Tuesday, July 29, 2008

Free will and Quantum mechanics

Because of the sort of internet locales that I frequent, I meet a lot of very philosophically minded folks. And sometimes, they spontaneously start talking about physics! I love it.

But I sort of hate it too. I feel like yelling, "Get off my lawn! Those aren't toys!" A lot of time, these people just don't know what they're talking about. And yet, everyone likes to think that there is solid scientific backing to their personal philosophy. That is not called science, it is called confirmation bias. It makes me sad, in a way. Is this the only reason that people enjoy science? So they can look into the depths of time and read it like a horoscope? I don't know... I guess that's marginally better than "to beat the commies".

In my metaphysics category, I aim to cut the line between physics and metaphysics, because this is where most of the abuse is.

Today's divorce: Quantum mechanics and Free will

First of all, free will is a contentious issue. A contentious philosophical issue, not a scientific one. Free will is one of those things that must, dogmatically, exist. Too often, people only care about the question of whether free will exists, when they should care about what "free will" really means. And what do we really mean by free will anyway? Does that mean that we're free from outside influences? Does it mean that we are morally culpable for our own actions? Does it mean that our actions are unpredictable? Is it necessarily a supernatural force? Definitions and details abound.

Does Quantum mechanics imply free will? It depends on what kind of free will we are talking about. If we're talking about unpredictability, maybe. But if we consider the moral definitions, I don't think science has the slightest bearing on any of them. "Unpredictable <=> morally responsible" just seems like a non sequitur to me, but hey, that's a problem for philosophy, not for physics.

But first, how about classical mechanics? The universe envisioned by Isaac Newton was like clockwork. All God had to do was wind it up. The universe would proceed in a single deterministic path. Now, Newton was quite religious, if a bit heretical, but that doesn't stop more modern folks from thinking that the determinism of classical mechanics was an obstacle to religion in some way. But is it?

In principle, classical mechanics are completely deterministic, but in practice they are not. If you've got a single particle, you can easily predict its motion, but if you have more, it's not so simple. If you have N particles, you have to keep track of 3N numbers to specify their coordinates, and 3N more to specify their momentum. Once you have at least three particles, the gravitational equations already become impossible to solve without approximations. In any typical system on the human scale, we'll have on the order of 10^22 particles. Because it is so vastly impractical to keep track of so much information, we instead use statistical descriptions of such large systems. Temperature is one example; it describes a probability distribution of energies for each particle. And that's why determinism does not imply predictability.

Having broken the connection between determinism and predictability, I have to wonder why determinism must be mutually exclusive with free will. Determinism at least allows for a very effective illusion of free will. (Bonus question: what's the difference between free will and its illusion?)

On to quantum mechanics. Quantum mechanics is thought to restore the possibility of free will (also miracles, but that's another topic) because it is completely random and therefore non-deterministic. But the more accurate description is that quantum mechanics is stochastic, not random. You cannot predict the outcome of a particular measurement, but you can predict the probabilities of different outcomes. In fact, in principle you can predict those probabilities exactly. If there were any way to influence the outcomes of the probabilities, there would, in principle, be an experiment that measures this skewing of probabilities. Such an experiment would contradict the stochastic nature of quantum mechanics. So this whole concept of "quantum free will"--a cosmic force capable of subtly influencing the results of wavefunction collapse--is in fact contradictory to quantum mechanics.

That is, unless this quantum free will is just as random as quantum mechanics itself. In that case, I have trouble discerning how this stochastic free will is any more free than a deterministic free will. Let's say you are to decide between two things--let's say, happiness or wealth. If you are forced to decide according to the result of a coin flip (don't forget: coin flips are a deterministic process), would you feel free? Would it make any difference if it were some sort of quantum coin flip?

As a side note, the current scientific consensus is that the brain is primarily governed by classical processes, not quantum mechanical ones.

Of course, things get still more complicated when we consider another respectable interpretation of quantum mechanics: the Many Worlds Interpretation.* According to this interpretation, quantum mechanics is neither random nor stochastic. It is deterministic in fact. Whenever a measurement occurs, the universe becomes a superposition of all the possible results. That is, all the possibilities occur. But subjectively, you only see one of those possible results. There are multiple versions of yourself observing each of the different possibilities, but you have absolutely no contact with those other versions of yourself. And no, you cannot "choose" which of the many possibilities will "really" occur--they all really occur, regardless of your state of mind.

*For details on why the many worlds interpretation might be preferred over the more common Copenhagen interpretation, see this previous post.

This is rather difficult to fit in with quantum free will. If your choices were truly based on quantum randomness, that means all choices must occur. Tell me, in what sense is this any more free than a classical universe? (Right now, I'm imagining God condemning half of your wavefunction to hell and allowing the other half into heaven.)

Now, there is one thing here that fits in with religion. Objectively (ie what God sees), you have no free will. But subjectively (ie what humans see), you have free will. Finally, a scientific solution to the omniscience/free will paradox! But that just misses the point. Determinism does not clearly imply predictability, nor does it clearly contradict free will and moral responsibility. And there all different kinds of ways to blur the lines between determinism and nondeterminism, free will and no free will.

So when you are looking for a way to back up your personal philosophy with physics, you must ask yourself: Am I talking physics or just practicing confirmation bias? If you find your confirmation in an idiosyncratic interpretation of quantum mechanics, it's probably the latter.

Of course, I still enjoy talking about it, regardless.

[This essay was partly developed in a discussion at the Friendly Atheist.]

Saturday, July 26, 2008

Confirmable but unfalsifiable?

In my encounters on the internet, I've found that people have all sorts of views on the relationship between science and religion. Here's one that I feel is just plain contradictory, as if someone had taken two very common views and stitched them together into a paradoxical Frankenstein monster.

View 1: God is unfalsifiable. Therefore, you can't prove that He doesn't exist. Those atheists are so irrationally dogmatic!

View 2: Religious experiences probably attest to some unknown. We call that unknown God.

Conclusion: It's a double-whammy! I can show that God most likely exists, and you can't disprove him. I win. Er... I mean, God wins.

See the contradiction? If you didn't see it, I'll eventually get to it.

There is a common theme in the reaction to the atheist movement. "Those atheists seem to have the same conception of God as do the fundamentalists! They probably think he's a bearded old guy in the sky in white robes. That's nothing at all like my religion. God is not something we need proof for." Sometimes, this complaint sounds very silly, as if people were saying, "Why are you giving all those B-movies bad reviews? You should be reviewing my movie." But I'll concede that there is some basis to the complaint. When it comes to fundamentalists, point by point refutations are common. When it comes to "liberal" Christianity, it seems like dismissiveness is the norm. I personally try to avoid this. As an atheist, I have little right to define what kind of God other people believe in. For all I care, you could define God as the ceaseless creativity of the natural universe. I can't really refute that kind of God. The best I can do is criticize your communication skills, and then be on the look out for the equivocation fallacy.

I want to focus on one particular part of the complaint. Most people will say that God doesn't need proof. Apologetics is not very important for them. God is not a scientific matter. God is unfalsifiable. Can they explain why they believe this? But never mind the reasons. The theist gets to define God, and I'll go with that definition at least for a while. Let us presume that we have all agreed that God is unfalsifiable, and therefore unscientific. Let us also ignore, for the moment, my misgivings about the definitions of science, the philosophy of falsification, and unprovable gods. So we agree that "God exists" is an unfalsifiable claim. This implies that "God does not exist" is also an unfalsifiable claim. For how can a claim be scientific if its negation is not?

So if God is unfalsifiable, that means it is also impossible to confirm God's existence with scientific evidence. You cannot refer to religious experiences as a confirmation of God's involvement with humans. You cannot refer to Big Bang Theory as a confirmation of God's creation. You cannot refer to quantum mechanics as a confirmation of God-given free will. If any of these scientific discoveries give you the slightest bit of "It's just like Christianity told us all along!" feeling, that means your god is confirmable, and therefore falsifiable.

So we're back to the top. The two views I presented, each of which I commonly encounter on the internet, are incompatible. One says God is unfalsifiable. The other says God is confirmable by religious experiences. But you have to pick one: confirmable or unfalsifiable. Otherwise, you've got a contradiction on your hands. And this is before I've even started talking about the argument from religious experience. Is it any wonder that atheists tend to be dismissive when people don't take seriously the meaning of "unfalsifiable"?

Friday, July 25, 2008

Desecration done

PZ finally desecrated a cracker.

I was impressed! It was the historical context that did it. The desecration of crackers is not so much a hate crime as it is a witchcraft-like myth that was historically used as an excuse to kill Jews. Superstition: there's a reason we think it's bad!

I know I questioned the effectiveness of cracker desecration earlier, but given his goals, and given the fact that he already promised, I can't imagine a better way for it to go. I still think most Catholics are going to somehow rationalize this to fit whatever worldview. But now I feel more comfortable saying that such people are completely wrong.

Wednesday, July 23, 2008

Colored maze discussion

See the original puzzle

Recap: The basic idea of the game is that player 1 chases player 2 on a circular board. If player 1 catches player 2 within twenty rounds, player 1 wins.

I have a policy of giving free link love to any bloggers that post good solutions. This time, Hugo of thinktoomuch.net wins! (Hugo's blog, by the way, has become a new favorite of mine.) Here's his solution:
Call the middle "ring 0", the next "ring 1", the outer is "ring 4".

If player 2 is in ring N, player 1 wants to be in ring N-1, always moving to a place that is adjacent to player 2's position. Player 2 can race around and around in ring N, with player 1 chasing in ring N-1, only until it gets to the point where player 1 is in the N-1 region that is adjacent to 3 N regions. That forces player 2 to go to ring N+1.

To start, player 1 goes to ring 0, from there heading out to get adjacent to player 2. To finish, player 1 traps player 2 in ring 4, at the bottom.
Allow me to illustrate this solution:
As long as player 1 stays one ring closer to the center, player 2 will eventually be forced outwards. When player 1 is in the cyan region and player 2 in the corresponding blue region, player 2 will have no choice to move outwards. When player 2 is stuck in the outermost blue region, the game is over.

Hugo also said:
New question: what's the maximum number of moves that player 2 can survive? I believe it would have player 1 on ring 4 to begin with, and player 2 playing in a way that player 1 has to chase player 2 all the way around every ring. I've not counted, but I place my bets on player 2 if player 1 only gets 20 moves.
Here, I admit to making a "mistake" in writing this puzzle. I meant to give player 1 plenty of time, but in a lapse of judgment I limited it to 20 moves. Player 1 might not be able to win that quickly! But regardless of my original intention, it is still an interesting question. I am not sure of the answer, but here are my rambling thoughts on the matter. I welcome any proofs you can come up with.

We can put some upper bounds on the number of moves required:
  • 4 moves to get to ring 0.
  • 3 moves to force player 2 to ring 2.
  • 5 moves to force player 2 to ring 3.
  • 6 moves to force player 2 to ring 4.
  • 7 moves to trap player 2 at the bottom.
  • 1 move to win.
That's 26 moves total. But we should be able to reduce some of those numbers.

One way to reduce them is by saying that the first player can choose which direction to go around the rings. This would reduce the number of required moves to maybe 18 or less. However, there is a way for player 2 to choose the direction, if player 2 jumps to the next ring before being forced to. I found a 21-move path in which player 2 constantly forces the direction to be clockwise. That's enough for player 2 to win! To win this way, allow 4 moves for player 1 to reach the cyan region below, and then run along the red path for 16 moves.
However, this path only works if player 1 strictly follows the strategy of remaining adjacent to player 2 at all times. I suspect that player 1 can slightly modify his strategy and win.

This game turns out to be more complicated than I thought.

Sunday, July 20, 2008

Unfeeling reason

"Cold logic"
"Unfeeling reason"
Why is rationality so often associated with a lack of emotion?

I can think of several good reasons, actually. Rationalism deemphasizes emotion as a way of gaining or interpreting knowledge. If you use emotions to determine truth, they can easily lead you astray by biasing your judgments. For example, if you're angry at a person, you're more likely to think them guilty. If you're happy with someone, it becomes as easy to miss their flaws as it is to miss one's own. Rationality doesn't stop you from feeling emotions, but it stops you from using them to twist reality.

The end result: rationalism diminishes the role of emotion. I'd like to think that it only diminishes the bad parts of emotion, but people are not perfect, and emotions can be messy. It's only inevitable that we throw a little of the baby out with the bathwater.

Another reason that people might think rationality and emotion can't mix is because of the sort of people who espouse logic and reason.

Well, first there's me. I bet I sound like a killjoy all the time. This, I claim, is an illusion. Not that I'm secretly the touchy-feely type or anything. It's just that this here is a medium in which the only emotion that can reliably be conveyed is anger. Thus the need for emoticons. It's said that eyes are windows to the soul, so I suggest staring into that colon until you know me. :-0

And then there's everyone else. I am a bad judge of stereotypes, but I suspect that people see rationalists as arrogant. Uh, maybe so. But I don't think arrogance is inherent to rationalism. Why should rationalists be any more arrogant than anyone else? Is it because rationalists think logic makes everything certain? If so, then they're just plain wrong. Is it because they believe they can judge some claims to be better than others? Then what's everyone else, a hardcore postmodernist?

But of course, arrogance is an emotion too. Arrogance can twist a person's perception of reality just as much as any other emotion. That should have been a no-brainer; not every emotion is the feel-good kind. Sure, there's love, hope, and happiness, but there's also anger, shame, and arrogance. When it comes to discussions, debates, or arguments--all of which are common places to encounter rationalists--"high emotional content" means an abundance of the negative emotions, not the positive ones. This doesn't indicate a lack of regard for the opponent's feelings, it involves a purposeful manipulation of the opponent's feelings.

I see it as a win-win situation. By avoiding arrogance, I avoid a potential source of bias and show respect for others. So forgive me if I am a little unfeeling in other respects as well.

Wednesday, July 16, 2008

The Authoritarians reviewed

Way back, Blake Stacey recommended to me The Authoritarians, by Bob Altemeyer. It is a free online book about the psychology of the authoritarian personality. I get the impression that Blake Stacey is in the habit of recommending this book to everyone. Allow me to echo this recommendation to you, my readers. It is a short, easy, and fun read. Bob is rather casual can chatty. He never gets bogged down with numbers, and yet he is clear about how all his conclusions are supported by scientific data. And did I mention it's available free?

The Authoritarians is one of those books that tries to answer the question, "What the hell is wrong with people?" The Bush administration, the religious right, the Creationist movements... Personally, I'm a moderate, an independent, but I won't touch the Republican party because it has gone to hell. Bob Altemeyer, I suspect is in the same position. But while I might advance few pet theories as to why this is, all I have to defend them is my super-humble rhetoric. Altemeyer's claims are not pet theories, but scientific findings. They could easily have been falsified, but instead they are strongly supported by a variety of surveys and studies.

His explanation? There is a certain kind of personality that is well-correlated with all these problems. Altemeyer calls it Right-Wing Authoritarianism (RWA). First, I should clarify a few things. Authoritarianism does not refer to the authorities themselves, but the people who would obey those authorities. Also, "right-wing" is used in the sense of being lawful or proper, not in the sense of being political conservative. RWAs in the US tend to be very politically conservative, but those in soviet Russia would probably be socialists. (There is also such a thing as Left-Wing Authoritarianism but that is not covered by the book.) Right-Wing Authoritarians exhibit the following qualities: submission to the established authorities in society, aggression in the name of these authorities, and wanting to enforce conventionalism on the rest of society.

The study of authoritarianism famously traces back to the Milgram experiments. In these experiments, the subject is told to shock another person with increasing voltage as part of a learning and punishment study. Soon the other person (an actor) starts screaming, going unconscious, etc. Of course, the study isn't really about learning and punishment, but about how far people will go if an authority asks them to. Amazingly, ~60% would go through the entire experiment (though they certainly don't enjoy it). This shows how even the small amounts of authoritarianism in all of us can make us do crazy things.

RWA is measured through a 22 question survey that scores people from 20 to 180. People who score higher, the "high RWAs", are correlated with the following:
  • Being soft on the crimes of the authorities themselves.
  • Religious fundamentalism and evangelicalism (which, incidentally, are very well-correlated with each other)
  • Ethnocentrism (which is in turn correlated with prejudice)
  • Fear of a dangerous world.
  • Self-righteousness
  • Illogical thinking and compartmentalization
There's a lot more detailed discussion of these and more in the book. There is also a similar discussion of the authoritarian leader's personality, which also looks bad but in different ways.

Now, if you're like me, you're skeptical of the efficacy of any such survey. But it turns out that there is a very rigorous way to create a valid survey that involves testing many possible questions and measuring their correlations. He briefly mentioned a similar survey developed in the 1940s that was discredited because of its poor design. The new one is scientifically tested. You might ask, "How do we know that this is all related to authoritarianism as opposed to religious fundamentalism?" We know because the RWA scale correlates with the above qualities better than any fundamentalist scale does. Altemeyer deserves lots of skeptical points for carefully explaining all this.

The most interesting part might be where Altemeyer suggests solutions to the problem. According to him, it would probably be ineffective to argue with these people directly. Instead, we should work with high RWAs them towards common goals, since lets them see outside of their community--high RWAs tend to feel a lot of pressure to be "normal", so we just need to show them. We should increase the visibility minorities. And we should promote higher education, which tends to decrease people's RWA scores. He also says it would help if we reduced fear-mongering, or if we taught kids to question authorities, but he doesn't think either of these things will realistically happen.

Aside from critical thinking, one of the major topics of skepticism is understanding why people think the way they do. By that standard, this is a great book for skeptics. It gives plenty of insight into RWAs and what makes them tick.

Sunday, July 13, 2008

In real life...

I got the most amazing job as a math camp counselor. I help with supervision, recreation, and maybe even a little teaching. I am pretty excited.

Of course, this might make me really busy... or not. So I might slow the blog down for the next few weeks... or not. I actually tend to have a bunch of completed essays in my drafts bin...

Saturday, July 12, 2008

Stealing the Eucharist

If you haven't heard the news, here's a brief summary. Webster Cook, a student of the University of Central Florida takes a communion wafer in mass, but doesn't consume it. He claimed that he wanted to show it to a curious non-Catholic friend. Now, he is receiving death threats. Bill Donohue of the Catholic League, whose business is to be professionally offended on behalf of conservative Catholics, declares it "beyond hate crime", and calls for expulsion of the student. PZ Myers, major science blogger and atheist activist, expresses dismay at all the fuss over a "frackin' cracker." To cap off his post, he suggests that people go out and get some wafers for him, which he will treat with "heinous cracker abuse". Bill Donohue responds by directing attention to PZ. Now people are sending PZ death threats, and calling for PZ to be fired from his tenured position.

You got that?

First, allow me to consider the whole issue emotionally. As in, who has my sympathies. I am sympathetic for Webster Cook. He's, what, my age? He wasn't intentionally trying to piss anyone off or anything. The Catholics just seem springloaded to make him or anyone into a pariah. As for the Catholics, I have very little sympathy at all. I was Catholic too, of course. I've searched the back of my mind for any way I might have been offended were I still Catholic. I just can't find anything. Transubstantiation? Jesus will be fine. Witchcraft? That doesn't exist.* I think the offended Catholics are just being silly. He was, no doubt, not the first person to smuggle out a wafer, so it's just arbitrarily hateful. So maybe I just wasn't ever a good Catholic?

*Sigh... Yes, I am aware of Wiccans, but Wiccans don't care about communion wafers, and are probably nice people.

As for PZ, I have a mixed relationship as always. PZ is actually a really nice, softspoken guy in person. Even when the Intelligent Design folks made a dishonestly editted interview of him, the worst part they can show is when PZ compares religion to knitting. If you look to his blog, Pharyngula, it may seem really shrill, but I think that's just an internet persona. Everyone looks angry on the internet, and PZ just puts a little extra effort into it. It's a way of making things more interesting. In other words, he's mostly just talk. And on the internet, talk is cheap.

Of course, that doesn't excuse PZ. He hasn't done any heinous cracker abuse yet, but he did ask his minions to smuggle out crackers. That's really the part that worries me. PZ isn't nearly as bad as some of his minions. All these people are going to go out to churches everywhere on false pretenses, and they're going to steal the Eucharist? That sounds like a bad idea.

Now, allow me to consider the issue pragmatically. (The voice in the back of my head is saying, "Between pragmatism, idealism, rationalism, and emotionalism, you can justify whatever conclusion you already had." Well, too bad, voice in the back of my head, because I'm continuing anyway.) What will be the effect of PZ's cracker desecration? Will Catholics realize the error of their ways? Will they see how silly they're all acting? Uh, no. Not going to happen. Look, the whole atheist blogosphere is split over whether PZ is doing something wrong. Catholics will not hesitate a moment to take the side against PZ. Is it really "silly" for Catholics to get angry at PZ if they think PZ's goal is to make Catholics angry?

Supporters may think this event is making a clear point about something or other, but they forget how easy it is to read one's own biases into a story. Everyone thinks their previous view was confirmed by current news. That's just confirmation bias. People who think PZ's actions send a clear message about the silliness of rituals are being affected by confirmation bias. Catholics, too, will be affected by confirmation bias, and read whatever they want into PZ's actions.

But since I'm in pragmatic mode, I must also consider this: I have absolutely no power over PZ's actions. None at all. He will do what he wants when he wants to. Sitting here and complaining about it just isn't pragmatic.

So allow me to wonder out loud what PZ might do. He might, of course, do nothing: it was all a joke, you know. Or he might do something really vulgar (which seems to be what everyone expects). I thought maybe he'd just eat it, but someone pointed out the problem with eating stuff sent to you by mail. I hope he does something funny, to make light of the whole situation. Or something totally innocuous, to show people that there is little to be afraid of. Let's see how it plays out.

Thursday, July 10, 2008

Quote: Fish and nets

Michael Shermer (in Why People Believe Weird Things) used this quote that struck a chord with me. The quote comes from Sir Arther Stanley Eddington's The Philosophy of Physical Science.
Let us suppose that an ichthyologist is exploring the life of the ocean. He casts a net into the water and brings up a fishy assortment. Surveying his catch, he proceeds in the usual manner of a scientist to systematize what it reveals. He arrives at two generalizations:

(1) No sea-creature is less than two inches long.
(2) All sea-creatures have gills.

In applying this analogy, the catch stands for the body of knowledge which constitutes physical science, and the net for the sensory and intellectual equipment which we use in obtaining it. The casting of the net corresponds to observations.

An onlooker may object that the first generalization is wrong. "There are plenty of sea-creatures under two inches long, only your net is not adapted to catch them." The ichthyologist dismisses this objection contemptuously. "Anything uncatchable by my net is ipso facto outside the scope of ichthyological knowledge, and is not part of the kingdom of fishes which has been defined as the theme of ichthyological knowledge. In short, what my net can't catch isn't fish.
Shermer was using this quote to say something about instrumental bias in science, but it struck me as being more relevant to the demarcation problem. The demarcation problem is the question: "What is and isn't science?" If we take the metaphorical ichthyologist's perspective, what you can't measure isn't science. What isn't science isn't real.

This quote resonated with me for a moment, as I thought, "I'll have to reconsider my thoughts on science in light of this!" But when I thought it over, I realized that it only confirmed my previous ideas, which is always a disappointment.

What are these previous ideas I speak of? First, I think it's possible for there to be real things which are nonscientific. I just don't think such things are likely to have any relevance to our lives, or that it is possible to know about them. Second, I also think there are scientific things that can't be measured. That is, they're scientific in principle, but not in practice. Therefore, nowhere must I take the absurd ichthyologist's perspective.

Any reactions to the quote, perhaps opposite or completely unrelated to my own?

Monday, July 7, 2008

Colored maze game

Time for a little exercise in game theory! Yes, there is a branch of mathematics called game theory. If you ever wondered what mathematicians do for a living, well, some of them research game theory. This game, however,is simple enough that anyone can analyze it without training.

We have two players. Each player has a marker in one of the colored regions in the picture above. The second player chooses the initial positions of the markers. The players take turns, the first player going first. During each player's turn, the player may either move his marker into an adjacent region or choose to do nothing. If the first player ever moves his marker into the same region as the second player's marker, then the first player wins. If the first player doesn't win after twenty of his turns, the second player wins.

Which of the two players can always win? I do not require a proof, but you get extra points for showing reasoning.

Now, if I may digress a bit, have you ever heard of the four color theorem? The four color theorem states that if I have any group of regions like in the picture above, and I want to color each region such that no two adjacent regions are the same color, then I only need four different colors. Interesting, huh? I am told that the proof is highly nontrivial.

ETA: my thoughts on the solution here

Sunday, July 6, 2008

Sorting a bookshelf: the solution

See the original puzzle

I am disappointed in all you readers, because no one corrected me! I thought it would require five moves to complete this puzzle, but in fact you can do it in four. I know I was amazed.

To represent the solution, 1s will represent fiction, and 0s will represent nonfiction. Now, hopefully the spacing will work out…


Thursday, July 3, 2008

Derren Brown

I've contributed another post to BASS about Derren Brown, the English magician. I feel a little silly reproducing the whole essay here, so I'll just put the video here. Read the whole thing!

Wednesday, July 2, 2008

Home experiment: Spinning box

Here's a physics experiment that you can try yourself right now. It's fun, I promise.

First, you have to find a small rectangularly-shaped object. Nothing valuable or breakable. A box works fine. A book works too, but you may have to tape the book shut for best results. It is important that there are no square sides on the object. All sides must be rectangles!

Here's my 3-d model of the box (created with Mathematica). Your own box might differ slightly in its shape, but it should be more or less the same. What are those sticks, you ask? They're just imaginary lines I drew to mark the three principal axes. If you have an object like a cube or a sphere, one axis is as good as another. But for an object shaped like above, there are three special axes of rotation, called the principal axes.

Now, take the box and toss it up into the air. Give it some spin as you toss it. First, make it spin around the blue line, then the green line, and then the red line.* Observe any differences between the three. I will wait.


The first thing you should notice is that it's harder to spin the box around some axes than others. It should take the most work to spin it around the green line, and the least work to spin it around the blue line. This is because the green axis has the greatest moment of inertia. The blue axis has the smallest moment of inertia. The red axis is somewhere in-between.

The other thing you should observe is that when you try spinning around the red axis, the box spins in a really odd way. After you let go of the box, it will not simply spin around the red axis, but spin and flip around in unexpected ways. If you draw a big "M" on the box, sometimes it will flip around so that you see a "W".

Why does it do this? The reason is because the principal axes with the greatest and smallest moments of inertia are stable. That is, if you spin around these axes, the object will continue to spin in more or less the same direction, even if you didn't spin it in exactly the right way. However, the principal axis with the middle moment of inertia is unstable. If you didn't spin it in exactly the right way, or if air friction pushes the box just a little bit, it will start spinning in all sorts of weird directions.

It's sort of like carrying a handbag. It's easy to hang it over your arm, because that is a stable position. But it's difficult to balance it on your head because that is an unstable position. Stability and instability are important concepts if you want to think like a physicist.

As for why two of the principal axes are stable and the other is not, that is a difficult question with a very mathematical answer. It has to do with three equations called Euler's Equations.
They are a mathematical consequence of Newton's Laws. I know many of you are looking at that and thinking, "Those equations look so ridiculously complicated!" In this case, you are absolutely right--these equations are ridiculously complicated, even after you learn about differential equations. But even if we don't solve the equations completely, we can still make qualitative predictions. If you have a cubical or spherical object, its rotation will remain constant. If you have a weirdly shaped object like your box, its rotation is stable around the principal axes of smallest and largest moments of inertia, but unstable around the third principal axis. By testing those predictions, you've just done some science!

*For the colorblind: blue goes from upper-left to lower-right, green is vertical, and red goes from lower-left to upper-right.