Sunday, March 30, 2008

Carnivals

A blogging carnival is an aggregation of the best essays in the blogosphere on a particular topic from the past few weeks. Here are the most recent carnivals.

Skeptic's Circle

Carnival of the Godless

Humanist Symposium

Saturday, March 29, 2008

A bridge and a flashlight

Here's a classic puzzle that everyone should solve at some point in their life.

Four friends are traveling at night. They have a bus to catch in 17 minutes, but it's on the other side of a questionable-looking bridge. They don't think it could reliably hold more than two people at a time. They need light to cross the bridge, but they have only one flashlight between them. Amy takes 1 minute to cross the bridge, Brian takes 2 minutes, Cassie takes 5 minutes, and Drew takes 10. If two people cross the bridge simultaneously, they must walk at the rate of the slowest person.

How can they cross in 17 minutes?

See the solution

Thursday, March 27, 2008

Experiments with relativistic asteroids

I've been playing around with this game: Relativistic Asteroids. It's the classic game of Asteroids, but it uses relativistic physics!* Light speed is set extra low so that you can see the effects of relativity. It is so awesome. This is the sort of game I dream of making. Thought experiments come to life!

Here's some relativistic weirdness that you can observe and experiment with in this game:
1. Lorentz contraction: If you are in the unmoving reference frame, your ship will appear to shorten when it moves near light speed. If you are in the ship's reference frame (press 'f' to switch between your own reference frame and the unmoving reference frame), the asteroids will shorten when near light speed.
2. Time dilation: In sandbox mode, you can create flashing squares by clicking and dragging on the screen. The faster the squares are moving, the more slowly they flash.
3. Tilting the plane of simultaneity: This one is a bit harder to observe. You must be in sandbox mode, and place two stationary flashing squares. If you time it right, you can make the squares flash in sync with each other. But if you change your reference frame, they go out of sync.
4. Make time go backwards: This is the effect I discussed in a previous post. While you are in an accelerating reference frame, clocks far behind you can tick backwards. The difficulty in observing this is that you have to build a clock. You may either use the flashing of a square as a clock, or you can set flashing squares to collide and then watch them reverse-collide.
But the game is not quite perfect. Here are a few "bugs" that I encountered, that are due to the programming, not due to relativity.
1. In sandbox mode, set light speed to 2 cm/s (use keys 'e' and 'd'). Make sure you are in the ship's reference frame. Place two squares, one directly above the other. Carefully navigate around the two squares, making sure to keep them away from the edges. If you go around the asteroids, you'll find that the one that used to be above will slowly move around to the side. I'm fairly sure this is impossible under Special Relativity. I suspect the programmer has incorrectly implemented the second dimension somehow.
[ETA: I may have been mistaken about this point.  After all, the commutator of two boosts is a rotation *mutter mutter*.]
2. The paths of the bullets (which move at light speed) should be affected by an accelerating reference frame in the same way light is affected by gravity.
3. One of the major obstacles in making Asteroids truly relativistic is that the playing field has a donut topology. That is, if you or an asteroid go off the edge of the screen on one side, you'll appear on the other. The problem here is that Lorentz contraction shouldn't simply affect the asteroids, but should also affect the entire screen. If you're going really fast, you should find that the distance required to wrap around the screen is much shorter than it was before. The percentage of total screen space taken up by asteroids should remain constant.

But I understand the programmer ignoring this fact, because combining Relativity with a donut topology opens the door to much more weirdness than anyone's bargained for. All relativistic hell breaks loose. A donut topology implies a "special" reference frame in which the screen is largest. It makes for a more complicated twin paradox. You might see multiple copies of the same asteroid in different locations. Finally, you would be simultaneous with your future and past self.
Nitpicking aside, it's still so awesome.

Next, I want to see relativistic billiards! And then I want to see a game based on Maxwell's equations, where you guide a charged particle through an obstacle course by inducing electromagnetic fields. And then we can add some plasma physics to the mix too. Oh, the possibilities!

*For my introductory explanations of basic relativity concepts, refer to my earlier posts, Parts 0, 1, 2, and 3. (I think my writing has much improved since I've written those posts...)

Monday, March 24, 2008

Framing debates resurface

It's time for a glimpse into the crazy world of science/skeptical/atheist blogospheric politics!

Almost a year ago, a bunch of science and atheism blogs erupted in the so-called "framing" controversy. (For the interested, I offer two links as reference: Sunclipse, Matt Nisbet.) What is "framing"? Well, it has something to do with how we approach the media, and communicate with people. Beyond that, no one can say what it really means, because it seems to mean something different to every person. The whole debate has as many facets as it has commentators, if not more.

Stated simply, one side, the "framers," say that scientists should be cautious when talking to the media and the public. In particular, people like Richard Dawkins and PZ Myers are doing it all wrong because they're combining science and atheism. When the framers stated their case, they stepped right into the lurking controversy of how "friendly" atheists should be (on which I've commented before). The New Atheists listen to the framers' advice but only hear, "Lie down and shut up!" The New Atheists say they're only trying to speak truth, and there is no reason to hide the connection between science and atheism. The framers reply that it is impossible to speak truth without using one frame or another, so they might as well use a working frame. So on and so forth.

"New Atheism," I should note, is a term that was coined, or at least popularized by a Wired article. It is a term created by the critics, and eventually reluctantly accepted by the New Atheists themselves. Nowadays, the critics will occasionally remark, "Isn't it arrogant of them to claim that they are 'new' in any way?" Some people dislike Wired because of that.

Back to today. First, we have PZ Myers' incident with Expelled!, and then the aftermath. Creationists expel prominent evolutionary biologist PZ Myers from their documentary, purportedly about academic freedom, even though they had thanked him in the credits for his interview. Matthew Nisbet, a prominent, but ironically uncharismatic "framer", weighs in to say that this whole thing is bad for science. He says, I quote, "Lay low and let others do the talking," (emphasis his) as if to emulate his opponents' straw men. Uh oh. Let's sit back and watch the blogosphere explode.

Among the many recent comments on the matter, I'd like to highlight Sean Carroll's at Cosmic Variance. He makes a distinction between politicians and critics, which is way more intelligible than the framer/non-framer distinction. Sean, why are you so awesome?

Now it's time for my commentary (if my biases aren't already obvious from how I report the facts). Now, I haven't really committed to either side. I don't need to if I don't blog about it. The whole discussion is a mess, so I don't want to pick either side. But in terms of Sean's critic/politician distinction, I'm definitely a critic. I have little interest in "spinning" my writing in order to achieve goals--I'm only interested in capturing the truth. I recognize that politics is important, but I have no interest in doing any of it myself. I'd probably completely botch it. It's not as if I have any political influence anyways. And if I do have influence, it's not on people who are representative of the general public.

So as a critic, my disagreement with the New Atheist faction doesn't have anything to do with politics, or with how the ignorant masses will react. My disagreement is in the truth itself. I don't think science leads to atheism at all! Or, at least, not directly, in the manner supposed by many atheists. My opinions on the matter are a little more complicated. The relationship between science, skepticism, and atheism has been one of my intended topics from the beginning of this blog, but I haven't quite gotten around to it.

There is an obvious correlation. There's a 1998 statistic that says 72% of the members of the National Academy of Sciences express "personal disbelief" (viewable in Nature if you have a subscription, and American Atheists if you don't). Should we ignore this fact in hopes of it going away? I don't think we have a choice. Ignoring facts is a collective effort; stating them requires only one loud voice, of which we have plenty.

The much better alternative, at least for me, is to argue that this correlation does not imply causation. As far as arguments against religion go, evolution is one of the poorest. Not every scientist is an atheist. An unknown proportion of atheist scientists think that atheism and science go together, and the rest don't. Barring the worst sorts of fundamentalism, religion is not, or should not, be an obstacle to scientific practice. The only people who will make fun of you are people like PZ Myers, and then, only online. In person, he's a really nice guy.

Furthermore, there is no reason to fear atheism. Atheists are not evil. If atheism is a religion (which it's not), it's not an evil religion. They're an indication of religious freedom. This is the same religious freedom that allows people to be one particular denomination of Christianity rather than another.

See, telling the truth as I see it is so much easier. I would also argue that this would be the correct way to "frame" it. This frame would allay fears about godless science by confronting them, while simultaneously serving the "evil atheist agenda" (Number one on the evil agenda: civil rights!). But maybe I'm just a critic who thinks he knows better than the politicians.

Sunday, March 23, 2008

Happy Easter!

During my spring break, updates may be more sparse.

Friday, March 21, 2008

dRive game

Check out this game: "dRive"

It has one of those magic derivative machines that we always used to talk about in high school physics. Oh! The memories. I remember back when the curly S thing would meet the letter d, and they would magically disappear in a puff of chalk.

Uh, yeah, so this game was part of a flash game competition, and there are 20 other games on the same web page. It's probably not the best thing to look at if you have finals to study for. I also like the game with the "doggs".

In other news, you have heard PZ's wonderfully ironic story about Expelled! by now, haven't you? Everyone in the blogosphere is talking about it.

Thursday, March 20, 2008

What's with Postmodernism?

When I write, I usually pick topics that I understand. Well, there's one topic in skepticism that I feel I don't quite get. What's up with skepticism's relationship with postmodernism? If you pay attention to the conversation that's going on (and I've heard this both offline and online), you find that most skeptics think postmodernism is one of their enemies. Why?

First, a few links to demonstrate what I'm talking about (and yes, I do bookmark these for months at a time).
• The Sokal affair - Alan Sokal famously published a nonsense article ("Transgressing Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity") in a postmodern journal without the editors catching it. This experiment suggests that postmodernism is indistinguishable from nonsense.
• Rob Knop runs into a postmodernist who promptly dismisses Big Bang theory as being a cultural projection.
• A postmodernist critique of evolution - The association between postmodernism and Creationism speaks very badly of postmodernism.
• A retrospective look at postmodernism - Rob Helpychalk gives us a more historical perspective on postmodernism. He gives a pretty good answer to my question "What's with Postmodernism?" but I guess I'm still confused.
What is postmodernism? It's so hard to define, especially by me, since I'm young and have absolutely no historical perspective, and do not study humanities. Everything I say on this topic is without the slightest bit of authority. But basically, postmodernism is a set of ideas that has cut across all fields of study, and has greatly affected our culture. Sometimes, it's defined as the rejection of all meta-narratives (meaning that they do not accept that there is any "correct" overarching worldview). Every view is ultimately affected by the cultural context, and in the more extreme forms of postmodernism, every view is purely a construction of its cultural context. In the even more extreme forms, scientific facts are no exception. You can make reality into whatever you want it to be.

When skeptics think of postmodernism, they mostly seem to think about the more extreme forms that reject science. Well, we're used to focusing on the bad parts of everything, because that's where criticism helps most. But to condemn all of postmodernism based only on the extreme forms is to construct a strawman. I mean, the idea that there is no reality separate from our worldview is silly, but the less extreme forms aren't all bad. It's true that there is some degree of bias from our culture, and we have to keep the uncertainty of our own beliefs in mind.

From virtually every other source, I get a very different view of postmodernism. We live in the Postmodern era, which started maybe around WWII. So really, we're all postmodernists. Here's my extremely apocryphal impression of modernism and postmodernism:

Modernism: "Look back at all of history. Those guys don't know what they're talking about! We can do much better than that! Instead of looking at the past, we should be looking to the future. In the future, there will be no war, and we'll have flying cars!"

Postmodernism: "Look back at all of history. Those guys don't know what they're talking about! And based on the historical results, we find that modernism didn't know what it was talking about either. We're no different. Everything we've ever known has been molded by our culture. How can we know what is true anymore? How can anyone know?"

If postmodernism is a cultural era, then it follows that even the skeptical movement itself is a postmodern movement. After all, the skeptical movement is usually traced back to, what, the 70s? I could draw similarities--skepticism rejects all sorts of meta-narratives, and is forever mindful of uncertainties. But one of those meta-narratives they reject is postmodernism, so maybe skepticism is really a modernist backlash against postmodernism? Or maybe it's something else entirely?

So I'm confused. It's up to you, the internet, to set me straight!

Tuesday, March 18, 2008

The Trial of God

I was reading who-knows-what when I came across a provocative reference to a play and novel called The Trial of God by Elie Wiesel. It's hard to find a good summary of the story online, but here's one.

The story is based on one of Wiesel's real experiences during the Holocaust. He witnessed three Jews indicting God for all their suffering and giving him a trial. After several days, the verdict came: guilty. Afterwards, they prayed.

Wiesel's story takes place in 1649 in a Ukrainian village after a pogrom. I believe it is referring to the Khmelnytsky Uprising, one of the many, many Jewish tragedies throughout history. At the beginning, most of Jews have just been killed in the latest pogrom. Some traveling Jewish minstrels decide to put on a play in which they prosecute God. They say that God has no justification for the death and suffering he has caused. No one is willing to defend God until a stranger Sam appears. In the very end, Sam reveals that he is Satan. Satan commands a final pogrom before the trial can end.

My first impression is, "Wow, Jewish philosophy is mature!"

I've got an intriguing quote from an interview with Elie Wiesel on this story.
For a Jew to believe in God is good. For a Jew to protest against God is still good. But simply to ignore God--that is not good. Anger, yes. Protest, yes. Affirmation, yes. But indifference? No. You can be a Jew with God. You can be a Jew against God. But not without God.
Wiesel is making an argument about the Jewish identity. Now, I'm not from a Jewish tradition, so it isn't particularly important to me what the definition of Jewish is. But I imagine that many secular Jews would take offense to Wiesel's comment. In case my readers didn't know, it's fairly common for non-theists to identify as Jews, because in their minds, being Jewish is about their rich culture and heritage. Wiesel apparently disagrees, at least during this particular interview.

From an atheist perspective, Wiesel's comment is rather ironic.

There is a disturbingly common misconception that atheists are angry at God. No I'm not. "Indifferent" is a slightly more accurate description. I'm indifferent to God in the same sense that everyone else is indifferent to the invisible pink unicorn standing next to them--the invisible pink unicorn in which most of society believes, and on which society bases many decisions. And of course, being indifferent to God does not imply that we are indifferent to anything else. Atheists are more God-ignorers than God-haters (though they do occasionally accuse the hypothetical God of hypothetically being responsible for evil). Most people would be relieved to know we don't hate God.

And yet, Wiesel seems to have flipped this around. In his story, it's God's prosecutors who are portrayed positively, and the defender who is evil. And from Wiesel's comment, we know that he places non-theists at the bottom of the ladder. Funny how we end up below Satan, huh? At least we don't try to defend God's ways.

But I guess he got us there--if the problem of evil is our primary argument against God, why don't we just argue with God instead of denying his existence? Partly it's because no one wants to believe in a God that isn't benevolent, but also because the problem of evil is not the only argument against God's existence.

Just for fun, I'll link to an opposite perspective. It's the typical morality-requires-God refrain, if you care to know.

Monday, March 17, 2008

I noticed that I've been getting a few hits from some military forum, where they're talking about how The Advocate "exposed" Planned Parenthood's racism. It seems they only really linked to my post because I put up the video, not because they actually read what I wrote. They go on to use the same quote mine I had pointed out. I'm not going to bother registering for some obscure forum, so instead I'm venting here. Is there no justice on the internet?

Sunday, March 16, 2008

Intro to the Quantum Measurement Problem

See the previous page: The double slit experiment

Intro to Quantum Weirdness

As previously explained, when we shoot a photon through a double slit, it creates an interference pattern. This interference pattern is only possible if some wave-like behavior is occurring, and if the wave goes through both slits simultaneously. And yet, when we watch where the photon hits the screen behind the double slits, the photon will always land in exactly one spot. Thus a photon has some properties of a wave, and some properties of a particle. I should also add that the exact same experiment works works with any kind of particles, not just photons. All "particles" have both particle-like and wave-like properties.

You may have wondered why this experiment must provide such indirect evidence. If we only need to show that the photon goes through both slits at once, couldn't we just put a measuring device on both slits? Yes, we can. But when we do so, we find that the photon goes through exactly one slit every time. Furthermore, the interference pattern on the wall disappears! It seems that when we try to gather more observations, the results change!

This is why Quantum mechanics is said to be counterintuitive. It defies common sense. Most everything we previously knew no longer applies. So on and so forth. Every time Quantum Mechanics is explained to popular audiences, I hear the same shtick over and over about how Quantum Mechanics is so weird. Personally, I get kind of annoyed that it's repeated to no end. So instead, I'd like to emphasize that while Quantum Mechanics is weird, not everything is up for grabs. It doesn't quite jive with intuition, but it does follow rules that can be studied and understood.

The Copenhagen Interpretation

To explain the basic gist of these rules, I will first consider what is called the Copenhagen Interpretation. According to this interpretation, particles can be described by their wavefunctions. Wavefunctions behave like waves. They propagate around walls, and can go through multiple slits simultaneously. They can diffract and interfere with themselves.

Unlike normal waves, we cannot observe wavefunctions directly. If we try to observe a wavefunction, something called "wavefunction collapse" occurs. When a wavefunction collapses, it suddenly becomes like a particle. It appears in exactly one location. If the wavefunction was originally spread out over a large area, the particle will appear randomly somewhere within this area. The probability that it will appear at any given location is based on the magnitude of the wavefunction at that location.

Let's apply the Copenhagen interpretation to the double slit experiment. First, we shoot a photon through the slits. At first, the photon is a wavefunction, and thus can go through both slits at once. The wavefunction diffracts, and interferes with itself, creating an interference pattern. But then the photon suddenly hits the screen, and collapses its wavefunction in a random location. Because of the wavefunction's original interference pattern, the photon is more likely to appear in some places than others. If we repeat the experiment many times, we can get a good idea of how the original wavefunction was shaped. And that's how we show that there was indeed an interference pattern.

If we put detectors on the slits, then these detectors will collapse the photon's wave function. The photon will become particle-like as it goes through exactly one of the slits. On the other side of the slits, the photon will spread out its wavefunction again, but since it has gone through only one slit, there is no opportunity for an interference pattern to form. If we repeat the experiment many times, we would find no interference pattern.

Observations and Observers

According to the Copenhagen interpretation, wavefunction collapse occurs when a particle is observed. But what constitutes an observation, and who is observing it? In popular imagination, the observer must be a conscious human. But that's not necessarily true. If we performed the double slit experiment with detectors on the slits, no interference pattern appears. This remains true whether we actually look at the data from the detectors. So do the detectors themselves count as observers? Further complicating matters are the experiments of quantum erasure. I will not cover the details, but it's possible to set up detectors such that the information from the detectors is erased after it has been measured. If the information is erased carefully enough, the interference pattern reappears. So sometimes a detector counts as an observer, and sometimes it doesn't?

At this point, I should clear up a common misconception about wavefunction collapse. Some people confuse wavefunction collapse with observer effect. Observer effect occurs because in order to observe the particle, we must knock it with another particle. Because we're hitting the particle, we change it when we measure it. This is not the same as wavefunction collapse. There are actually other ways to observe a particle without knocking it with another particle. Wavefunction collapse can occur whether you physically touch the particle or not. I should also add that the observer in no way "decides" where the particle will appear. Wavefunction collapse is entirely random, and does not depend on the state of mind of the observer.

Back to the detectors. It turns out that it does not matter whether we consider the detectors to be observers or not. Further research has developed a mechanism called "quantum decoherence". In a complicated system, wavefunctions become "decoherent," and no recognizable interference patterns can occur. Any such system will act like an observer and appear to be able to collapse wavefunctions. This is the idea behind the Many Worlds interpretation, an alternative to the Copenhagen interpretation. According to this interpretation, wavefunctions never actually collapse, but only appear to collapse through the mechanism of decoherence. The Many Worlds interpretation implies that our universe's wavefunction is equal to the sum of many non-interacting parallel worlds. In other words, all quantum possibilities are realities in a parallel universe. That may seem like a lot to swallow, but the advantage of the Many Worlds interpretation is that there are no awkward distinctions between observers and non-observers.

There are also other, less popular interpretations to quantum mechanics. Some interpretations say that the wavefunction is not real, but is a representation of what we know about a particle. I understand the philosophical appeal of such interpretations, but in practice they require other nonintuitive rules, and generally just make things harder. Note that the scientific results of every interpretation must agree with the Copenhagen and Many Worlds interpretations, otherwise we would quickly disprove one interpretation or the other.

The end. Questions? Corrections?
After this post, I think I will take a short break from quantum mechanics.

Friday, March 14, 2008

Talk like a physicist!

Today is Talk like a Physicist Day! It coincides with Pi Day.

Many people seem to be interpreting this in different ways. From my perspective, I always talk like a physicist, by definition, at least insofar as I'm a physicist. I coauthored a paper once, so I think that qualifies me! So what is the point of setting aside a special day to talk like I always do?

Well, it must be so I can get all of you to talk like physicists too!

Here's some physicist-speak that deserves to be normal-speak:

Negligible - This word describes something so small that we can easily neglect it without affecting our calculations. In fact, we should neglect it, in order to simplify the calculations. Example: "Walking to the trash can takes a negligible amount of time, so stop littering!"

First-order approximation - This is the best rough estimate we can get of something by only considering the biggest numbers in our calculations. If we look more closely at the details, it becomes a second-order approximation. Example: "To a first-order approximation, I like all music."

Non-trivial - This describes a problem that is so complicated that the first-order approximation is wildly inaccurate, and the details are not negligible at all. Example: "Figuring out what he wants for his birthday is a non-trivial problem."

There's probably more that I'm not thinking of, but those are the most important ones. Did you expect me to say things like "muon", "Fourier transforms", or "wavefunction collapse"? Don't be ridiculous! That's not at all how a physicist normally speaks! Except perhaps when they speak to each other. ;)

Update: See Uncertain Principles and the comment discussion for a more complete list! How could I have forgotten "orthogonal"?

Wednesday, March 12, 2008

Guess the meaning

What word or phrase is suggested by this photo? Click for a bigger version.

Monday, March 10, 2008

Probabilistic ethics

So, I was looking at these online games from The Philosophy Magazine. In particular, I want to discuss the game "Taboo". They ask you some questions about the morality of things that are taboo. You can be assured that involves things like eating cats, incest, and so forth. The basic idea is that people usually don't actually think about these things rationally. They just have an emotional reaction to the situation, and then they come up with some after-the-fact rationalization for the judgment. Afterwards, they often claim they had been using that reasoning all along.

So here's my rationalization. Of course, I'm going to claim that I was thinking about this particular line of reasoning all along. ;-)

I claimed that an action cannot be wrong if "it is entirely private and no-one, not even the person doing the act, is harmed by it at all." Later, it gives some situations that sound bad, but in which no one was harmed, not even emotionally. Well, I should have qualified my previous answer on the quiz, but it was difficult to do when the only choices are yes and no. An act cannot be wrong if there is no possibility of harming anyone.

To elaborate, consider a hypothetical situation. Let's say there is a lottery. Like all lotteries, the odds are not in your favor. Let's also assume that the lottery does not donate a few pennies to the education system like real lotteries do. All profits and losses go directly to Al Qaeda (or you can insert some other unequivocally evil cause here). Lastly, assume that your participation does not affect anyone else's chance of winning.

Obviously, participation in this lottery is wrong. But what if you ignore this fact and play anyway? What if you beat the one to a billion odds, and win, thus taking funds directly from Al Qaeda? Does the outcome make your previous action ethically correct?

I would argue no. The right/wrongness of a particular decision should not be determined by the outcome, but by all the possible outcomes and their respective probabilities. These probabilities are determined by the decider's knowledge (or by what the decider should know). The whole purpose of labeling past actions right or wrong is to better choose between future actions. So the label should not depend on the outcome of that particular situation, but on the possible outcomes of a similar future situation. So even though you won the lottery, your participation was wrong because you would probably not win if you participated again.

This is why most traffic rules are illegal to break, even when no one actually gets hurt.

Of course, such an ethical model would never work out in fiction. Think about all those heroes who take stupid risks, but are saved by some lucky coincidence. Would they be heroes in real life?

Other implications I like: Ethicists should study probability theory? Mathematicians are naturally ethical?

I leave it as an exercise to the reader to imagine how this relates to taboo.

So... that was easy to rationalize. For my encore, I will prove black is white so you no longer have to worry about those pesky zebra crossings.

Saturday, March 8, 2008

Quote: On prayer

To seek to win peace through others, as priests or sacrificers, is the same as if a stone were thrown into deep water, and now people, praying and imploring and folding their hands, came and knelt down all around saying, "Rise, O dear stone! Come to the surface O dear stone! But the stone remains at the bottom.
--The Buddha

Thursday, March 6, 2008

Impersonal science writing

I've got my first single-authored science paper in the review process right now. It is awesome probably. Guess what it's about. Ok, ok, I'll give it away... partly. It's about magnetospheric waves. But that's not what I'm going to talk about.

One of the revisions that they asked for was to remove all first-person mentions from the paper. I disagree with this idea. I'm not angry at the reviewers or anything. I suspect they're just students who are following guidelines, or doing what their past teachers have taught them. In truth, I didn't even hesitate to follow through with the changes, because I don't really care. But I'll put on my internet-angry face just for flavor. >:-( *wink*

So there's this idea that in science writing, you never use the first person. The first person is the use of pronouns like "I" or "we". The second person is "you". And the third person is "he", "she", "the experimenter" or "the present author", etc. The reason you're supposed to avoid the first-person is to make science look more objective, and to place less emphasis on the people doing science.

I disagree because, for one thing, it only creates the illusion of objectivity. Merely changing around the sentence structure of your paper cannot actually change the degree of objectivity of the research. Avoiding the first person does not actually make the research any more objective, it only makes it appear objective. And how objective is the research, exactly? The research was, after all, performed by a person or persons. Should we be trying to make the research look as objective as possible, or as objective as it really is? Trying to make a study look more objective than it really is just smacks of subjectivity.

On the other hand, I understand wanting to place less emphasis on the people. When you read a paper, you don't particularly care which scientists wrote it, nor which students did the grunt work. The study should be replicable, meaning that any other scientist can try the same experiment and get the same results. If other scientists can't replicate the work, its conclusions are called into question. Furthermore, prescriptive rules are entirely appropriate for technical writing. A uniform writing style makes for clearer communication. Scientists basically deal with information, so clear communication is essential. Individualistic styles, though flavorful, might be harmful to clear communication.

But what is the alternative to using the first person? There are two major alternatives. One is to use the third person, and the other is to use the passive voice.

In the third person, I would refer to myself as "the researcher", "the programmer", "the present writer" or something along those lines. The present blogger thinks that's pretty awkward. And is it really any better than the first person? I'm still mentioning that there are *gasp* people involved in my scientific research. So how exactly does this make it more objective, and how does it deemphasize the people involved? Well, it's true that "he" sounds more objective than "I", but this is, again, mostly an illusion. And I suppose this makes it easier to conceive of a replication of the study, since you only need to replace "the researcher" with a researcher of your own. Still, using the third person just sounds weird.

The other alternative is the passive voice. In the active voice, I would say, "I analyzed the data," "You do not amuse us," or "This researcher dislikes the third person." In the passive voice, I would say, "The data was analyzed by me," "We are not amused by you," or "The third person is disliked by this researcher." The basic idea is that the thing that is [verb]ed becomes the subject of the sentence. The advantage of the passive voice is that you can omit any mention of who or what is doing the [verb]ing. I can say, "The data was analyzed," "We are not amused," or "The third person is disliked." So this is the primary way to avoid the first person.

The problem is that the passive voice is sometimes very awkward, and some people are adamantly opposed to it. Some crazy people even think the passive voice should never be used. Orwell once said: "The passive voice is wherever possible used in preference to the active," apparently expressing extreme disapproval of the same passive voice he had just used. (An aside: someone way back asked me what I thought of Orwell's essay on language, so there you go.) I don't think it's a deadly sin to use the passive voice, but using it all the time is just as bad as using the active voice all the time. If you're forced to always use the passive voice, occasionally you'll get sentences that are suboptimal. Case in point, convert one of my earlier sentences into the passive voice: "Ok, ok, it will be given away (by me)... partly."

So, you see, writers are stuck between a rock and a hard place. Using "I" doesn't give us that oh-so-important illusion of objectivity. Using "the researcher" is awkward and contrived. Using the passive voice is aesthetically displeasing, and widely disapproved of. You can't satisfy everyone.

I prefer using the first person, because creating an illusion of objectivity seems relatively unimportant. I think nowadays, most science journals no longer require avoiding first person. But it seems that this particular undergraduate science journal does. Of course, even I flinch at the mention of "I" in formal writing, so I prefer "we" instead. Of course, that doesn't make much sense in a single-authored paper. We guess we're using the royal "we"? In the end, I simply switched to the passive voice. It's not a big deal, really.

Tuesday, March 4, 2008

Hypercubes and hypercube nets

Question: What is a hypercube? What are hypercube nets?

To understand the answer, we must first look at cubes and cube nets.

Cube nets

You all know what a cube is, right? In case you are in doubt, I give you the cube.
Ok, so I admit that I actually gave you two cubes. So I like drawing cubes. But if you think about it, I didn't really give you any cubes (sorry, no refunds). A cube is a 3-dimensional object, and all I gave you was a 2-dimensional image. I work with what I have.

The green image is how you would normally draw a cube. The blue image is a little more unusual. In the blue image, the outer square represents the face that is closest to you, while the inner square represents the face furthest from you (as we all know, things look smaller when further away). In both images, I drew all edges, even the ones behind the cube that you wouldn't normally see.

Let's say we want to build a cube by folding some paper. We need one square for each of the six faces of the cube. Now, we could cut out six little squares, and paste them all together. But then, we'd sometimes be cutting squares apart only to glue them back together in the same place. So what we should do is leave some of the squares connected together. Like so!

If it's unclear how this can be folded into a cube, I suggest cutting out this shape yourself, and folding along the dotted lines.

The shape I just showed you is called a "net." A cube net is basically a cube that has been unfolded into a bunch of connected squares. (See MathWorld for a more technical definition.) There are other ways to unfold a cube to form a net. How many ways? Eleven. (Obviously?)

The Hypercube

A hypercube is a generalization of the cube. A cube is 3-dimensional. A n-hypercube is n-dimensional. That means a 3-hypercube is, well, a cube. A 2-hypercube is a square. A 1-hypercube is a line segment. A 0-hypercube is a point. You can also have higher-dimensional hypercubes, such as a 4-hypercube, a 5-hypercube, or a 100-hypercube. Usually when people just say "hypercube", they refer exclusively to the 4-hypercube, which is our focus. The 4-hypercube is also sometimes called the Tesseract.

So I give you the hypercube.

Well, it's not really a hypercube. Again, I can only show a 2-dimensional image. In this case, even if you were to imagine it in 3-d, it would still just be a 3-dimensional image of a 4-dimensional object. The hypercube is hard to draw! I often try to draw hypercubes in the margins of my notebooks when I should be listening to lectures (true story!).

The hypercube image is directly analogous to the blue image of the regular cube at the top. To create a cube, you take the outer, larger square and connect it to the inner, smaller square. To create a hypercube, you take the outer, larger cube, and connect it to the inner, smaller cube. These two cubes are not actually different sizes. The smaller cube only appears smaller because it's in the "back" of the hypercube. Remember how I said that objects further away appear smaller?

I put "back" in quotes because that's not really what it is. It's really in a new direction that we have no word for. See, in 2 dimensions, there are two different directions. One direction is North/South. Another direction is East/West. If we enter the 3rd dimension, we get a third direction: up/down. If we enter the 4th dimension, we get a fourth direction. That's what it means to have an extra dimension.

Hypercube nets

Just like 3-dimensional polyhedrons, 4-dimensional shapes also have nets. To make a net from a 3-d object, we must unfold it and flatten it into 2-d. To make a net from a 4-d object, we must unfold and "flatten" into 3-d. That's right--hypercube nets are 3-d objects! A cube is made up of 6 faces, each one a square. A hypercube is made of 8 "hyperfaces," each one a cube. Finding all 8 in the above image is a difficult exercise.

It's really hard to visualize how exactly you can fold cubes into each other, but thankfully, we have the internet for that. I strongly recommend this site, which shows the folding of a cube and hypercube. Study it carefully.

By now, your mind might be spinning, but there is one more layer of complexity to this. The video linked above only showed one hypercube net. But there are many more, just as there are many nets for the cube. How many more are there? This is a very difficult question, not one I could have figured out myself. The answer, it turns out, is 261. The explanation of how to get there is shown here. Summary of the solution: 50% inspiration, 50% perspiration, 26100% awesomeness.

Concluding remarks

The reason I decided to write this up was primarily because I found out that by merely mentioning "hypercube nets," I became the first hit on Google--not that many people are searching for hypercube nets. My above explanation is very brief, and I just know many people will react with, "Wait, what?"

If you don't understand, I recommend doing some googling, since there are just a ton of people on the internet who have tried to explain the hypercube, with all sorts of approaches. I particularly like this site, which includes excellent videos. You may also drop me a question, though I do request that you be specific. (If you just say, "I don't understand!" I won't know where to begin.)

Sunday, March 2, 2008

Carnival of the Godless #86

The Carnival of the Godless #86 is up at Life Before Death. Go read it!

My submission was "The Mountain Theologians."

This little meme has been making the rounds in the blogosphere. It's Googleoetry! I basically look at all the Google search terms that have landed people on my blog, and then organize them into a poem. Here's one example on Greta Christina's blog (slightly NSFW language). Of course, Science after Sunclipse has been doing this since way back, but now I get to jump on the bandwagon!

Now, my blog is relatively small, so I have less search terms to choose from (none of which are dirty). Also, I don't know the first thing about poetry, nor do I even like poetry. Mostly, it's just fun to look through search terms to see what odd things people are searching for. So I guess this will be more fun for me than for anyone else. Well, here goes my random little poem.