Contrary to what you might have read, the U.S still annually produces more engineers per capita than either India or China:

After an exhaustive study, researchers at Duke University also pummeled the numbers. In a December 2005 analysis, "Framing the Engineering Outsourcing Debate," they reported that the United States annually produces 137,437 engineers with at least a bachelor's degree while India produces 112,000 and China 351,537. That's more U.S. degrees per million residents than in either other nation.

Now consider this statistic from Business Week.

Currently, 451,000 Mexican students are enrolled in full-time undergraduate [engineering] programs, vs. just over 370,000 in the U.S.

The U.S. enrollment number is a little under thrice the U.S. number from the Duke study, which makes sense if most undergrad engineering students enroll in an engineering program at the beginning of sophomore year. This consistency check inclines me to believe the Mexican number is also accurate. Interpreting these numbers is dangerous without making a qualitative comparison of these countries' schools' engineering programs, so I won't draw any policy conclusions. My point is that the empirical world is much more interesting than the caricatured world.

CH in simple terms II

First, notice that a set has size N+1 if and only if it can be linearly ordered such that every element has at most N lesser elements. Similarly, a set is countable if and only if it can be linearly ordered such that every element has only finitely many lesser elements. The continuum hypothesis is equivalent to the existence of a (very strange) linear ordering of the reals with respect to which every real has only countably many lesser reals.

For comparison, consider the classical statement of CH: for every infinite set X of reals there is either a one-to-one correspondence between X and the integers, or a one-to-one correspondence between X and the set of all reals. Which version is easier for you to understand? I find linear orders easier to visualize than one-to-one correspondences, but others' imaginations might work very differently than mine.

(This post is the sequel to "CH in simple terms," which presents CH in terms of strange colorings of a cube.)

I was just reading some Calvin Coolidge quotes and it made me feel like I was born eighty years too late. Coolidge was the last president who governed in accordance with the Tenth Amendment. I'll just reproduce a few quotes here.

Collecting more taxes than is absolutely necessary is legalized robbery.

We do not need more intellectual power, we need more moral power. We do not need more knowledge, we need more character. We do not need more government, we need more culture. We do not need more law, we need more religion. We do not need more of the things that are seen, we need more of the things that are unseen. If the foundation be firm, the foundation will stand.

If you see ten troubles coming down the road, you can be sure that nine will run into the ditch before they reach you.

Perhaps one of the most important accomplishments of my administration has been minding my own business.

Since the 2004 elections, my policy has been to give a bit of money to the Club for Growth, but none to the RNC. Unlike some frustrated conservatives, I also still plan to vote in November, especially given the competitiveness of the Wisconsin gubernatorial race. Jim Geraghty has been blogging at length about how sitting out is a bad strategy for conservatives in 2006. He also suggests some more productive tactics.

Via Instapundit, I learn that Bush's immigration speech is polling very well. Now I'm having doubts about my earlier prediction of an enforcement-only bill.

Update: More recent polling is more in line with my expectations.

Some potential good news about oil prices:

Well, a New York Times article about a United States Air Force plan to shift toward jet fuels made from coal reports that the USAF and industry sources think coal-to-jet fuel would cost the equivalent of $40 to $45 per barrel oil. If they are correct then current oil prices are above long term sustainable prices.

Hopefully this bit of positive change makes its way into whatever immigration legislation the House and Senate eventually agree on this year.

If the Immigration Reform Act passes, the means to bring and keep foreign scientists and engineers in the U.S. -- the H-1B visa -- would increase (from its 65,000 limit to 115,000) and eliminate caps for advanced-degree holders.

That's what I call a very good start.

Beyond raising the cap on H-1B visas, he [John Margburger, Science Advisor to the President and Director of the Office of Science and Technology Policy] also believes the current immigration policy needs reworking. Applicants should not be expected to return to their native countries after receiving their degrees. "We ought to be doing just the opposite," Marburger says.

Arnold Kling proposes to cut the Gordian knot of the looming explosing in government spending on retirement benefits by a "stroke of the pen": raise the retirement age. I wholeheartedly support this proposal, but I know that it's very, very unpopular. Unpopularity is why "policy apparatchiks of both parties" mock Kling's idea. The Pew poll I linked to shows that it is nearly equally unpopular (22% to 23%) among all age groups under 65. Support is at 40% in the 65+ group. The Kaiser poll notes that 41% percent of respondents are prepared to vote against their representatives in Congress if they raise the retirement age.

To the 77% of my fellow Americans aged 18 to 29 who apparently want to start collecting government benefits at age 65, would you please consider using a 401K to finance your refusal to adapt to greater lifespans and lower birthrates? Or would you please raise lots of kids to widen the base of the great government-mandated pyramid scheme founded by FDR and expanded by Johnson and Bush?

Malaise is back. Gas prices are rising and approval ratings are dropping proportionately. As of this moment, intrade.com has the probability of the Republicans keeping the House between 49% and 50%. What are Republicans doing about all this? Fighting amongst themselves about immigration and spending.

Bush's recent immigration speech has just dug the hole deeper. Immigration hawks won't trust Bush's promises to secure the border. We all know Bush is only two-thirds of a real conservative, and a big part of the missing one-third is about immigration. (Though a bigger part is about small government.) As for the guest worker plan, who actually supports this other than some businesses? Why settle for a mere guest worker when we could get a new citizen instead? And what about the many guest workers who would inevitably end up staying permanently? These we would like to assimilate; hence, it would be foolish to deny them a path to citizenship.

My prediction: Congress will pass an enforcement-only immigration bill, though not as tough as the House bill.

My wish: Congress would also reform our foolishly overly restrictive H-1B system so as to encourage more skilled foreigners to come here and become citizens. (While I'm at it, I can always wish Bush would force Congress to cut spending.)

Let me add that I like the idea of securing the Mexican border a lot more than I do of increasing internal immigration enforcement. The former does far less damage to the liberties of the people for whom the United States government is supposed to secure liberties. Furthermore, those liberties include property rights that are being poorly protected if you live near a popular crossing point. As for the unhappy choice between amnesty or deportation for illegal immigrants already here, I wonder if we really have to make that choice. If we could reduce the rate of illegal immigration by an order of magnitude with increased border security, then why not just maintain the current level of internal enforcement? Current illegal immigrants chose to live and work here off the books; let them live with that choice. If we can be confident their numbers will drop in the long term, then perhaps we can live with that choice too.