All Done (Mostly)

I still need to write a teaching philosophy statement, but other than that, I'm all done with my first semester of grad school. Woot.

The analysis exam was not as dire as I had anticipated. We had to do 6 problems out of 9, and I finished 5.5 problems. I don't think my answers were completely correct, but the fact that I'll be getting graded out of 90+ points is very cheering. I got a 55% on the midterm and I don't think I'll have less than a 75% on this exam, so that's a large improvement. Given that our professor has told us not to worry about grades (including telling one woman who did much worse than I did on the midterm specifically not to worry about her grade), I'm expecting a B in this class.

The logic final (our only exam in that class) was today. As expected, it consisted of basic skills from the class rather than proofs or things that required us to have memorized a lot of the theorems and tricky things from the assignments. Given that I needed less than 50% credit on it to have an A in the course, I'm fairly secure in that A.

I also think I'll have an A in probability and in my math pedagogy class. That gives me a good GPA for the semester and means that I passed all of my courses (meaning that I got at least a B), which is really what counts. So: woot!

I need to do better in analysis next semester, though. The main key in that class seems to be working through the exercises in the book, so I'm going to plan to do that. Another student in the class and I are planning to work together to read the sections and work on the problems before the material is taught in class, so that if we have questions we'll know what they are in advance. We'll see how that works out, but hopefully I'll have time; I think my course load will be easier this coming semester. (I will need to make time whether I have time or not.)

Now I have a month off. I feel weird about it already. The next semester doesn't start until mid-January. (Yes, this is where you people with real jobs can want to kick my ass. Believe me, I get it.)

Coming up next semester: statistics, the second half of real analysis, and an introductory topology course.

The Probability Exam

Today, we had our final exam in Probability. I got a perfect score on the (very easy) first exam, and then did very poorly on the second exam. Fortunately, the two questions I couldn't answer on there (worth 32/100 points) were left mostly blank by the vast majority of the class, and the professor took them away, so that I ended up with a 90%. Nevertheless, it was a bad testing experience.

I had had an analysis exam the previous day, that I'd done very poorly on, and as I sat to take the probability exam I was exhausted and really couldn't think straight. I hadn't prepared well for it at all, and couldn't do basic things like subtract correctly (even using a calculator) or perform simple algebra tasks, much less think creatively about problems.

I felt reasonably well-prepared for this exam - the last few weeks, the material has seemed to come together for me much more than it did in the middle of the course, and I had good formula sheets written up - but I also worked hard to be rested, correctly fed, hydrated, etc., for the exam. I knew that I would need (because both probability and tests in general demand it) mental flexibility in order to be able to answer the questions.

And I did it. I completely killed the exam - I should have a perfect score, or at least within epsilon of a perfect score. (Really I could have as low as a 95% - who knows what weird errors I could have made - but I definitely got the questions basically correct.) And I didn't just kill the exam by being prepared; I killed it by being smart (relative to my baseline) and mentally flexible.

One question asked us something about three independent random variables, each uniformly distributed on the interval [0,1]. (For the "probabilists" out there: we had to determine the CDF and expected value of the minimum term. Pretty easy stuff.)

The next question asked us to consider the same three variables, and then had some questions that only involved two of the variables. I had a few moments of confusion (of the type that totally derailed me on the secon exam) before realizing that the irrelevance of the third variable meant I could draw the standard [0,1]x[0,1] box and fill in the areas I was being asked about and do the computations using areas (e.g., "What is the probability that Y1 > Y2 given that Y1 > Y2^2" - which is the just the ratio of two areas, given that the distribution is uniform).

The exam wasn't hard either, I should admit, but it did take me just about the entire time.

There were five problems (some with multiple parts) worth 15-20 points each, and then the sixth problem was worth 6 points. He's urged us to consider these last problems as pretty much optional, even though they are part of the full score. If you make sure you can do the basic problems, then it's OK if you can't do the fancy problem. But this fancy problem turned out to be exactly the type of fancy problem that I am good at. It went something like this:

An urn contains 6 red balls and 14 blue balls. Two balls (selected at random) are removed and discarded without noting their colors, and then another ball is drawn. Given that this last ball drawn is red, what is the probability that both of the two discarded balls were blue?

This is exactly the kind of thing where if you just draw a little probability tree it is pretty obvious how to compute it. (I shouldn't say it's "obvious." Many things in probability should be obvious but take me a long time to figure out or I can't figure them out at all. But this type of problem is intuitively easy for me, for whatever reason.)

I have my analysis exam tomorrow, which is triple express doom, and then the (low-stakes) logic exam on Wednesday. After that, I have to write a [maximum] 3-page teaching philosophy and fill out a short survey for one of my courses, and then I'm done.

Heartbroken

My life is so weird and messed up lately, and the worst part of it, I feel like there is almost nobody I can talk to about it other than Ed. It feels like he is the only one who actually understands all of our bizarre circumstances well enough to get it. But talking to him is hard on both of us.

I can't get over him and our break up, and I don't even know how to try. I feel a deep bond and partnership with him that isn't going away. I miss every single thing that we had together and no longer have. A lot of the time I would do anything to go back a few weeks and do things differently. (I'd go back further than this, but even the night he broke up with me I didn't make an effort to stop him. We had just started making things better. But I was so worn down and it felt so inevitable that he was leaving me - he had been so relentlessly dissatisfied - that I couldn't fight it anymore.)

I can't express even these simple feelings to people very well, because I just don't say ridiculous things to people even when I feel them. I think this makes me seem robotic or something, but I don't know how to change that about myself. Also, I don't want to say bad things about him to our mutual colleagues (and, even if I'm sometimes tempted, the truth is that in my heart of hearts I don't think he did anything wrong, and he's been amazingly kind and supportive all along).

It would probably help if I didn't see Ed all day every day, but I don't want him to go away either. I certainly can't stand the idea of moving or of having him move and then having to get a new roommate. I want us to continue having this close friendship that we still have.

My life is just really hard right now.

Zu Ende

Ed and I began dating in May of 2007. Last night, we broke up.

It's been an interesting and mostly great three years, but I won't get into all of that now. Why did we break up? Well, I keep thinking that it's a long and complicated story, but I think that really it is a short and simple one.

My relationship with Ed has always required high inputs of energy. It has been a high-drama, high-maintenance relationship, which has mostly suited me well.

But grad school takes up all of my energy. It's not that I don't have time left over for talking or hanging out or whatever, but I don't have mental energy and space left for being an extremely involved partner. I was thinking about this last night, and what I think is, I could only be a really involved partner to someone new (where you have that crazy "new relationship energy") and, if that happened, I would probably fail my classes, because I really can't do those two things at the same time. Maybe if it were someone more studious than I am and also in grad school, then it would work out, but otherwise, I don't see how it could. (I am certainly not looking.)

Ed tried to deal with my benign neglect as best he could, but it made him increasingly hurt and angry. This came up a week or so ago in a big way and we made some changes to try to resolve it, but I think the changes were too little, too late, and last night he decided to call it quits.

It wasn't a big surprise. I had felt (and said, a few days ago) that I thought our breaking up might be inevitable. There was a lot that I valued in the relationship - so much that I couldn't decide to break up with him myself - but there was no more that I could do to fix things, I didn't think. I decided to proceed as though the relationship would continue in the best possible way and let the chips fall where they might. And this is where they fell.

We are still friends. I consider it nobody's fault that the romantic part of the relationship is over. (I started to say that it was nobody's fault that it "didn't work out," but it did work out, very much so, and the fact that it was of limited duration doesn't change that.) I don't think either of us is moving out of our shared apartment anytime soon, so we will have to get through this awkward stage of being newly broken up. I think we will.

Thanks for three and a half great years, Ed.

Small Revelation about Time Management

Grad school life has been pretty great for me so far, but the major thing that I struggle with is getting work done. I don't usually have an actually overwhelming amount of work to do, but I waste a large number of hours each week procrastinating or trying to start working, when if I just worked I would have more free time to do things like read.

I have, however, realized one thing that has made a big difference over the past few weeks, and that is that I really hate doing things at the last minute. When it's "do or die" and you will stay up all night to finish something due the next morning, it feels like some giant metal rod is pressing against you. Sometimes the thought of doing the work is intolerable but, of course, not doing it at all is unthinkable.

The "correct" way to avoid this is to do the work ahead of time, but I sometimes struggle with that. My revelation is that just moving that "last minute" point up by a day has a huge impact. So my current strategy is staying up all night the night before the night before something is due, rather than just the night before.

You would think it wouldn't matter or help. Staying up all night is staying up all night, right? (I've not literally had to stay up all night yet; I'm using the term loosely.) But it actually makes an enormous difference to me. I have that "I am not going to bed until I [more or less] finish this" urgency to keep me going, but without the horrible iron bar feeling. Instead, I have the virtuous and enjoyable feeling of kicking ass by getting something done early. Also, once I get to the point where I have only a little bit left to do, I can leave off and finish up the next day with minimal stress.

It's sort of exciting to have a working, specific strategy to avoid being crushed by things at the last minute.

Prank

Just a story I enjoyed...

When my real analysis professor was a graduate student, he had a Number Theory professor who made the homework sets available by leaving copies at local copy shops, where you would go and pay for them to make a copy of the problem set for you. One time, the week before an exam, the professor hadn't left any problem sets, so my now-professor and his pals typed up a page of unsolved problems in the field and left them for the other students.

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.

Google Voice

I've been wanting to check out Google Voice for a long time, and I finally got an invitation from Google to sign up. It is fantastic and I'm very excited about it.

You can use Google Voice either with your existing phone number, or you can get a phone number from Google. I chose one that is local to where I'm moving to. You can search for phone numbers that spell things, and I tried my first and last name with no success, but eventually got a phone number that ends in MATH, which is pretty cool.

What GV does at this point is that, when someone calls my new number, GV will ring whatever phones I've told it to. I can tell it to ring my office phone, home phone, and cell phone all at the same time from that one number that belongs to none of the phones. I can also, if I choose, set up classes of my contacts and have GV treat them differently. (For instance, perhaps business associates get to ring only my office and cell phones, but family get to ring all three phones.)

GV also catches all of my voice mails and will email me when I get a voice mail or a text message. Voice mails are automatically transcribed (not very well, but better than nothing) and there will also be a link to play the voice mail recording on the computer. Text messages come as they are, of course, but best of all, I can text the person back just by replying to the email. (I don't do a lot of texting, but now it is at least easy to do with those few people I know who do text me.)

I can place phone calls from my Google number from any of my phones (though I forget how) and I can also place them using the website as a helper. I tell Google who I want to call and from what phone, and they ring first my phone, and then the other phone, and make the connection. It's sort of like having a secretary. One of the advantages is that I can manage all of my contacts in Google (same contacts as in Gmail) and not in my cell phone. (Of course, I might also want them in cell phone if I want to place calls when I don't have access to a computer, but there are not that many people I call regularly from outside of my home or office.)

My favorite aspect is the voice mail capture and emailing. I am pretty bad at ever getting phone calls and I especially don't notice voice mails (much less texts), but I check email all the time. This will make my chances of receiving and returning phone calls much higher.

I also really like the idea of having one phone number that will stay the same no matter what kind of phone I have. I'm considering, once I move, having a prepaid phone plan so that I don't have to pay $40/month for the five or six phone calls I make every month. I know that you can keep your numbers when you change plans these days, but this seems so much easier - just give everyone the Google number and only you and Google have to know where it's ringing. (For that matter, if I wanted to make even fewer phone calls than now, I could just have the Google number and no actual phone plan, then find a phone booth or something to place calls when necessary.)

Anyway, I'm a big fan of Google Voice so far. I have one invitation left that I can send someone, so if you're interested in trying this, just let me know.

Money Fairness Without Marginal Costs

As I mentioned earlier, Ed got his driver's license last week, and I included him in my new insurance policy with Progressive. It's great (even for me) to know that he can now borrow my car and go wherever he wants. I expect this will come in very handy in grad school, where neither of us will commute to school by car, but where we may not live in (easy) walking distance of a grocery store. So far, Ed hasn't taken much advantage of this new ability, which is partly due to a lack of opportunity, and partly because I think the idea of being able to just drive somewhere hasn't penetrated his consciousness yet.

The question that arises for me is, how much (if any) of the car insurance and other car-related costs should Ed bear? I asked him this question, and he suggested that as a starting point, I find out how much extra it costs for him to be on my insurance.

At Amica, this was going to be $400/year, but according to Progressive, it is $0. Having him on my policy does not add anything to the cost. And yet, it doesn't seem that it should be free to him. If I were to move in with Sally, even if she found this desirable and enjoyable, I should pay some rent even though my being there would not affect the rent. People who benefit from a thing that costs something should bear some of the costs.

So he shouldn't pay nothing. If we drive the car about equal amounts in grad school (as opposed to now, when I drive it to work every day), should he pay half? On the one hand, borrowing your girlfriend's car is not as nice as having your own car; I'd have first dibs on the car and thus more convenient car access. On the other hand, I paid for the car and its depreciation falls on me, not him. And, of course, it might be that what I think is fair is more than it's worth to him for me to have a car that he can borrow.

It's hard for me to figure out what seems reasonable in this type of situation.

Resume Pet Peeve

I realize that even having pet peeves is obnoxious. Nevertheless, I really hate it when resumes (we are looking at some this week for the person who is to replace me) have a bullet point list of the duties associated with the job and the entries in the list are not in the same grammatical category, e.g.,

Massive Oil Company, Melbourne, Australia, 2008-2010

• Worked extensively with Aries.
• Finding and maintaining city and county records.
• Assist engineers with daily tasks.

Bah! Fie on thee!

Swimming

Today, I went swimming at the Wheat Ridge Rec Center. I haven't been swimming laps much lately at all - in fact it's been months, I think, since I've swum laps at all - but I decided on an ambitious goal for the day: swimming a mile. I wasn't sure that was realistic at all, so I wasn't really determined to make it, but I thought having a stretch goal would be fun.

A mile is just slightly over 35 laps in our 25-yard-long pool. I actually count lengths and not laps, as I'll explain later. I used the crawl (or freestyle, as I think it's sometimes called) for almost all of the laps.

I got slower as the laps went on, but ultimately I did make my goal! I think it took me about an hour and a half, which is pretty damn slow, but I don't care - I am excited about swimming such a long distance at all.

I really enjoy swimming. The environment underwater is beautiful and feels wonderful to me. Swimming is also no-impact; I suppose it's possible to get injured swimming, but I've never hurt myself. For me, it is kind of a low-stress, high-rep, light muscle exercise situation that is not extremely aerobic.

I used to have trouble counting laps, but the technique I use now is that I say the number I'm on in my head with every breath, which is a bit hypnotic too. I count lengths rather than laps so that I always know that on the way out I should be saying an odd number, and on the way back it's an even number. That helps prevent the thing where my mind drifts and suddenly '51, 51, 51, 51' turns into '51, 51, 51, 52, ...'

I also wear a mask and snorkel to swim. I first tried this when I had my neck injury, because I couldn't handle the neck strain of swimming back then. The mask and snorkel made it possible for me, since I didn't have to move my neck around to breathe, and could just keep it in a nice neutral position. And what I discovered is that swimming is much more relaxing and nice if you don't have to worry about breathing at all.

Every 5 laps or so, I come up, take off my mask, and have a short break. I try to keep some water with me and drink it during my breaks, because it is kind of easy to get a little dehydrated while swimming. I don't tend to ever feel thirsty while submerged in water.

Anyway, I had a wonderful time. I hope that the pool at my grad school will be as nice as the one at the rec center and that I can swim there on a more regular basis. I can't swim in the winter here, because the chlorine does unbearable things to my already-dry skin, and I'm hoping that won't be a problem in the new locale.

Auto Insurance

Many years ago, when I first moved to Denver, I had Progressive auto insurance. I don't remember what they were charging me, but when I called up Amica, I got a quote that was something like half as much as Progressive's, and I switched over. I've had excellent service from Amica for about 8 or 9 years now.

Ed got his driver's license a couple of weeks ago, and when I went to add him to my Amica policy, it would have added $400 to the year, and my total insurance costs (for full coverage with fairly high deductibles) were going to be about $1200. In the meantime, I had pulled up a quote from Progressive that was much less - about $700 for the year for the same coverage.

So I switched to Progressive again.

All this is to say that it might be worth checking your insurance coverage every few years to see if you get a much lower rate with another company (and to ensure that you're getting only/exactly the coverage you want).

Try. First.

I have a coworker who was hired as an engineer right out of college (by us, I mean, a year or so ago). I imagine he's relatively intelligent, yet the way that he works drives me up the wall. Today, for instance, he called me to find out the easiest way to get a map of an area.

"Probably just make the map in Petra," I said. Petra is software we use very commonly and I have walked him through many processes in Petra before.

"OK," he said, "well, I've never made a new project in Petra. I was wondering if you could walk me through it."

Now when you start up Petra, the very first screen asks if you want to open an existing project or make a new one, so it's not mysterious how to at least start making a new project. And I really resent this guy asking me to "walk him through" something in a program he already uses without even trying it himself first.

Nevertheless, I walked him through a few initial stages, at which point he had some steps to do on his own, and then I just happened not to take his follow-up phone call. (Yes, I realize it's unprofessional, but I wanted him to have the opportunity to try the next steps on his own, and I don't have the balls, I guess, to just tell him so.) He sent me an email a while later so I sent back some hints.

The next time he called, I did take the call. He was stuck at a certain point, which is a reasonable time to call someone. But when I walked him through what he was doing, he (a) repeatedly did not listen to what I was saying, (b) indicated an inability to figure out the simplest things, and (c) simply failed to try obvious things in the software.

Of course, since he never takes notes or anything like that, I expect someone will have to walk him through his next new Petra project as well.

The Perils of Lesbianity

Via Andrew Sullivan:

War and Peace: My Review

I have now finished War and Peace.

It's hard to know what to say about a book that is a famous classic, so I will give you some random assorted thoughts, in no particular order.

• Parts of the book were amazing, life-altering, crazy good, in characteristic Tolstoy ways. If you were very moved by Anna Karenina you should be moved by War and Peace too, and W&P is much longer, so there is more.
• More of the moving parts of W&P are about characters facing death (or the possibility of death) or suffering.
• The book inspired in me an interest in the Napoleonic Wars (especially the Russia parts) that felt very similar to how I think a lot of people feel about the Civil War. I now want to independently read about this. I am not usually interested in battles or wars, so that's strange for me. If you tend to enjoy books about soldiers or wars (say, similarly to how Sally enjoys books about life on ships), W&P might hit your buttons.
• That said, Tolstoy is not big on describing the exact tactical moves or positions of armies taken in various battles, largely because he does not believe such things exist in a meaningful way or that they determine outcomes. He's rather adamant about this. There is one map showing the positions of the armies, but for the most part you get a broad overview and then specific details concerning the characters we care about.
• Most of the book isn't about war, but about the lives of various people, similar to how Anna Karenina was, and a fair bit concerns who will ultimately marry whom and how various fortunes will be disposed. There were many times that the book made me gasp in surprised delight or feel real despair over what happened to the characters.
• It is fantastically written.
• I got extremely annoyed reading Part II of the Epilogue, which is basically a very long essay about history and free will. I was heard to say out loud, more than once, "Tolstoy, shut up." Maybe I simply missed the brilliance of it all, but I think it could have used some serious editing and been a much stronger essay with 1/5 as many words. Since it was the last thing I read, it made me not like the book as well overall. If I reread W&P, which I hope I will someday, I will probably skip that part.
• It is long, but, by the time you get near the end, you'll wish it were longer, at least until you get to Part II of the Epilogue.

I certainly recommend it unconditionally. I also have a rather pretty softcover edition that someone is welcome to have.

A Little Tolstoy

This is the beginning of Volume III (Pevear/Volokhonsky translation):

Since the end of 1811 an intense arming and concentration of western European forces had begun, and in the year 1812 those forces -- millions of men (including those who transported and fed the army) -- moved from west to east, to the borders of Russia, towards which, since the year 1811, the forces of Russia had been drawn in exactly the same way. On the twelfth of June, the forces of western Europe crossed the borders of Russia, and war began -- that is, an event took place contrary to human reason and to the whole of human nature. Millions of people committed against each other such a countless number of villainies, deceptions, betrayals, thefts, forgeries and distributions of false banknotes, robberies, arsons, and murders as the annals of all the law courts in the world could not assemble in whole centuries, and which, at that period of time, the people who committed them did not look upon as crimes.

What produced this extraordinary event? What were its causes? Historians say with naive assurance that the causes of this event were the offense inflicted upon the duke of Oldenburg, the non-observance of the Continental System, Napoleon's love of power, Alexander's firmness, diplomatic mistakes, and so on.

Consequently, it needed only that Metternich, Rumyantsev, or Talleyrand, between levee and rout, make a little better effort and write a more skillful dispatch, or that Napoleon wrote to Alexander: Dear sir, my brother, I agree to give the duchy back to the duke of Oldenburg* -- and there would have been no war.

Understandably, that was how the matter presented itself to contemporaries. Understandably, it seemed to Napoleon that the war was caused by the intrigues of England (as he said, in fact, on the island of St. Helena); understandably, to the members of the English Parliament it seemed that the war was caused by Napoleon's love of power; to Prince Oldenburg it seemed that the war was caused by the violence done to him; to the merchants it seemed that the war was caused by the Continental System, which was ruining Europe; to the old soldiers and generals it seemed that the chief cause was the need to make use of them; to the legitimists of that time, that it was necessary to restore les bons principes [Good principles]; and to the diplomats of that time, that it had all happened because the alliance between Russia and Austria in 1809 had not been concealed skillfully enough from Napoleon and because memorandum no. 178 had been clumsily worded. Understandably, these and a countless, endless number of other causes, the number of which depends on countless different points of view, presented themselves to contemporaries; but for us, the descendants, who contemplate the enormity of the event in all its scope and delve into its simple and terrible meaning, these causes seem insufficient. For us it is not understandable that millions of Christians killed and tortured each other because Napoleon was a lover of power, Alexander was firm, English policy cunning, and the duke of Oldenburg offended. It is impossible to understand what connection there is between these circumstances and the fact of killing and violence; why, because the duke of Oldenburg was offended, thousands of men from the other end of Europe should kill and ravage the people of Smolensk and Moscow provinces and be killed by them.

I could read this over and over. (And now I have.)

[* Original in French, but I didn't feel like typing it.]

War and Peace

Now that I have gobs of spare time, I've started reading War and Peace. It took me a while to get into - at first I could only read in short patches - but around 100 pages in I finally started to get invested. I've just finished Book 1 (of five, each divided into parts, each of which is divided into short chapters).

There are a lot of characters, all with the Russian patronymics and whatnot. It doesn't help that a lot of names are used over and over for different characters (e.g., in the Bolkonsky family, Prince Andrei is the son of Prince Nikolai, but over in the Rostov family, there is a Count Nikolai who is part of Prince Andrei's generation. And there are two Vasilly's as well.) It also doesn't help that a lot of the book concerns the Napoleonic Wars. I am both ignorant of the history here, and generally uninterested in (and cannot easily follow) military history and descriptions. For instance, I don't know the different ranks in an army so whether a corporal or a captain or a sergeant is of higher rank, I couldn't tell you. (Yes, it is possible to look these things up, but it's not fun to read a book if you continually have to look everything up.)

On the eve (in the book) of the Battle of Austerlitz, I did stop and read the Wikipedia article about it, out of pure curiosity. I wasn't concerned about spoilers since it seems likely that Tolstoy would have assumed his readers would be familiar with its outcome. But it was very surprising to read the names of some characters from the book in the article. It is as though in some alternate reality, these characters in a novel were living people. I enjoyed looking at paintings of them as well. I've also been supplementing my reading by doing google image searches on words like "hussar" and "Cossack."

As with Anna Karenina, there are parts of this book that sort of blow me away and that I find myself thinking of over and over again. Unlike Anna Karenina, I don't find it a totally captivating read. But it's captivating enough to be worth it, given that it's also a great work.

DIY U

This morning, I greatly enjoyed Community College Dean's takedown of DIY U by Anya Kamanetz (it's the "edupunk" one you may have heard about). I haven't read Kamanetz's book, but I already basically think it's full of crap, so I surely won't.

Arroz con Pollo

Friday evening, I made this arroz con pollo recipe. I pretty much followed it exactly except that I also put in two jalapenos and two red peppers. I used chicken thighs.

It came out pretty good, though it was much improved with a few sprinkles of cayenne pepper (which I'll add next time), and it was the kind of dish that, once you've made it once, doesn't require a recipe at all. It's dead easy.

It was also cheap. I think I spent about $12 total (and you could economize by buying less-fancy chicken broth or using green rather than red peppers), and it made six generous meals, plus we had rice left over afterwards.

Next time, I don't think I'll bother dredging the chicken in flour - I don't think it added much taste relative to how much trouble it was. I would probably use even more peppers and possibly slightly less rice. But anyway, this recipe gets a big thumbs up from me.

Dreaming False Memories

When I was very young, perhaps around 4, I had a nightmare. In this dream, I would be in a room, and the floor would tilt a little bit and bubbles would start seeping in at the base of the wall. I'm not sure why this was dangerous, but it clearly was. It was something that had happened before, too. When I woke up, I knew that the bubbles had been a dream, but I still believed that it was a dream about something that had really happened before. It took me a long time (months or years) to convince myself that the bubbles were only a dream, and not even a dream I had had more than once.

Until recently, I hadn't often (as best I can recall) had dreams that implanted false memories like that, but lately, I have them all the time. I will dream of something, let's say smurfs, and wake up thinking, "God, I have dreamed of smurfs every day this week! What the hell is with the smurfs!" And then I'll think, "Shit, is this one of those dream memories?" And sooner or later I will realize it is.

Sometimes it has stages. I'll wake up being annoyed that I've dreamt about a smurf revolution all week, then realize almost immediately that, although I've been dreaming about smurfs all week, the revolution part is new, and then realize hours later that I hadn't been dreaming about smurfs at all, up until that point.

Sometimes the dream memories aren't about dreaming. Last night in bed I realized that all week, or all month, or something like that, I had been thinking and fantasizing (while awake) about something like foursquare (the playground game, not the iPhone app). And then I slowly started to question that and to realize that I hadn't even been thinking about that while awake at all, much less more than once. I only dreamed that I was, and had been, doing such a thing.

I'm starting to find the frequency of this experience disturbing. I think it happens several times a week. (And I'm pretty certain that that is not itself a false memory; I clearly remember thinking about this while awake many times over the past year or so.) I like dreaming, but I don't like waking up believing things that are not true. Is this common?

PawPaw Jimmie

Last night before the exam, I got a chance to talk on the phone with my grandfather. This is my father's father, who is (or was, before retiring) a Southern Baptist minister. He's a delightful and warm person, full of humorous stories. I told him about my exam, and he told me a story from when he was in seminary.

He had a professor there who I'll call Dr. Smith, since I can't remember his actual name. At seminary, apparently they started every class off with a prayer, and though most professors would ask one of the students to lead the prayer, Dr. Smith always led it himself. My grandfather said that he would start in to praying and you got the feeling that he was always in conversation with God and you were listening in at this one moment.

But before exams, the prayer was chillingly different. "Father," he would says, "provided that these students have studied diligently, please help them to recall what they have learned." My grandfather said this was not the most encouraging message; during an exam you'd rather have unconditional bolts of knowledge!

At the end of our conversation, he asked if he could pray with me over my exam, and I readily agreed. (I am more or less an atheist, but I never mind being prayed over or with.) He left off the "provided she has studied diligently" condition. Whew.

(An actual picture, found online, of my grandfather and late grandmother.)

The End

Tonight is my abstract algebra final. I have a take-home part to turn in, and then the final itself is supposed to take about an hour, though we have two hours for it. I'm not as ultra-prepared as I have been for some other tests, but I think I am prepared enough. The take-home part was difficult but I think I'll have close to full credit on it, and I only need a high D or low C on the final in order to have an A in the course.

This is not just a final exam, it is the final exam. Barring the unforeseen, this will be my last act as an undergraduate. My other classes are finished. Sunday is the graduation ceremony, which I am not attending, but after which I will consider myself to have graduated.

Taking my last exam would feel stranger, of course, were I not starting grad school in the Fall. It will be different from this, but will still feature math, homework, exams, and all of that. Leaving my job in a couple of months is going to be weirder than graduating, I think.

I was thinking about my family earlier, the two sides. On my mother's side of the family, everyone goes to college. My grandfather, mother, aunt, and two cousins (which is everyone I know from my side of the family) all have degrees (did my grandmother? I wonder), and my aunt and cousins either have or are working on graduate degrees of some stripe.

College seems more rare on my father's side of my family. My grandfather went to college and seminary, but my grandmother didn't go to college. Of their four children, I believe only one of my aunts has a degree. My father took some college courses but did not graduate. Two of my three cousins started or are about to start college; probably the older has graduated by now (assuming she did graduate).

I have mixed feelings about graduating. It's not really much of an accomplishment for an intelligent person with a middle-class background. You expect it. I had a perfect opportunity to go to my dream school right out of high school, basically for free, and the only reason I didn't get my degree there was that I wasn't mature enough to actually go to classes, do work, study, and so on.

At the same time, it has taken me a number of years to get this degree while working, and I did, over all that time, develop a work ethic (at least towards school), learn how to tackle difficult material, and gain various academic skills, such that I am, these days, a good student. So I do feel a certain sense of accomplishment in finishing something that was initially hard for me. And it was certainly enjoyable as well.

Anyway, tonight is it - the end of my undergraduate career.

Data-Driven

This New York Times Magazine article "The Data-Driven Life" was pretty interesting. An excerpt (not particularly well-chosen):

For a long time, only one area of human activity appeared to be immune [to numbers]. In the cozy confines of personal life, we rarely used the power of numbers. The techniques of analysis that had proved so effective were left behind at the office at the end of the day and picked up again the next morning. The imposition, on oneself or one’s family, of a regime of objective record keeping seemed ridiculous. A journal was respectable. A spreadsheet was creepy.

And yet, almost imperceptibly, numbers are infiltrating the last redoubts of the personal. Sleep, exercise, sex, food, mood, location, alertness, productivity, even spiritual well-being are being tracked and measured, shared and displayed. On MedHelp, one of the largest Internet forums for health information, more than 30,000 new personal tracking projects are started by users every month. Foursquare, a geo-tracking application with about one million users, keeps a running tally of how many times players “check in” at every locale, automatically building a detailed diary of movements and habits; many users publish these data widely. Nintendo’s Wii Fit, a device that allows players to stand on a platform, play physical games, measure their body weight and compare their stats, has sold more than 28 million units.

This sort of thing appeals to me but I won't usually keep up with it if it's not very easy.

One Down, Two To Go

My math seminar met this morning for the second-to-last time. I was hoping we wouldn't meet during our final exam period (as required by law), and indeed we will not. And I was hoping the homework assigned today would be the last one. Instead, the professor assigned no homework today. ("I know it's the end of the semester," he said.) Next week will be a little bit of a wrap-up plus a show and tell from him about Daubechies wavelets.

Even though not having this last homework is a very small thing, I'm immensely relieved by it. I'll go next week, of course, but as far as having to do actual work, the course is over for me. He did say that if we aren't quite at an A, we can have an extra assignment due finals week to make it up. My average, however, is something in the A+ range, so I can safely skip that.

Whewwwwwwww.