Saturday, August 25, 2007

A Whiff of Fascism

Everyone knows the basis of Senator Clinton's political appeal: she and her husband are the most ruthless employers of mass propaganda in contemporary political life. The interesting thing about Senator Clinton is that she's the first person to admit to it:
It's a horrible prospect to ask yourself, 'What if? What if?' But if certain things happen between now and the election, particularly with respect to terrorism, that will automatically give the Republicans an advantage again, no matter how badly they have mishandled it, no matter how much more dangerous they have made the world," she said.

"So I think I'm the best of the Democrats to deal with that as well," she concluded.
In other words, if a major terrorist attack on the United States succeeds between now and the election, Senator Clinton claims to be the Democrat best able to undermine the government and seize power (in the election, of course). Does anyone else smell that whiff of fascism in the air?


Senator Clinton, the so-called democrat, issues dictation to the Iraq parliament:
In a statement released by her Senate office, Clinton echoed a call by Senate Armed Services Committee Chairman Carl Levin for Iraq's Parliament to oust al-Maliki in favor of a leader who could restore order to Iraq's unity government.

"During his trip to Iraq last week, Senator Levin ... confirmed that the Iraqi government is nonfunctional and cannot produce a political settlement because it is too beholden to religious and sectarian leaders," Clinton said. "I share Senator Levin's hope that the Iraqi Parliament will replace Prime Minister Maliki with a less divisive and more unifying figure when it returns in a few weeks."
In other news, a Huffington Post columnist calls for a military coup to remove President Bush as Commander-in-Chief (boldface in original, hat tip: instapundit):
General Pace - you have the power to fulfill your responsibility to protect the troops under your command. Indeed you have an obligation to do so.

You can relieve the President of his command.

Not of his Presidency. But of his military role as Commander-In-Chief.

Thursday, August 23, 2007

A Physicist's Take on the M-Door Monty Haul Problem

The M-door Monty Haul Problem is very simply stated. You are a contestant of a game show in which a collection of M closed doors is present on the set. Unobserved by you, one door has an expensive car behind it and the others doors have goats behind them. Neither the car nor the goats are switched between doors or replaced with a different prize at any time. To start, you pick a door and then host Monty Haul opens one of the doors (not the one you picked, of course) to reveal the goat behind it. You then alternate between choosing to switch or not the door you have picked and Monty Haul opening doors to reveal the goats behind them. Once you are down to only two doors, you have one final chance to switch doors and then Monty Haul reveals the prize behind your picked door.

It turns out that my previous proof of the optimal strategy for the M-door Monty Haul problem has a few errors in it. The most important was an assumption that switching doors on any round other than the final two-door round hurt one's chances of winnings. This must be false. To see this, let's suppose that at the start of the game you've picked door #1. Suppose also that, after making a series of switches or non-switches, you switch back to door #1. Can it really be said that your odds of winning the car are now lower than if you had never switched from door #1 at all?

In physical terms, this property is called the Markovian Postulate:
If K is any observational state and T is a trial whose preparation stage invariably ends with the system in the state K, then T is statistically regular. (O. Penrose, "Foundations of Statistical Mechanics", p.34)
In particular, suppose you go into the two-door round having picked a certain door and with a certain other door remaining (call them #1 and #2). You can think of this as one long trial T which invariably end with you having picked door #1 with door #2 remaining at the end of a preparation stage of a certain length. The Markovian Postulate says that your probability of winning the car at this point will only depend upon whether or not you switch in this final two-door round, regardless of the past history of switches or non-switches in the previous rounds.

In the M-Door Monty Haul problem, the probability of winning the car by making no switches at all except for one final switch in the two-door round is (M-1)/M. So this must be the probability of winning the car by switching doors in the final round, regardless or whether or not you switch or not on any previous round. So the optimal strategy is simple: switch doors in the two-door round.

Wednesday, August 15, 2007

Foolish Atheism

There's a bumper crop of Vacuum Energy posts today! I started reading Christopher Hitchens' new book "god is not Great: How Religion Poisons Everything" the other day, and this paragraph threw me for a loop (p.4):
There still remain four irreducible objections to religious faith: that is wholly misrepresents the origins of man and the cosmos, that because of this original error it manages to combine the maximum of servility with the maximum of solipsism, that it is both the result and the cause of dangerous sexual repression, and that it is ultimately grounded on wish-thinking.
My first problem with this is that if one objection only occurs because of one of the other objections, then the list is not irreducible as claimed. Ok, so my first objection might be splitting hairs. Let's move on.

I haven't read the book past page 4 yet, so I haven't read Hitchens' argument for the "dangerous sexual repression" objection to religious faith. In the modern era at least, it seems as if the problem with religious faith is sometimes exactly the opposite one: a dangerous sexual liberation. What I mean by this is that the very servility expected by some religous leaders can act as a very compelling temptation to them. Put even an average person in a situation where his or her every wish must be obeyed as the word of God with no harmful consequences permitted and he or she is quite likely to start "losing it". One moment you're a successful religious guru preaching to the faithful; the next moment you're using biblical verses to redefine the concept of "virginity".

Stupid Creationism

Vox Day wields the "Argument from Personal Incredulity" against the Darwinist enemy:
From my admittedly layman's perspective, the Neo-Darwinian Theory of evolution looks remarkably like a historical model, except that it doesn't explain historical events half as well as my stock system did. It's not a reliably predictive model like the Law of Supply and Demand and it doesn't provide what I consider to be convincing answers to simple questions like why one population evolves and another does not when they share the same environment; declaring one to have reached equilibrium while the other is unstable is simply not convincing over the lengths of time that are supposed to be involved.
One would think that merely invoking the phenomenon of extinction would be sufficient to disprove Vox Day's point. In any given environment, some species will adapt to it and some species will die out within it. It is an obvious empricial fact that the abilities of species to adapt to a given environment are different.

There is another perfectly simple reason why one population in an area might evolve rapidly while another population in the same area does not evolving as rapidly. Evolution is ultimately changes in the DNA of members of a species over time. It would be extremely unlikely for the DNA of all organisms to have exactly the same potential for beneficial changes to occur at exactly the same rate when placed in a certain environment. What I would expect is that some species, because of the exact nature of their DNA and the way it is expressed, are going to be more resistant to changes than other species. In the absence of, say, a complete genetic profile of every species ever to have existed on Earth over the last 4 billion years, biologists might therefore have to come up with empirical relations to investigate mutation rates.

Senator Barack Obama, loser

The blog "The Reality-Based Community" posted this commentary, which was too good to pass up. Helpful campaigning tip: When running against Senator Hillary Clinton for the presidency, it's probably not a good idea to keep drinking the Clinton Kool-Aid (hat tip: The Daily Dish):
The Clinton campaign, both the candidate and the surrogates, have been going after Barack Obama hard and personally. He's "naive" and "irresponsible," too inexperienced to trust as Commander in Chief. Now Obama says that, largely through no fault of her own, Clinton is not the best person to bring the country back together.
So, according to Senator Obama, the same Republicans who spent the 90s attacking Hillary Clinton just because she is a woman are going to be civil gentlemen with respect to a President Obama.

Yes, you read that correctly. Senator Obama has just told a Democratic Party that is questioning his "blackness" that racist Republicans who hate and despise all African-Americans will love and adore him when he becomes president. Short of walking into the YearlyKos convention was a sign reading "No, I am not black enough to be president. Ask me why.", it's hard to imagine an admission more damaging to Obama's liberal support.

Tuesday, August 14, 2007

A foreign policy decision that took real courage to make.

The first sentence of the article speaks for itself (embedded hyperlinks removed):
The United States has decided to designate Iran's Revolutionary Guard Corps, the country's 125,000-strong elite military branch, as a "specially designated global terrorist," according to U.S. officials, a move that allows Washington to target the group's business operations and finances.
All summer, we've been hearing reports that Iran is sending support to the Iraqi insurgency. Now we're finally ramping up the pressure on Iran to cut it out. Contrast this with the Obama Doctrine of "Protect our enemies. Invade our allies."

I'd like to think I'll be proven wrong with this, but my prediction is that the Democratic Presidential candidates are going to denounce this decision with varying degrees of vehemence. Their Left-wing base isn't going to like measures that threaten the "revolution", after all.

Monday, August 13, 2007

Michelle Obama gets it right.

Michelle Obama came out and said it:
The wife of Democratic presidential hopeful Barack Obama on Sunday admonished those who question her biracial husband's credentials as a black man, calling the issue "nonsense."

"We're still playing around with the question: Is he black enough?" Michelle Obama told a campaign event on Chicago's South Side. "Stop that nonsense."

Wednesday, August 08, 2007

Absurd separation of Chuch and State

The latest attempt by those evil Right-wing Christians to establish theocracy in America:
David Wallace Croft and his wife, Shannon, of Carrollton, Texas, have three children at Rosemeade Elementary and argue that the moment of silence is unconstitutional and amounts to state-sanctioned school prayer.
So what is the remedy to this problem? All public schools will have to install Constitutionally-mandated noisemakers in all school facilities to prevent students from having more than 59 seconds of silence at any point in the school day. Helpful tip: according to Liberals, the seperation of Church and State requires the government to monitor your thoughts and behavior on a second-by-second basis to make sure you aren't doing anything religious (like thinking).

Tuesday, August 07, 2007


At the present time, 755 home runs is still the real home run record of major league baseball. Hank Aaron cranked out every one of those home runs the hard way with hard work, determination, and professional integrity. Hank Aaron busted his ass and wore himself out to set that record. He deserves every single second of the accolades and every single penny of the rewards he has received since then.

* Technically speaking, San Francisco Giants player Barry Bonds finally acheived his 756th career home run tonight. To recognize the stain that has been placed upon the honor of major league baseball, the asterisk on Hank Aaron's record will be maintained until Barry Bonds has been banned from baseball.

Friday, August 03, 2007

The M-Door Monty Hall Problem

The M-Door Monty Hall problem assumes that you are a contestant in a game show trying to win a new car. You start off with M doors, one of which has a car behind it and all of the others have goats. After you pick a door, host Monty Hall opens a door to show the goat behind it (other than the one you picked, of course). He then gives you the choice of keeping your picked door or switching your pick to one of the other doors. After you make your choice, Monty and you continue alternating between opening doors to reveal the goats behind them and choosing whether or not to switch which door has been picked until the game is down to only two doors. Monty then gives you one final chance to switch your picked door before revealing your prize.

The problem is to determine the optimal strategy of either switching doors or not switching doors in each round starting from the initial pick from one of the original M doors. Also note that Monty is not allowed to switch which door has the new car behind it.

The key here is to have a probability that the door one has picked has the car behind it is a far from 1/2 as possible going into the two-door round. The further this probability is from 1/2, the more confident one can be in either switching one's pick or keeping one's pick as appropriate to win the car.

My proof of optimal strategy is as follows. Suppose that you go into round N+1 (here N>=2) with a probability x of having picked a door with a goat behind it.

  • If you don't switch your door, Monty opens a door with a goat behind it and you go into round N with a probability x of having picked a door with a goat behind it.

  • If you switch your door, a fraction
    • (N-1)/N of people who picked doors with goats behind them switch to another door with a goat behind it;

    • 1/N of people who picked doors with goats behind them switch to the door with the car behind it;

    • all people who picked the door with the car behind it switch to a door with a goat behind it.

    If you switch doors, you go into round N with a probability x*((N-1)/N)+1-x = (N-x)/N of having picked a door with a goat behind it.

Now (N-x)/N can equal 1/2 if N=2 and x=1. That is, if you were absolutely guarenteed that you picked the goat going into the 3 door game, then switching doors would reduce your chance of winning the goat to 1/2. In this case, the optimal strategy is to not switch doors, let Monty open one of the two remaining doors with goats behind them, and then switch doors to win the car with absolute certainty. In any other case other than N=2 and x=1, since x is at most 1, it follows that (N-x)/N is larger than 1/2.

Under what conditions is (N-x)/N closer to 1/2 than x? Start with the inequality

x - 1/2 > ((N-x)/N) - 1/2

This inequality is satisifed if

x > N/(N+1)

In other words, if x > N/(N+1), then switching doors in the N+1 round and then never switching doors again until a final switch in the 2-door final round will lead to a reduced probability of winning the car.

Notice also that if one switches in the N+1 round, thus altering the probability that one has picked a door with a goat behind it from x to (N-x)/N, it is also the case that for 1 > x,

(N-x)/N > (N-1)/N > (N-2)/(N-1) > ... > 2/3

Of course, if x=1 going into the N+1 round, then the optimal strategy is to never switch doors until the 2-door final round, thus winning the car with absolute certainty. What this means is that, if you go into the N+1 round with a probability 1 > x > N/(N+1) of having picked a door with a goat behind it, then switch doors in the N+1 round, then no matter how many rounds you refuse to switch doors before the two door finale, the next switch of doors still further hurts your chance of winning the car. This same argument can be repeated as many times as necessary to show that, as long as one starts with 1 > x > N/(N+1) going into the N+1 round, every time you switch doors before the 2-door final round, no matter when, you hurt your chance of winning the car.

So the conclusion is that, if you go into the N+1 round with N>=2 with x > N/(N+1), every switch of the doors before the 2-door final round, no matter when, will always hurt your chance of winning the car. Notice that your probability of having picked a goat is always going to be at least 2/3, so you will always want to switch doors in the final 2-door round.

Now, one starts the game by picking from M doors with M>=3, then allowing Monty to open a door to reveal the goat behind it. The probability of picking a door with a goat out of a selection of M doors with M-1 doors having goats behind them is x = (M-1)/M. You're forced to allow Monty to open at at least one door before your first switch. So you go into the M-1 round with a probability x = (M-1)/M of having picked a door with a goat behind it. Since

(M-1)/M > (M-2)/(M-1)

it follows that switching doors in the M-1 round or any subsequent round hurts your chances of winning, no matter how many rounds you wait and refuse to switch doors. So the optimal strategy must be to never switch any doors until reaching the two round finale, and then and only then switching doors. This is consistent with all of the special cases above as well, so this is the optimal strategy.

Thursday, August 02, 2007

Political lightning strikes twice

Senator Barack Obama screws up again:
In another broadside indicating the increasingly heated race for the Democratic nomination, Sen. Hillary Clinton, D-N.Y., implied Thursday that comments made by Sen. Barack Obama, D-Ill., were careless and unpresidential.

Sen. Clinton was referring to Obama's statement earlier in the day that he had ruled out using nuclear weapons against al Qaeda targets in Afghanistan or Pakistan.

Clinton also suggested Obama's high-profile speech earlier in the week in which he said would be willing to invade Pakistan to attack high-profile al Qaeda targets, given actionable intelligence, was inappropriate, further evidence that she is painting her challenger as unprepared for the job of commander in chief.
It looks like Senator Obama is turning out to be the biggest loser for the Democrats. Coincidentally, Senator McCain seems to be adopting this same role for the Republicans.

On the other hand, perhaps we are watching the embryonic stages of the formation of a new "All Losers Party". Is it possible that we might see a McCain-Obama ticket in 2008?

The Fall of Chameleon

What we've seen this summer is a great man watching his great dream collapse in front of his very eyes. His proud designs for the future have been reduced to dust. His triumphant entry into the capital city of his enemies has been transformed into a humiliating retreat that has only just begun.

The actor in this drama is Senator John McCain. His downfall was the comprehensive immigration reform:
Republican presidential hopeful John McCain on Thursday backed a scaled-down proposal that imposes strict rules to end illegal immigration but doesn't include a path to citizenship.

The move away from a comprehensive measure is an about-face for the Arizona senator, who had been a leading GOP champion of a bill that included a guest worker program and would have legalized many of the estimated 12 million illegal immigrants living in the U.S. It failed earlier this year.

"We can still show the American people that we are serious about securing our nation's border," McCain said in a statement, adding that the new bill would "provide an essential step toward achieving comprehensive reform in the future."
It seems just yesterday that McCain was piously accusing "secure the border first" advocates of being racist xenophobic klansmen gestapo brownshirts who would plunge the American economy into chaos out of sheer hatred for "the Other". Now McCain himself -- apparently the last Republican alive to learn this particular lesson -- wants to secure the border first.

2008 is over for McCain, but like an aggrieved Shakespearean prince, McCain will not let go of his ambitions for the throne. The humiliation, then, must go on... and on... and on...

Wednesday, August 01, 2007

Barack "Empty Suit" Obama nails himself, big time

Senator Barack Obama is looking increasingly more inept on foreign policy concerns. Last week he attacked Senator Hillary Clinton as being "irresponsible and naive" for not meeting face-to-face with dictators:
"The notion that I was somehow going to be inviting them over for tea next week without having initial envoys meet is ridiculous," he said in an interview outside his Senate office. "But the general principle is one that I think Senator Clinton is wrong on, and that is if we are laying out preconditions that prevent us from speaking frankly to these folks, then we are continuing with Bush-Cheney policies."
This week, Senator Obama is even more Bush-like than Bush himself:
He offered harsh words to Pakistani President Pervez Musharraf, who has been the target of assassination attempts for his efforts to aid the United States in rooting out terrorist havens in the northwestern region of his country.

"I understand that President Musharraf has his own challenges. But let me make this clear. There are terrorists holed up in those mountains who murdered 3,000 Americans. They are plotting to strike again," Obama said. "If we have actionable intelligence about high-value terrorist targets and President Musharraf won't act, we will."
Senator Obama's foreign policy as president seems to be "negotiate with our enemies; invade our allies".

Really dumb Supreme Court commentary

Conservative judges are typically opponents of judicial activism and proponents of the idea that laws have some fixed meaning that does not evolve with time. With a great deal of deliberate irony, the liberal media likes to attack these conservative judges with the claim that, in reality, it's conservatives who are the judicial activists. This article discussing the "faux originalism" of Supreme Court Justice Clarence Thomas actually goes a bit further than that. The claim here is that conservative "originalism" is a silly way for a judge to make desicision; so silly, in fact, that even Clarence "Mr. Originalist" Thomas just votes his conservative bias rather than take it seriously.

For example, here's how the article analyzes Thomas's ruling in the "Bong hits 4 Jesus" case:
Despite the vast differences between public education then and public education today, Justice Thomas evidently believes the question of whether students have free-speech rights should be answered by conducting an imaginary séance with 18th- and 19th-century Framers and ratifiers, who should be asked: Do you think public-school students have a constitutional right to free speech while in school? This line of inquiry is about as productive as asking an only child: Imagine you have a sister. Now, does she like cheese?
I'm not a lawyer or a legal scholar, but I'm pretty sure that Clarence Thomas isn't staring into a crystal ball to make decisions.

Let's look at the article's argument in a bit more detail. The author states Thomas's opinion and criticises it with:
Thomas wrote a concurring opinion in both cases. In the first, he made the bold claim that students simply do not have any right to free speech in school. Why? Because those who framed the relevant constitutional language would not have expected students to have First Amendment rights while in school.

This is an extraordinary claim for many reasons, not the least of which is the fact that public schools did not exist when the First Amendment was drafted. Even by the time the 14th Amendment was adopted, making the First Amendment applicable to the states, public schools were just getting started. Few students attended school for more than five years; public high schools were virtually nonexistent; and compulsory education was still decades away.
The game being played here is obvious: the author is assuming a narrower focus to his argument than Thomas might have done. Whether or not the Founding Fathers did or did not have the slightest apprehension of the specific concept of a compulsory public school, they would have been more likely to have known the more general concept of compulsory attendance in general for citizens at the behest of government. Would the Founding Fathers have had an opinion about free speech rights of citizens, in general, who were compelled to attend some government function such as a jury trial? Yes, they most likely did.

The next attack follows up with the charge of hypocrisy:
But it gets worse for Justice Thomas, considering the second school case, this one about voluntary integration. Thomas also wrote a concurring opinion in that case, in which he lambasted those who try to integrate public schools, calling school integration an elitist fad. He also claimed that using race to integrate schools was obviously unconstitutional and made an impassioned argument in favor of colorblindness—the idea that governments can never take race into account, even to protect or assist minorities.

But guess what's missing entirely from this sweeping opinion? That's right: any consideration, whatsoever, of how the Framers and ratifiers of the Equal Protection Clause of the 14th Amendment would have viewed voluntary integration of public schools. The touchstone originalism of his Morse opinion is nowhere to be found.
Again, I'm not a lawyer or a legal expert, but it seems obvious that not every case that comes before the Supreme Court must go all the way back to some Constitutional touchstone. Perhaps, instead of starting with the 14th amendment and working his way forward, Thomas conceeded that some later law -- one of the subsequent civil rights acts maybe -- was undoubtedly constitutional and more relevant to the case. The whole point of originalism, after all, is that future legislators can change the meaning of the existing laws by enacting new legislation. If Thomas judged that the latest, most authoritative, constitutional legislative commentary on the 14th amendment with relevance to the case was, for the sake of argument, the Civil Rights Act of 1964, then there would have been no need to "hold a séance" with Charles Sumner and Thaddeus Stevens over the 14th amendment.