when I was working.

It feels like in general, my life is more tightly circumscribed than before. And I pretty much like it.

For the most part, I don't find myself struggling as much as usual with motivation. Having clear deadlines and more difficult, interesting work makes it much easier for me to get stuff done. I've been operating in a pretty high gear (for me) since school started. I have found, however, that I will need to kick that up a notch to really do well, because my high gear isn't quite adequate to keep me out of the danger of not getting things finished on time. Work comes due in little clumps, so I have the option of relaxing for a few days and then having a few more stressful days, and I'd like to smooth that curve out a bit more than I've been doing.

But there is no question that this life is more enjoyable in just about every way than working for a living.

Landslide

There are certain songs that speak to me very strongly, sometimes for reasons I don't understand. "Landslide" by Fleetwood Mac is one of them. I've always felt an affinity for the idea of speaking to my younger self, or more generally the relationship between younger and older selves, which is what the song strikes me as being about, at least today.

The Problem of Measure

One of the central ideas, perhaps the central idea, of my real analysis course concerns something that is called "the problem of measure." Measure Theory is important in analysis and, eventually, probability theory and other things as well. (During my visit here in the Spring, I asked a grad student studying measure theory whether that was an area in probability and she said, no, it was more like probability was an area within measure theory.)

Anyway, the basic idea is like this. If you have the real line, or a plane, or 3-dimensional space, or as many dimensions as you want, can you measure every subset of it? I'm just going to talk about the real line (all of the real numbers). If you have an interval, we usually talk about the length of the interval as its measure. But not all subsets are intervals. For instance, the rational numbers are a subset of the real numbers, but they don't have a "length." Is there something like length, but more general, that we can use to measure all subsets?

Remember Riemann integration, where you find the area under a curve by approximating with boxes? One way to do that is to measure the boxes that go outside of the curve (the brown ones) and the ones that go inside (the orange ones), then take the limit as you make the boxes narrower, and then see if the two limits are the same, in which case, that limit is the area under the curve. (Intuitively, you can see that if you make the boxes "infinitely narrow," the inside and outside boxes would be the same under a smooth curve like this one. That's what it means to take the limit.)

There is a similar definition of measure, called Jordan Measure. Unfortunately, it doesn't exist for quite a lot of subsets of the real numbers (just like not every function is integrable).

What we really want is a happy kind of measure that satisfies at least the following intuitively obvious conditions:

1. The measure of an interval is the same as its length.
2. If you have two (or more) sets, and they are disjoint (don't overlap), then the measure of their union (both together) should be the sum of their individual measures. (In other words, if you cut something up into pieces, the sum of the sizes (measures) of the pieces should be the same as the size of the original.)
3. If you have two sets, A and B, and A is a subset of B, then the measure of A should be less than or equal to the measure of B. (In other words, if A fits inside of B, then A shouldn't be "larger" under this measure.)
4. It is "translation invariant" - moving a set around (like by adding something to every number in it) doesn't change its measure.
5. The measure of the empty set is 0.
6. Measures are never negative.

What we're studying now in analysis is called Lebesque Measure. Actually, what we have is Lebesque Outer Measure, which is the Lebesque equivalent of the outer box method (the brown boxes above). Here is the difference between Jordan measure and Lebesque measure. In both of them, you are looking at intervals (the 1-dimensional equivalent of boxes; of course when you do this in more dimensions you use boxes or rectangular solids, etc.). In Jordan outer measure, the intervals can't overlap, and they have to be finite in number. In Lebesque outer measure, the intervals CAN overlap, and they can be countably infinite (you can have one for each natural number, going up to infinity). In both cases, you then take the infimum (which is basically the lower limit) of the sum of the lengths of the intervals, for all such sets of intervals.

There is no Lebesque inner measure. Lebesque outer measure exists for every subset of the reals and it has a lot of the nice qualities we want, but it doesn't have criterion 2 (called "additivity") above for all sets. So what they did was, they said, hey, if a set is additive with every other set, then it's "Lebesque measurable." Otherwise, we don't care about it. (Ideally you'd have an even better measure that works perfectly for all sets, but such a thing either doesn't exist or hasn't been figured out yet, as best I'm aware.)

Basically, every kind of set you'd easily think of is Lebesque measurable. Certainly all of the intervals, all singletons, plus sets like the rational numbers are measurable.

Right now, what I'm struggling with is that we have approximately three kadrillion theorems about Lebesque outer measure and about Lebesque measurability, and I'm having a really hard time keeping them all straight, even though I've written out each one with proof and even though I've (several times) made lists of all of them. The idea that I might have to be able to reproduce any or all of these proofs on an exam is terrifying but possibly true. So...that's my own little personal addendum to this otherwise no doubt extremely boring post about math.

Eating on Campus

This semester, at least, I'll be on campus every weekday. I'd like to be on campus more hours than are technically required just to go to my classes, because it's usually easier for me to do productive work away from home. So the question arises of what to do about lunch.

I considered bringing food from home, which is cheap and offers a lot of control over content. But honestly I've always sucked at follow-through on that, and every idea I have sort of sucks. A cold lunch is not that appealing. A hot lunch requires more forethought, and then you have to heat it up, and usually bring the containers back home for washing. That's a lot of trouble.

There are a various places to eat near my building. On campus there is a food court with many inexpensive options like Taco Bell and Chik-Fil-A. Off campus, but still nearby, are some more sandwich shops and the like. The downsides to this plan are that the food tends to be both unhealthy and more costly than I'd prefer on my stipend.

Instead, I opted for a meal plan, like any student. The one I got gives me a meal every day of the semester (85 in total) and the cost per meal is $5.09 including tax. The $5 cost fits into my original budget pretty well, the meals are all-you-can-eat, and it's very convenient. But is the food tolerable?

I've now eaten at a dining hall twice, and the answer is yes. Yesterday I ate at the dining hall that emphasizes more healthful foods (nothing fried, for instance) and I had a very reasonable, healthy, and enjoyable meal. Today I ate at the dining hall nearest to my office and had another decent meal. In addition to the usual hot cafeteria foods (which tend to have very reasonable options, at least so far), there is a salad bar (self-serve) and a sandwich bar (not self-serve). The place I ate yesterday also had a pasta bar and a panini bar. The biggest dining hall has a grill-type area with burgers as well. And there are numerous drink options including a tolerable imitation of iced tea.

I won't say it's gourmet, or even particularly well-prepared, but it's easy to get a healthy protein, some good vegetables, a to-die-for roll, and a salad, and that's a steal for $5. I also like the fact that I'm not wasting much packaging. I kind of hate when you get fast food and everything is all individually wrapped and it comes in a bag. The dining hall is, of course, real plates and silverware and non-disposable cups. I like getting out for lunch, going somewhere, and the atmosphere of the dining halls has been all right so far, with good music in the background too.

Next year, when I'm a TA/TF for real, the deal gets even better. If you are willing to invest in 40 meals, which roll over from semester to semester, then as a faculty or staff person, you only have to pay $3.79 per meal (including tax). At that price it starts to seem silly to bother doing anything else.

But the Worst Is...

Monday's xkcd tickled me:

But for me, the worst random sound in a song, and this occurs in a few KSAL songs, is the sound of a bicycle bell. Do you know the kind of bell I mean? It's the kind you put on a bike and it has a little lever on the side and when you pull it, the bell goes "zhing, zhing." Hearing that when you're backing out of a parking spot or tooling along in a neighborhood is definitely enough to trigger a heart attack.

Ikea Cartoons

Ed and I recently bought some furniture from Ikea. When you buy from Ikea, you typically have to assemble the furniture yourself, and you get a large booklet full of instructions. Aside from a safety warning that is printed in 30 (!) different languages, all of the instructions are in pictures. The first page of our booklet contained the following general pieces of advice:


I find these drawings immensely charming and I love the details like the different styles of frowns on the left-hand people.

But the drawing that gets to me the most is in the second row, where it is recommended that you assemble your furniture on carpet rather than a bare floor. The guy who has broken his furniture breaks my heart:

In contrast to his carpet-kneeling alter-ego, who strokes his new furniture with pride and delight, this fellow is greatly saddened and disappointed by his error. I realize that this is somewhat humorous, but I've always noticed that I find other people's disappointment very painful to empathize with (more painful than grief, for instance), and I actually find this drawing kind of upsetting. I found myself thinking about it in bed at night and feeling sad.

Fall 2010 Schedule

This morning, I met with the graduate advisor and we hammered out my schedule for the fall. I'll be taking four courses rather than the usual three since I have a fellowship and don't have to work as a TA this year. The final schedule is as follows:

5000 Instructional Issues for the Professional Mathematician
M/W 3:30-4:50PM
This is the class for new TA/TF's. I guess I get to take it this year even though I won't really be a TA/TF until next year. This one also meets twice before the semester starts (so, next week).

5010 Mathematical Logic and Set Theory
M/W/F 10:00-10:50AM
This isn't a normal course in the sequence, I don't think, but more of a one-off. The advisor recommended it as being probably very interesting and possibly a good prep for topology later on.

5310 Functions of a Real Variable
Tu/Th 2:00-3:20PM
This is the first course of the core sequence for real analysis. After this course and its successor, I could be ready to take the qualifying exam in real analysis.

5810 Probability & Statistics
M/W 2:00-3:20PM
Prob/stats is not a required core sequence at UNT, but they do have a qualifying exam in it (new this year; nobody has taken it yet, ever), and this is the first course of the sequence for that one.

Dr. B originally had me starting the Algebra sequence instead of Prob/Stats, but I told him I might want to do research in probability ultimately, so we swapped it out so this would happen earlier in my graduate career.

My first job at this stage in the game is to pass two qualifying exams, so it's important to get to the four required core sequences (real analysis, complex analysis, algebra, and topology) as soon as I can. If we count prob/stats (which we can since it has a qual associated with, even though it's not one of the required four sequences), I'll be taking care of two of those this year. Dr. B would like me to take my first qualifying exam next August and the second one in January of '12. I technically have four years to pass two of these exams, but doing it earlier is better.

I also got my campus ID and access to the computer labs (password, etc.) so I'm doing pretty well.

The plan for next semester is that I will take the continuation of the prob/stats, analysis, and logic courses, plus either the introductory topology course (the prelude to the core sequence in topology) or a reading course in something or other (to help me prepare for one of the exams).

My Visit with Mosch

Saturday, I flew to Albuquerque and spent the day with Mosch in the rehab hospital. When I parked and walked up to the building, he was waiting for me outside, standing with his sitter and with Nancy and another friend. I was astonished to see this guy who looked kind of like Mosch and then have it turn out to be actually Mosch. He recognized me as I walked up, which was awesome.

Back inside the hospital, we walked around some. He asked me to tell him about what's going on with me right now, so I did, taking a couple of videos of him on my phone. He wanted to play cards, so we fetched some from the room and played a 5-person version of War. He was able to cut the deck, deal cards to each player when it was his turn, and determine which person won each round. (The only card he didn't recognize, at least before he got a little tired out, was the Joker.) When we stopped, he was able to count his cards in his head, and arrive at the right total (15).

Mosch is walking now, which is great. When he walks, he wears a wide canvas belt around his stomach, and his sitter walks behind him, holding onto the belt. His balance isn't perfect - he walks a little like a drunk guy, basically. But one of the great things about rehab, vs. the hospital he was in before, is that he can walk anytime he wants, and has a sitter 24/7 to go with him. Before he was apparently spending hours restrained and frustrated, trying to get out of bed, which was terrible and unhealthy.

Talking to him right now is like talking to someone who is mildly mentally retarded and/or has alzheimer's or has just woken up from a compelling dream. He talks just like Mosch, with all the verbal tics of Mosch, but sometimes the things he says don't quite make sense (they make, to me, "dream sense"). For instance, Saturday night he kept asking everyone for a screwdriver, which he said he needed to "unscrew his screwdriver."

He was at his best and most alert when I first got there. He was just realizing how impaired he is, and he said to me, "My brain isn't working right, and it's so important to me, it's such a big part of who I am." (It sounded so much like normal Mosch.) Upon my saying that he was doing much better, he said, "Better than what??" He wanted to know whether he had in fact been good (smart or with it or whatever) in the past. At one point he asked if he always walked like he was drunk.

After lunch, Nancy went to the library for a while to return some books, and I sat with Mosch in his room. I told him that I knew a lot about his life, and he asked me to tell him about it, so I told him basically his whole life story as I know it, and then some more little stories about himself. Through it all he had his eyes closed a lot and was nodding, smiling with recognition. Afterwards he said, "Wow. I had no idea you could tell it like that!" When I asked him if he remembered specific things, he would say something like "vaguely." I really enjoyed that whole conversation, which felt very natural and Mosch-like.

He gets frustrated and irritated a lot. They don't really do therapy on the weekends, so there wasn't much to do all day. He seemed to be looking for a purpose a lot. He would ask, "What's next?" We would go somewhere and he'd want to know what we (his visitors) wanted to do, and we didn't really have an agenda, of course, but that was annoying too. Why did we come out here if you didn't want to do anything? was what he seemed to wonder.

At one point we had a long (for him) walk and when we got back to his room, he said, "This is the same place we started out from hours ago. This whole place is BULLSHIT!" I'm sure it's very hard to have so much energy and restlessness without having any attention span or anything you're supposed to be accomplishing. I hope it's better for him during the week when "What's next?" can be answered with the different kinds of therapies. It's obvious that he wants to work. (When we were in the dining area looking at the TV, he said, "I'm waiting for him to take off his clothes so I can practice doing that." They've been doing that in occupational therapy, I guess. While I was there I saw him unbutton and remove a long-sleeved men's shirt, twice, which is pretty great for someone who couldn't use his left hand just a week or so ago.)

He's not so easy on the nursing staff, because he's often not cooperative and doesn't remember instructions. If he wants to get up, he is supposed to let the sitter know, and then s/he will help him with the belt, but instead he usually just starts clambering over the bed rails or bolts up. He often tries to remove the belt, which I'm sure is a little uncomfortable, sometimes over and over again while it's being explained why he shouldn't. He can't seem to hold information about that in his head, or else he just doesn't care. But the sitters have pointed out that having that drive and energy will help him get better faster than if he were more complacent, and I'm sure that's true. Mosch has always been careful to call a baby "easy" rather than "good" and that's kind of what applies here - Mosch isn't an easy patient but he's a good patient.

Overall, I really enjoyed being with him. Of course, with a person who is fully unconscious, like he was on my other visits, you can imagine that they'll wake up and just be normal, and you can't do that with a person who is awake and functioning but not normal. But you can still get some of the Mosch personality and it's much more interesting to interact with someone who is walking around and talking. He seems to be improving day to day and (vastly) week to week, so now it's just a question of how far he will come in his healing process. I'm feeling pretty optimistic about his future.

Poor Leno

Lately I've been listening to a lot of Royksopp. I came here to post something about the song "Poor Leno," but then I saw the video on Youtube, and it is awesome. So instead of the other thing, I am going to post about the video. Go see!

Catalog Blog

I've been enjoying a new catalog blog. This post in particular reminded me of Debbie for reasons I can't identify. (Debbie, is this your sense of humor?)

Hardiness

When Sally was last in town, she talked about a psychological trait called "hardiness" that I hadn't heard of before. What she said about it was something like that people with high hardiness get bored easily and have trouble motivating themselves to do things they don't want to do. (That's my paraphrase, anyway; feel free to correct me in the comments.) I think she indicated that I might have high hardiness.

I became quite curious about this, because "hardiness" sounds like something good, and if there is something good associated with my slacker qualities, I want to know what it is! (Although in fact I misunderstood her completely and when I did my Google search today, I typed in "heartiness." But anyway.)

Apparently we hardy types (assuming I am one) are unusually stress-resistant. I would say that is true of me. It's not so much that I handle stress well by rising to the occasion as that I feel somewhat immune to stress (not entirely, of course). Apparently hardiness has three components:

1. Commitment - feeling involved in life (as opposed to alienated)
2. Control - believing that you can control/influence your circumstances (as opposed to feeling powerless)
3. Challenge - being excited (as opposed to threatened) by changes; finding satisfaction in difficulty

It's hard to say how much these three ideas apply to me. The third one, "challenge," is a no-brainer. I've written before about how excited I always am about changes (even ones you might think of as probably bad; if I found out I was going to prison instead of grad school, I'd be on one level devastated, but I'd still be pretty excited to see what prison was like), and how I think difficulty correlates positively with satisfaction. (I view myself as kind of an excitement junkie - not in the sense of being a thrill-seeker, but in the sense of always finding things in the future to feel excited about.)

I don't have reason to think I have higher than usual levels of commitment and control. I can sometimes feel alienated, though not severely. I rarely feel powerless; I almost can't remember ever having felt that way.

In my cursory searching, I wasn't able to find anything about hardiness and lack of ability/motivation to do boring work. One article I saw said that hardiness was negatively correlated with neuroticism but positively correlated with the other big five personality traits (openness, conscientiousness, extraversion, and agreeableness). I would guess I am more open, less conscientious, slightly less extraverted, and slightly more agreeable than the average bear. I don't think I am very neurotic.

Going with the general meaning of the word, I do think of myself as "hardy" in ways that relate to what I've read. I usually look back at a stressful and difficult experience with joy (assuming nothing actually bad happened; I mean something like getting lost in the woods, not something like seeing your buddy gunned down in front of a liquor store) and I am fairly resilient. Hardiness is also associated with expressing satisfaction about one's life, and I'm definitely high in that area.

To cite any sources for this would suggest that it's not completely half-assed and basically along the lines of comparing oneself to characteristics expected for one's astrological sign. Still, I had a good time looking into it a little bit, and am happy (as one tends to be) to find a positive word that might describe me.