Alethiography

Socialization

2012-02-18T15:33:00.005-07:00

I have experienced an interesting attitude change since starting grad school.

Ed (my ex-boyfriend, with whom I still share an apartment) and I are in grad school together, as most readers of this blog know. Before coming here, we'd had one class together at my undergrad institution, and that was when I learned that we have similar classroom styles (as students), except that his style is more extreme. We both tend to ask more questions (and answer more questions posed by the professor) than other students, and are prone to...well, sort of acting as though we are the only student in the room and can just freely interact with the prof without regard to what s/he is trying to accomplish with the class.

In the math pedagogy class that I took, our professor once gave us a list of problem student types, one of which he called "Mr. Non-Sequitur," giving the example of that guy who always asks you how such-and-such relates to fractals. At the time, this reminded me of Ed, who will often ask tangentially related questions.

Last year, I found Ed's classroom behavior pretty obnoxious, and worried that mine was obnoxious as well. But then this year, I observed that, in talks, many of the professors in our department behave exactly the same way. Whether the speaker is internal or external, they will interrupt with questions, make nitpicky corrections, and ask about strange tangents. And, though there is no way to put this on my public blog without risk, I will say that the professors who act this way are some of the ones I respect the most (independent of their behavior in talks). This is also the talk-watching style of the genius among the grad students of our department.

Maybe this is normal, socially appropriate behavior for my discipline.

I was curious what would happen when Ed took another class with our pedagogy professor, who is a bit strict in his classroom management style. Would he quash Ed's interrupting tendencies? The answer turned out to be a pretty big no. If anything, I think he appreciates being interrupted, nitpicked, and asked weird questions. He told me once that we were his best class in many years because we are so engaged and challenging, and I think he also gave private positive feedback to Ed once.

So I have basically totally revised my opinion of this style of behavior, and now think it must, indeed, be socially appropriate in our field. This led to an interesting conundrum recently, however, when one of my cohort gave a talk.

The talk was very interesting. At one point, though, Ed stopped the speaker to ask, basically, "So what?" He didn't use those words but wanted to know about the motivation for something she was talking about. She didn't have an answer right away, and he said, "I just think I would get more out of this if I knew why we were talking about it."

I felt like it was a bit over the top, given that she is our friend, is a bit early in her career (like we are), and may not have been completely confident in giving the talk. I wouldn't have pushed her in that way myself.

Now, I think Ed just asked the question because it was on his mind. But I wonder...maybe it is our job to socialize each other by asking these kinds of tough questions, even if it makes the speaker uncomfortable. You could argue that we should refrain so that our friends can be more comfortable, or that we should intentionally not refrain so that they can toughen up and not be stymied in (e.g.) a job talk later, when someone in the audience is of this more obnoxious cast.

Fortunately, our department has a good mix of people who like to speak up and people who don't, so I guess it will all just average out. But these are just some thoughts I've been having lately.

Teacher Follies

2012-02-16T14:40:00.001-07:00

An amusing/embarrassing thing happened to me today.

Because I write so much, I am very careful to keep paper that I've only used one side of to use as scratch paper. I have a big stack of this on my desk, and when students come to see me, I usually write with/for them on some of this paper, and then if they want, I let them take the paper with them. I figure the graduate math on the other side won't hurt them any (though it hurts me plenty, I can tell you).

Anyway, sometimes when I am working on problems, I write notes to myself in the margins. Often the notes say something like, "I suck at this type of problem :(" or "I will never get this!!!!" I try not to give papers like that to students, but I don't try very hard.

Yesterday, a guy came to my office hours and I sent him away with three sheets of my scratch paper. Today before class, he was showing it to another student, and I overheard this conversation:

Other student: Huh. It says "I am a bad ass" on this side. Did you [to the first student] write this?
First student: No, I think she wrote that. This is her work for some other stuff.

So I wandered over and sure enough, I had written "I am a bad ass" in the margin of my work. We had a good laugh over it.

It's kind of embarrassing, but I'm glad it was positive self-talk for once, and not the negative kind. One of my friends in the program pointed out that it was good that I had at least not written that I was a BAMF, which is also something I might write (either as an abbreviation or written out).

So anyway, there's that.

Measure-Theoretic Probability

2012-02-04T11:37:00.003-07:00

This is definitely my hardest semester of grad school so far, for the simple reason that I am taking two core courses (which are the kind here that require the most work) plus a reading course in measure-theoretic probability, which is taking as much time and effort as a core course (and more than either of mine, actually). But I'm increasingly wanting to go in a probability direction with my studies, so I'm thrilled to be doing it, and I'm really enjoying it so far.

The core course I took last year was in measure theory. I've written about it a little before, but today I'm going to (briefly) explain its relationship to probability. Then I'll end the post with my real reason for posting, which is a quote that excited me this morning.

Measure is just (more or less) a generalization of length. Let's say you're on the real line and you want to know how big a set is. If the set is just an interval, like (0,2), it's easy enough to say its length (or measure) is 2. But what if your set is much weirder? Like, what if you want to be able to say what "size" any subset of the reals is, in a sensible way that accords with our notion of length? That is, you'd like the interval from 0 to 2 to still have length 2, but you still want to be able to measure anything you want?

Well, unfortunately that is impossible, but what we can do is come up with a measure that works for pretty much any set that anyone cares about. In fact, coming up with a set that you can't measure requires using the axiom of choice to construct some bizarro thing that just doesn't arise in normal life.

So, let me tie this to probability. Let's say you want to pick a random number between 0 and 1, with all numbers equally likely. I'm just talking about a uniform distribution on the interval [0,1]. It's pretty obvious (I think) that the odds of getting a number between 0 and 1/2 is 50%. This corresponds to the length of the interval that you're talking about.

But what about the odds of getting a rational number? Or the odds of getting a number without a 2 in it anywhere? Or the odds of getting a number whose first three digits (after the decimal point) are repeated 9 times?

These are questions which can be answered with measure theory. In particular, there is only one measure (it's called Lebesgue measure) which both assigns to each interval its length and gives a measure for every Borel set (the ones I'm characterizing as "all the sets anyone cares about").

You might ask, "Who cares about the odds of getting a number whose first three digits are repeated 9 times?" But let's unpack that a little bit.

Let's say we roll a 10-sided die an infinite number of times. If the sides of the die are labeled 0 through 9, then if you wrote out the results, after a decimal point, you'd get a number in the interval [0,1]. For instance, it might look like .98362819501... and so on.

If we assume all combinations of die rolls are equally likely (which is true if the die is fair), then the odds of the die roll meeting whatever criteria we give are exactly the measure of the set in [0,1] that corresponds to the numbers that the roll represents.

For instance, let's look at my question about rational numbers. I should note that we're not going to let anything terminate, so for instance, we wouldn't write 0.4 (because that wouldn't correspond in any obvious way to an infinite series of dice rolls) - we would write 0.399999999..., which is the same number.

So what is a rational number? It's one that repeats forever when you write it out like that. For instance, 1/3 is 0.33333333.... You could also have a rational number like .123123123123... where more than one number repeats.

So, if we randomly choose a number between 0 and 1, the odds of it being rational are identical to the odds that, if we roll a die infinitely many times, eventually we hit some number or group of numbers that then repeat forever (for instance, we start rolling 1,2,3 over and over again for all eternity). Common notions of probability suggest that the probability of that happening is basically nil, which turns out to be right - the measure of the rational numbers is 0. (This is proved in an entirely different way in a measure theory course.)

Or, to use my other example, the odds of having your first three rolled numbers happen again like that 8 more times in a row is the same as the measure of the set I mentioned earlier - numbers with their first 3 digits repeated nine times. (So in other words, you can use this to measure probabilities that happen in a finite number of dice rolls too.)

This leads me to my quote, which is from Section 4 of my textbook, Billingsley:

Complex probability ideas can be made clear by the systematic use of measure theory, and probabilistic ideas of extramathematical origin, such as independence, can illuminate problems of purely mathematical interest. It is to this reciprocal exchange that measure-theoretic probability owes much of its interest.

So there you have it. Nifty, no?

Two Easy Recipes, and a Bonus Low-Rent Dessert!

2012-01-19T20:00:00.004-07:00

I basically only cook things that are extremely easy, so here are two simple recipes, plus a bonus dessert.

Chicken and Rice Soup

1 package chicken thighs (bone-in)

1 cup rice

1 bag frozen mirepoix (diced carrots, celery, and onions)

1 tsp salt

Put chicken thighs, salt, and mirepoix into a pot and cover with plenty of water. Boil until thighs are cooked (about half an hour). Remove thighs. Remove and discard skin, and separate meat from bones. Return meat and bones back to the pot and simmer another half hour or so. Then remove the bones and add about a cup of rice. (Confirm by eye that there is at least 2 cups of liquid in the pot; more if you want genuine soup rather than, as I prefer, something more like chicken and rice.) Simmer for another 20 minutes.

Beef Stew

1 package (1-2 lbs) stew meat

1-lb bag baby carrots

2 or 3 large potatoes

2 cups beef broth

1 cup wine (optional)

1/2 tsp salt

pepper if desired

Cut up potatoes (peel first if desired) and place all items into a large pot. Simmer gently until cooked, about 2 hours, or cook all day in a crock pot on low.

Low-Rent Banana and Chocolate Dessert

1 banana

part of a chocolate bar (I use 2 squares of a Lindt 85% cocoa bar, but any chocolate bar should work)

plain yogurt (I prefer whole milk)

Cut up the banana into a bowl. Break the chocolate into small pieces and microwave for 30 seconds at a time in a tiny bowl until melted. Gently spoon/pour the chocolate on top of the banana pieces. Glop a bunch of plain yogurt on top. Enjoy!

Reading Course FTW!

2012-01-19T18:50:00.004-07:00

This semester, I am doing a reading course in probability & measure (using Billingsley). It's the first time I've ever done a reading course or any kind of independent study (other than my grant, but that was very different).

This was the first week of school, so last week I emailed the professor to ask when he'd like to meet or whatever, and we set a meeting for today. He gave me a section to read and some exercises to look at.

I've spent probably literally (not counting Internet-procrasting-time) 20 hours on that section and the exercises this week. The book is very dense for me and the exercises were difficult. I ended up with 10 typed pages of answers. I wasn't sure if he would want me to turn those in or just discuss them or say that I had done them or what.

So we met today. The scoop is that, whatever questions we don't discuss to his satisfaction in our meetings, he will have me turn in (I ended up turning in the whole set since I had it all stapled together, though we talked about most of the questions). The meeting went well - I was comfortable presenting answers on the board and discussing the material. He told me how to do the problem I hadn't managed to figure out, and the answer was really cool (really cool).

I've been exhausted all day. The first week of school is rough and I've been working hard. I'm the kind of tired where my head naturally goes slanty and I become slack-jawed. I'm the kind of tired where I think I must look really tired even from the outside.

But that meeting was so energizing, and I think this course is going to be great. I'm realizing that, actually, I think reading courses are super fun, way better than classes. Instead of sitting in class for 3 hours a week (which I hate even when it is informative), you get to work on your own with a book (which I love even when it is really hard). It's fun in the way that my summer of qual studying was fun.

Guess what? Reading and figuring out math on your own is more fun than a class. That's a really cheerful thought for me.

I'm still worried about my workload this semester. I have two core courses plus this reading course. But I feel motivated towards at least one of my courses, and of course towards the reading course, so I'm feeling pretty good right now. And I'm looking forward to doing more reading courses in the future, bigtime.

Silas Marner

2012-01-16T01:49:00.005-07:00

I just finished reading my second George Eliot book, Silas Marner. I chose it to read because I wanted to read another book by her and I had heard of it. I got it for free (in Kindle form) from Amazon.

The basic idea of the book is that a man named Silas Marner has lost his faith after being (in essence) exiled from his (what we would now call) fundamentalist religious community, and has settled in a new town, where he becomes a miser and a recluse. Then a series of strange events involving a nobleman and an unwanted child alter the course of his life.

Before I read it, I read a review on Amazon, by a Susan Hallander, which begins thusly:

Question: How can you ensure that a person will hate a book? Answer: Make her read it for 7th grade English class, make sure that the language is old-fashioned, and above all, make sure that the ideas and concepts are over her head. If that's what happened to you, and that's why you have an aversion to Silas Marner, and you are now over 30, pick it up again. Read it twice. Silas Marner is one of the greatest novels in the English language.

As a result, while I was reading it, I had that context in the back of my mind - what would it have been like to read this in 7th grade?

Ultimately, while I enjoyed reading it, and was always reasonably eager to continue, I found Silas Marner disappointing. In some ways I would have enjoyed it less in 7th grade, but in other ways, 7th grade might have been a better time to read it. I probably would have appreciated its folksy moralism better when I was younger and less cynical.

I don't know what to say about this book in terms of anyone's decision of whether to read it or not. The book it most reminded me of, that I did read in school, was The Scarlet Letter, but that's probably a rather ignorant comparison.

My Changing Musical Preferences

2012-01-13T11:28:00.002-07:00

I was emailing with Sally today about the increasing distaste I feel for the habit of rating everything one encounters, and it occurred to me that this relates a bit to my changing tastes (or, really, a change in the way that I have tastes at all) in music.

When I was a kid (through middle school or a bit beyond), I liked most of the music I heard, though of course I liked some things more than others. But I was largely unconscious of what I liked - I usually didn't know what bands or artists or albums the songs I liked came from (with the exception of the music my mom really liked, which she would tell me about). I just listened to the radio and liked what I heard and was crazy about a few things. (Some songs I remember being crazy about: Do Ya Think I'm Sexy? by Rod Stewart, Strip by Adam Ant, We Built This City by Jefferson Starship.)

Sometime in high school, I started to really have taste. There was some music I loved (Erasure, Depeche Mode, Midnight Oil, Jane's Addiction, The Cure, plenty of other stuff I'm not thinking of at this moment) and other music I loathed and detested (New Kids on the Block, Tiffany, Madonna - who I had loved when I was younger - and in general most top 40 things). Through college and beyond, I developed and expanded and refined these tastes, and they were a part of my identity. (This identity-by-tastes seems really common among my friends, particularly younger ones.)

When I was 19, I think, I did have a surprising experience. I hated the song "Vogue" by Madonna. I was visiting the Netherlands at the time, and I walked into a club with some friends. In the club was a leather-clad half-naked guy in a cage, and he was dancing to "Vogue." And it was the perfect music for exactly what was happening in that moment. I had not known such a phenomenon could occur: that a song you hated could turn out to be perfect for a particular occasion.

I've noticed over the years since college that my musical tastes are not only expanding but in general just loosening. There began to be a ton of music that I enjoyed hearing despite not officially "liking." (For instance, I am now ready to admit that I really do love hearing the song "Dust in the Wind." I will always sing along.) Sometimes I felt as though, if my friends learned of my real tastes, they'd think less of me.

That kind of anxiety is part of why we (some of us, anyway) identify with the famous xkcd cartoon about Pandora:

It seems silly that there is such a thing as "embarrassing music" in a way. People make all this music for us to listen to and enjoy - what is embarrassing about enjoying it? I mean, I'm embarrassed about liking "Dust in the Wind" which is not exactly nazi death metal or anything. It's pretty innocuous.

I am moving more and more towards viewing my musical tastes as being more probabilistic (I tend to enjoy dance music, alternative, 80's pop, blue grass, dixieland jazz, and Beethoven, and don't tend to enjoy metal, classic rock, new country, or jazz, but I can enjoy a lot of things in the right context) and not really related to my identity. It's actually hard for me to let go of the idea that musical tastes have more than practical importance.

But I am getting more and more to the point where it seems useless to describe various artists as good or bad. Sally and I both remember a time that Robin defended Pearl Jam (who Sally didn't like) as "a quality product," but most commercially produced music could be so described (depending on what qualities you think are important). Does Garth Brooks suck just because I don't really like his sound and his lyrics aren't clever and edgy or deeply meaningful (for me)? Or is he great because his music (apparently) brings pleasure to millions of people? Who cares what I think anyway?

Where My Money Goes

2012-01-10T21:27:00.012-07:00

Unlike in my former life as a corporate worker bee, these days I spend more money than I earn. Not counting the tax hit from the bonus I got when I left my last company (which, after all, came with a bonus), I'm about $2000 poorer (in terms of cash and short-term savings) now than I was a year ago.

I'm not too upset about that. I started grad school with some savings that I expect to partly deplete by the time I graduate. At the same time, considering that I live in a relatively cheap apartment ($675/month) with a roommate (so that my rent + utilities is typically under $400), my TA stipend (about $22,000 a year including the extra summer work) really ought to be enough to live on. Many people are supporting families on such a wage.

I keep track of my finances in Mint, so for your amusement and/or horror, let's take a look at how I spent my money in 2011. First, here is an overview of all of my spending:

A few things really stand out:

Wow, I spend a lot of money on food!
And shopping!
What am I spending all that "Auto & Transport" money on?
I wonder what is in "Other"?

(In case you wonder, the Education spending includes $5 of tuition and the rest is books and office supplies. Some of the books are textbooks and others are supplemental reading. I also spent $180 on eBay for the tablet I teach from.)

Let's look at where my food budget goes:

So, it turns out that I eat out a lot. This shouldn't surprise anyone who knows me. And this aspect of my life has proven extremely unresponsive to my attempts to apply budgets to it. It turns out (via the magic of revealed preferences) that eating out, and in general having nice things to eat, is important to me. I'd still very much like to spend less money on food. Over $20 a day seems a bit excessive.

Now, about the shopping:

I'll admit it shocks me that I spent over $1000 on clothes in 2011. I don't think of myself as buying many clothes (even including shoes, which are included here). I'm fine with the money I spent on books. The 'hobbies' money here was the money I spent having the photo albums of my childhood digitally scanned and I don't regret that either.

Now let's take a look at where my "auto & transport" spending is coming from:

The parking is mostly for school, of course. I shouldn't need to spend money on this at all given that I live half a mile from campus, but I started buying parking because I developed chronic foot problems that seem best remediated by avoiding walking. Hopefully over time I can cut that expense. The rest of this is just the normal costs of car ownership.

Let's take a look at "Other":

I'm happy with the money I spend on travel - I think it's money well-spent, relatively speaking. Visiting my loved ones is important to me, and if anything, I wish I spent more money on this. (That is to say, I wish I traveled more. If I could travel more for the same money that would be great too.)

What about that $418 on entertainment?

You might think from seeing this that I buy movies, but that is not the case: if you look at the individual records, it turns out that a few of these are movie rentals and the rest are actual theater tickets. (There is also my Netflix subscription for $10/month.) I hardly ever used to go to the movies, so it's a bit shocking that I apparently saw 25 in the theater this year.

Seeing movies in the theater is a bit of an extravagance, but it results from the social life I have these days that I never used to have. I really relish that aspect of my current existence and don't regret it in the slightest. I will continue to see movies with friends as much as I want.

So that's how I spent my money in 2011. I would like to cut back on shopping and on eating out; otherwise I'm relatively satisfied with my current choices, and very grateful that my life affords me so many opportunities.

Middlemarch, and Being Human

2012-01-05T00:13:00.002-07:00

A long time ago at a college far, far away (well, about 6 hours away by car), I was supposed to read Middlemarch by George Eliot for a 19th Century British Literature class. I ended up dropping the class and never reading the book, but then recently, Ta-Nehisi Coates has been talking it up, and I love him, so I was inspired to pick it up. I haven't finished the book yet - I've been reading it several hours a day for over a week, but it's a long book - but I want to talk about it a bit.

Middlemarch at first reminded me of Jane Austen's novels - the setting appears similar (Eliot was born around the time Austen died, but from this distance in time, it feels the same) and the book has a large and interwoven cast of characters and is heavily about courtship and marriage. There are three really clear differences, though:

Eliot is much harder to read than Austen; the sentences are longer, use more fancy vocabulary words, and are structured with more complexity.
If you read Austen novels and think, "But what about once they are married? These people barely know each other! Marriage is every day for years and years and years! Also women especially had no options and they didn't even have divorce back then," Middlemarch may be for you, because getting married is just the start of each story, and you get to find out exactly how the matches turn out.
Eliot doesn't limit herself to describing conversations between women or between women and men; she also describes conversations that solely involve men.

There are other differences, one of which relates to an obsession of mine. The obession is the one I'm thinking of when I say, "I don't know how to be a human being," so let me digress for a moment.

Life to me seems like a constant struggle between being a decent human and being a shitbag, and we have two choices - unabashed shitbaggery, or shitbaggery accompanied by struggle and abashedness. I don't see any cure for it, and this, to me, is almost the sole appeal of Christianity - that it starts with a frank admission that we are basically horrible.

Pondering one's own "stuff" gets into what I call fractal territory, which is to say, it leads to an endless descending cycle of realizing what a crappy excuse for a person one is, at the end of which cycle I usually declare, "I have no idea how to be a human being."

I'm not talking about temptations like lying or theft, but actual internal attitudes. I'm talking about things like mocking people we don't like for qualities we readily accept in our friends, or detesting others for traits we ourselves possess, or continually (despite any efforts to the contrary) seeing the world as revolving around ourselves, or constant unremitting disregard for sometimes even really obvious things about the experiences of the people around us, or the bizarre selfish pride most of us feel.

So I guess what I'm really talking about is fundamental selfishness. Of course, some people simply embrace their own selfishness - either by conveniently not noticing it or by taking up a philosophy that justifies it. I know some people who actually seem not to be shitbags at heart, but I have no idea how they attained this state, or whether it's basically illusory. But I know that when I look at myself in terms of my internal states I basically disapprove of my overall implicit attitudes.

And the thing about Middlemarch is that George Eliot seems to really get this. She writes about this sort of thing a lot, and I like it.

Here are some good quotes (not all relating to this topic):

For my part, I have some fellow-feeling with Dr. Sprague: one's self-satisfaction is an untaxed kind of property which it is very unpleasant to find depreciated.

***

We are angered even by the full acceptance of our humiliating confessions - how much more by hearing in hard distinct syllables from the lips of a near observer, those confused murmurs which we try to call morbid, and strive against as if they were the oncoming of numbness!

***

There are answers which, in turning away wrath, only send it to the other end of the room, and to have a discussion cooly waived when you feel that justice is all on your own side is even more exasperating in marriage than in philosophy.

***

She leaned her head back against the window-frame, and laid her hand on the dog's head; for though, as we know, she was not fond of pets that must be held in the hands or trodden on, she was always attentive to the feelings of dogs, and very polite if she had to decline their advances.

***

But Duty has a trick of behaving unexpectedly - something like a heavy friend whom we have amiably asked to visit us, and who breaks his leg within our gates.

***

It is true Lydgate [a doctor] was constantly visiting the homes of the poor and adjusting his prescriptions of diet to their small means; but, dear me! - has it not by this time ceased to be remarkable - is it not rather what we expect in men, that they should have numerous strands of experience lying side by side and never compare them with each other? Expenditure - like ugliness and errors - becomes a totally new thing when we attach our own personality to it, and measure it by that wide difference which is manifest (in our own sensations) between ourselves and others.

***

The spiritual kind of rescue was a genuine need with [Bulstrode]. There may be coarse hypocrites, who consciously affect beliefs and emotions for the sake of gulling the world, but Bulstrode was not one of them. He was simply a man whose desires had been stronger than his theoretic beliefs, and who had gradually explained the gratification of his desires into satisfactory agreement with those beliefs. If this be hypocrisy, it is a process which shows itself occasionally in us all, to whatever confession we belong, and whether we belief in the future perfection of our race or in the nearest date fixed for the end of the world; whether we regard the earth as a putrefying nidus for a saved remnant, including ourselves, or have a passionate belief in the solidarity of mankind.

***

I think any hardship is better than pretending to do what one is paid for, and never really doing it.

***

There is no general doctrine which is not capable of eating out our morality if unchecked by the deep-seated habit of direct fellow-feeling with individual fellow-men.

So there you have it, folks: Tam's guide to Middlemarch.

Sucking at Life

2011-12-15T08:39:00.003-07:00

Yesterday, I did a load of dishes. And it's important that we're really clear about what happened here, so let me elaborate.

Ed and I collectively have quite a few dishes, and a large number of them were dirty. I was picking up these dirty dishes, one by one, and placing them on the dishwasher racks. Once I was done, I would I put a little square of soap into the dishwasher, close it, move a small lever to lock the door, and slightly rotate a dial. A couple of hours later, there would be clean dishes.

This is not at all difficult or taxing, and yet we are a couple of days behind on dishes. As usual. Whence the following conversation as I was loading:

Me: We suck at life.

Ed: Oh, I know.

Me: How could anyone have this easy of a life...

Ed: And suck at it this much?

Me: Yeah.

Ed: I don't know, but we do.

[pause]

Ed: We can't solve any real problems, that's why we solve made-up problems.

Me: Right! So that's why we're in math?

Ed: Yep.

Me: So we can be like, "Oh, what if we had this type of thing, and we called it a blah de blah, then what else could we say about it?" and just give ourselves easier problems to work on?

Ed: Yep.

Me: My god, I think you're right.

Self-Description

2011-11-30T11:37:00.004-07:00

Once upon a time, Sally and I used to talk about something we called "being demonstrative," by which we meant not excessive displays of affection, but rather statements like, "Oh, isn't Paris lovely this time of year?" or the way that someone we knew once took out chopsticks to eat a burrito, claiming that the year she had just spent in Japan had made it difficult for her to eat with a fork. In other words, we were talking about statements calculated to demonstrate something - a practice akin to name-dropping.

I've recently been thinking about another type of obnoxious behavior. It's one in which many people sometimes engage, and I find myself tempted by it often. It's also something I have learned to recognize as an immediate warning sign about a person's personality. It is an almost universally obnoxious trait: self-description.

Some (hypothetical) examples:

I'm not the kind of person who watches TV.
I guess I'm just more cynical than that.
I'm just a big ole country girl.
Most people either love me or hate me.
I'm one of those people who can't stand pedantry.

It's interesting - it's hard to write examples of this, because some of it comes down to intent. If your intent is (honestly) humble or self-denigrating ("I'm kind of an asshole before I have my coffee"), then that's not what I'm takling about. Likewise if you're being ironic. But often these types of statements come from a demonstrative type of intent - a strong desire to demonstrate your characteristics to others, especially people you have just met. And in that context it somehow becomes really obnoxious. It is like you have this obsession to present yourself. I guess an obsession with oneself is never attractive in a social context.

A few months ago, a friend and I had a conversation via IM. Afterwards, I thought, jesus, we just had a fight - I hope she didn't notice. I could feel myself being obnoxious during it and I thought she was a little obnoxious too. Later she texted me to apologize for being that way, and I apologized too.

I'm pasting in the transcript of this because the whole thing drips with self-description of exactly the kind I'm talking about...on both sides:

Friend: Hmm. That [story about cheating] does sound bad. I don't know.

It just makes me so upset that cheating is a thing here... cheating wasn't an issue where I went to high school or where I went to college and I hate that it's prevalent in this environment.

me: I know what you mean. I think it's pretty common here.

Friend: I just don't think I'll ever be able to teach somewhere like that ultimately, I think it would bother me too much.

me: I am cynical so it doesn't bother me, I guess. So far anyway.

Friend: I'm cynical about some things, but education isn't one of them, probably because of where I went to school.

me: I don't think that's really why. I mean, I have a lot of similar school experiences to yours.

Friend: maybe i'm just an idealist then

me: I mean, I want cheaters nailed to the wall, but it doesn't bother me that they exist, if that makes sense.

A Time Capsule from 2005

2011-10-25T13:43:00.002-06:00

In May of 2004, I had some blood tests done by my doctor. My cholesterol was a bit high, so she recommended that I cut back on saturated fat. I ended up making a lot of changes to my diet then - cut saturated fat significantly (I was logging everything back then, so this was easy to say), cut back on fast food, and ate a lot more whole grains and vegetables at home.

I remembered today that I had a c-reactive protein test back then, and I thought I might have emailed Sally about it at the time, so I searched my Gmail for "CRP" and turned up an email I wrote a year later when I had more tests done. I'm interested in CRP because it is a marker of inflammation, which may be one of the causes of leptin resistance, which may be a major cause of obesity.

Anyway, I now present, for your reading pleasure, this email from 2005.

Last May, when I got my high cholesterol numbers (from tests taken
in April), I radically changed my diet. Remember? Sure you do.

I have pretty much kept with those changes, and I have also lost 29
pounds since then.

Well, I just got my blood test results back. Here is a comparison:

April
-------
total cholesterol: 211 (should be < 200)
hdl ("good"): 43 (should be > 40)
ldl ("bad"): 151 (should be < 130)
triglycerides: 85 (should be < 150)

Now (February)
----------------------
total cholesterol: 219 (should be < 200)
hdl ("good"): 38 (should be > 40)
ldl ("bad"): 166 (should be < 130)
triglycerides: 112 (should be < 150)

So basically, all of my numbers have gotten WORSE rather than better,
despite my having lost a substantial amount of weight (13% of the
weight I had in April, in fact) and changed my diet in all the
recommended ways (if not to all of the recommended extents).

In addition, this time I had that Cardio CRP test. I got a 10.7.
Here is what the reference numbers are:

< 1.0 Low Risk
1.0 - 3.0 Average Risk
3.1 - 10.0 High Risk
> 10.0 Persistent elevations may represent non-cardiovascular inflammation

Yuck. My doctor wants to have all of this retested in November, and
meantime recommends continued weight loss, exercise, and avoiding
animal fats. (What animal fats? I hardly eat any fucking animal fats
anymore anyway.)

This is kind of freaking me out.

Notice that eating less animal fat, cutting saturated fat from my diet resulted in HIGHER triglycerides (very bad) and slightly worse cholesterol numbers (probably bad), despite the fact that I lost 29 lbs over that time, which would be expected to improve things.

This proves nothing, of course, but unlike most anecdotes, this one at least applies to me specifically.

My Current Beliefs about Diet and Obesity

2011-10-21T22:54:00.004-06:00

I thought it would be good to set out my current beliefs about diet, nutrition, the causes of obesity, and so on. They are what guide my (perhaps wacky-seeming) current dietary guidelines. I'd also like to distinguish them from other beliefs with which they might be confused.

Food Reward Hypothesis

I think the food reward hypothesis is the best-supported current idea about why so many of us are overweight and obese these days. The basic idea of this is that we now have the ability to make (in many cases manufacture) foods that are both hyper-palatable (really delicious) and high reward (very tempting/craveable/"addictive" in a loose sense), and that eating such foods causes our bodies to try to keep us at a higher weight than is healthy.

This shouldn't be confused with the "thrifty gene hypothesis," which is the common-sense idea that we evolved to live under the threat of starvation and are going nuts now that food is so plentiful. According to the food reward hypothesis, if our food were still the sort of plain, comparatively unvaried food eaten by our ancestors, abundance itself wouldn't cause overeating.

Stephan Guyenet has a great series on the food reward hypothesis here: Part I, Part II. He talks about the thrifty gene hypothesis as well.

(Note: I will be linking Guyenet a lot in this post. He is not my only source of information here, but he has informed a lot of my thinking, and seems to have done his homework. In many cases he's the best concise link I can give.)

Conclusion: I should eat simple foods prepared at home.

The Role of Carbs

Books like Good Calories, Bad Calories by Gary Taubes make convincing arguments that overconsumption of carbohydrates, particularly sugar and refined flour, are responsible for the obesity epidemic. Certainly, obesity travels together with insulin resistance (a problem that is all about carbs, and is the fundamental cause of Type II diabetes), and insulin resistance is a big part of what causes heart disease in general.

Guyenet, the same guy as above, has a long critical post about the idea that carbs (or insulin resistance) cause obesity. He doesn't buy it at all.

I honestly don't know what to think about this topic. But what everyone (at least, everyone I'm currently reading) seems to agree on is that if you are insulin resistant, eating a ton of carbs is a bad idea. This is contrary to the official recommendations for diabetes patients (which stress a high-carb, low-fat diet), but I've read enough to convince me that that is bunk; I'll write more below about why.

I've been testing my blood sugar lately, and my fasting morning glucose levels are slightly elevated - not in the diabetic range, not quite in the "pre-diabetic" range, but not where they should be or where they have been in the past either. I have a strong family history of diabetes and I have other signs (like PCOS) of having trouble with insulin resistance.

Insulin resistance definitely leads to heart problems and a lot of other issues. Exercise and reduced carb intake definitely combat insulin resistance.

Conclusion: I should take care not to eat too many carbs.

Dietary Fat

The dominant hypothesis of the last half-century or so of medical advice has been that overconsumption of fat is what causes obesity and (separately) heart disease. This is why diabetics and overweight people (and, really, everyone) is encouraged to eat a low-fat diet.

It is a fact that you cannot eat a low-fat diet without eating a high-carb diet. Humans can't eat the bulk of their calories as protein (you will get sick if you try, but you'll also find it very hard to try, because you will start very very badly not wanting to eat any more lean meat).

The evidence that high fat intake causes obesity is based partly on common sense (fat has more calories per gram than carbs or protein) and partly on the observation that Americans got fatter and started (perhaps) having more heart trouble around the early part of the 20th century, when (it is believed) we may have started eating more fat.

We also started eating way more sugar and refined flour and packaged products and that sort of thing at the same time, so it's very hard to tease out the effects of fat vs. carbs vs. high-reward foods (vs. unknown other factors, of course). There seems to be very little evidence that eating a high fat diet causes weight gain. Many traditional cultures (Inuit, Masai) eat very high fat diets and are very lean (despite not facing any regular food shortages).

Conclusion: It's OK to eat a high-fat diet.

What about Saturated Fat?

As someone who has lived in our culture, it is very difficult not to believe that saturated fats, especially from meat and animal products, are dangerous. I feel as though I know in my very bones that these types of fats are unhealthy and cause heart disease. This is one of the very strongest messages about food from the medical establishment.

From what I can tell from my reading, it's just not true, or at least, many very large, long-lasting studies designed specifically to support this hypothesis have completely failed to. Now, my reading isn't (can't be) exhaustive and it's possible my sources are looking at the data in a really biased way, but it doesn't seem so to me.

Here's Guyenet on saturated fat and cholesterol, the diet heart hypothesis, coronary heart disease, and on findings about full-fat dairy. I also found Good Calories, Bad Calories pretty convincing on these topics. And, of course, when you look at recent studies comparing low-carb to low-fat plans for weight loss, everyone gets healthier on both sides.

An additional bit of common-sense thinking: for a very long time before agriculture, our human ancestors got most of their fat from animals. Either they ate a very high-carb diet (and probably some did), or they ate a lot of animal fats (definitely some did). It's likely we evolved to be able to handle eating these fats.

Conclusion: It is truly safe and healthy to eat saturated fats, including from animals.

Pre-Western Cultures

The fundamental idea of the paleo and primal advocates is that we should eat the way that our hunter-gatherer ancestors did, rather than the way that our immediate agricultural ancestors did. In other words, rather than relying heavily on grains, legumes, and dairy for our food, we should eat more meat, vegetables, perhaps occasional tubers, berries, nuts, and things like that. We certainly spent a lot more time evolving to eat a hunter-gatherer diet than we have spent evolving to eat grains.

The only populations on the planet today who don't suffer from a lot of heart disease, obesity, diabetes, cancer, and other "diseases of civilization" (periodontal disease, appendicitis, gall bladder disease, etc.) are the ones people used to call uncivilized - small pockets of people living a traditional culture. It is true that they largely lack these health problems even when you adjust for age.

These groups are very different from each other. The Masai have a diet made up almost exclusively of milk, cow blood, and meat. Traditional-living Inuit have a diet that is something like 90% animal fat. On the other side, there are traditional cultures who live very healthy long lives (when they don't die in infancy) on diets composed almost exclusively of yams or sweet potatoes, and others who eat more balanced diets. But in general, my point is that there are very healthy cultures living on high-fat and on high-carb diets. It appears that healthy diets can have a wide range of macronutrient ratios.

What these cultures have in common is that they eat very little refined sugar, very little refined grains, and they don't eat "food that comes in boxes" - highly processed food manufactured to be as delicious and tempting as possible. They eat diets of mostly plain foods, with not a lot of variety by our standards.

It's hard to tease out what aspects of the western diet and/or lifestyle cause all of our problems. Is it the sugar? (There is some evidence that high-fructose foods like table sugar and corn syrup may have especially bad effects.) The comparatively recent introduction of grains to our diets? The refining of those grains and sugars? The even more recently introduced cottonseed, canola, corn, etc. oils (polyunsaturated fats)? Or the excessive variety and deliciousness of the manufactured food products that surround us?

At any rate, if the problem is dietary (as seems likely), then, while we can't say exactly what the problem is, we do know that simple diets of plain, pre-agricultural foods are healthy. (Of course, no food that I eat is actually pre-agricultural. I don't hunt or gather anything myself. But I think we can all agree that grass-fed beef or an apple is more "paleo" than a Big Mac.)

Conclusion: It may help to avoid modern agricultural products like sugar, refined grains (or any grains in large quantities), and seed oils.

Exercise

Exercise decreases insulin resistance and has many other beneficial effects, but I seem currently incapable of incorporating much into my life. If I explained why, I would just be making excuses, so I'll just say it's not a big focus for me right now.

Based on what I've read lately, I do think that high-intensity interval training is way more effective than regular steady moderate-intensity cardio. If I were designing an ideal exercise program, I think I'd go with something like Mark Sisson's recommendations in The Primal Blueprint, which means a good base of low-intensity exercise (walking, slow swimming, jogging if you're much more fit than I am), small amounts of interval training (two or three times a week for 5 or 10 minutes), and regular natural, whole-body strength training (two or three times a week for 30 minutes or so).

Conclusion: I should exercise, but I don't.

I hope this helps to make sense of why I'm doing what I'm doing, or was at least interesting on its own.

Current Diet Protocols

2011-10-20T11:34:00.004-06:00

These are the dietary rules under which I currently (try to) live.

Don't Eat
Sugar
Grains
Legumes
Seed oils (corn, cottonseed, soybean, canola, etc.)
Restaurant meals & fast food

Eat freely
Meat (any non-processed kind)
Non-starchy vegetables
Nuts
Non-starchy fruits (berries, apples, etc.)
Full-fat solid dairy products (cheese, butter, yogurt, etc.)
Coconut oil, olive oil, animal fats

Eat in moderation
Very dark chocolate
Starchy vegetables (potatoes, etc.)
Starchy fruits (bananas, etc.)
Whole milk

I am OK with eating some of the "don't eat" items a couple of times a week in order to eat at restaurants with friends. Other than that, I am trying to make my food at home and keep it relatively simple.

Ch-Ch-Ch-Changes

2011-10-09T10:32:00.003-06:00

This morning I hit a new low weight. Overall I've lost 22 pounds since early May, which is pretty awesome. And today is my 7th day of largely eschewing grains and legumes and of keeping my carbohydrate intake between 50 and 100 grams per day.

So what am I eating?

Yesterday I had a fajita chicken salad (w/ cheese, sour cream, and guac) for breakfast, eggs with turnip greens and cheese for lunch, and chicken tikka masala at a restaurant for dinner. I was trepidatious about eating chicken tikka masala without rice or naan. Frankly, it seems a little insane. But I managed it and it was still extremely delicious (though I did crave the naan and rice that were on the table, so that was a little uncomfortable).

Today I got up early, worked for three hours, and then made myself a breakfast of scrambled eggs mixed with tri-color peppers (from frozen), a big chicken sausage link (cut up), and cheese. I cooked this in ghee (clarified butter) and it was extremely delicious.

It's no longer the case that I don't get hungry. I do get hungry. But the hunger is like the hunger of my childhood - it doesn't really interfere with activities. You think "Where's dinner?" but then you can happily go run around some more in the meantime. It's not urgent. (More precisely, it feels urgent, but only intermittently.) I really like this change.

There has been one more change. Before I started losing weight in May, I was taking 150mg of ranitidine for heartburn twice a day - so, 300mg per day total. Eating smaller meals to reduce calories let me drop that to 1 pill per day, so in half. Then I bought some smaller ranitidine pills (75mg each) and was taking two of those a day. Now I am taking at most one of those per day, and some days I don't need any at all. I would love (so much) to stop using heartburn medication, and it seems within reach. Yesterday I didn't take any, not even a single Tums, which is amazing considering all of the spicy, fatty things I ate, which are usually exactly the things to cause heartburn.

Other than the changes to hunger and acid reflux, and the accelerated weight loss, I haven't noticed any changes. I feel good, happy, etc. Most of my meals are very satisfying due to the high fat content. It is sometimes tricky to figure out what to eat, but I've always tended to obsess over what I was eating next anyway, so this has just channeled that into a different direction.

Primality

2011-10-05T18:51:00.002-06:00

Last week's no-wheat experiment went pretty well. It wasn't too hard not to eat wheat (I ended up eating a fair bit of corn tortillas and tortilla chips) and it seemed to cut my hunger a bit. I lost a pound a day for about 4 days in a row and then gained one or two back after that, so that was kind of exciting.

This week I've been reading The Primal Blueprint, and I'm experimenting with completely not eating grains or legumes and keeping my carbohydrate amount between 50 and 100 grams a day, which is the level at which the author of that book claims effortless weight loss will occur.

I'm still eating dark chocolate, having coffee if I want to, and I'm not avoiding things like soybean oil, largely because it's much easier for me to have salad at the school cafeteria if I can have ranch dressing rather than the nutritionally superior olive oil and vinegar type of thing. So I'm still basically eating sugar (which is a grain) and some legumes. Other than that, I haven't (to my knowledge) had anything - no wheat, no rice, no oats, no beans, etc.

It's a sort of radical thing to do, obviously. But it wasn't a huge transition since I'd already been eating no wheat and keeping my carbs low for a week. I haven't noticed any untoward effects this week, while last week I did have some serious crankiness and headaches.

What I have noticed is that I have absolutely no perceptible blood sugar changes. I sort of still get hungry - at least, there is a kind of feeling that grows over time that tells me I should eat something. It's kind of a gaunt or empty feeling. But it no longer seems to carry with it much urgency. (For instance, I had no breakfast today, a small lunch at 10:15, and I was fine not having dinner until 6:30.) And I never have blood sugar crashes, which I frequently did before. That's kind of a big deal.

My weight has been dropping pretty seriously - like about 2.5 pounds since Monday. I'm not recording these new weights yet, since they may settle back down. I'm still tracking everything I eat, and I'm pretty easily creating calorie deficits of 700-900 calories a day basically without trying. (I'm not really trying to limit my food intake.) So that's kind of amazing.

It could be that some of the "this is so easy!" aspects of doing this are basically just me being excited about doing something new. I could get really tired of this and find it just as hard as anything else. It's certainly extreme to not be able to eat virtually anything that normal people eat (sandwiches, pizza, tacos, muffins, fried rice,...). But I'm finding I can eat something at most places I ever go, and that's working for me just fine for now.

If this does prove to be a way to maintain a much lower weight without the extreme effort of resisting eating all the time, I think I would have to choose many extra years of healthy life over the ability to eat these common and delicious foods. So basically if this keeps up, I'd like to keep doing it. We'll see, of course, whether I feel that way in a week or a month or whatever.

It's probable that the weight loss comes more from the effects of low-carb than from avoiding grains and legumes per se. When you don't eat carbs you don't set up part of the insulin cycle that makes you hungry again a few hours later, which is a particular issue for people who are blood-sugar-challenged, like me.

But the advantage of eschewing grains and legumes while doing low-carb is that you don't end up prioritizing a muffin over the day's vegetables. I'm eating tons of vegetables most days, and some fruit as well, plus dark chocolate, plain yogurt, nuts, and other carb-bearing foods. If I were just trying to keep carbs down I think I'd trade some of that for, say, white rice, and that would be less healthy, in general.

Anyway, I'm kind of excited, and I hope this keeps up.

Wheat Experiment

2011-09-25T00:57:00.002-06:00

Starting yesterday between breakfast and lunch, I am experimenting with not eating wheat for the next week. I'm also trying to go (moderately) low carb in general, but I'm much more dedicated to the no-wheat aspect than to the low-carb one.

I read the book "Wheat Belly" by William Davis. Davis argues that grains in general are not great for us, and that wheat is the worst. He thinks that genetic changes to wheat over the past 50 years (through modern but not genetic-engineering-based methods) have made it particularly dangerous to humans and responsible for a host of different medical problems. Celiac disease is an obvious thing that is indeed (indisputably as far as I know) due to wheat; the rest is more speculative, I think.

He has a lot of references in the book, which is good, but the way he argues leaves holes you could drive a truck through. It's not the worst pseudoscientific bullshit I've ever read - even the term "pseudoscientific bullshit" might be an exaggeration - but it's not fully convincing either.

Still, it's hard for me to resist the pull of sense-making conspiracy theories about food. I do think that the overconsumptions of carbs, especially from grains, is a big part of the obesity problem for some people (including me), and not just because it's easy to eat a lot of carbs. I think they actually encourage overeating beyond just being tasty, readily available, and cheap, by changing your body chemistry such that you have more blood sugar fluctuations (which cause eating) and possibly by encouraging your body to store fat (through insulin-related stuff).

With my family history of diabetes and my PCOS, it seems pretty clear that I will (do) struggle with insulin resistance. My odds of avoiding diabetes feel pretty low at times (assuming I'm not already diabetic, which I haven't been so far when tested, but which of course could happen anytime).

I think that if I can eat less carbs over my lifetime, I'll be doing myself a huge favor. Aside from non-starchy vegetables and a moderate intake of fruit, I don't think there's any biological reason that humans need to eat carbohydrates at all. I think grains are completely unnecessary to a human diet. (They're practically necessary as there is no other way to feed the number of humans on this planet, but that's a different issue.)

So, Dr. Davis claims that when his patients stop eating wheat (without making any other changes, but in the context of generally trying to have a healthy lifestyle), they magically lose tons of weight and all of their mysterious ailments (IBS, chronic fatigue, acne, arthritis, asthma, acid reflux, etc.) miraculously disappear. This is pretty clearly not a clinical finding that would hold up.

Nevertheless, if giving up wheat did make it a lot easier for me to lose weight, I feel like it would be worth it, and if I gained more energy or a better overall life feeling in the process, that would be even more awesome. It seems worth a try given that I think it's basically a healthy choice anyway.

Hence my exploratory week of non-wheat-eating.

So far I've been having meats, salads, vegetables, eggs, and today I had about 1/2 cup of a straight-up starch (rice or potatoes) at my meals. I also ate some extremely dark chocolate today, plus raw walnuts and almonds. It seemed like a very healthy day of eating overall.

I've also been feeling like shit, which was true other times that I tried to dramatically cut carbs as well. (Carbs made up 25% of my diet today, so I haven't cut them to a really extreme extent. It's usually more like 50%, though.) I've often felt a bit hungry yet nauseated at the thought of eating, and I've been a little headachy and extremely irritable. I think these aren't just nocebo effects, but of course they could be, and I have no way of distinguishing them. I expect them to get worse but I hope they subside before the week is up (and before I give in and eat 15 pieces of naan) so I can see what life is like afterwards.

Dreams

2011-09-16T09:41:00.002-06:00

I've had a few strange ones lately.

Dream 1

Apparently in this dream, Sammy (my cat) was my romantic partner. In the manner of all dreams, this was not strange. He was standing on an ironing board talking to me about how dissatisfied he was recently, and how sad, because I was not spending enough time with him, or giving him enough attention. I felt very sad too. I was petting him while he spoke, though it occurred to me that this was disrespectful because I knew he didn't want to be petted - he was unhappy with me. But of course I always pet him when he is nearby because I like to.

Then I (very insensitively) asked him how he'd feel about us getting a new kitten, because I thought that would be fun. I knew it was insensitive when I asked it. It also felt a bit novel to me - just asking the current cat whether to get a new kitten or not. I wondered why I hadn't thought to ask in the past.

Dream 2

This dream took place in an enormous old house that apparently all of the grad students in my program used for parties. Our director of grad students was there. Sally was also visiting. There were a ton of rooms, all with different things going on. The decor sort of looked like the Old Spaghetti Factory, if you've ever been to one of those (or in other words like an old or possibly haunted house).

For a long time I was trying to track Sally down, but couldn't because she was planning some sort of big surprise or show or experience for the rest of us. In the meantime, I talked to the DGS. He was funny as always. I asked him whether this house had always been owned by the department, or was loaned to us by some kind of alumn, or how it had come to be used for parties this way? (In the dream, I don't think anyone lived in the house full time.) He told me that, no, actually, it belonged to [something like] an aunt or uncle of Lee Ann (who has only been in our program a short time). I was telling him how I could now understand the appeal of being in a fraternity or sorority, just so you'd have that big house for parties.

The Midnight Conundrum

2011-09-11T02:09:00.004-06:00

Here you are, it's midnight on a Saturday night. You feel tired, you could definitely go to sleep, but you also feel able to continue working. You have two big assignments due on Tuesday and have put a few hours into one of them already today, and you're primed to continue. But if you stay up late doing this, you'll sleep late tomorrow, and then getting up Monday will be even harder than usual.

Go to bed or keep working?

For me, the answer usually has to be "keep working." This is because I really cannot (or, at any rate, do not, ever) get up in the morning and get right to work. So if I go to bed, I may never recover the momentum that I feel right now, or at best I may recover it hours after getting up on Sunday. For the most part, I get stronger and find it easier to work more and more as the day goes on, at least when I'm vaguely able to structure my time that way.

I made the choice to continue working and I got some really excellent work done despite also feeling tired. Now it's 3:15 and I'm really quite tired and ready for bed, but I have big tasks completed. I also happened to stop at a "downhill" point, which is good. (By "downhill" I mean a point from which it is easy to continue. It's like riding on hills with your bike - if you need to stop, it's better to stop on a downward slant so that you can easily start up again.)

Basically when I feel "tempted" to work I have to make use of that temptation unless there are truly compelling reasons not to. As long as I get overall something like enough sleep, getting my work done is more important than sleeping at any particular time.

Grad School vs. Working

2011-09-04T16:27:00.003-06:00

Back when I was thinking about going to grad school, I had one hope that I was almost afraid to confess. I hoped, despite how hard grad school was reputed to be, and how many hours it was said that I would have to work (i.e., way more than 40 per week), that it would take me away from the horrible feeling associated with having a regular job.

I don't know exactly how to describe the feeling, and I feel like a spoiled brat or a wimp for even having it, but I'm basically talking about that kind of bored feeling of waiting for the day to be over, killing time, trying to think of a good reason to leave work early, etc. I mean the basic feeling of just not wanting to be at work.

It turns out to be true that grad school, for me, totally does not have this feeling. I had it over the summer when I worked in the math lab (a worse job than any I've had in many years, though still not bad in the overall scheme of possible jobs), but I don't have it during the regular semesters at all.

It's interesting. I spend more hours at school now than I ever have at a job, and (more or less completely independently) more hours working than when I had a job. But I simply do not have that feeling of being required to be in a place for 8-9 hours every day. Aside from my office hours (4 per week), I am always either doing a specific thing (teaching or attending class or a seminar) or I am free to go if I want to. Everything now is about accomplishing specific tasks on time rather than spending a particular amount of time appearing to work.

Consequently, my office, and the building where I work, doesn't feel like a workplace to me. It feels a lot like my dorm felt when I was originally in undergrad, actually - like a cool place to hang out, the place where I do most of my work, and the place where, at all hours of the day and night, some of my friends and acquaintances are around.

I was able to confirm this when I was working in the math lab. I left there one day during my shift to go to the restroom, and when I walked out into the hall, past the offices of my friends, I had a feeling like, "Oh, I am trapped in the math lab, and all these people out here get to have their regular lives."

That dreadful feeling of being trapped at work was a really large feature of my previous life, and it's pretty fantastic for me that I don't have it anymore. It's like, as I wrote once before, my work life and life life have all become the same thing. Some people hate that aspect of grad school but I think, for the most part, I really like it.

The Difference a Year Makes

2011-09-03T01:55:00.003-06:00

Last week, I started my second year of graduate school. It feels so very different from my first year - really almost astonishingly so.

I spent the entire summer studying for my qualifying exam in real analysis. I wrote over 300 pages of notes, by hand, working through proofs and ideas, some over and over again. I worked about 2-4 hours pretty much every single weekday, and many weekend days, for all but about 2 weeks of the summer. (I also tutored students in the math lab.)

Even though that may not seem like a huge amount of time to spend (because it wasn't), it was huge for me. I've historically been terrible at making myself work to a far-off deadline, and this work was both hard and sort of ambiguous. How much would be enough? Was it even possible for me to pass (like, ever)? Had others passed these exams in the past only because they were smarter than I am, or had better memories? I struggled with these thoughts a lot, but I kept working.

The qual was an 8-hour exam. It took me 6 hours and 40 minutes, which is somewhere in the typical range. And I passed. I passed it. Amazing.

Now that I've passed it, the material doesn't actually seem like it was that big of a deal. Now that I know the proofs, they don't seem to have all that much to them. Ha.

I also, of course, made it through my first year of classes last year. I struggled with the material a lot at times, but I did well in terms of grades. I didn't seriously screw anything up. I was never one of the worst students. Occasionally I was mildly praised.

Last year, when I started grad school, I was extremely enthusiastic, and then when it got hard, I was really scared a lot. Especially that first semester I had really dramatic mood swings. I sometimes fantasized about leaving, going back to my old job, resuming a better life with more money and things and free time and less failure and stress.

This year, honestly, I wasn't that enthusiastic at the start of school. When I went to the mandatory all-TA/TF meeting, I remembered how exciting it had been the previous year, but I was pretty meh about it. I was mildly interested in meeting the new first-years, but that was about it. I was still recovering from the qual.

But...I'm not scared anymore, either. I still don't know if I can actually do research, but I now know I can pass classes and quals. (I need to pass one more qual, and I have four tries.) I now know I am not borderline for the program, barely clinging to life.

Last year, I remember the first homework that I got with a problem I couldn't easily figure out. It really freaked me out. I'm pretty sure I cried. I calculated what percentage of my grade this one problem would be and thought about the fact that I was already losing that much so early in the term. I wondered whether I belonged here. I did eventually solve the problem, but man, the stress.

Last week, my topology homework had a problem I couldn't figure out. I worked on it on a few different days, but never with any real feeling of stress. I figured out all of the other problems. This one remaining one wasn't a big deal. Turning it in unfinished would not harm my grade or standing or anything like that. I wanted to get it but there was no fear there. It certainly did not drive me to tears.

And that, my friends, is the difference that a year makes.

Hated Professors

2011-09-03T01:29:00.003-06:00

Back in 2007, I took "Introduction to Proofs," the class at my alma mater that was designed to transition you from the computational type of math with which most people are familiar to proofs-based theoretical math. It is kind of a grab-bag course at that school, dabbling in proposition logic, (abstract) algebra, analysis, discrete math, etc.

I hated my professor, Dr. J.

Hated him.

He would talk to the class in this sort of angry way all the time. He barely graded our homework. One time he gave us a quiz and then, when he returned it, and someone asked him how to do one of the problems, he couldn't do it on the board. One time he mistakenly declared that "Fish only bite when the moon is full" would translate to "The moon is full implies that the fish are biting" instead of the converse.

Ugh. I hated that guy. He was ugly too.

I did hear from someone else that their proofs class had covered way fewer chapters than ours. So we covered a lot of material, and at the end had to write a paper (ugh!). I wrote about taxicab geometry, which was very interesting for me when I did it. (The taxicab metric has appeared in so many courses since then it's not even funny - including this year in topology.)

Over the years, my hatred of Dr. J faded. I'd see him in the halls or elevator and he was always friendly to me. I guess he remembered me, probably as a good student. He was happy that I was going to grad school. For all I know he was a nice guy after all.

And in the meantime, time after time, these weird "obscure" (to me at that time) topics that we covered in that class came up. When I took my second non-Euclidean geometry course in undergrad, the abstract algebra we'd done in Proofs was really useful. Having covered (very well) the definitions of sets, relations, functions, etc., made them so much easier to understand in future classes. Cardinal numbers didn't show up again until my second semester of grad school, so it's great that I learned about them in there. The Peano axioms showed up in the first semester of grad school and nowhere inbetween.

Did I mention I really did not know the first thing about writing math (as opposed to logic) proofs when I started that class, but totally learned how?

Man, that class was awesome. It was easily one of the most useful classes I ever took. From an outcomes perspective, Dr. J was brilliant. I bet he was one of the best Proofs professors at my school. I bet he still is.

All of this is to say that my feelings about a professor can have very little relationship to how much I am learning or how useful the course is. This is not the only example of me hating someone and then thinking later that they were pretty great, or that I learned a ton. What it tells me is that I should put a lot less stock in my own feelings in situations like this.

Qual Cloud

2011-08-20T09:27:00.003-06:00

I took my real analysis qual yesterday, which I hope to write more about later. This morning I wrote Sally another long email about it. Reading it over after I sent it, the language itself seemed obsessive. Perhaps this tag cloud will give you some sense.

(P.S. Try saying "qual cloud" five times fast.)

That Which Doesn't Kill You

2011-08-04T10:33:00.002-06:00

In mathematics, a statement and its contrapositive are equivalent. So, for example,

If I bake bread, then the house smells nice.

is equivalent to

If the house doesn't smell nice, then I didn't bake bread.

The contrapositive of the saying from the title of this post is, "That which doesn't make you stronger kills you." When this first occurred to me, I saw it as a funny way to disprove that that which doesn't kill you makes you stronger.

But there is a way in which it's actually true, and almost more motivational than the original. Think about it. What doesn't make you stronger? TV? Donuts? It could be argued that those things do kill you.

If you radically limited your intake and activities to things that at least arguably make you stronger (taking a broad view of "stronger"), you'd probably be pretty bad-ass.

Tricking My Brain

2011-07-28T14:38:00.004-06:00

Disclaimer/spoiler alert: The following insights are brought to you by the miracle of introspection, and should not be confused with factual statements about the human brain.

Sitting down to do work for a few hours at a time is very hard for me. Hell, sometimes even sitting for half an hour to do math (which I like better than most kinds of work) is hard for me. I sometimes think that I have ADD, though I can certainly read a novel for hours.

It feels like there is a part of my brain that is fundamentally discontent to sit and work. It feels like a relatively animal part of my brain - not a conscious, smart part. And it is somewhat easily tricked.

I usually listen to music while I work. I can work to a variety of music, but I find that dance music (the kind you'd hear in a club - any kind of dance club) is one of the most effective kinds. It seems to trick my brain into thinking I am having fun and moving around rather than sitting and working. It's like a part of my mind is actually moving and doing something with a rhythm, and gets soothed/tricked into letting me get some work done.

Today, Pandora on my phone was acting up and sounding shitty as it sometimes does, so I switched to Simply Noise, which I haven't tried to work to before. I have an app for it on my phone.

Of the different noises, I like the brown noise the best, and I like to make it oscillate. It sounds like ocean waves to me.Very soothing.

After listening to this for a while and working, I realized it was extremely soothing indeed. It feels very much like it makes that part of my brain think I am actually asleep. That part doesn't seem to mind sleeping - in fact, it's pretty much content to let me sleep forever. It was really an amazing feeling. I think I may try this more often in the future.

"How Can We Memorize All That??"

2011-07-28T11:42:00.002-06:00

Memory is a funny thing.

I've spent vast hours this summer (enough time to have produced 174 handwritten pages of work and notes) studying for my real analysis qualifying exam, which I'll take three weeks from tomorrow. I have to take and pass two of these exams to be a PhD candidate. Of all of the exams available (real analysis, complex analysis, algebra, topology, and prob/stats), the word on the street is that the real analysis is the easiest (ha!) and the most memorization-heavy. Many of the other exams rely more on fundamental concepts that you have to cleverly apply to solve the problems (or so I'm led to believe).

I have a stack of the old exams going back to the 1980's. There are a lot of repeat questions, so I've been studying from the list I put together, which has the most often repeated questions of about the past ten years on top, followed by others that have appeared. These are hard questions. Many of the proofs take me 2 to 3 pages to write out, and I'll have to do 8 of them in 8 hours.

Studying for the exam has been difficult but also one of the most fulfilling experiences of my life. I mean that very sincerely. It's been amazing.

One of the amazing aspects, and this always amazes me, is that you can actually learn and remember things. I'm sure if you've taken classes this has happened to you - you had to apparently memorize some amount of material, and it seemed impossible. For instance, if you take calculus, you have to know all of these different derivatives (polynomials, trig functions, natural log, inverse trig functions, etc.) plus things like trig identities, if you didn't already memorize them in a previous class. It seems (to many people, at least) crazy, like a totally unrealistic expectation.

And yet I myself know large chunks of those things, and it doesn't even feel like something I have memorized so much as something that I just know. So I know that it's completely possible to learn that information and internalize it usefully.

The amount of stuff I have to memorize for this qual seems outrageous, but there are a lot of things that, during this past school year when I took the class this qual is based on, I knew I would never be able to remember, but that I now simply know - for instance, Hölder's inequality. When I first saw it, it was totally random garbage. Now, it's something that I know, and that I know some contexts in which it can be used, and so it is just part of my mind.

If you think about all of the things you know, it's actually an amazingly gigantic amount of crap. (Do you know drink recipes? Mathematical formulae? State capitols? Song lyrics? Phone numbers? Email and web addressses? Passwords for various web sites? Avogadro's number? The chemical formula for salt? The plot of "Anna Karenina"? The name of that one British actor who was in that recent "Hitchhiker's Guide to the Galaxy" movie? The details of your sister's divorce? It just goes on and on.) Even though new things sometimes seem random at first, and thus difficult to memorize, it actually seems virtually limitless, our ability to remember things.

The only thing more amazing than how much crap I can actually learn and remember is how easily I forget this, and thus how much despair I feel when faced with new piles of crap to know.

Surely You Jest: Universe Edition

2011-07-04T13:07:00.002-06:00

So, 10 or 20 billion years ago, mass, energy, time, and everything we know about emerged in the Big Bang. What was before or outside of that? The question is meaningless because time was part of what was created, and so was space - there is no "before" or "outside" as far as we are concerned.

Stuff expanded, and after a while, through processes that are not too mysterious, our sun and planet came onto the scene. At some point(s), matter on our planet, which of course was busy colliding and interacting and doing all of the things matter does when you shine the sun at it, happened to fall into a shape that was self-replicating. Naturally, once you start self-replicating, it's hard to stop, and stuff that is better at self-replicating will manage to incorporate more matter into itself than stuff that is less good at it.

Over time, these self-replicating bits got better and better at it through the addition of defensive barriers, the incorporation of other, smaller self-replicating bits, and so on, and after a very long while indeed, many of them were conglomerating together to build absolutely enormous machines to carry them around and help them replicate. (No, no, I don't mean hippie vans. That came later still.)

Some of those replicating machines are us, humans. And because I am one of the humans I can testify that, somewhere along the line, some of the matter started to have subjective experiences. Now, if you think about it, that is just fucking weird. It's hard to even think how to describe subjective experience. If some cosmic overlord machine came along and demanded to know what the hell you were talking about, you'd have trouble being convincing. You start with, "You know how you, like, feel stuff inside? Like you can really tell you're there and stuff? Yeah, me too." If the machine didn't have that experience it wouldn't get it.

So, here I am, a gene vehicle, on this little piece of space dust. In 100 years, I'll be at best an old photo in someone's family photo album. In 1000 years, nobody will remember a damn thing about me. In 100,000,000 years it's extremely unlikely anyone will remember my species. And sometime after that, there won't be any life on this planet, and sometime after that, there won't be any planet earth, and not only will nobody remember us (not even our best art and most fantastic thoughts and culture), nobody will even know that we were forgotten. And eventually, one way or another, the universe will devolve or crunch up to the point that there will not even be anyone of any kind left to know or not know anything whatsoever.

There could be other parallel universes, whatever that means.

These questions and the answers given by science don't really make sense to me. But then, why would they? My brain is evolved for life on this planet. There's no reason I would have the mechanisms needed to understand the nature of reality itself. Nevertheless, I do find the whole thing implausible.

One could embrace a religious view instead. The ones I'm most familiar with replace the grand mysteries of the material universe with a single mystery - some god or gods. We have no evidence for these deities, but a big controller entity is in some sense more workable for my socially evolved brain than a bunch of causeless, purposeless, endless, meaningless universe. I can grapple with an entity. I am one myself. I get that.

It'd be really nice to wake up from this weird-ass life at some point and get some answers. I guess if that's what happens at death, I'll find that out at some point. If, as I suspect, nothing happens at death, then I just won't ever know it (or anything else, ever again).

Stand By Me

2011-06-26T14:47:00.004-06:00

There is a movie theater here in town where they have a "retro movie" (projected from a blu-ray or dvd) every Saturday night at midnight. It's a tradition that a bunch of us go see this movie every week for $5. (Nobody goes every single week, I guess, but we all go as we see fit.)

Last night's offering was "Stand By Me." I thought I had never seen it before, though I remember when it came out, which I think was middle school for me. I remember the song being really big on the radio around then, I think. There was also a scene in the movie that was completely familiar - the one with the leeches. Maybe I saw part of the movie on TV one time or something.

I was very surprised to see a pre-pubescent Wil Wheaton as the main character. He was pretty good.

There was also this blond boy in the movie, who was the best friend. Even though he was pretty rough-looking in the movie, he was so beautiful that I couldn't keep my eyes off him whenever he was on screen. I was really eager to see the credits to find out his name, whether he acted when he grew up, whether he was as attractive as an adult, etc.

Then the credits: River Phoenix.

Wow.

See, when I was but a young lass, a freshman in high school, so about 14 years old, my best friend Susan had a poster of River Phoenix on one wall of her bedroom, and one of Johnny Depp on the other. I remember sleeping over at her house, lying on sleeping bags on the floor, and talking about fine they were, and which one we liked better. We both liked River Phoenix better. He was pretty much the finest guy I could imagine. (Ultimately, I said she could have River Phoenix and I would take Johnny Depp, since they were her posters, after all.)

Sally and I were talking lately about the fact that I don't really have an anti-type (vs. Sally, who for instance doesn't like men who look have that Jesus look with long hair and sandals), and Drew has been wondering what my type is, which I agree is hard to pin down. But I'll tell you that when I was in high school, River Phoenix was my type. (When Cary Elwes came along, he was right up there as well. Dreamy.)

River Phoenix died the year after I graduated from high school. I wonder if he would have stayed crazy hot or gone more of a Leonardo DiCaprio route. This picture is chosen to best reflect what I think I would have found hottest as a youth, although to be honest this still makes me catch my breath a little:

Bonus Cary Elwes:

Weight Watchers vs. MyFitnessPal

2011-06-26T10:30:00.002-06:00

I've been doing Weight Watchers lately. I haven't told most (hardly any, actually) of my local friends about this, because I always feel private about trying to lose weight. It's also ridiculously boring for other people to hear about, I think, and sort of tedious and typical.

I told one local friend other than Ed - the one I'm closest to. I told her I wasn't going to tell anyone else, not because it was a secret (I didn't want her to feel obligated to keep it as a secret, because that's always a burden and this isn't very important), but just because I didn't want to talk about it with anyone else. But it's good to have a couple of friends for support.

Anyway, where was I? Oh, yeah. Websites.

Weight Watchers is pretty cool these days. I just do it online. They still have a program based on "points" which are calculated for a food based on its protein, fiber, carb, and fat content. In reality, it works out to about 1 point per 40 calories, though WW doesn't want you to think that way. Non-starchy vegetables cost no points and, even more astonishingly, neither do any fruits (except avocados).

You get a daily points allowance, and then you also get this weekly pool of points that you can use for extras. You can have a few of these every day or you can have them all at once if you want to.

I really like the program. They reduced the points totals to allow for what they think will be typical fruit/veg consumption, and the free fruits really encourage you to snack on fruit, vs. forcing you to choose between a banana and a 100-calorie snack pack of mini-oreos, where most people will choose the oreos, which is clearly not the way to go for overall health and well-being (or, most likely, satiety). And I like the pool of weekly points - it really helps me manage social occasions and things like that.

Recently, the site myfitnesspal was recommended to me. It is a dieting site based purely on calorie-counting (or you can track whatever nutrients you want). Unlike Weight Watchers, it's free (ad-supported). For about the past week I have been logging my food intake in both places.

The calorie budget that myfitnesspal gives me based on my various statistics and desire to lose 1 lb per week basically comes out to be the same as what WW gives me if you include the weekly points. (WW "requires" you to eat all of your daily points, but you can forgo the weekly ones if you wish.) Of course, WW lets me eat fruit on top of that allowance, and myfitnesspal does not. Myfitnesspal doesn't have any software-supported way for me to bank calories to eat on other days, either, or anything like that.

However, myfitnesspal does have a truly excellent food database, the easiest one to use that I've encountered since the tragic demise of BalanceLog. In addition to their database, users can enter foods for anyone to use, and other members can verify that the nutrition is correct. If 43 people agree that this entry for McDonald's fries is right, you can pretty much trust it.

In addition to these aspects, myfitnesspal has a community aspect. There are message boards, but, more importantly, it has the whole "friends" thing from Facebook. That part of the site is almost a direct clone of Facebook - you get a news feed of your friends' updates, which (depending on their preferences) will include posts when they log their food for the day, update their weight, etc. So if you have friends on the site, you can get a ton of social support. Also, if your friends' food diaries aren't set to private, you can go see what they ate every day, which is fun if you like that sort of thing.

I'm considering abandoning WW (esp. since it costs money) and just using myfitnesspal. I want to continue enjoying the social aspects of myfitnesspal in any case, and it would be nicer to only be using one site rather than two.

What's a little sad for me is that I really do like and prefer the WW program itself. I like the points and the weekly extra points and the free fruit and all of that. It sort of turns the whole thing into a game rather than being more of a dreary regime. It takes things slightly out of the realm of reality.

But I feel like I can only really enter into the playful fantasy world of WW if I don't at the same time do actual calories. They don't layer well for me.

To be clear, I think these systems are pretty much equivalent in terms of the bottom line of encouraging the energy deficit that leads to weight loss - it's just a matter of what works better psychologically. And of course, one doesn't need to decide once for all time. But those are the issues I'm pondering right now.

Motivational Techniques

2011-05-30T15:46:00.003-06:00

One of the hardest things I've had to do recently was study for my real analysis final exam. It was hard because I had a lot of things going on that week, and I was tired, and I did not want to do it, and it felt futile because I knew I could not master the material in the time available, even in a best-case scenario. That last thing made it especially hard.

Yet somehow I did study, at least enough that I got an A in the class.

I wrote a while back about negative motivation. It used to be that threatening myself ("if you don't study you're going to fail this class") was the only type of self-motivation I knew how to deliver, and of course that type of motivation is not really very helpful. Eventually you become immune to your own threats, and the truth is that even many important things don't come with immediate terrifying consequences (e.g., it is not true that if I eat this particular donut I will die of diabetes at a young age).

Ever since realizing that I always resorted to negative motivation, I've been trying to cease making threats to myself. Instead, I've been trying to remind myself of positive reasons to do what I should do ("I'll feel good when I get this homework done"). And that has been moderately successful.

But neither type of motivation was enough to get me to study for my analysis final. Instead, what I did was pretty continually push myself simultaneously with various different motivations, of all types. Among them (and yes, I talk to myself in the second person)

If you study enough that you can get 3/4 or more of the exam done, you'll feel pretty good about it afterwards (as has happened on the other analysis exams you've successfully studied for).
It's going to really suck to sit in the exam and not be able to write much for many of the questions. You'll feel really stressed and doomed in that situation.
If you get through this semester with good grades, you're going to feel really great about your chances in the program.
You have some good friends here - you don't want to let them down by failing classes or dropping out. To continue this happy lifestyle you need to be like them and actually do well.
If you finish strong, you can send an email to Dr. P (undergrad analysis prof who wrote me LOR's for grad school) and tell him you finished your first year including this analysis core sequence! (You'll feel sad if you can't send that email or if you can't report passing this class.)
You're really just pre-preparing for the analysis qual in August. You'll feel good studying for that if you already have this head start.

So, basically, thinking of a lot of creative good reasons to want to study or to want to avoid not studying really helped. I mean, it helped just enough. It was barely enough to get me to actually do the stuff I needed to do, and I needed to apply it pretty constantly over the days I was struggling.

Screw Index Cards

2011-05-18T16:35:00.003-06:00

In my last post, I mentioned using index cards to write down the past qualifying exam questions. And I did indeed write about 50 of them before saying, you know what, screw this.

I'm now putting them into Access. You can't easily represent formulas in Access, so what I've done is set it up so that I put in TeX code for the problem statements, and then I wrote some code in Access so that it will spit out a TeX file with my problems (in a variety of orders).

I feel pretty awesome about that, and I've now entered about as many problems as I had written on index cards. The process is much faster and the results are way better.

Go me!

Moving Right Along

2011-05-14T23:37:00.002-06:00

This week I had three final exams and a project due, but everything was done by Tuesday afternoon. Wednesday, I flew somewhere to do a little bit of work for my old company, for a client I hadn't met before but who turned out to be someone who immediately strikes one as crazy and/or full of shit. I now have more work to do for this guy. I sort of wish I hadn't gotten involved at all, but I guess making some extra money is a good idea.

This summer I am also lined up to make about $3000 doing (paid by the hour) math lab and grading work. I think that comes out to about 140 hours (based on my guess of what the hourly rate is). I hope that instead of interfering with my summer plans, this work will help keep more organized and moving along. (Have you noticed that it is easy for a day with no fixed plans to glide competely by with nothing to show for itself?)

My main goal this summer is to pass my real analysis qualifying exam in August. It's an 8 hour long, written exam. I think there are typically 12 questions, of which you choose 8 to complete. They are typically rather meaty questions, though not usually very novel. (An example might be, "State and prove [famous theorem].") My understanding is that you need to get 6 completely right in order to pass.

I'm worried about whether I can pass this exam, even under ideal conditions and having studied a somewhat large amount, but I need to, as they say, give it the old college try. I have a stack of the old exams (going back so far that the earliest ones are handwritten). The first thing I intend to do is write questions on index cards. I want to determine what types of questions are asked, which questions are asked most often, and so on. If I can at least have answers to the most commonly asked questions down cold, it should help, and of course there is a lot of overlap of material and technique between different ones, so it's helpful in general.

In undergrad, I had a professor who would always point out, when we were starting a project, that you always wish, at the end, that you had an extra day or so, and so you ought to make very good use of the first few days (the ones you might otherwise kind of blow off, feeling that you have plenty of time). I have thirteen weeks before this exam, so I'd best get started.

Why We Get Fat

2011-05-11T10:46:00.000-06:00

A few months ago, I read Gary Taubes's Why We Get Fat: And What to Do About It. I've been wanting to comment about it ever since. I found parts of the book very convincing and others less so.

Taubes is a low-carb (practically no-carb) advocate, which is always suspect. The book presents a pretty strong argument against the view that people are getting fat because they eat too much and exercise too little.

I was amazed and convinced by the way that Taubes argues agains the "calories in, calories out" way of thinking about weight change. It's not that he disagrees that you gain weight by taking in more calories than you expend; it's just not a useful way of looking at it, because it doesn't answer the question of why that is happening.

By way of analogy, if you were in some particular room in a museum and after a while you noticed that the room was becoming very crowded, you might ask your companion, "Why is this room getting so crowded all of a sudden?" It would be true but not at all helpful for your companion to answer, "More people are coming in than are leaving." That's how Taubes views the calorie situation.

He points out that, for instance, children gain quite a bit of weight as they mature, yet this is not because they take in more calories than they expend. Obviously they do, but the causality goes the other way - they take in more calories than they expend because they are driven to grow. Similarly, adolescent girls develop fat deposits on their chests and hips, and this is not because they are eating more than they need; they eat more because biology pushes them to in order for them to develop secondary sexual characteristics.

He also points out that something like a 35-calorie-a-day difference (a bite of a brownie, basically) adds up over a 30-lb weight gain (or loss) in 10 years. Given that math, how is it possible that so many people do maintain a consistent weight?

Obviously there are processes in our bodies that balance our food intake and energy expenditure. Experiments with rats show that at least some types of rats can stay fat or thin (according to genetic predispositions) on various amounts of food by modulating their energy expenditures. This is presumably not because the skinny rats read Vogue and the fat rats watch too much television.

Taubes then presents his case that the reason people are getting so fat now is that we're eating so many carbs. His line of reasoning involves insulin regulation. If I remember correctly (which I may not), the basic idea is that eating more carbs causes our bodies to produce more insulin, and insulin promotes fat storage, which is to say it causes (basically) our fat cells to become hungry and thus prompt us to eat more so that they can grow.

I find that argument reasonably convincing. What I found less convincing is Taubes's line of reasoning that goes something like, "Everyone in the past knew that you lose weight by cutting down on starches, before all this low-fat bullshit came along." I agree that the low-fat craze of the 80's/90's was mostly b.s., but I don't find it that meaningful that people have historically known to cut back on starches. It's pretty obvious if you consider what people usually eat (even in the past) that we're much more likely to overeat bread, rice, potatoes, pasta, desserts, etc., than we are to gorge on meats. And of course it's almost impossible to overindulge in veggies. (Most people historically probably couldn't even afford to overeat meat. Also, it's much more fun to overeat starches, IMO.) Of course, that's on top of the general thing that citing the wisdom of the past is always selective.

Taubes's ultimate recommendation is the standard Atkins type of diet, with extremely restricted carb intake. He justifies this partly in the common paleo way - apparently our caveman ancestors mostly ate corn-fed beef from the Safeway, and we should too.

I find the general recommendation to cut back on starches pretty convincing, but I don't find that cutting all of them from my diet is any easier or more possible than keeping myself on a general starvation regimen that makes it impossible to gain weight anyway (even as one of the fat rats). A mostly-meat diet is expensive and, after a while, sort of disgusting, and it's obviously not at all environmentally sustainable.

I also, of course, know plenty of skinny vegetarians and vegans, who are clearly eating very high carb diets, suggesting that there are various types of diets on which one can maintain a healthy weight (even effortlessly, if you're lucky in that way). So...yeah.

But the book is probably worth reading if you're into this type of stuff.

The Problem with Moving

2011-05-06T11:55:00.006-06:00

I've been thinking lately about the downsides of moving to a new place (whether it's a new state or a new country or whatever). Everyone is aware of the struggles around not knowing the conventions or how to accomplish things in the new place (which can range from how to get a license plate in Nebraska to the need to give bribes to bureaucratic functionaries in some countries or whatever), but I think there's another negative thing that isn't as obvious: the loss of features.

Every place has certain features that are positive. Texas has, for instance, Blue Bell ice cream, which is pretty great for a non-premium brand, and Tex-Mex, and South by Southwest. New Orleans has Mardi Gras. Colorado has skiing.

But often the best "special" features of a place are not very accessible. Sometimes a new resident wouldn't know that the feature exists (like you might not notice Blue Bell ice cream and think to try it). Sometimes the feature is an acquired taste (as Tex-Mex might be). And sometimes the feature is something that can be enjoyed much more thoroughly (or at all) if you grew up with it, like Mardi Gras. (As a kid, we were thrilled to get beads and doubly-thrilled by doubloons. Mardi Gras was a whole season with parades all the time, not just one day in the city but on weekends in the suburbs as well. I knew a kid who moved to New Orleans and thought the whole thing was stupid - little cheap aluminum coins? Who needs it?)

So when you move, basically you lose all of the special features of your old place, yet can't fully appreciate the special features of the new place.

The grocery store is kind of a microcosm of this experience, and it's kind of what brought it to my attention when I moved back to Texas. If you're just moving within the U.S., then your old store will have had major national brands of everything, plus better local brands of some things. The new place won't have the old better local brands, and its own local brands won't look familiar or inviting, so you'll only have the least common denominator of big national brands to choose from.

Groceries are even worse if you move internationally, of course. I read a blog post sometime about living as an American in China. Apparently breakfast cereal is really expensive there, so that would be diminishment of your quality of life. I guess it's not what Chinese people traditionally eat for breakfast, though, so it's not that they suffer under the yoke of expensive Cheerios so much as that Cheerios is a weird foreign luxury item. So basically if you want to live cheaply and comfortably in a foreign country you have to either try new, weirder things or else stick to very basic things that are available everywhere (produce, meats, etc.)

I think we've all known people who have moved to wherever we live and then proceeded to hate it for not having the right features (like Sally's college roommate who lamented the lack of real bagels down here). I was like that when I moved to Houston from New Orleans as a kid, and I wish someone had encouraged me to have a different attitude about it. I think if you can be a little bit adventurous and non-judging, you can probably have a better time in a new place. And if you're flexible enough to live like the locals, you might have a very good time indeed.

Jerk

2011-05-03T22:37:00.004-06:00

There is an older grad student in my department who I am pretty well convinced by now is a jerk. I've heard of various jerky behaviors, but the most egregious (to me) is that he's made a friend of mine, who is a fairly gentle person, upset on several occasions, always by criticizing and/or yelling at her about ways that he thinks she has slighted him or not treated him with proper consideration. None of his complaints have seemed valid to me in the slightest. (For instance, on one occasion my friend canceled a weekly get-together with him because she had out-of-town guests.)

I've expressed my opinion that he is just a jackass, and she basically agrees. "But," she told me, "I really don't think he knows that he is being a jerk."

The idea of this as an excuse sort of fills me with rage. Most people, after all, have no problem justifying their behaviors to themselves. Most people do not set out deliberately to cross boundaries or be jackasses. So it is practically the definition of being a jerk to not know, or not be aware, when you are doing something wrong/mean/rude/whatever. One of the jobs of a human being is to actively prevent oneself from being a jerk, which often involves being aware of other people's feelings and perspectives, actively curbing one's natural self-centeredness and inclinations, and so on.

I mean, you know, I'm glad he isn't intentionally evil. But that's not really saying much.

Anti-Woo Cleverosity

2011-05-02T23:19:00.001-06:00

Via the Barefoot Doctoral, this:

Lifestyle, Redux

2011-04-23T21:44:00.003-06:00

I posted a long time ago about Brooks Brothers ads. Lately, this one has been catching my eye:

All I can say is wow.

Potluck Success

2011-04-22T20:00:00.007-06:00

I normally don't enjoy potlucks very much. I'd rather eat out than eat a bunch of random food prepared by other people, and I'd rather pay for a restaurant meal than have to make something (which often ends up costing me as much as a restaurant meal anyway). I also hate the hassle of how it's impossible for everything to be served warm/cold/whatever. I am just a grump about them.

However, I was invited to a Passover seder last Sunday. The host made a fine brisket as well as matzo ball soup, and we were asked to bring a side item, dessert, or drink, etc., made without leavened flour and without pork or shellfish or both meat and cheese, etc. So it was kind of a semi-potluck, but a great opportunity to participate in a seder, so that was all right.

I decided to roast some brussels sprouts. I'd never tried this before, but it seemed like it ought to work, and the Internet seemed to agree. At the store, there were boxes of fresh sprouts that were not as fresh as I would have liked, and then there were these enormous stems of sprouts which were much fresher (presumably because the stem sustains them).

This thing was amazing - huge and bulky, like a big club made of brussels sprouts. And it had way plenty of sprouts on it for roasting. Cutting them off wasn't much extra work since you normally have to trim the flat end anyway.

It was $4.49.

So I cut the sprouts off, tossed them in olive oil and salt, and roasted them at 400 degrees for about 40 minutes (whole). Cutting them in half would probably have been more delicious, but I was actually running out of time.

I don't have two ovens and I wanted a warm dish to transport these in (I was afraid a cold vessel would coldify them right away), so when they were getting done, I poured boiling water into a lidded casserole dish. When the sprouts were done, I poured the water out, dried the dish thoroughly, and put the sprouts in. I carried the casserole dish to the seder wrapped in a towel, and I got the hosts to put their oven on warm as I drove over, so I could pop it right in the oven when I got there.

The ritual part of the seder went on for a while, so by the time we ate, my sprouts had been kept warm in the oven for perhaps 45 minutes. This is not an ideal situation for maintaining any kind of roasted quality, but when we ate them, they were still delicious - not totally toasty but still considerably different from boiled or steamed sprouts. I got a ton of compliments both from people who like brussels sprouts and from people (well, one person) who had previously regarded them with fear.

I felt pretty kick-ass at bringing a healthy, well-liked dish that cost me under $5 to make.

Non-Zero Probability

2011-04-21T18:52:00.004-06:00

It now appears that there is a non-zero probability that I will finish the semester. For the first time, I can actually see the end from here. We have two more weeks of classes, and then finals, but I had a big exam today and really couldn't see past it until it was over.

In some ways, the class I had the exam in was my most important one (real analysis, which I'm taking a qual in this summer), and of my four classes, it has gone the worst. There is a lot of material I really struggle to understand, and what I do understand, I have trouble holding on to from moment to moment. Studying for the exam did greatly increase my knowledge, but there were topics I couldn't study because I just couldn't face them. And yet...the qual.

I'm feeling better now, but the past couple of days I have felt pretty down on school. As happened during the stressful part of last semester, I found myself fantasizing a lot about quitting and going back to my old job (I think they would hire me back, but I could probably get a similar job in any case) and having an easier life with more money and not as much math. I think that terrible negativity might be passing now, which would be nice. Most of the time, I prefer my life here to my old life by a moderately large margin.

I actually probably did all right on the exam. Last semester, I got a 55% on the midterm and ended up (somehow) with an A in the class. I estimate that I got about a 70% on this one. If I do a good job on the final, I should be able to at least pass with a B, I think. (If I fail the class, all hope is not lost, but passing would be better, of course.)

I posted a while back about my doom-laden decision to take four courses this semester. I'm happy to report that that decision, at least, was not in fact a mistake. Reports of my impending doom turned out to have been exaggerated. The logic class has been very interesting and our professor dramatically decreased the workload relative to the first half, and the topology class has been as vital as I'd thought it might be, and I'm really glad that I had the opportunity to take it.

So, that's my life these days, anyway.

Do Not Want

2011-04-05T23:29:00.003-06:00

It seems to be the case that after a serious relationship ends, I discover that certain aspects of it are things I do not want in any future relationships. Some of these are senseless allergies (omg no more Alex Chilton fans!!!*) but others, I think, are legitimate discoveries. It's hard to know how living with someone who does x or y or believes z will turn out. Sometimes I was blind to signs that I can now recognize, and others times, it just requires playing the experience out all the way to find out how it goes.

One thing I learned from my relationship with Ed that I don't want anymore is a little bit subtle, but important. One of the very noticeable features of Ed early on was that he was very emotionally literate (which I really appreciated, and continue to think is cool) and wanted to understand in minute detail what I was thinking and feeling about various aspects of the relationship. He didn't feel safe if he didn't understand my exact feelings.

This went both ways. If Ed found a feeling in himself that he thought might be a deal-breaker or bad news for me, he always told me about it. He was very open with me (which is a good thing, in general) and scrupulously honest, to the best of his ability.

All of this is why "radical honesty" was a tenet of our relationship.

I'm not against radical honesty. I think as an experiment it's fun. In fact, as long as you remember that it's called "radical" for a reason, it's all good.

But I don't want to be in another relationship with someone for whom that is of prime importance. I want my future partners to trust me to manage my own thoughts and feelings. I want them to trust that I'll tell them what's important, but be content with my being somewhat of a black box. I want to be with someone who doesn't worry about it that much, and/or who just figures me out as we go along. And I want to be with someone who manages his or her own inner thoughts and emotions as well, sharing as appropriate or desired but sometimes holding things back that are counterproductive to share.

(* not actually on my list)

Strange Advertisement

2011-04-04T22:41:00.004-06:00

A few blocks down from my apartment is a big complex that is mostly inhabited by students at my school. Out front is a sign that caught my eye a few weeks ago because of its nonsensical slogan:

Live like you "Mean" it!

It's a weird slogan to begin with (don't I really mean it? how am I living now? what does it mean to mean living, anyway?), and not improved by the scare quotes.

Then I started looking at the picture more closely:

Now, here we have these four...college students, I guess. But this picture is so weird. Notice the following:

At least three, possibly all four, are wearing oversized sunglasses.
Both of the boys are carrying helmets.
Three of them are wearing large headphones of the kind people use almost exclusively at home.
All humans come in couples.
The way a couple walks is that the boy puts his arm around the girl and then she reaches up near where her neck and his arm meet.
The boy on the left is wearing a sleeveless hoodie and a very slender bracelet.
The boy on the right appears to also be wearing at least one, and possibly two, bracelets.
75% of the people pictured are wearing hats. (Note that both boys are wearing hats in addition to carrying helmets.)
At least one girl has rollerblades; both boys seem to have skateboards attached to their backs.
The girl on the right is disturbingly narrow from the waist down, and has the hips of an 11-year-old boy.

Who are these people? Why are they all dressed/accessorized so similarly? Are they living like they "mean" it?

Wikipedia and Math

2011-04-03T03:02:00.006-06:00

I am a relatively big fan of Wikipedia. It tends to be my go-to source for things I want to know that are of a general nature - for instance, when I finished Bleak House the other day, I read/skimmed the Wikipedia articles on Charles Dickens, Bleak House, and the Chancery court that is such a big feature of that book.

But for professors in many disciplines, Wikipedia is a kind of sore spot, because students will often try to cite it. Not only is it generally inappropriate to cite an encyclopedia in a college class, Wikipedia is extra-suspect since anyone can edit it, and so it may or may not be rife with errors. (Everything in life is full of errors, really, but at least published encyclopedias have editors.)

But in math, people seem to like Wikipedia a lot. Several of my professors have referred to looking up things in Wikipedia themselves before presenting them in class, or to using it in general.

In fact, a few weeks ago, we had a visitor from the NSA who came to talk about careers there. It came up that of course (for security reasons) they don't have Internet access at their workstations there. I asked the woman how they did math without Wikipedia, and she immediately replied, "Oh, we have our own copy of Wikipedia." She didn't seem to find the question bizarre (like if I'd asked, "Oh, how do you do math without Facebook?")

I think there are some legitimate reasons why Wikipedia is different for math than for other subjects.

First of all, I imagine that when, say, history professors read Wikipedia, they find errors that irritate them. (This is probably true of many encyclopedias as well, but I doubt it comes up much that professors read encyclopedias.) You can make a lot of factual errors in history, or you can simply write an article that is unbalanced - that goes into a lot of detail on one small point and completely fails to include other major points. This is especially likely if the topic is controversial.

In math, on the other hand, there are not so many facts. When you look up a math topic in Wikipedia, you want to answer questions like

How is this thing defined?
What areas is it used in?
What are some theorems about it?
What are the different notations or ways that it is conceptualized?

You might think of definitions as being akin to facts, but actually they're quite flexible. It's true that some things are simply NOT the definition of an algebraic group, for instance, but there are several different definitions to choose from, and you can do math from a lot of different standpoints or bases.

I commented to Ed the other day that, unlike in other fields, in math it's the facts (definitions and axioms) that are matters of taste or opinion, and the conclusions drawn from those facts (theorems, etc.) that are either right or wrong.

The second reason I think Wikipedia is different for math is that, honestly, it's difficult to abuse it. You can't read and understand a Wikipedia math article unless you actually know enough math that any errors are probably not going to be dangerous to you. Is there a proof that is erroneous? You should be able to tell. (Nobody sophisticated enough to read proofs in Wikipedia should be foolish enough to treat any proof as authoritative.)

So if you were going to write a paper about Hausdorff spaces and you looked up the Wikipedia article and started there, it wouldn't really hurt you any. Either the definition in the article would work for you as a starting point in your research or it wouldn't. Once you know generally what's being discussed, you can make up your own definition if you want (though of course if it's not roughly equivalent to a commonly-used one, you'll only confuse your audience by calling it "Hausdorff"). You don't need a source for a mathematical definition, so you're not likely to mistakenly cite Wikipedia.

So, math Wikipedia - all upside, no drawbacks (if you can read it at all).

As a side note, my ability to read Wikipedia articles in math has absolutely skyrocketed since I started grad school. I'm actually starting to get enough background in the various general areas of mathematics for these things to make sense.

Spring Break 2011

2011-03-09T12:15:00.005-07:00

My Spring Break is next week - yippee!

I don't have any particular plans, and so there's a danger the week will go by in a kind of haze of boredom and too many "Without a Trace" reruns and vague intentions of doing some kind of academic work.

I don't know all of what I'll have due when I get back. Guesses:

Logic: We're getting 6 homeworks total and have finished 3. I'm guessing no homework over the break.

Analysis: We usually have an assignment every week, so I think this one will be no different. We should have a midterm at some point, so that could be the week after break instead. I am a bit behind on my notes/studying for this course anyway.

Stats: I imagine we'll have a normal homework assignment like every week.

Topology: I have an assignment due the Friday after break.

So I've written up a schedule (complete with checkboxes next to every item) for how I want to spend by Spring Break. It reads as follows:

Saturday

Groceries
Launder towels
Clean master bathroom
Dishes

Sunday

Have fun

Monday

2 hours analysis
2 hours topology
Dishes

Tuesday

Podiatrist appointment
2 hours analysis
2 hours statistics

Wednesday

2 hours analysis
1 hour statistics
1 hour topology
Dishes

Thursday

2 hours analysis
2 hours topology

Friday

2 hours analysis
1 hour statistics
1 hour topology
Dishes

Saturday

Finish statistics assignment
2 hours analysis
Groceries

Sunday

Have fun
Dishes

I'm hoping this schedule will overall maximize my fun and relaxation over the week, since I'll know what I want to accomplish each day, and trying to get it done will allow me to really enjoy the rest of the time. By my calculations, after sleeping, eating, grooming, and everything on this list, I'll have about 70 hours left over for pure fun and doing whatever the hell I want. (Of course, "whatever I want" may well include additional academic work, and that's fine.)

The Work-Life Boundary

2011-02-13T11:58:00.004-07:00

Earlier this week, I was reading some posts about how many hours people in academia work every week. Some people claimed to work about 35 hours a week, and others claimed more in the 70-80 hour range. Some asserted that professionals in "9-5" jobs typically work 60 hours a week anyway, and others that comparing an academic job to a 9-5 job is folly.

I've come to realize that one of my favorite things about being in grad school, as strange as this is, is that I always have something I should be doing. I don't actually work all that many hours (certainly not 60), but every single day my focus is on what I can get done that day, and how, and when. I don't have any days off. And I love it.

When I had a job-type job, there were hours I was required to be at work (not necessarily working) and hours that were my free, non-work time. I had a job and, separately, the rest of my life. Now it feels like my life is my work. I still spend most of my time not working, but I am never not thinking of work and how to get back to it.

I'm not sure why I like this but I really do.

A Partner but Not a Boyfriend?

2011-02-09T11:02:00.005-07:00

Ed and I started dating in May of 2007, and last November (2010), he broke up with me. Things hadn't been working well since around the beginning of the semester, when all of my attention went to school and I had no energy for relationship maintenance, and also, I think, some longstanding patterns between us weren't working well for me anyway. I had a distinct and increasing lack of interest in making things work. Sometimes I felt on the verge of breaking up with him, but doing so also felt unthinkable.

Since then, in many ways, things have only improved between us. We are still living together (not planning to change that anytime soon), sleeping in the same bed (which could change), getting along well (better than before, I'd say), and doing all of the things that boyfriends and girlfriends do. There are a lot of "I love you"s and other romantic things. We're experimenting with ways to be in a relationship with each other.

I often call him my "semi-ex-boyfriend." (I guess if this ends, I can start calling him my "ex-semi-boyfriend.")

It occurred to me the other night that he's sort of my partner but not my boyfriend. But given that our relationship is indistinguishable from a regular boyfriend-girlfriend one, what makes him not my boyfriend? Is it just that we're not using those words? Is it purely a technicality?

I don't think so, necessarily. For one thing, our relationship isn't exclusive at all. It has always had a degree of openness to it, but it's more blatantly non-exclusive now than in the past. And for another thing, we lack a certain sense between us that we are staying together. In general, the assumption with a boyfriend is that if nothing goes wrong, you're going to stay together, possibly forever, maybe leading to marriage if you are the marrying type. Our relationship lacks that sense right now, because it clearly doesn't meet the conditions for us to be happy together long-term, at least as each other's primary partners. This just isn't where I'm laying my bets for the future.

So for now I am just living with, hanging out with, and loving one of my closest friends. I'm sure it's confusing for other people, but it seems to be working for us pretty well right now.

The Leg (with Bonus Song!)

2011-02-07T19:12:00.002-07:00

On MLK, Jr. Day, the day before school started, I had a nasty fall in the bathroom and sprained my knee. What happened was that I got into the shower, then realized I wanted to see something on the bathroom counter, got back out, stood with my legs too far apart, and my feet slipped outwards in opposite directions. I'm nowhere near flexible enough to do a split, and what gave first, I guess, was my right knee.

There was some screaming.

After a while, the pain subsided and I began to gingerly see if I had any serious injuries. Everything seemed all right. I carefully got onto my knees and then stood up on my lef (uninjured) leg. I was very heartened to find that nothing was seriously wrong with me despite the pain I'd felt. I put my right foot down...and promptly my knee gave out again and I found myself on the floor, screaming again (though not as much the second time).

I live on the second floor, Ed wasn't coming back from Austin until that night, and I felt pretty doomed. I considered calling Drew (grad school friend) to see if she could come help me, but what could she do?

I managed to reach some clothes from the floor so that I could at least be dressed, and then I called 911. Once the paramedics were en route, I used my elbow to drag myself over to the door so I could unlock it for them. They showed up pretty quickly and ultimately carried me down the stairs in a special ambulance chair and took me to the hospital.

Nothing was broken; I got crutches, a pain med prescription, and advice to stay off it for a bit. Drew came and picked me up in her big truck, which was interesting because I had no way to get in. If you think about trying to get into a full-sized truck while only putting any weight on one leg, it's pretty much impossible, at least if you don't have the upper body strength to do a pull-up using the panic handle. Ultimately she folded the back seats up and I was able to sit on the floor back there and scooch in.

Anyway, it's been three weeks now, and the knee has healed pretty quickly compared to what I expected. I can walk unassisted (with a pretty heavy limp), but have been carrying a cane for longer distances. (When I use the cane, my limp isn't as noticeable to me. I also like the way it is a signal to other people that I have an issue and am not just slow or obstructive.)

My knee seems to be OK from a weight-bearing perspective. I've been careful. I went up and down the stairs at my complex on my butt for a long time, but these days I can walk up in the normal way (a bit slowly). I walk downstairs as well, but I put both feet on each step before going to the next one.

It used to hurt a lot when my lower leg went in or out from my knee (to the inside or outside, I mean), but that seems to have pretty much gone away. The only thing that hurts now is when my knee goes into an acute angle, especially suddenly (for instance, when I sit on the edge of the bathtub to scoop out the cat box), or when I bend my knee at all if it's been straight for a while (like rolling from my stomach onto my side when I'm asleep). I also can't easily straighten my leg all the way out, so when I stand, most of my weight is on my left (good) leg. I guess that flexibility will return in time.

Other than that, I'm pretty good. I'm really glad this has resolved so quickly. I walk to and from school every day normally, so not being able to walk was putting a lot of strain on me and on the people I was bumming rides from, and of course there's no way to bum rides from one building to another on campus, so that was annoying too. (I found walking on crutches truly exhausting and difficult.)

I promised you a bonus song. I was torn between this one and "Montana" but this one worked a little better for me.

Types of Proofs

2011-01-31T12:06:00.003-07:00

When you're first taking a course in math proofs, you learn about things like direct proof, proof by contradiction, proof by induction, and so on. Now that I have more experience, these are the types of proofs that I've experienced:

Proof by Algebra
These are the types of proofs most often encountered in a math class that isn't very proof-oriented, like statistics or (sometimes) linear algebra. The problem will say something like

A Palanquin Duo is a pair of numbers, x and y, such that x+ y = a for some real number a. Then the product xy is called a Palanquin Product. Show that the minimum Palanquin Product for a given a occurs when x = y = a/2.

[Yes, I made this up completely.] You see this and you go "shit, that's a bunch of weird crap" but when you go to do it, it just requires some algebra (or calculus, or whatever - basically some calculations/math that are sort of obvious in context). Often these are pretty easy because it's sort of obvious what the next step is, and you just have to have faith that if you keep going, the proof will work out.

Proof by Definition
These proofs usually ask you to verify that something specified in the proof is, in fact, an Thing, where the Thing is something that is defined in the course. For example,

Let A1 and A2 be two topologies on a space, X. Show that A1 intersect A2 is also a topology on X.

When you first, in your math career, encounter this type of proof, you often think something like, "My gosh, why would that be true?" But if you look at the definition of a topology (or whatever), you can easily verify that all of the conditions are easily met using the assumptions that you're given.

Proof by Construction
I may not be using the word "construction" here as it is usually used in math. But sometimes you are asked to show that something exists and the easiest way is to actually show how it can be made. For example,

Show that every Lebesque-measurable function may be approximated by a step function such that [blah blah conditions].

I see these in analysis, mostly, where you end up doing a lot of stuff with epsilons and deltas and building up a giant edifice step by step. These types of proofs can be very hard.

Proof by Induction
The canonical induction proofs are when you want to prove something for every natural number, for instance,

For $n>1$, show that $2 + 2^n + 2^3 + ... + 2^n = 2^(n+1) - 2$

To do this, you prove that the statement is true for n=1 and then that, if it is true for some n, it is true for n+1. But there are much more complicated and interesting types of induction proofs out there as well. Induction is fun - when you can get it to work, it often feels like cheating.

Proof by a Trick You'd Never Have Thought Of
I assume this is self-explanatory. Usually the professor will show these proofs in class rather than expecting you to do them as homework. There is a reason some theorems are named after the mathematician who first proved or formulated them!

Terrifying Product

2011-01-15T18:25:00.002-07:00

Every time I go to Kroger, I pass this product, and am gobsmacked by how horrifying it is:You may not be able to read the jar in this image, but it says 'Walden Farms Calorie Free Alfredo Sauce.'

Good luck sleeping tonight.

My Spring Schedule

2011-01-13T16:03:00.004-07:00

This is my schedule for Spring 2011.

Mondays & Wednesdays
10:00-10:50AM Logic & Set Theory
2:00-3:20PM Statistics

Tuesdays & Thursdays
11:00AM-12:20PM Intro to Topology
2:00-3:20PM Real Analysis

Fridays
10:00-10:50AM Logic & Set Theory

So I have basically a pretty consistent schedule every day except that on Fridays I have no afternoon class.

Doomed. Doomed, I Tell You!

2011-01-12T01:02:00.002-07:00

I've been facing a dilemma (two conflicting lemmas!) for the past few weeks, and I have finally resolved it, though I have resolved it in the direction of ultimate doom. Pray for my sanity, friends.

The dilemma is this. Last semester, I took the first semester of a two-semester logic & set theory course. I sort of hated it a lot in the middle, but I look back at it very fondly, and the stuff to be covered this coming semester is stuff that seems to come up a whole lot and that I really want to understand. I'm extremely tempted to take the second semester, and normally one does take both semesters of such a thing.

However! I took four courses last semester, and, though it was originally planned for me to take four this semester as well, the graduate advisor asked both me and the other fellowship recipient to only take three courses this semester. One of the courses I need to take is an Intro to Topology class. I think that class will be relatively easy ("relatively" being the key word here), and I'm not that excited about it, but I have never taken a topology class and I am planning to take the topology core sequence next year, and that just won't work. So: topology ho!

But I still want to take logic, and I don't know when the course will even be offered again. Also, though this may sound silly, all of my favorite people from my cohort are in that class. They are the brightest and (especially) the hardest-working of us, and being around them is really great for me.

I had decided in favor of topology - we must be practical, after all. But then Ed let me know that the logic professor is worried the second half of the class won't even make. So I changed my mind and have now signed up for both courses. This means I'll have four classes again, except that, unlike last semester, none of my courses will be a total blow-off like the pedagogy one was.

There are two reasons this should be possible, and one fairly compelling reason that it shouldn't be. First, other students routinely take three classes and have a TAship that is supposed to be half time. Many don't work 20 hours a week at their TAships, but some do work many hours. Second, I did not, objectively speaking, work all that many actual hours last semester. There is theoretically enough room for the extra hours topology will add to my life, without compromising time to eat, sleep, relax, and so on.

However, last semester there were at least a few weeks (perhaps the middle half of the semester) when I was really and truly stressed, basically walking around like a zombie and fantasizing about going back to my old job and having an easier life. The stress subsided near the end, partly (perhaps) because the analysis prof stopped assigning homework, but also partly (I feel) because I figured out how to chill out a little bit. I think maybe--maybe--I can make that skill carry over to this new semester.

The following things are clear:

It's possible for me to drop a class if I need to, but I would feel bad about how it would look (not on my transcript, but in terms of how the professor teaching the course would view me).
I'll need better time management; I need to get better at working early and often.
If I succeed at this, I'll feel really good about it.
If I succeed at this, I'll have learned some extra math that I'll be really happy and excited about.
If I succeed at this, it will have made me stronger.

So that's that.

A Second Chance

2011-01-05T01:08:00.002-07:00

A couple of weeks from today, I start my second semester of grad school. The first semester went great, in retrospect - I ended up getting A's in all four classes (woot), and I remember it all extremely fondly. If I didn't remember having complained about how stressed out I was, I'd think I enjoyed the entire thing start to finish. I guess, as usual, I enjoy it retroactively. This probably bodes well for my real-time enjoyment of future semesters.

This whole grad school thing is really amazing. One of the most awesome things about it is the other people in my cohort (and in other years, potentially). There is a large social group I feel very comfortable in, and I am really close to two people in particular. I'm not used to having so many acquaintances and friends to enjoy, close at hand like this.

I went to a New Year's Eve party at Drew's parents' house in Missouri this year, and stayed for a couple of days. Jared and I drove up together. (These are the two I am close to.) I actually saw midnight on New Year's Eve for the first time in a few years, and I stayed up very late drinking somewhat heavily (though not so much that I became ill, passed out, or had a hangover the next day). I actually felt socially likeable and accepted. I felt like a fun person whom other people would naturally like.

Counting Drew, there were five people from our program there, but the majority of the attendees were Drew's other friends, most from her undergraduate school (a SLAC, I think). I liked many of them very well indeed, and there was nobody I felt I didn't like.

It is a little strange to think about. I am about halfway between Drew's friends and her parents, age-wise. Is it creepy to be 36 and hanging out with a bunch of people who (on average) just finished college? They seemed to accept and like me. I didn't feel out of place. I don't feel, moment-to-moment, like I am not one of them, despite the ~13 years of work experience I had before starting grad school.

What all of this feels like is a great big giant miraculous do-over for me. I feel like this is the life I should have had, but couldn't grasp when I was these people's age, but here I am now, getting to do it. I'm pretty immensely grateful for it, too.

All Done (Mostly)

2010-12-15T15:47:00.002-07:00

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

2010-12-13T21:54:00.004-07:00

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

2010-12-06T19:27:00.004-07:00

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

2010-11-24T15:43:00.006-07:00

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

2010-11-08T00:04:00.003-07:00

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

2010-11-04T19:53:00.003-06:00

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

2010-10-31T01:11:00.004-06:00

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

2010-10-24T02:34:00.006-06:00

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

2010-10-20T16:31:00.003-06:00

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

2010-10-18T22:54:00.007-06:00

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

2010-10-17T01:32:00.005-06:00

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

2010-10-14T15:39:00.005-06:00

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

2010-10-08T07:54:00.003-06:00

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

2010-10-05T14:57:00.002-06:00

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

2010-10-03T21:19:00.003-06:00

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

2010-09-30T15:25:00.002-06:00

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

2010-09-25T17:52:00.003-06:00

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

2010-09-23T10:14:00.004-06:00

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

2010-08-24T12:53:00.002-06:00

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...

2010-08-18T10:25:00.004-06:00

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

2010-08-16T10:58:00.004-06:00

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

2010-08-11T13:33:00.004-06:00

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

2010-08-02T14:12:00.006-06:00

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

2010-07-20T10:29:00.003-06:00

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

2010-07-01T13:28:00.001-06:00

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

2010-06-23T17:40:00.005-06:00

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:

Commitment - feeling involved in life (as opposed to alienated)
Control - believing that you can control/influence your circumstances (as opposed to feeling powerless)
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

2010-06-23T11:32:00.002-06:00

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

2010-06-22T15:24:00.003-06:00

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

2010-06-21T16:01:00.002-06:00

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

2010-06-20T15:20:00.004-06:00

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

2010-06-18T14:51:00.003-06:00

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.

2010-06-10T15:03:00.002-06:00

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

2010-06-09T16:30:00.000-06:00

Via Andrew Sullivan:

War and Peace: My Review

2010-06-07T17:15:00.004-06:00

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

2010-06-01T18:36:00.004-06:00

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

2010-05-27T17:03:00.006-06:00

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

2010-05-26T07:58:00.003-06:00

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

2010-05-25T14:59:00.004-06:00

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

2010-05-22T20:32:00.002-06:00

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

2010-05-14T16:20:00.005-06:00

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

2010-05-13T13:59:00.006-06:00

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

2010-05-05T10:23:00.003-06:00

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

2010-04-30T11:39:00.001-06:00

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.

Tigerlily's Unfortunate Adventure

2010-04-28T07:42:00.005-06:00

This morning, around 7 AM, I awoke to the sounds of Sammy meowing, and Ed starting his shower. It's not unusual that Sammy wakes me up before my alarm goes off at 7:30 (which happens 7 days a week so that he is fed at more or less the same time every day), so I promptly went back to sleep.

But Sammy kept meowing, wandering around, and I realized that (a) it is unusual for him to meow in the morning - he usually wakes me up by purring or touching me, and (b) hey, wait a minute, that's not his feed-me meow, that's his Tigerlily meow!

And I remembered wondering about why Tigerlily hadn't come to bed yet, when I went to bed.

And I remembered closing the open balcony door right before bedtime.

And I got up and rushed over to the balcony and opened the door.

And Tigerlily was pressed into the opposite wall-hugging corner of the balcony, looking terrified. She meowed piteously several times after I opened the door, but wouldn't come in right away, so I went to tell Ed what had happened, and she came in shortly afterward, still looking all scared and moving around in the tail-down, low-running way of scared cats.

Poor Tigerlily! She seems fine now (all rubbing on everything in the house), and I'm just really grateful that it wasn't a super cold night. (We've had snow and freezing temps lately, so this isn't a silly consideration, but I don't think it got much lower than 40 last night. She felt cool when she came in but didn't seem to be shivering or trembling.)

I am such a bad cat mommy.

The Trouble with Infinity

2010-04-27T21:48:00.004-06:00

Infinity has been giving me some trouble lately - not the concept, but the symbol. You see, when I write it, it comes out all wonky-looking. You'd think it's just a sideways 8, so what's the trouble?

Actually, there are two ways that I write the number 8 - I either start at the top, go counter-clockwise, and make (not coincidentally) a figure 8, or I draw the two ovals separately. It kind of just depends on my mood.

The infinity symbol doesn't look good either way, when I write it, but I recently realized that part of the problem is that, when I write it in the "figure 8" way, I start off going clockwise, which is opposite to how I write an 8. So I started writing it counter-clockwise instead. Now my infinities look great!

...and my 8's look like crap.

Exams

2010-04-27T16:27:00.004-06:00

This week, I have exams in abstract algebra and advanced calc. Next week is the last week of school. The following week, I'll have finals in those two classes.

The abstract algebra exam is tonight. I'm well-prepared for it, and should do well, though the tests in that class are harder than the class generally is, so I'll still have to think and work hard to do well tonight. I'm on track to get an A in the class, which I'd like to do, especially since I really enjoy the material.

Tomorrow night is the advanced calc test. I'll finish studying for that tonight, but I don't feel very well-prepared for it. There is also a take-home portion due next Monday that I'm not looking forward to. I feel in some ways really done with this class. Of the three test grades (not counting the final), one is dropped, and my other two grades are an 83% and a 92%, so I could let this one go non-catastrophically, but I'll need to know the material for the final exam anyway, so I might as well apply myself and try to do well.

Assuming this test grade is not higher than an 83% (and is thus dropped), I'll need about a 10% on the final exam in order to pass the class with a C (required for graduation), or about a 50% to get a B. It's very unlikely I would get less than a 50%, but I'd hate to scrape by with an F on the final.

My third class, the "seminar" that is not, has becoming increasingly abstruse to me. I still need to finish up the homework that was due last week, that I got stuck on and got some hints in class about, plus this week's homework. I am hoping that we'll only have one more assignment after this, rather than having one due finals week. (We won't have a final exam, at least.) I can usually fake my way through the homeworks; I have about a 98% average in the class so far.

I'm ready for the semester to be over. It still boggles my mind that I'm actually graduating.

America's Next Top Model

2010-04-23T13:48:00.006-06:00

America's Next Top Model (hereafter ANTM) is one of my favorite TV shows. This might be surprising, considering that I have never shown any interest in fashion, conventional female attractiveness, hair and makeup, or anything you'd normally associate with modeling.

I started watching because I am basically a sucker for reality shows in which someone is dismissed at the end of each episode (I will watch almost any show of that type) and because there are a lot of ANTM episodes out there to see. I think there have been 14 seasons of the show by now, and every weekend, Oxygen broadcasts an entire season back to back, which I have my DVR record, so that basically whenever I want to just space out in front of the TV, it's likely to be ANTM that I'm watching. I think I've seen 6 or so seasons in their entirety at this point.

The setup is the same each season. Out of thousands of women who send in videotapes or are recruited in malls and the like, Tyra Banks (the supermodel who produces and hosts the show and is like a "mother hen" to the contestants) chooses 35 or so to show up. During the first episode, this gets narrowed down to about 13, and these finalists move into a fabulous house. Each week, there is a "teach" (where they learn more about runway walking, acting, posing, dancing, makeup, or some other relevant skill), a challenge (where whatever was taught is tested, with some prize for the winner), a photo shoot (or sometimes commercial shoot), and a judging, in which one woman is sent home. The finale each season has them choosing between the last three girls to see who will become "America's Next Top Model." (The prizes for winning the show include a modeling contract with Cover Girl, representation by a modeling agency, and a cover and spread inside a magazine, usually Seventeen.)

The contestants are generally all (or almost all) within the physical parameters of models - that is, tall, and thin, except that usually one or two are plus-size models (which is a specific range of size as well). Some are conventionally very pretty and others are more odd-looking. The odd-looking ones can generally skate by a bit longer in the competition by virtue of their odd looks; conventionally pretty women need to shape up quickly or they will be kicked off for being too commercial or relying on their looks.

All of this doesn't exactly sound appealing to me, but the actual show is very interesting to watch. They are always striving to make the women more edgy, less commercial, more editorial, and basically more strange. (On one episode, Tyra helped the women develop a "signature pose." One of the women - Marjorie, shown at left in a different pose - wanted to do "the hunchback of Notre Dame" as her pose, and Tyra loved it, and helped her mold it into something awesome.) The women who look strange, like Marjorie, tend to be my favorites. I usually have a favorite every season - someone I could look at for hours - and my favorite usually makes it pretty far, but so far has never won.

One thing that interests me is watching and cataloging, over time, what traits are needed to succeed on the show. The most important one I've seen is that you have to be simultaneously completely aware of your body (how it looks, how it's catching the light, what positions you personally look good in) and completely un-self-conscious (willing to try anything, look foolish, be over the top). You need to be confident but also open and willing to learn and listen to advice. Being either arrogant or insecure will not work.

I'll never be a model, but this is an attitude I want to work on having more of for grad school especially - the willingness to try things, and work hard at them, without any guarantee of success, but also without apology or insecurity. And, of course, I want the ability to receive and profit from advice from people who know more than I do.

In my own experience, humility is the key to hitting both points. Humility makes you not too afraid about failing, because you don't see your awesome glorious self as being put on the line. You're just there doing your best and learning as you go along, and you basically don't view everything as being about you and your image. I mean, I don't know any of this for sure, since I don't really have the quality that I'm talking about, but it seems to me that if I could cultivate it, it would help.

Brand Recognition

2010-04-20T17:58:00.003-06:00

When the very first slide (shown at left) of this semi-animated ad came up in my browser, it drew my eye. More than that, I knew exactly what company it came from -- a combination, I think, of the font and what is shown in the ad (which I had not seen before, as far as I can recall). I think it's pretty impressive that the company in question has made its mark on me to this extent.

Do you recognize it too?

My SOP Word Cloud

2010-04-14T16:16:00.003-06:00

I think it's safe to say my SOP was a bit less focused than Sally's. It also looks, to me at least, a bit more me-me-me.
Incidentally, when I made this word cloud it contained the name of a state my university is not in. I really hope that was an artifact of saving drafts at the wrong time and that I did not tell University of [Delaware] that I looked forward to studying at University of [North Dakota]. I guess it worked out all right regardless, but sheesh.