Thursday, January 31, 2008

My Erdős number is 5

Back in high school, when we got around to it (about once a year) the Neighborhood would publish an issue of the Menlo Math Magazine. It was sort of a random collection of real-world-relatedness, whimsy, and interesting problems. Not an academic publication by any standard. But that didn't stop us all from facetiously claiming an Erdős number of 6, when we heard that Mr. T's was 5.

I just found out that mine is actually 5, and this time it's damn near official, not tenuously based on a high school pamphlet. Over the summer of 2005 I worked on the Stanford ALL project. Mostly as unpaid labor, admittedly, but I did sit in on the meetings and I did point us to a couple of valuable data sources. This meant I got to interact with some big names, however briefly.

According to Language Log, the lowest Erdős number known for a linguist is 2, and Geoff Pullum's is 3. A quick Google Scholaring shows that Arnold Zwicky and Thomas Wasow, therefore, have Erdős numbers not greater than 4. And they were both involved in the ALL project, as was I, which makes my Erdős number not greater than 5.

...All right, none of us are actually authors of the paper in question. I appear in the acknowledgement footer on the first page, along with the other students involved in the project. But Zwicky and Wasow appear in the same footer, as does John Rickford (who doesn't have any papers coauthored with Pullum, at least on Google Scholar). (Well, OK, all those big names appear in the references, which I don't.) Their contributions to the project were certainly substantive enough to qualify criteria for what counts as `collaboration'. My contributions were far less substantive, but I still think they counted for something, and if I appear in the same acknowledgements (the same parenthesis in the acknowledgements, even), that's got to be worth something.

(Naturally, this all comes with the caveat that we've been counting non-strictly-mathematical publications, but that has plenty of precedent.)

Wednesday, January 23, 2008

It makes a fella proud to be a scientist

Pharyngula linked to this amazing video that "compares creationism and science". Really, it's no comparison. [3:54]

You could watch it without the music -- none of the strictly visual beauty would be lost -- but instead, I highly recommend turning your speakers up to eleven, putting the video on fullscreen, and inviting all your officemates to come watch. Better yet, invade a conference room or a lecture hall for five minutes. It'll be worth it.

I found it incredibly affecting. Some parts had me cheering and yelling "SCIENCE: IT WORKS, BITCHES!". And some had me tearing up. I felt like a little kid again, all "when I grow up I wanna be a scientist!" I'm damn proud to be a part of it (or at least to be on track to become part of it).

Monday, January 21, 2008

Math lagging (or leading) physics

Senior year of high school, I took AP Physics C and AP Calculus BC concurrently: allowable, but not advisable, the admins said. For a good part of the year, I struggled with physics because I hadn't `really' learned the math yet. Reading the textbook, I'd just skip over derivations that I didn't understand, and hope that the end result was something I could memorize, if not comprehend. Mr. T held a session or two of `physics math', which helped a little, but didn't make me feel less intimidated.

Last semester, I was in pretty much the same situation, only with line and surface integrals instead of all integrals. Oh, we never had to evaluate any -- they were always of the simple kind that reduce to multiplication problems -- but it took several tries to be able to recognize those situations, and remember how to reduce them to multiplication problems. Didn't solve the intimidation problem, either. On the final exam, even though I knew what to do and how the problems worked, I still felt like a trespasser for writing down those fancy-schmancy closed-surface double integral signs, knowing I didn't really know how they worked.

At one point Prof. Hudson said something (can't recall the exact words) that gave the impression this math-lagging-physics business was a dreadful intractable plague, oh me oh my, whatever shall we do. And at the time, struggling to understand everything, I was rather inclined to agree with him. But since then I've somewhat reversed position, or at least become neutral.

Back in high school, after I'd learned to fudge my way through integration, I had a much, much easier time with it when we `officially' learned it in math class. This was especially noticeable in the case of integrating (still in a single variable, though!) over 3D objects. We'd been doing this routinely in physics, to find the moments of inertia of various shapes. So while the rest of the calculus class was struggling to put together the relatively new concept of integration with the relatively new concept of bizarre-shaped objects in 3-space, I could relax.

Recently (within the past two weeks), the same thing happened for me in multivariable calculus. I'm in 18.01A/18.02A, which is a blend of two courses: a quick six-week review of single-variable, and then the regular multivariable curriculum, finishing over the January term. Because of the way things are timed, I never saw a line integral in 18.02A until just now, well after the end of my physics class. And the same thing happened: I'd learned to fudge my way through easy line integrals, and that gave me a leg up on people who'd never seen them before. I had a well-developed intuition about what line integrals meant in terms of the real world, which kept me from getting confused. That in turn allowed me to focus on the complicated aspects that we hadn't worked with in physics.

Given these experiences, I don't think it's a very bad thing at all that math education tends to lag physics education. It can often be a good thing: physics is leading math, to frame it positively. When you tackle something complicated and abstract, having `live-fire' experience with simple cases and workarounds can hardly do anything but help.

This comes with some caveats. It's a classic example of delayed gratification: I sure didn't feel happy about math lagging physics when I was actually struggling with the physics, and it was only a month later that I was able to grin to myself in calculus recitation, watching the people around me struggle with a problem I'd found obvious. (Schadenfreude, too, is not necessarily a good thing. In my defense, I do help my peers if I can, and if they're not already being helped.) And naturally, it's a tradeoff; who can say if knowing the math beforehand would have brought my physics grade up a little?

But most importantly, if physics is going to lead math, physics has to be taught right. I approve very strongly of Prof. Hudson's philosophy here: conceptually difficult problems with easy math = win. If you absolutely must be bashing your head against the wall at midnight the night before the problem set is due, it shouldn't be because you can't solve a differential equation. It should be because you can't figure out which way the induced current goes. Physics can be taught adequately without using too much complicated math (though of course the definition of `complicated' will vary with the physics). You learn just as much integrating (read: multiplying) over a sphere as you do integrating (read: flailing) over the surface of some crazy-shaped thing.

You wouldn't expect it, but knowing too much math can be a problem. Last semester's physics class was taught in a rather unusual format, about which more later. The relevant thing is that I spent the whole time in a group of three. There was me, there was S, and there was L. S had excellent intuition, and tended to approach problems by thinking them through qualitatively first, and then seeing if the math bore him out. This was really a very effective strategy -- a lot of the time the math looked right, but his intuition cried foul, and then we found the sign error twenty steps back. L, on the other hand, was advanced in math, and already pretty far beyond what the physics course used. She approached problems very mathematically, instead of with intuition like S. Even when something made complete physical sense, she wasn't satisfied until she justified it mathematically -- even if it was a qualitative problem and didn't have any equations in it to begin with. and because of how every other thing is backwards in E&M, she tied herself into an awful lot of knots. (Not that she wasn't brilliant; I think she outscored both S and me on every test.) L and S complemented each other, and they were a great group to work with. But I have to say that S's intuitive method was the more effective. To the same question, S might answer "because the charge is over here so the potential is higher here, and then this happens"; L might answer "because the potential is [insert equation here] and the electric field is the negative gradient of the potential."

I admit that this is based on my own experience, and what's better for different students will vary. I said that it's easier to learn complicated abstract math if you've first grounded it in physics; you could just as well say that it's easier to learn physics if you're well practiced with the mathematical tools already. But I think the first argument is more valid than the second. It's easier to abstract from the concrete than it is to learn the abstract first and only then get concrete examples. You see the same thing in computer science classes: pick up a copy of the blue wizard book and on every other page you'll find a discussion of how to abstract some instance, not how to instantiate some abstraction. Even though physics was made genuinely more difficult by not knowing the math, I'd still rather have done it this way around.

Briefly on Sitemeter and privacy

For the sake of full disclosure: yes, I have a Sitemeter on this blog. It's the free version, which means I can't see anyone's full IP address (just the first three numbers). I can, however, see your location, your ISP, a crappy estimate of your latitude & longitude, what page you came from, and what page you exited to (sometimes; this last one seems to be borked).

I have it on the "medium" privacy settings, which means that all those details are not visible to members of the public, but that certain stats may be given out to indexing sites -- the textbook example is giving out the hit count to a service that ranks sites by number of visits.

I'm not all that interested in most of the information that Sitemeter collects. I mostly have it as a hit counter, not anything fancier. I do get a kick out of seeing what random cities people are visiting from, or what random Google search terms bring me up in the results. It's rather annoying that Sitemeter's privacy options are pretty much all-or-nothing: I can't allow members of the public to see, e.g., just the Google search terms or just the geographic locations, without giving them everything, including partial IP addresses. Grr.

But at some point I think I'll compile a list of the more interesting Google search terms that bring this blog up. Might be amusing.

Friday, January 18, 2008

Feeling a teacher's love

In high school, we had a teacher, Mr. T, who taught computer science and some of the advanced math courses. And he was wonderful. Everybody loved him. I've never encountered so much infectious enthusiasm, even at the ungodly hour of 8am on a Monday morning. He could light us on fire by drawing box-and-pointer diagrams. We had a party the day we learned the Fundamental Theorem of Calculus. Mr. T was a mentor, a friend, a father, a rock; his room was a haven for geeklings. Everybody loved him, and he loved us too.

I understood his love in a rather abstract sense back then, and up until this morning. But this afternoon, I understood it from the inside.

The research I'm doing at the moment involves teaching pairs of people a constructed language by immersion, and then having them take a test. (More details on this (very interesting) paradigm in an upcoming post!) Today was only the second time this experiment has ever been run, so I'm also happy just because it worked. We ran two pairs of people.

I had an awfully hard time teaching the first pair. They just seemed to fundamentally not get a lot of the grammar. It was very difficult to keep myself from grabbing one guy and telling him, loudly and in English, that "the way to turn a sentence into a question is NOT just to say the sentence with a rising intonation at the end!!!". And so on, and so on. Teaching them was frustrating, occasionally painful.

And then the second pair came in, a pair of undergrads, and they more than made up for the first pair. It only took them twenty minutes to get to more than adequate proficiency, where it had taken the first pair almost an hour to get to less than adequate proficiency. They seemed to pick everything up right away. It was like watching a rose bloom in time-lapse. My favorite moment was when I taught the question form, using only one verb in my examples. When I prompted one of the participants, she immediately came up with several correct question-form sentences, and she generalized to all the verbs we'd learned, not just the one I demonstrated with. If we hadn't been in an experiment, I might have proposed to her on the spot.

I graded the four tests just now. The first pair had decidedly mediocre scores, no surprise there. But the second pair did extremely well, and they both did just about perfectly on the part we're most interested in. I was overjoyed to see them using linguistic terminology correctly to explain their answers (even though their knowledge of terms had nothing to do with how well they acquired the language). When I was done grading, I spontaneously picked up the last test and kissed it.

Tonight, I think I experienced a little of what made Mr. T such a good teacher, what made him love his students and his work. It's not an easy feeling to articulate. Pride and joy in students, enthusiasm for the subject, and a little bit of self-satisfaction that, yeah, I taught them that. The feeling was very powerful, even though the teaching I did today wasn't very real. What if I were teaching material that was beautiful and meaningful, instead of an arbitrary constructed language? What if I could teach for an entire semester and witness long-term progress and synthesis, instead of bidding goodbye after an hour? What if I were teaching students who learned for love of the material, not because they were paid to be subjects in a study?

For the record, this is not the first time I've taught, nor the first time I've found it satisfying. For a couple of years I tutored 6th graders in math and Japanese, and it was always great when they'd get a flash of insight after a long hard slog. (They were remedial students, so it wasn't often.) And in the Karate club, it's traditional that you help teach the people who rank below you. I was co- leading brown belt my senior year, so that meant I taught just about everybody. I always enjoyed seeing some yellow-belts perform a technique really well, and thinking "Yay, they remembered X subtle point I taught them about!". But I've never felt a teacher's love as strongly as I did today; certainly not strongly enough to merit using the word `love'.

If I follow the track I'm planning to follow, I'll end up a professor. I understand that teaching is mostly tedious, frustrating, and difficult, not full of brilliant-student-love. But it's the possibility, the hope that springs eternal, and when it's fulfilled it makes up for everything else.

Tuesday, January 8, 2008

Problems with the LJ feed

I recently made some minor edits to "my experience with lab mice", and everything seemed normal. But for some reason the LiveJournal feed saw fit to repost the entire post, clogging up people's friends pages. Meep, sorry!

Funny thing is, this didn't happen anywhere else. The native feed is normal, the blog itself is normal. Only on LJ did the post show up again. And apparently there's no way to go into an admin panel and fix this; it's fully automated. Grr.

Monday, January 7, 2008


You might have noticed the shiny new section in the sidebar. Yes, I finally got around to making a blogroll.

...Well, more like a catalog of the RSS feeds I follow. Everything in that list is something I read religiously (which, given Google Homepage, is a much weaker statement than it used to be). I've seen blogrolls that have hundreds of links to blogs whose names start to seem awfully similar, and which sound like they cover mostly the same content -- so, more of a "recommended reading" list than a reflection of what the blogger actually reads on a regular basis.

Eventually, I'll flesh it out into a proper blogroll, but for now, I'm not experienced enough to evaluate a blog without following it for quite a while.

Edit: Also, I would have included my brother over at Mage's Plane, but he's just gotten started, so I'll give him a little time to build up steam. Right now what he gets is a tongue-in-cheek for using the same Blogger template as me, right down to the color choice. *shrug* Yes, this is a very common template.

Black vs. white backgrounds (also, chalk)

(No, this post is not about race).
The other night, I and my friend 4pq1injbok were discussing the compelling, overarching, enormously important issue of black text on white ground vs. white text on black ground. (Woo, having spare time!)

Of course, each option is appropriate in different contexts. If you're printing something out, you better have a good reason to do it in white on black, because that wastes so much ink/toner. But for viewing on screens (including projection screens), I vastly prefer black on white because it reduces glare and seems to make my eyes less tired. Mostly the former. Glare is a problem especially on very large projection screens: you can dazzle (in a bad way) an entire lecture class with a white-backgrounded Powerpoint, especially if the projector is having an off day. Not fun early in the morning.
What troubles me, then, is that there seems to be some kind of unspoken rule in academia that you can't use black backgrounds, and I'm not entirely sure why. I watched a dry run of a job talk a couple summers ago, and in the midst of everybody commenting on every facet of every slide, my mentor explained to me that there's just a certain way scientific presentations are done, which includes black text on white ground. The Google example is telling, in one sense -- Google is renowned for the "clean" look of its pages, which I'm sure has a lot to do with being white-backgrounded. Perhaps there's a lot of pressure from older academics who are more comfortable with print on paper. Perhaps, also, it makes pictures easier to see, but you can fix that with a relatively narrow white border. I think we should take a hint from the movie industry; when was the last time you saw the end credits in black on white?

(Also, using black backgrounds probably saves energy -- I don't know any numbers, but the savings must be considerable for large screens. There's even Blackle, an almost entirely black version of the Google homepage. Supposedly if everyone used it, we'd save ~750 MWh a year (hat tip for the calculation to ecoIron).)

Chalkboards are the only common medium I could think of where the default is light text on dark ground. (Not to say there aren't others; it's just that I couldn't think of them.) Nothing profound about it; chalkboards are this way because CaCO3 is white, and slate is dark gray. But it does raise an interesting question. Suppose you draw two circles on the board, and fill one in with chalk while leaving the other one empty. Which is black, and which is white? Do most people just seem to naturally agree, or is there some kind of consistent convention, or is there no consistency at all?
In my music theory class, and anywhere I've seen musical notation on a chalkboard, the convention is that quarter notes are filled/white while half and whole notes are empty/black. In print, it's the other way around, at least with regard to absolute colors. But in this case, you can define it in terms of filling, not color, so it's a bad example. I'm rather tempted to crash a game theory class on the day they discuss chess/checkers, or some kind of visual arts/design class on the day they discuss positive vs. negative space, or take a poll of professors, or some such.
Related linguistic issue: on the Improbable Research blog, a prof rants about the suckiness of Crayola's new chalk, complaining that "the new pieces are thinner, shorter, and don't write as dark", using "dark" to denote degree of whiteness. But "don't write as well" lacks specificity, and "don't write as lightly" would be interpreted the wrong way around. Sounds like "heavily" (or perhaps "cleanly") might be the way to go.

And finally (and randomly): hooray for profs who know how to use colored chalk well, to highlight information and obscure noise, without overusing it. More on this subject if I ever get around to reading Tufte's books.