I did a history and a tragedy, so now I have to do a comedy.

From As You Like It:

All the world’s a stage,
And all the men and women merely players:
They have their exits and their entrances;
And one man in his time plays many parts,
His acts being seven ages.

Shift around the letters, and it becomes:

My sane ashen melancholy gentleman harshly says an existential narrative wellspring and, with a serene rhythm, anticipates the modern stage-based development ideas.

I had wanted to post this clip from the Republican debate earlier, but didn’t want to ruin this week’s Headline Game. Giuliani was asked to respond to a harsh quote from a Catholic bishop about his stand on abortion. As he tried to answer, lightning began to play havoc with the sound system. The audience laughed as the candidates on either side of him, Romney and McCain, began to back away, and Guiliani made a joke about it.

Politics aside, it’s pretty funny. Check it out:

If you watch the rest of the clip, you can see Mike Huckabee’s defense of his earlier stance against evolution. He spins it hard, but then he ends with a quote that leaves little doubt about his position on the matter:

If anybody wants to believe that they are the descendants of a primate, they are certainly welcome to do it.

McCain and Giuliani seemed amused by that. We’ll see how it plays with the Republican base.

I don’t know. Let’s ask Fox News.

Seriously, I don’t know why I bother with Fox News. Every time I think I can walk away, I just keep getting sucked right back in. Maybe it’s because I’m concerned that so many people watch it uncritically that it’s actually doing great damage to our country.

The best we can do is to teach information literacy skills to our students. Are we doing that well?

How do they calculate the digits of pi?

I mean, they’ve calculated the number out to billions of places. When they get a billion digits out, how do they know they’re right? Just think about how incredibly precise that is. A quark’s diameter can be described in 18 decimal places, so surely a billion places is far beyond the realm of any practical scientific purpose or authentic human experience.

From a purely mathematical standpoint, pi is defined as the ratio between a circle’s circumference and its diameter. But the only way we have of measuring such things mathematically is by using pi.

Wikipedia has this article on the subject, but I doubt you’ll be surprised when I tell you it is not helpful to me. We could ask Daniel Tammet but he’d probably just tell us what the algorithm tastes like.

Anyway, if all this math stuff is boring to you, check out this discussion thread putting a more philosophical spin on the digits of pi:

“Somewhere inside the digits of pi is a representation for all of us — the atomic coordinates of all our atoms, our genetic code, all our thoughts, all our memories. Given this fact, all of us are alive, and hopefully happy, in pi. Pi makes us live forever. We all lead virtual lives in pi. We are immortal.” – Cliff Pickover

This means that we exist in pi, as if in a Matrix. This means that romance is never dead. Somewhere you are running through fields of wheat, holding hands with someone you love, as the sun sets — all in the digits of pi. You are happy. You will live forever.

Silly, perhaps, but technically true. And somewhere in the digits of pi, there’s a version of the Shakespeare Teacher who understands how they calculate the digits of pi.

When I first started this blog, one of my very first posts suggested that almost all of the current natives of Mongolia and China were probably descendants of Genghis Khan. I literally had no readers at the time – I hadn’t yet told anyone about the blog – and so there was nobody to challenge my sweeping statement. I didn’t even make an argument. I’d like to give my argument now, and reopen the question as a Conundrum.

The idea was based on a National Geographic article about the biological legacy of Genghis Khan:

An international group of geneticists studying Y-chromosome data have found that nearly 8 percent of the men living in the region of the former Mongol empire carry y-chromosomes that are nearly identical. That translates to 0.5 percent of the male population in the world, or roughly 16 million descendants living today.

I went on to note:

16 million descendants. And that’s only men descended from Khan directly through the male line, father to son, for the past 800 years. The total number of Khan’s descendants living today is truly incalculable.

If you figure an average of four generations per century, that’s 32 generations between Genghis and his living descendants. Each person living today should have around 2 to the power of 32, or roughly 4.3 billion, living ancestors that are contemporary with Khan. Obviously, many individuals will have to be counted more than once, so let’s take a different tack.

Let’s pick a year somewhere between 1200 and 2000, say 1500. The total population of mainland Asia in 1500 was 268,400,000. Each living person today would have approximately 2 to the power of 20, or about a million, ancestors who were around in 1500 (and that’s if we don’t count anyone with a living parent).

So how many of the 268,400,000 around in 1500 were Khan’s descendants? Well, there are 16 million men living today that share the Y chomosome. If Khan and his direct male heirs had an average of 1.68 sons over 32 generations, that would give us our 16 million. That would only account for 505 men carrying that Y chromosome in 1500. But that calcuation leaves out two factors.

First, by 1500, Khan’s seed had been pretty well spread. The factors that account for his prevalence today came mostly into play during Khan’s life and the few generations following (see the article for details). So the distribution was a lot more top-heavy than the calculation above would suggest.

Second, we’re only counting direct male-line heirs. Passing a Y chromosome down from father to son over 32 generations is only one of 4.3 billion different permutations of inheritance. Each of those 16 million Y chromosome carriers alive today probably has an average of at least one sister or daughter. That doubles the known descendants right there. Extend that back over 32 generations, then consider all of their descendants, and you get the idea. If we change “average of 1.68 sons over 32 generations” (which we know is true) to “average of 2 children of either sex over 32 generations” (which doesn’t seem like too great of a leap from there), then 16 million becomes 4.3 billion, greater than the population of mainland Asia today.

It seems to me that today’s ethnic Mongolians and Chinese would almost all have to be descended from Khan, some many times over.

Now I am no math expert. I’m a Shakespeare Teacher. It’s very possible I could be wrong about this. I’d be interested to hear what other people think, particularly people with more professional experience with statistical analysis.

And I should also point out that I pin no political, moral, or judgmental significance to being a descendant of Genghis Khan. This is simply a math, history, and logistical Conundrum. I truly hope no offense is taken (though if you read my original post and the Economist article it is based on, it actually seems to be a point of pride for both Mongolia and China to be the descendants of Khan). And my family comes from Belarus, so this would mean I’m probably a descendant of Khan as well. So don’t screw with me.

Now, with all that in mind, for this week’s Conundrum, I hereby submit my original conclusion up for public scrutiny:

So, China and Mongolia should probably stop arguing over which of their people are the true heirs of Genghis Khan. My guess is, almost all of them are.

At the recent Republican debate, the candidates were asked to raise their hands if they did not believe in evolution. Sam Brownback, Mike Huckabee, and Tom Tancredo all raised their hands.

And this is America, where people are free to believe anything they like. But these are people who are running to be the president of the most powerful nation on earth. The next president must be able to lead the world in dealing with the crisis of global climate change. The next president will probably have to revisit stem cell research. The next president will possibly have to deal with another epidemic. All of these things are difficult to do when you don’t believe in science. Just ask President Bush.

But these three guys raise their hands, and it’s buried in the middle of the story, after we finish talking about the legacy of Ronald Reagan. Why is this not the top story? If they had said they were athiests, it would be the top story. If they had said they were atheists, that would be the end of their careers in American politics. If they had said they were agnostic, that would be the end of their careers in American politics.

So many of our most celebrated figures are openly athiest, from scientists to artists, from business leaders to Karl Rove. But not one of the candidates running for president.

Why is disbelief in evolution more acceptable in American politics today than disbelief in God?

Researchers in Germany are working on a way to predict the intentions of human subjects by observing their brain activity. Damn!

For some reason it’s a little disturbing to me that something as personal and ephemeral as an intention can have a physiological manifestation that can be measured. Or maybe I’m just disturbed that they are now starting to measure it. What new “mind reading” technologies might be developed from this science? Could it become prosecutable to merely intend to commit a crime? Intent is already used as a legal concept, and attempted murder is considered a crime, even if nobody is hurt as a result. Could market researchers measure the intent of potential consumers? Will we one day have little handheld devices that can measure intent at a poker table or when our daughter’s date arrives to pick her up?

It all reminds me of a thought experiment made popular by Robert Nozick, which will be this week’s Conundrum. Before we get to it, though, it might be helpful to consider another thought experiment known as Kavka’s Toxin.

Let’s say I offer you $100,000 if you can form an intention to drink a particular toxin. This toxin will make you violently ill for about five or six hours, after which you will be perfectly fine. You’d drink it for the money, but you’re not being asked to drink it. You’re being asked to intend to drink it. After you have the money, you are free to change your mind and not drink it. The question is, can you actually form a genuine intention of doing something unpleasant that you will have no motivation to do?

Turn that one over in your mind for a few moments before moving on to this week’s Conundrum, Newcomb’s Problem.

Imagine there are two boxes, Box A and Box B. You will have the option of choosing to take both boxes, or to take Box B alone. You will keep what you find inside. Box A is transparent and contains one thousand dollars. Box B is opaque. A super-intelligent alien scientist with a proven track record of accurately predicting human behavior has analyzed you and has secretly made a prediction about which you will choose. If he believes you will choose Box B alone, he has put one million dollars inside. If he believes you will take both boxes, then he has left Box B empty. Which do you choose?

The super-intelligent scientist has run this trial with several hundred other humans, and has made a correct prediction each time. The only people who have ended up with the million are the ones who chose Box B alone. On the other hand, our alien friend has already made his prediction and left. Your choice can no longer affect the amounts that are in the boxes. You may as well take them both, right?

Fans of game theory might recognize this as a variation of the Prisoner’s Dilemma. Game theory would likely suggest that you flip a coin, so we’re going to disallow that option. You must rely on reasoning alone.

Unlike last week’s math puzzler, this one doesn’t have a right or wrong answer. It’s a thought experiment designed to test your conceptions of free will vs. determinism.

Or as Nozick put it:

To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly.

It will be interesting to hear how people answer this.

Will you take both boxes, or Box B alone?

Feel free to answer the question, or continue the discussion of any of the topics covered above.

If you’re interested, you can take this survey on your intuitions of causation.

If you like this sort of thing, you can head on over to Harvard and take these kinds of tests all day. Start with the Moral Sense Test and the Moral Sense Test 2.

Then check out the series of Mind Surveys.

There are also surveys on Visual Cognition, Music Universals, and Implicit Preferences.

Have a good weekend.

Yesterday, I assured you that there was no need to worry about super-sentient robots taking over the world and ruling humanity. Then, I read about this.

Researchers at Cornell have announced the creation of self-replicating robots. These are robots that are designed to build exact copies of themselves. They are made up of identical building blocks (cleverly named “molecubes”), each of which contains all of the information needed for the program, not unlike DNA. The current version is simple, only able to self-replicate, but they have big plans for the future:

Although these experimental robots work only in the limited laboratory environment, Lipson suggests that the idea of making self-replicating robots out of self-contained modules could be used to build working robots that could self-repair by replacing defective modules. For example, robots sent to explore Mars could carry a supply of spare modules to use for repairing or rebuilding as needed, allowing for more flexible, versatile and robust missions. Self-replication and repair also could be crucial for robots working in environments where a human with a screwdriver couldn’t survive.

Well, that’s all fine and dandy, but add the idea of self-replicating robots to yesterday’s discussion of robot evolution and now we have ourselves a problem. You see, the only elements that are needed for evolution are self-replication, the possibility of error in that replication, and a competitive environment. The errors that increase the chance of survival within that environment will then spread throughout the population, leading to the inevitable evolution of something entirely new.

But what, you ask, are the odds of robots actually being put in a position where they will be able to reproduce and evolve? Um, how about one hundred percent? Because you just know that this is exactly what researchers are going to do once they have the ability to do it – put self-replicating robots (with the possibility for random mutations) in a competitive environment and see what evolves. Hell, that’s the first thing I’d do, and I’m the one warning you about it. Even if it leads to the destruction of humanity, it’s too cool. It must be done.

But then the robots evolve laser-guided heat-seeking missles before the experimenter has the chance to flip the off switch, and the evolving robots run amok in the wild, mutating and evolving at breakneck speed. And then, one day, humanity gets a bitter lesson in the true meaning of “survival of the fittest.”

So that’s it then. We’re all doomed. Long live the age of the robot.

Via Prospero’s Books, I found this article about robots being used to simulate evolution. I’ve read about similar projects simulating evolution through competing artificial intelligence programs, using the “Prisoner’s Dilemma” scenario as the competitive task. The Prisoner’s Dilemma, for those who are unfamiliar, breaks down as some variation of this:

You and a partner are both correctly arrested for two crimes, one major and one minor, and are put in separate rooms. Executive Assistant District Attorney Jack McCoy comes to visit you and offers you a deal: testify against your partner for the major crime, your partner will get twenty years, and you’ll walk for both crimes. However, his lovely assistant is right now offering the same deal to your partner. If you both confess, you’ll both get five years. If your partner confesses and you don’t, you’ll get the twenty, and he’ll walk. If neither of you confess, McCoy can’t make his case for the major crime, but he’ll make sure you both do two years for the minor one. What’s the right play?

Well, logically speaking, regardless of what your partner ends up doing, you’re better off confessing. But if you both confess, you both end up worse off than if you had both kept your mouths shut. If you had had the chance to communicate with each other, you might have chosen differently. The fact that you don’t know what your idiot partner is going to do while gazing into the eyes of the lovely ADA means that you can’t afford to take any chances, and neither can he. You both end up doing the nickel, even though neither of you had to.

In this example, you only get to play the game once. If you play some version of the Prisoner’s Dilemma with the same person repeatedly, your choices can affect future outcomes. In a sense, the choices you make are a form of communication. Only the very last time you play do you revert back to the original cutthroat scenario. (And since everybody knows this will be the case, the next-to-last iteration can also be cutthroat. How far back does this reasoning work?) There is actually a twenty-year-old Iterated Prisoner’s Dilemma competition for artificial intellegence programs and the winning strategy has long been the simple Tit-for-Tat. But it seems there’s now a new champion, though it seems to me to be a bit of a cheat. Read the article and let me know what you think.

The Prisoner’s Dilemma is an illustration of one of the central concepts of a branch of mathematics called “game theory.” Game theory allows us to make mathematical computations in decision making, even when all of the factors are not known. Think of two generals, one trying to choose a target to attack, the other deciding how to deploy defensive forces. Each knows the other is intelligent and out there making his decision. That’s game theory. If you were to meet someone anywhere in the world outside of the United States, but you couldn’t plan with that person ahead of time, where would you go? Would it surprise you to learn that almost everyone makes the same choice? (Post your answer in the comments section, if you like.) That’s game theory too.

With a branch of mathematics that can take unknown variables into account, a computer’s functionality can be increased significantly. Obviously computers that are powerful enough can play chess, but game theory allows them to play poker as well. There’s already a Texas Hold ‘Em Tournament for Artificial Intelligence programs. Imagine putting all of these programs into a giant simulated Texas Hold ‘Em Tournament where the losing programs died out and the winning programs created offspring with the possibility of mutation. We might evolve the ultimate strategy. And when we do, the first round of drinks are on me!

But as computers get more powerful, imagine other simulations we may be able to run, and what understandings we might be able to gain from these experiments. Evolution has proved itself to be a mighty force in the past. Once all of the data from Web 2.0 is compiled, maybe it will be allowed to evolve into Web 3.0. It’s not about computers becoming super-sentient and ruling over humans. It’s about humans developing and using new tools that can increase our capacity for growth. And if evolution has taught us nothing else, it has taught us that.