Tuesday, January 31, 2006

Doesn't the president's oath to protect and defend the constitution require that he veto what he believes unconstitutional? Yet I read that "by the end of 2004, Bush had issued 108 signing statements presenting 505 different constitutional challenges. He has yet to veto anything." Am I missing something?

Sunday, January 22, 2006

I have a lot of hope that Shadegg's candidacy is a harbinger of reform and something a lot closer to fiscal discipline than what we've seen over the past five years. Maybe, just maybe, we can get to the point where GDP grows faster than government again. I'd like to set my hopes higher, but for now I'm trying to stay realistic.

Thinking more long-term, Medicare and Social Security costs will force big cuts and/or tax hikes that will dwarf all the current budget allocations that are being argued over. It's too soon to say when we'll stop delaying that choice, and who will be in power at that time.

Friday, January 20, 2006

Chaitin's limits of mathematics

Godel's incompleteness theorem says that if a formal axiomatic system that consistent and expressive enough to do arithmetic, then it will bite off more than it can it chew. That is, there will be formal propositions that the system is powerful enough to express, but not powerful enough to prove or disprove. In this sense, all interesting (read: consistent and sufficiently expressive) formal axiomatic systems are incomplete: they pose questions that can only be answered by more powerful systems.

So, formal mathematics is incomplete, but how incomplete is it? About fifty years after Godel's theorem, Gregory Chaitin gave a quantified answer to this question. You can read excellent, relatively nontechnical expositions by Chaitin on his results here and here. The gist of it is that if you can unambiguously describe a formal axiom system with N bits, then that system cannot compute more than N bits of the binary expansion of the halting probability.

Chaitin calls the bits of the halting probability "irreducible mathematical information" and "random." I agree with the former but not the latter. Yes, to compute more bits you need to add more axioms to your system, but you need not add axioms randomly. Set theorists have built an elaborate heirarchy of proposed new axioms; this heirarchy has a beautiful structure that is anything but random. One could claim that the truth of these new axioms is random. However, such a claim is inherently metaphysical, for it is impossible to produce empirical evidence directly for or against the axioms in question. (There is empirical evidence in favor of their consistency, but that's not the same as truth.) I don't know if Chaitin intends to make this metaphysical claim, and at any rate I can't disprove the claim, but I can say I find it implausible. "God does not play dice."

Okay, enough complaints for now. Chaitin argues that incompleteness implies that mathematicians needs to use experimentation to produce tentative axioms to use to prove theorems that cannot be deduced from of our currently accepted axioms. I agree wholeheartedly. That heirarchy of new set-theoretic axioms I mentioned earlier is believed (by most set-theorists) to be consistent essentially because no one has been able to deduce a contradiction from them (yet). In fact, for a few years many set theorists believed in the consistency of the existence of a Reinhardt cardinal, until a contradiction was deduced.

Wednesday, January 04, 2006

I read more details at Slate on how some of the NSA's warrantless searches are inherently not the kind of thing for which you can get a warrant. Essentially, they are conducting traffic analysis (e.g. looking for certain patterns of, say, length and frequency of phone calls) on all Americans--at least all who communicate with foreign people or websites. This is in addition to the more targeted eavesdropping of electronic communications between Americans and individuals with known links to Al Qaeda. (Why such "known" links weren't used to get FISA warrents is a separate issue.) Traffic analysis is arguably a great tool for producing probable cause for conducting eavesdropping on particular individuals, but the traffic analysis itself is far too broad to have any justifying probable cause or reasonable suspicion.

I don't know enough about FISA to say whether or not the act has are loopholes big enough to let through all this surveillance. On the other hand, I've no trouble throwing in my two cents on its compatibility with the 4th Amendment. First, I don't accept the "border search" exception to the warrant and reasonableness requirements even in the case of the targeted NSA eavesdropping. Searching for contraband at the border is very different from reading the letters carried by a courier trying to cross the border, which is the low-tech analog of what the NSA is doing. It's not a reasonable search without additional information, the kind of information that is good enough for a warrant. As for the broader NSA traffic analysis, the "border search" exception makes even less sense.

I also don't believe the President has any "inherent authority" from Article II or anywhere else to conduct these warrantless searches. On this point, I shall link to a post of Orin Kerr rather than repeat his arguments.

I only see one way for all this surveillance to be constitutional: all the access given to the NSA by telecommunications companies is truly voluntary. If that's the case, then expect the Supreme Court to ultimately decide whether FISA has been violated. I expect this because although Bush might get Congress to retroactively legalize warrantless eavesdropping on communications involving essentially anyone the government asserts is linked with terrorism (see this poll), I strongly doubt Congress will acquiesce to the NSA's broader, TIA-style data mining of domestic communications. Yet, I don't expect Congress to muster a veto-proof supermajority to close all the alleged loopholes of FISA. Enter: the judicial branch.

Sunday, January 01, 2006

Via MR , I read the following invocation of Richard Hamming:
In his famous essay You and Your Research (which I recommend to anyone ambitious, no matter what they're working on), Richard Hamming suggests that you ask yourself three questions:
1. What are the most important problems in your field?
2. Are you working on one of them?
3. Why not?
Just be sure to read all of Hamming's talk. Hamming also said,
When you are famous it is hard to work on small problems. This is what did Shannon in. After information theory, what do you do for an encore? The great scientists often make this error. They fail to continue to plant the little acorns from which the mighty oak trees grow. They try to get the big thing right off. And that isn't the way things go.