Monday, May 30, 2005

The (mis)evalutation of science textbooks

As a follow-up to this link (from a few weeks back) that detailed the horrible way in which physics textbooks for public schools are evaluated, read Kent Budge's similar experience with evaluating math textbooks.

Wednesday, May 25, 2005

CH in simple terms

CH is an abbreviation for the continuum hypothesis. Taking my audience into account, I'm not going to formally define CH here. Instead, I'm going to present a statement equivalent to CH yet expressable in terms of high school (middle school?) level math.

Picture three-dimensional (Euclidean) space. For reference, add an x-axis, a y-axis, and a z-axis to the picture. (My usual picture is the x-axis running from left to right, the y-axis running from front to back, the z-axis running from bottom to top.) Now imagine trying to assign to every point in this space one of three colors: red, green, or blue. Too easy? Well, not just any coloring will do. There are three requirements:

1) Every line parallel to the x-axis contains at most finitely many red points.
2) Every line parallel to the y-axis contains at most finitely many green points.
3) Every line parallel to the z-axis contains at most finitely many blue points.

Is there such a strange coloring? The answer is "yes" if and only if CH is true.

If you don't like trying to color things of infinite length, then just try to color all the points inside a cube (or any other solid shape) so as to meet the above three requirements. The existence of such a coloring is still equivalent to CH.

The above equivalent form of CH is originally due to Sierpinski (cite: Simms, John C.; Sierpinski's theorem. Simon Stevin 65 (1991), no. 1-2, 69--163).

Tuesday, May 24, 2005

Pax Americana

Consider the following paradox. Since the end of the Cold War, the United States has become involved in many "small wars" and a few big ones, yet there is actually less war overall in the world. Don't try to deny the second half of the paradox; Gregg Easterbrook brings some encouraging numbers to our attention to back it up:
The University of Maryland studies find the number of wars and armed conflicts worldwide peaked in 1991 at 51, which may represent the most wars happening simultaneously at any point in history. Since 1991, the number has fallen steadily. There were 26 armed conflicts in 2000 and 25 in 2002, even after the Al Qaeda attack on the United States and the U.S. counterattack against Afghanistan. By 2004, Marshall and Gurr's latest study shows, the number of armed conflicts in the world had declined to 20, even after the invasion of Iraq. All told, there were less than half as many wars in 2004 as there were in 1991
Global military spending is also in decline. Stated in current dollars, annual global military spending peaked in 1985, at $1.3 trillion, and has been falling since, to slightly over $1 trillion in 2004, according to the Center for Defense Information, a nonpartisan Washington research organization. Since the global population has risen by one-fifth during this period, military spending might have been expected to rise. Instead, relative to population growth, military spending has declined by a full third. In current dollars, the world spent $260 per capita on arms in 1985 and $167 in 2004.
Today, the United States accounts for 44 percent of world military spending; if current trends continue, with many nations reducing defense spending while the United States continues to increase such spending as its military is restructured for new global anti-terrorism and peacekeeping roles, it is not out of the question that, in the future, the United States will spend more on arms and soldiers than the rest of the world combined.
Easterbrook attributes part of the cause of fewer wars to democratization: "In the last two decades, some 80 countries have joined the democratic column, while hardly any moved in the opposite direction.... As ever-more nations become democracies, ever-less war can be expected, which is exactly what is being observed." I have to agree, with the proviso that eventually the trend of democratization may reverse (see ancient Greece and Rome).

Easterbrook mentions several other causes, including the end of the Cold War, peacekeeping troops, and nuclear deterrence, but he fails to mention the pacifying effect of the overwhelming dominance of the American conventional military. A country with a nuclear second-strike capability has an excellent deterrent against nuclear attack and against any external attempt to overthrow its government. However, it is not really a deterrent against conventional war. It is quite possible the U.S. and China could end up fighting a ruinous, massive conventional war over Taiwan sometime in the next few decades. Yet, there's little reason to worry about such a war escalating into mutual nuclear annihilation, because there is a mutual desire not to be annihilated. The actual deterrent to fighting a war over Taiwan lies with having a conventional military strong enough to make such a fight long and costly.

As another example, consider the Gulf War. If the U.S. had had only nuclear ICMBs with which to threaten Iraq, then Kuwait would not have been liberated, because we couldn't have credibly threatened to use them. We only hinted of nuclear retaliation in the event of chemical weapons being used against our troops. It is U.S. conventional military dominance that maintains an equilibrium in which most countries--the big possible exception being China--find it pointless to try to create or maintain a conventional military strong enough for regional conquest. For countries living in a Kantian democratic peace, military conquest may already be undesirable, but about a third of the nations are not democracies.

Thursday, May 19, 2005

Dave's filter

Sunday, May 15, 2005

Dr. Pepper stats

Average consumption for first semester at Madison: 2.84 cans per day.

Average consumption for second semester at Madison: 2.82 cans per day.

My overall Madison average is only 2.64 cans per day if I include the days during Christmas break when I wasn't in Madison. Extrapolating linearly, I should reach 1000 cans before the end of August.

For comparison, during my last 26 months (give or take a few weeks) at MIT I accumulated over 1259 (empty) Dr. Pepper cans (here's 1240 of them), implying an average consumption of 1.6 cans per day.

The roots of terrorism

From the abstract of this paper:
In line with the results of some recent studies, this article shows that terrorist risk is not significantly higher for poorer countries, once the effects of other country-specific characteristics such as the level of political freedom are taken into account. Political freedom is shown to explain terrorism, but it does so in a non-monotonic way: countries in some intermediate range of political freedom are shown to be more prone to terrorism than countries with high levels of political freedom or countries with highly authoritarian regimes. This result suggests that, as experienced recently in Iraq and previously in Spain and Russia, transitions from an authoritarian regime to a democracy may be accompanied by temporary increases in terrorism. Finally, the results suggest that geographic factors are important to sustain terrorist activities.
Hat tip to Econopundit, who has posted a copy of the paper's graph relating freedom to terrorism.

Thursday, May 12, 2005

Is my "sitting on its hands" remark already out of date? One can hope, but my prediction is that Iran will string the West along with negotiations until they have a nuclear bomb. Pessisimistic, you say? Consider the North Korea precedent.

Dave's filter

As Thomas Friedman notes, the best hope for nonviolently persuading Iran to forego nuclear weapons lies with Europe. Alas, Europe is sitting on its hands.

The intrinsic value of science or: how not to write a physics textbook

The rise of nonviolent rebellions

Yay for federalism

Don Luskin disputes this warning about the administrative expenses of individual Social Security accounts

The 2008 race according to Tradesports. (See also the UK and Canadian stuff at the bottom.)

The shores of Tripoli

Friday, May 06, 2005

Tuesday, May 03, 2005

Dave's filter

Because of this, I'm surprisingly having second thoughts. I hope to write more later (after I do some more research); for now I'll just note that if there shall be private accounts, then they probably should be voluntary for employers as well as for employees.

Monday, May 02, 2005


As regular readers know, I'm a data junkie. As such, I'd just like to name three particularly data-filled and excellent books of science that are accessible to the intelligent lay reader and that I recommend to the intelligent citizen:
The Skeptical Enivronmenalist: Measuring the Real State of the World
Bowling Alone: The Collapse and Revival of American Community
The Bell Curve: Intelligence and Class Structure in American Life
These books have all greatly added to my understanding, and I can't stress enough how delightfully empirical and thorough they are.

Would you recommend another book with lots of data presented in an accessible way? Then please leave a comment. One potential example that comes to my mind is Freakonomics, but I haven't read this (yet).


David Brooks writes about an alleged secret deal offered to Frist by Reid - sacrifice some appeals court nominees in exchange for a promise not to filibuster the next Supreme court nominee - and argues that Frist was foolish to have allegedly "said he'd think about it, but so far he's let it drop." If David Brooks really believes what he wrote, then why would he kill the deal by making it public? Was someone else going to publicize it? As for the merits of the deal itself, Brooks himself lists and then ignores several strong reasons for Frist to reject Reid's offer.

Sunday, May 01, 2005