evolution

I have a lot of blogging to do — and frankly, I can’t think of a better way than spending the Independence Day weekend availing myself of the freedoms guaranteed by the Constitution, at least one of which is applicable here — but I’m tired.

I was just at Kelley’s in Basehor with my family (including one of my nieces who I hadn’t seen in quite a while, because they live in Missouri with their mom, my step-sister), and I ate a chicken fried steak dinner that must have been in the neighborhood of ten thousand calories. And, I had a long week at work, plus I had to make two trips to see my folks in Tonganoxie — we’d swapped cars to get my car’s broken power window repaired.

Not that you care about any of that, but I’m going to bed. More this week.

UPDATE: At least I didn’t eat a beer-battered deep-fried bacon double-Quarter Pounder with Cheese.

“Huge asteroid hurtles toward Earth” (UPI/PJM).

Jun. 29, 2006 (UPI delivered by Newstex) — An asteroid that’s about one-half-mile wide is hurtling toward Earth, expected to narrowly miss the planet early Monday.
Astronomers say the space rock, called 2004 XP14, will pass “exceptionally close” to Earth in astronomical terms — 268,624 miles away at its closest approach, The Scotsman reported. That’s a little more than the moon’s average distance from Earth.

If you have Java, you can see this disturbing animation (click on “Orbit Viewer”) that predicts the asteroid’s orbit in relation to Earth’s. I let the time index run through the year 2006, and found that the asteroid’s maximum distance from Earth is 1.008 AU (astronomical units; 1 AU = 149,597,870.691 km = 92,955,807.267 mi), and its minimum distance — which will occur on 07.03 — is 0.0029 AU, or roughly 270,000 miles, which is only slightly greater than the Moon’s distance from Earth.

NASA doesn’t believe the object is a threat. It’d be interesting to sit down and figure out by how much they’d have to be wrong to fail to predict a collision.

If it did produce a collision, you wouldn’t want to be standing near it. If it struck the KU Campanile, it would make a crater the size of the entire city of Lawrence, and release energy equivalent to 28,000 megatons of TNT; or roughly three times the combined stored energy of all the world’s nuclear weapons. Douglas (Lawrence, Eudora, Baldwin City), Shawnee (Topeka), Leavenworth (Tonganoxie), and Jefferson (McClouth, Oskaloosa) Counties would be utterly annihilated. Kansas City would make New Orleans after Katrina look like Paradise. Those as far away as Manhattan, Emporia, and Blue Springs would get away with only severe third-degree burns and widespread property destruction. People in Salina, Chanute, and Columbia, MO would get away with a mild sunburn — from a fireball eight miles in diameter.

Oh, and people as far away as West Lafayette, IN — my former home, 660 miles from Lawrence — will experience the gentle faraway rolling of a magnitude-7.6 earthquake.

The good news is that most of the rest of the world won’t be affected that much. The Earth will not shed very much mass, and its orbit shouldn’t be affected. Nice to know.

“Lastango” at Daily Pundit:

The second point — the extension of the Geneva Convention to detainees — is more troubling because it will actually have some sort of impact. The decision would seem to apply not only to Gitmo inmates but to Al Qaeda members taken prisoner in any military theatre, from the moment of capture. One critical aspect of our GWOT has been the quick transfer of AQ prisoners from the battlefield to other countries where they can be interrogated by foreigners using methods our own military is barred from employing. The prisoners are then held in those locations for extended periods, and repeatedly interrogated to cross-check new intelligence information as it becomes available. Prisoners captured by foreign authorities and turned over to the US are often processed the same way. This program may be the single most important component of our post-capture handling of terrorists captured abroad, and I’ll be interested in knowing if the Supreme Court’s decision threatens it. If so, that may even have been the liberal majority’s goal.

I don’t know much about the Geneva Convention, but my impression is that it applies only to uniformed combatants of nation-states waging conventional war against their counterparts and against enemy nation-states. AQ fighters hardly fit this description, so I want to get a sense of how the Supreme Court explains its reasoning. If the justification is thin or out of whole cloth, the Court may have been acting on an ideological bias dressed up as a legal opinion, or on a professional, institutional bias against the notion that anyone or anything might fall outside the reach of national and transnational legal structures.

It seems to me that al-Qaeda qualifies on that score. It also seems to me — and I want to stress that I haven’t read through the decision, only bits reprinted elsewhere — that it puts non-uniformed al-Qaeda terrorists hiding among civilian population on equal legal footing with uniformed soldiers clearly engaged in military actions, which is what I thought the Geneva Conventions were supposed to prevent. Furthermore, it seems to me that we are somewhat hamstrung now: we are expected to apply the Geneva Conventions to people (people I do not believe they apply to) who will never, ever apply them to us. I thought the Conventions were supposed to guard against that too.

Allahpundit (yeah, I know, I should just channel the RSS feed here and be done with it):

It’s obvious that the clause about non-international conflicts was meant to apply to civil wars within signatory states. Stevens admits as much. It’s a way of having the Conventions apply intranationally to nations that have ratified them. But if you’re dealing with a political entity that’s explicitly transnational and that’s rejected the Conventions repeatedly by deed if not in word, why deem them included? Article 3 leaves you with the absurd paradox of affording more protection to Al Qaeda members caught inside a signatory country than to members of a hypothetical group that scrupulously follows the Conventions operating inside a nation that’s not a High Contracting Party.

That’s about the impression I got, from my own limited reading. I hope to do more this weekend, rather than be lazy and crib other bloggers.

Follow the brewing chaos in Israel/Palestine at Hot Air.

It’s getting out of control fast.

Executive summary: Palestinian terrorists kidnap settler, soldier (that was Hamas, the Palestinian “government”, now there is a third kidnapping by Fatah, Abbas’s people). Israel moves in with force to look for its people. Al-Aqsa Martyrs’ Brigades (”loosely affiliated” with Fatah) claims it shot a chemical-weapons munition into Israeli territory, IDF denies it; possibly, as Allahpundit puts it, “to keep the genie in the bottle”.

None of it is good news.

It’s time to begin down the path to real numbers, but we have some things to do first. Namely, we’ll construct the natural numbers using basic concepts related to sets. We shall assume the validity of the standard (Zermelo-Frankel with choice) set theory, which is known believed to be a consistent logical system as discussed previously. To enhance readability(!), I shall paper over some subtleties. I’ll assume that you know (at least intuitively) what a set is, and that you know what the union of two sets is (the collection of all elements in both sets; it helps to recall the Venn diagrams you did in school).

We are all apparently innately familiar with the natural numbers. So, we have some idea where we are going. Any model set we hope to build that does what we intend must accomplish the following:

1. Every member of the set must have a “successor”, i.e., given an element of the set, there must be a way to construct the elements that “come after”. These elements are also members of the set.
2. There is one element that is not the successor of any other element. We shall christen this element 0. (This is just a name, it need not correspond to what we know as zero. But, the only other number we know of that would work is 1.)
3. Elements with the same successor are equal.
4. Any subset of this model set which contains our 0, and given any element the subset also contains its successor, then this subset must in fact be the whole set. You may have heard this called the “induction principle”.

It has been proven that at least one set with these properties does in fact exist, assuming the validity of set theory.

Very well, let us plod on. Throughout, we denote the empty set ∅ and the phrase “defined to be equal to” by “:=”. Then, define:

• 0 := ∅
• 1 := {∅} — “a box containing an empty box”
• 2 := {∅, {∅}} = {0, 1}
• 3 := (∅, {∅}, {∅, {∅}}} = {0,1,2}

Let us define the successor S(a) of a element a to be a ∪ {a}. I claim that this construction satisfies the conditions outlined above (known as the Peano axioms).

All right — so how do you “add” two of these things together? Define an operation called “addition” and denoted by + as follows:

• a + 0 = a; and
• a + S(b) = S(a) + b

This is an example of a recursive definition; i.e. a definition that is applied repeatedly until one arrives at the first of these statements, and then unwound from there. For example, substitute 3 for a and 4 for b. One gets from the definition that 3 + 4 = 3 + S(3) = S(2) + S(3) = S(2) + S(S(2)) = S(S(1)) + S(S(S(1)), and so forth.

This operation we call “addition” is commutative; i.e., a + b = b + a for any choice of a or b. 0 is also what we call an “identity” element; by definition a + 0 = a for any a. Furthermore, 0 together with addition “generate” the entire set — remember, if the set contains an element, it also contains the element’s successor. (In jargon, this set with addition is a “free monoid on one generator”.)

You can define “multiplication” thusly: a * 0 = 0 and a * S(b) = (a * b) + a. This is also a recursive definition. You can test it if you like by substituting 3 for a and 2 for b. If you apply the definition correctly, you will get the expected result. (The set with multiplication is a “commutative monoid with identity 1.” The set with both operations together is a “commutative semi-ring”.)

With some effort it can be shown that these operations satisfy the expected properties of arithmetic, like the distributive law.

The mathematician Leopold Kronecker asserted that “the natural numbers are the work of God, all else is the work of man.” Here, we see that it is not required to assume their existence, although even infants have been shown to grasp the concept of “two” or “three”. They may be constructed from scratch out of a consistent logical system that does not assume their existence.

The question of whether this construction and the theory behind it expresses some fundamental concept inherent in our existence or is simply a word-and-symbol game is another matter entirely.

[References: Wikipedia, Kenneth Ross's accessible Elementary Analysis: The Theory of Calculus, which basically continues where I left off here. It had been a while since I thought about the ideas in this post! UPDATE: And thanks once again to David's fact-checking.]

After four years, more than two thousand posts, and nearly half a million words, it’s possible that almost every English sentence one searches Google for could land you here.

I note this because I saw someone get this blog in a search for “egyptian teabag”.

UPDATE: Note to family members — please, for the love of all that is holy, do not repeat this search. Especially not at work.

Don’t ban gay marriage, don’t ban flag-burning, and don’t do this.

I don’t smoke.* I can’t imagine why anyone would want to.** I don’t usually go to places that allow it. That’s my choice.

Where does it stop?

UPDATE: I suppose it depends on the definition of “public places”.