High School Math and Computer Science Curriculum

I went to Brookline High School, which had a very good math and science program. Still, though, (as I expect it is almost everywhere) the focus of the math was on calculations. We saw proofs in geometry, and calculus, but these are often technical, and only steps along the way to deriving some theorem that can help solve some poorly motivated practical problem (Why do I want to calculate the rate that water rises while filling a solid created by a swept polygon??). Also, ideas from computer science were completely missing.

Its not that the more beautiful ideas in mathematics are out of reach of high schoolers -- indeed, my favorite proofs are short, simple, and profound.

If I were designing a highschool senior level introduction to mathematics, I would include:
-- The infinitude of primes
-- The uncountability of reals
-- The notion of polynomial time computation, NP completeness, and the power of randomness
-- The idea of undecidability, through the halting problem

Each of these topics can be presented with elementary mathematics, and each seems to say something profound about the universe. I think that with a course like this, rather than another course focussing on calculation, mathematics and computer science would seem like sexier topics.

Maybe the course could be called "The Nature of Infinity and the Possible"

The government is creepy

New Jersey has filed subpoenas to telephone service providers to try and discover if they violated New Jersey consumer protection acts when they disclosed thousands of phone records to the NSA. The federal government, however, has filed a lawsuit to block these subpoenas.
Check out this quote from the Times:

"Compliance with the subpoenas issued by those officers would first place the carriers in a position of having to confirm or deny the existence of information that cannot be confirmed or denied without causing exceptionally grave harm to national security," wrote Irene Dowdy, an assistant United States Attorney, in the 14-page lawsuit. "And if particular carriers are indeed supplying foreign intelligence information to the Federal Government, compliance with the subpoenas would require disclosure of the details of that activity."

I cannot imagine what sort of "grave harm" it would do to national security for the public to know exactly what data was given to the government, and under what circumstances. Given all of the publicity that has surrounded this, if I were a terrorist, I would have to assume at this point that the NSA has all of the data that is available about all of my electronic communications. What seems to be at issue now is whether the NSA did this legally. Perhaps the grave harm that will be done if the truth is revealed is that the government will be forced to abide by its own laws? If this is the case, the correct course of action should be to change the laws, not prevent state investigations into violations of those laws...