28 March 2008

Work paralysis

I have a bad habit.

When I have an important but short task hanging over my head, I will often neglect it and other less important tasks, and waste time on the internet instead.

It is strange in that, in the absence of the first task, I would generally have been happy to work on the other tasks rather than waste time. This is not only obviously suboptimal for my productivity, it probably also violates some basic criterion of economic rationality.

22 March 2008

The state of mathematics education

Keith Devlin recently published in his MAA column an essay by Paul Lockhart titled A Mathematician's Lament, a critique of American primary school mathematics education. It's a fascinating read, and the quickest 25 pages I've read lately.

Marvin Minsky has written an essay, What makes Mathematics hard to learn? In it he suggests some ideas for teaching math effectively, and relates a couple of poignant anecdotes about math education, my favorite of which is this one:

...that child [who had been struggling with learning to multiply] had a larger-scale complaint: "Last year I had to learn the addition table and it was really boring. This year I have to learn another, harder one, and I figure if I learn it then next year there will be another one and there'll never be any end to this stupid nonsense." This child imagined 'math' to be a continuous string of mechanical tasks— an unending prospect of practice and drill. It was hard to convince him that there would not be any more tables in subsequent years.

These got me thinking about my mathematics education. Perhaps the single most lasting skill I've picked up from doing math is learning how to prove things: not those two-column geometry proofs that everyone is tired of, but really knowing how to put together a line of argument that is both easy to follow and watertight. And there is not just one way to do that. Like writing, there is both art and science in it: choosing terminology and metaphors carefully; designing the structure and scaffolding of an argument; putting in enough details, but not too many; being economical with words.

Moreover, from mathematics I picked up an inclination to ask why things are true. In math— unlike in any natural science— you can always get down to the bottom of things by asking "Why?" until you get back to the axioms. Frankly, that's an amazing idea.

Yet, I saw very little of the "art of proof" and the "mathematician's skepticism" until I started going to a math circle in high school. Most of my public school math classes focused on learning recipes rather than talking about the why. When we learned, say, the quadratic formula, we did the derivation (based on completing the square) in class. But that derivation was soon squirreled away so we could do "applications", which is a fancy name for plugging numbers in ad nauseum. Personally, I find this tragic: the trouble is that in mathematics, the process is far more important and interesting than the result. More pragmatically, a student who remembers the idea of completing the square can derive the quadratic formula (and more) anytime, but students are given little incentive to think about, or remember, that beautiful idea. Most students will forget the quadratic formula once they have stopped using it for a few years, and if their experience with mathematics is that it is just a bunch of facts, they are more than likely never going to get that quadratic formula back.

The result of these methods, as Lockhart notes, is that pretty much no one today knows what mathematics is (not even math teachers). And students are being led to think that they dislike math when they actually just dislike whatever it is that they're being taught in math classes. Doing math is a deeply creative and enlightening process, but those aspects of mathematics are very rarely seen by the general public.

11 March 2008

Investors spend $100 billion a year trying to beat the market

Kenneth R. French has circulated a working paper titled "The Cost of Active Investing" summarizing an analysis in which he tried to quantify the costs of investors trying to beat the market. The price tag is huge: over $100 billion in 2007 alone. This represents money those investors would have saved had they simply bought an index fund.

The New York Times has this punch line :

One [implication] is that a typical investor can increase his annual return by just shifting to an index fund and eliminating the expenses involved in trying to beat the market. Professor French emphasizes that this typical investor is an average of everyone aiming to outperform the market — including the supposedly best and brightest who run hedge funds.

Vatican articulates seven new "social" sins

The Vatican has declared seven new "social" sins, parallels to the seven deadly sins of yore (lust, sloth, pride, envy, anger, greed, gluttony). Bloomberg has summarized them thus:

  1. "Bioethical" violations such as birth control
  2. "Morally dubious" experiments such as stem cell research
  3. Drug abuse
  4. Polluting the environment
  5. Contributing to widening divide between rich and poor
  6. Excessive wealth
  7. Creating poverty

Doing drugs? Seriously? And leave it to the Vatican to cast the first stone with respect to "excessive wealth".

I hope we can be forgiven for forgetting that trampling on the Earth is bad, but overpopulation is good. Poverty is bad, but life-saving technologies are bad too.

I'm reminded of this joke: for Catholics, acceptable forms of birth control include biology, but not physics or chemistry.

08 March 2008

Swapping memory into compressed pages

When you are using more virtual memory than you have physical memory, the usual solution is to swap pages out to a hard disk.

What about compressing those pages, sticking them in a corner of physical memory, and decompressing them when they're needed again? This is what compcache does. It's a win for read times because zero latency + decompression time is still faster than hard disk latencies. And at a high level it makes sense because new computers typically have many processors but only one hard disk.

02 March 2008

Making Pork Vindaloo

I made pork vindaloo this past weekend, using a recipe out of The America's Test Kitchen Cookbook.

It was very tasty. Unlike the vindaloo I have had at Indian restaurants, it was not painfully spicy. It consisted of country style pork ribs, tomatoes, onions, spiciness to taste, and the secret ingredient, red wine vinegar, all stewed in a crock pot for about five hours.

Some people swear that it isn't vindaloo without pork, but the sauce was sufficiently tasty that I will try it with chicken or just vegetables next time.

People who are not in our league

MIT's very own Kiran Kedlaya is going to the American Crossword Puzzle Tournament. He practices on New York Times crosswords:

For a really good solver, Monday's puzzle would take about three minutes, while Friday and Saturday puzzles would take seven to 10 minutes, says Kedlaya. Sunday's puzzle, which is larger, could take eight to 15 minutes.

Enough said.

I prefer the Wall Street Journal's myself, although that may be because it's harder for me to get my hands on a NYT.

01 March 2008

Thinkpad X61s and the Lenovo ScrollPoint Mouse

If you've been in the general vicinity of me in the last six months, you have likely heard me raving about my new Thinkpad (I got an X61s last September). It's powerful, durable (I've dropped it on the ice once already), well supported by free software, and has great battery life. It's light enough that I don't think twice about taking it with me everywhere. But the thing that has impressed me the most has been the TrackPoint (the pointing device with many other names.)

I was somewhat apprehensive about buying a laptop without a touchpad, but after getting used to the TrackPoint I can't imagine going back. Touchpads are crude and error-prone input devices. They are easily confused if you let an extra finger or the side of your hand stray onto the surface. You have to constantly re-place your fingers to move or scroll long distances. Touchpads get grimy and crumby and acquire little dead zones. And, of course, touchpads are typically located many centimeters away from where you want your fingers to be while typing. So you have to move your wrists to switch between pointing and typing. It's practically uncivilized.

The TrackPoint is right in the middle of the keyboard, so you only have to move your index finger over the width of one key in order to use it. You can use it for both pointing and scrolling (just hold down the middle button and point; this works out of the box on Windows, and you can easily configure it under Linux as well). Just by pushing and holding in one direction you can move or scroll arbitrary distances. And the finger displacement needed to use the TrackPoint is on the order of millimeters, not centimeters.

The TrackPoint is a solid-state device which senses pointing via resistive strain gauges, and I have not had any reliability problems with it. Lenovo has developed some pretty sophisticated software which continually recalibrates the device so it doesn't drift.

When I heard that the scroll ball on Apple's Mighty Mouse (which is supposed to permit scrolling along two axes) acquires dust and grime really easily, I wondered if there was some more reliable two-axis pointing device you could put on top of a mouse.

Putting an optical sensor on top of the mouse might work, but I suspect that there wouldn't be enough feedback to make it feel natural, and you would also have to have a pretty fine optical sensor to figure out when your finger was (or was not) in contact with the thing.

But what about putting a TrackPoint on top? Is there a firm, I wondered, that was crazy enough to put a pointing stick on top of a mouse? As it turns out, Lenovo itself makes such a thing; it's called the ScrollPoint mouse.

From a quick Google search, you can apparently get one of these for around $25.