In my Jesuit (read: Catholic) high school, my religion teacher (great guy) liked to use String Theory to think about God. String Theory is this horribly advanced physics theory that attempts to explain everything. While not proven, many say it's our best candidate theory so far. Among other things, String Theory states that our universe doesn't have just 4 dimensions (3 of space, 1 of time), but 11 dimensions. My teacher suggested that, like the strings in String Theory, God is hidden in extra dimensions.
My initial reaction was, "Why bring up String Theory?" Sure, maybe God is hidden in extra dimensions. I could have told them that before String Theory existed. Extra dimensions, while difficult to visualize, are actually a very simple mathematical concept. In three dimensions, you describe position with three numbers: <x,y,z>. For eleven dimensions, you simply give 8 more numbers, nothing to it.
It doesn't matter whether String Theory is true or not; you can posit extra dimensions just for God either way. Because you can posit extra dimensions either way, I think it's equally likely either way. If you think it's unlikely that God is in an extra 5th dimension, why should it be any more likely that he's in an extra 12th dimension? String Theory suggests the idea of extra dimensions beyond the physical world, but does not really support it.
But all of this is fine, because I realize it wasn't meant to be an argument for God. It's just food for thought. But I feel one problem remains: this idea is abusing science.
As far as I can tell, there are two possible answers to "Why bring up String Theory?"
The first possibility is to invoke science's authority. This is an abuse because scientific authority, contrary to popular opinion, does not derive from fancy words or difficult math. Scientific authority derives from empirical evidence and inductive reasoning. There is no such reasoning to actually connect String Theory to God's extra dimensions. Inserting the words "String Theory" into an idea gives a false appearance of authority. Besides, as far as theories go, they didn't even pick a very authoritative one.
The second possibility is that String Theory is a metaphor for understanding the concept. I am not necessarily against the use of metaphors. I like to analogize lots of things to physics myself (though it usually only helps the physicists understand). But there is just no point in drawing analogies to a theory so horribly complicated as String Theory. Analogizing to String Theory does not simplify things, but obfuscates them. What is the topology of God's extra dimension? Are the rest of us confined to some sort of 11-dimensional brane? Such a metaphor will only end up distorting String Theory, and obscuring its own philosophical flaws in pseudo-technical language. Also, if it's a metaphor, it should be explicitly a metaphor, so as not to mislead people.
What they're doing with String Theory is not too far off from how Deepak Chopra abuses Quantum Mechanics. When asked by Richard Dawkins, Chopra admits that Quantum Mechanics is simply a metaphor* for his theory of consciousness. But the rest of the time, he acts as if it is something more. He puts it all together in a confusing mess, doing violence to both quantum mechanics and psychology. The analogy with String Theory isn't quite as bad as Deepak Chopra's analogy, but it's only one step away.
My advice: If you want to talk about extra dimensions, leave talk of String Theory behind. String Theory doesn't actually support your ideas, nor does it elucidate them. Seriously, if you try bringing up String Theory to any normal person, you'll get lots of comments like, "I'll never understand it!" and never anything like, "Oh, so that's how extra dimensions work! It's just like in String Theory!"
*For those who watch the video, I should note that Chopra gets everything completely wrong. "Observer effect" is the only real science I heard in there, but, contrary to popular belief, it is not quantum mechanics. "Discontinuity", as far as I know, is not a term used in quantum mechanics, but rather, an ill-defined scientific-sounding notion Chopra made up. Also, Hillary Clinton is a follower? *shudder*
Thursday, January 31, 2008
Tuesday, January 29, 2008
2007 TU24 and the magnetosphere
Today, the asteroid called 2007 TU24 narrowly missed us. By "narrow," I mean about 85 earth radii--1.4 times the distance of the moon. Of course, there are some doomsayers who think this will somehow negatively affect us. They're wrong (duh). Bad Astronomy made an awesome debunking video.
The closest approach has already occurred, but the people at tu24.org don't seem to be letting up. They say they never thought it would hit the earth, and instead think it will cause magnetic disturbance. As it happens, the magnetosphere* is my area of study (mind you, undergraduate research only), and I declare bunk.
They claim that the asteroid traverses the magnetosphere. Well, this is difficult to confirm, since the magnetosphere is constantly changing shape. The magnetosphere extends roughly 15-25 earth radii from the earth, but there is also a very long tail that extends away from the sun. The asteroid just might be in the tail region, but I don't see them actually substantiating such a claim with anything other than this diagram they put together.
In any case, if it did traverse the magnetosphere, this would be of no consequence. Contrary to their claims, the asteroid is electrically neutral, like all large objects. If it had an overall negative charge, then all the surrounding positive ions in interplanetary space would very quickly be attracted to it until it no longer had a charge. So I just don't know how this rock could possibly have a noticeable effect on the magnetosphere. Furthermore, if it did have an effect, we already would have seen it. It doesn't take that long for waves to travel across the magnetosphere--maybe twenty minutes at most.
They throw around ideas like "magnetic reconnection", which is a real phenomenon. But guess what? It's a very common phenomenon that happens all the time even when there is no magnetic activity. Speaking of activity, there was a magnetic storm on November 20. This storm was not, and could not have been caused by a rock. Usually, storms are caused by solar flares and coronal mass ejections. These phenomena are far larger than Earth, and they really do have magnetic properties, since they're made of ionized gas. This gas has no overall electric charge; there are an equal number of positive and negative charges. And yet, do you remember anything happening on November 20? I didn't, and I study this stuff! I only know about it because I checked SpaceWeather.
Really, magnetic storms can have negative effects (see Wikipedia), which is why we need to study it. But mostly they just make pretty lights for the people in auroral regions. And these lights are caused by processes that are far less trivial than 2007 TU24.
*pronounced "mag (as in magnet)-KNEE-toe-sphere"
The closest approach has already occurred, but the people at tu24.org don't seem to be letting up. They say they never thought it would hit the earth, and instead think it will cause magnetic disturbance. As it happens, the magnetosphere* is my area of study (mind you, undergraduate research only), and I declare bunk.
They claim that the asteroid traverses the magnetosphere. Well, this is difficult to confirm, since the magnetosphere is constantly changing shape. The magnetosphere extends roughly 15-25 earth radii from the earth, but there is also a very long tail that extends away from the sun. The asteroid just might be in the tail region, but I don't see them actually substantiating such a claim with anything other than this diagram they put together.
In any case, if it did traverse the magnetosphere, this would be of no consequence. Contrary to their claims, the asteroid is electrically neutral, like all large objects. If it had an overall negative charge, then all the surrounding positive ions in interplanetary space would very quickly be attracted to it until it no longer had a charge. So I just don't know how this rock could possibly have a noticeable effect on the magnetosphere. Furthermore, if it did have an effect, we already would have seen it. It doesn't take that long for waves to travel across the magnetosphere--maybe twenty minutes at most.
They throw around ideas like "magnetic reconnection", which is a real phenomenon. But guess what? It's a very common phenomenon that happens all the time even when there is no magnetic activity. Speaking of activity, there was a magnetic storm on November 20. This storm was not, and could not have been caused by a rock. Usually, storms are caused by solar flares and coronal mass ejections. These phenomena are far larger than Earth, and they really do have magnetic properties, since they're made of ionized gas. This gas has no overall electric charge; there are an equal number of positive and negative charges. And yet, do you remember anything happening on November 20? I didn't, and I study this stuff! I only know about it because I checked SpaceWeather.
Really, magnetic storms can have negative effects (see Wikipedia), which is why we need to study it. But mostly they just make pretty lights for the people in auroral regions. And these lights are caused by processes that are far less trivial than 2007 TU24.
*pronounced "mag (as in magnet)-KNEE-toe-sphere"
Sunday, January 27, 2008
On grading curves
According to the powers that be, one of the lab classes I'm currently taking is graded on a curve. This means that a person's grade is determined by how well the class as a whole scores. Whatever the average score, whether it is high or low, it is assigned a B.
The lab notebook makes an odd suggestion that grading curves are justified because the laws of statistics are the "laws of common sense". It also suggests that the grading curve is an excellent example of an application of statistics. So let's analyze it!
The equation for a student's gpa* is as follows:
gpa = 3 + (x-m)/σ
Where x = the student's score
m = the average score of the entire class
σ = the standard deviation of the class's scores, a measure of how variable the scores are
Luckily, they gave us the mathematical tools to know exactly how accurate a grading curve is. If we have a class of 20 students, then the uncertainty of m is equal to σ/sqrt(20). That comes out to an uncertainty in gpa of about 0.22. That's almost a third of a letter grade!
If you're a student like me, the words "grading curve" inspire a nebulous fear--what will happen if the whole class is above average? Now, I can tell precisely how inaccurate my grade is. Thanks, statistics!
Another justification they used is that this how real life works. Maybe so, but I'm betting that real life has a sampling size larger than 20.
*gpa is the grade point average. A gpa of 4 is an A, a gpa of 3 is a B, and a gpa of 2 is a C.
The lab notebook makes an odd suggestion that grading curves are justified because the laws of statistics are the "laws of common sense". It also suggests that the grading curve is an excellent example of an application of statistics. So let's analyze it!
The equation for a student's gpa* is as follows:
gpa = 3 + (x-m)/σ
Where x = the student's score
m = the average score of the entire class
σ = the standard deviation of the class's scores, a measure of how variable the scores are
Luckily, they gave us the mathematical tools to know exactly how accurate a grading curve is. If we have a class of 20 students, then the uncertainty of m is equal to σ/sqrt(20). That comes out to an uncertainty in gpa of about 0.22. That's almost a third of a letter grade!
If you're a student like me, the words "grading curve" inspire a nebulous fear--what will happen if the whole class is above average? Now, I can tell precisely how inaccurate my grade is. Thanks, statistics!
Another justification they used is that this how real life works. Maybe so, but I'm betting that real life has a sampling size larger than 20.
*gpa is the grade point average. A gpa of 4 is an A, a gpa of 3 is a B, and a gpa of 2 is a C.
Friday, January 25, 2008
The infinite bag of billiards balls
Difficulty: 5 of 10
This is a classic puzzle that often provokes lively discussion among puzzling communities.
We start with an empty bag at 11:00. We put in 10 billiards balls, which are numbered 1 through 10. But then we take out the ball labeled #1. At 11:30, we add 10 more billiards balls, which are numbered 11 through 20, and remove the ball labeled #2. At 11:45, we add balls 21 through 30 and remove #3.
This process is repeated infinitely. At each step, the next ten billiards balls are put into the bag, and the lowest number in the bag is removed. There are an infinite number of steps before 12:00, since the time between each step decreases at each step.
Obviously this puzzle is meant to be abstract, as you cannot actually perform an infinite number of steps within an hour, nor can a bag actually hold that many billiards balls. But we can still ask a genuine mathematical question about the situation: what's left in the bag after 12:00?
Variation 1:
Instead of removing the lowest numbered ball in the bag at each step, we instead remove the highest numbered ball. So on step 1, we remove #10, on step 2, we remove #20, and so forth. What's left in the bag after 12:00?
Variation 2:
On the first step, we add only billiards balls labeled 1 through 9. Instead of adding #10, we just take #1 and paint an extra zero at the end. On the second step, we add numbers 11 through 19, and add an extra zero to the end of #2, resulting in #20. On the third step, we add numbers 21 through 29, and add an extra zero to the end of #3. This process is repeated infinitely before 12:00. What's left in the bag after 12:00?
Solution
This is a classic puzzle that often provokes lively discussion among puzzling communities.
We start with an empty bag at 11:00. We put in 10 billiards balls, which are numbered 1 through 10. But then we take out the ball labeled #1. At 11:30, we add 10 more billiards balls, which are numbered 11 through 20, and remove the ball labeled #2. At 11:45, we add balls 21 through 30 and remove #3.
This process is repeated infinitely. At each step, the next ten billiards balls are put into the bag, and the lowest number in the bag is removed. There are an infinite number of steps before 12:00, since the time between each step decreases at each step.
Obviously this puzzle is meant to be abstract, as you cannot actually perform an infinite number of steps within an hour, nor can a bag actually hold that many billiards balls. But we can still ask a genuine mathematical question about the situation: what's left in the bag after 12:00?
Variation 1:
Instead of removing the lowest numbered ball in the bag at each step, we instead remove the highest numbered ball. So on step 1, we remove #10, on step 2, we remove #20, and so forth. What's left in the bag after 12:00?
Variation 2:
On the first step, we add only billiards balls labeled 1 through 9. Instead of adding #10, we just take #1 and paint an extra zero at the end. On the second step, we add numbers 11 through 19, and add an extra zero to the end of #2, resulting in #20. On the third step, we add numbers 21 through 29, and add an extra zero to the end of #3. This process is repeated infinitely before 12:00. What's left in the bag after 12:00?
Solution
Wednesday, January 23, 2008
Proving negatives and burden of proof
The Skeptic's society has a weekly online newsletter called eSkeptic. A month ago, they had a great essay titled "You Can prove a Negative". It includes lots of things that I've tried to explain or was thinking of explaining in the future. All claims can be stated as negative claims. Absence of evidence is evidence of absence under certain circumstances. Inductive arguments do not imply their conclusions with certainty, but they still suffice as evidence. Inductive arguments are required to prove most positive claims as well as negative claims.
But I disagree on one point. Why do people think you can't prove a negative? Hales thinks that it's because of confirmation bias and disappointment in the uncertainty of induction. I think he missed an important reason: because it's true! Or at least partly true.
It's true that there is no fundamental difference between positive and negative claims. If we have a claim P, then there exists a negation of this claim which we might call Q. Q is equivalent to not-P (symbolized as ¬P or ~P) and P is equivalent to not-Q. P and Q are in a symmetrical relationship, and there is nothing in the logic to tell you that one claim is harder to prove than the other.
But in practice, this symmetry is often broken. In practice, one of these claims is what we call the null-hypothesis, and the other is not. The null-hypothesis states that there are no unknown processes at work. When we say "you can't prove a negative", the "negative" refers to the null-hypothesis. In practice, the null-hypothesis is not impossible to prove, but it is usually a little harder to prove.
For example, let's take the hypothesis that bigfoot exists. Let's assume that this hypothesis predicts approximately 1% chance of finding bigfoot behind any given tree. We look behind 300 trees. If the bigfoot hypothesis is true, then we have a 95% chance of finding him. If it's false, than we have a 0% chance of finding him. That means that if we don't find him, it's very unlikely that he exists. But if we do find him then that's some smoking-gun evidence for bigfoot (of course, I am making the spectacularly false assumption that our perceptions cannot be tricked). Either way, the evidence is fairly conclusive. But it would take hundreds of trees to prove the null-hypothesis, and only one to prove bigfoot (provided that we pick the right one). The null-hypothesis simply takes more work to prove.
Now, the reason I'm arguing about this asymmetry between "positive" and "negative" claims is not because I care about bigfoot or anything (seriously, bigfoot is boring). It's because the asymmetry is used as the basis for the concept of "burden of proof." Let's face it--proving stuff takes work. Proving the null-hypothesis takes more work than proving bigfoot. Therefore, the people who should be doing the work should be the bigfoot folks (known as cryptozoologists). They have the burden of proof.
The burden of proof concept is abused fairly often, I think because people detach it from its justifications. If you want to know when it's valid, you have to remember why it's valid!
But I disagree on one point. Why do people think you can't prove a negative? Hales thinks that it's because of confirmation bias and disappointment in the uncertainty of induction. I think he missed an important reason: because it's true! Or at least partly true.
It's true that there is no fundamental difference between positive and negative claims. If we have a claim P, then there exists a negation of this claim which we might call Q. Q is equivalent to not-P (symbolized as ¬P or ~P) and P is equivalent to not-Q. P and Q are in a symmetrical relationship, and there is nothing in the logic to tell you that one claim is harder to prove than the other.
But in practice, this symmetry is often broken. In practice, one of these claims is what we call the null-hypothesis, and the other is not. The null-hypothesis states that there are no unknown processes at work. When we say "you can't prove a negative", the "negative" refers to the null-hypothesis. In practice, the null-hypothesis is not impossible to prove, but it is usually a little harder to prove.
For example, let's take the hypothesis that bigfoot exists. Let's assume that this hypothesis predicts approximately 1% chance of finding bigfoot behind any given tree. We look behind 300 trees. If the bigfoot hypothesis is true, then we have a 95% chance of finding him. If it's false, than we have a 0% chance of finding him. That means that if we don't find him, it's very unlikely that he exists. But if we do find him then that's some smoking-gun evidence for bigfoot (of course, I am making the spectacularly false assumption that our perceptions cannot be tricked). Either way, the evidence is fairly conclusive. But it would take hundreds of trees to prove the null-hypothesis, and only one to prove bigfoot (provided that we pick the right one). The null-hypothesis simply takes more work to prove.
Now, the reason I'm arguing about this asymmetry between "positive" and "negative" claims is not because I care about bigfoot or anything (seriously, bigfoot is boring). It's because the asymmetry is used as the basis for the concept of "burden of proof." Let's face it--proving stuff takes work. Proving the null-hypothesis takes more work than proving bigfoot. Therefore, the people who should be doing the work should be the bigfoot folks (known as cryptozoologists). They have the burden of proof.
The burden of proof concept is abused fairly often, I think because people detach it from its justifications. If you want to know when it's valid, you have to remember why it's valid!
Monday, January 21, 2008
Uri Geller retracts psychic claims
Uri Geller was a famous psychic in the seventies known for bending spoons. James Randi famously debunked these psychic powers, as you can see in this excellent video. These days, Uri Geller is still around, doing TV shows and stuff.
From James Randi, we have some interesting news about Uri Geller. In an interview with Magische Welt, Geller admitted to not having supernatural powers.
But this feeling passes. People really do believe this stuff. James Randi says it best.
Anyways, I think it's good that Geller is retracting his claims of being psychic, provided that he stands by it. Maybe now he'll have to improve his act?
Update: I wasn't reading Randi's article carefully enough. Randi says that Geller has not stood by his answer. His interview with Magische Welt was in November 2007, and Geller has already claimed telepathic powers yet again in January 13th, 2008.
Update 2: Randi made a video about this story.
From James Randi, we have some interesting news about Uri Geller. In an interview with Magische Welt, Geller admitted to not having supernatural powers.
I’ll no longer say that I have supernatural powers. I am an entertainer. I want to do a good show. My entire character has changed.You know, sometimes I wonder if Randi is simply a bitter old man with a magician rivalry against Uri Geller. It's like a real life version of The Prestige (anyone here seen that movie?). Sure, Uri Geller somehow still manages with the same boring routine as he did decades ago, with the spoon-bending, key-bending, and remote-viewing. But he's an entertainer, and his whole act is about his character as a psychic. Nobody actually believes this stuff, right? It's like Disneyland--no one actually believes that hitchhiking ghosts will continue to haunt you outside of the haunted mansion!
But this feeling passes. People really do believe this stuff. James Randi says it best.
Try to remember these names, Mr. Geller: Andrija Puharich, Brian Inglis, Byron Janis, Charles Panati, Claiborne Pell, Colin Wilson, Edgar Bronfman, Edgar Mitchell, Eldon Byrd, Guy Lyon Playfair, Harold Puthoff, John Hasted, John Taylor, Jonathan Margolis, Jose Lopez Portillo, Maria Janis, Moshe Dayan, Russell Targ, Ted Bastin, Val Duncan, Wernher von Braun, Wilbur Franklin, William Cox, and Yascha Katz. These are just a couple dozen of the hundreds of people you lied to, people who put money into your pocket, wrote supportive books about you, validated your claims, brought you to the attention of prominent persons, or otherwise helped you because they believed you when you told them you were the real thing, and played your tricks on them! Now you’ve admitted that it was all just a big joke?Playing on people's suspension of disbelief is fine. But intentionally fooling people, including naive experts, separating them from their money, is just plain unethical. If Uri Geller were doing the former rather than the latter, then his response to Randi would properly be, "Don't be such a spoilsport! I'm just an entertainer." Instead, Geller is known for responding with frivolous lawsuits.
Anyways, I think it's good that Geller is retracting his claims of being psychic, provided that he stands by it. Maybe now he'll have to improve his act?
Update: I wasn't reading Randi's article carefully enough. Randi says that Geller has not stood by his answer. His interview with Magische Welt was in November 2007, and Geller has already claimed telepathic powers yet again in January 13th, 2008.
Update 2: Randi made a video about this story.
Sunday, January 20, 2008
Peer Reviewed Carnival of the Godless
The Carnival of the Godless is up at Tangled up in Blue Guy. They have taken a lesson from Answers in Genesis' new research journal. If they make it look like science, it must have the authority of science!
My entry, "How to recursively divide atheists", successfully passed this rigorous peer-review process. I credit my success to the use of such technical words as "recursive" and "satirical".
My entry, "How to recursively divide atheists", successfully passed this rigorous peer-review process. I credit my success to the use of such technical words as "recursive" and "satirical".
Saturday, January 19, 2008
The metaphysics of Relativity?
One of the things people like to ask about physics is, "What is the meaning of it all?" What does physics tell us about metaphysics--the ultimate reality behind all that is? Does Special Relativity support Moral Relativism? Does Quantum Mechanics provide a mechanism for consciousness or miracles? Does the Big Bang Theory prove God? No, no, and no.
In general, I feel the answer is that, no, physics does not tell us much about metaphysics. Furthermore, people who try to connect physics and metaphysics are often engaged in gross abuse of the science. Much more often, physics only helps us realize how much we don't know about metaphysics.
I've already tried to explain Special Relativity (Explained: 1, 2, 3), so I'm going to use it as an example to demonstrate my point.
First off, Relativity is not even related to Moral Relativism, or indeed any sort of subjectivist philosophy. They have nothing to do with each other. Yes, Relativity suggests that different observers can have different perceptions of time and space. But "observer" is a technical term that ultimately has no connection to humans, much less human ethical theory. Similarly, the details of time and space have little to do with ethics. If I say that time and space depend on your frame of reference, "frame of reference" is a technical term that depends on your velocity, not your point of view. People seem to think that Relativity tells us, "It all depends on your point of view," but the more accurate statement is, "It all depends on your direction and magnitude of motion." I guess that just doesn't have the same ring to it.
Another problem with the idea is that Special Relativity doesn't say everything is relative. Previous to Special Relativity, we used what we retrospectively call Galilean Relativity. In Galilean Relativity, the distance between two objects, and the time between two events would always remain the same, no matter your frame of reference. Time (Δt) and distance (Δx) are what we call "invariants". In Special Relativity, there is an invariant that combines space and time: what we call the "interval".* That means that though space and time are relative, space-time, taken as a whole, is not. Changing reference frames is analogous to rotating a keyboard (only you're actually rotating space-time). You may have changed the positions of the keys, but the shape of the keyboard stays the same. You may have changed space and time, but some things about space-time never change. For example, the speed of light always remains the same.
What Relativity does tell us is that our intuition of time and space can be incorrect. Our common experiences bias us towards thinking that time is absolute and independent of space, but that's not necessarily the case. Therefore, if you want to philosophize, you should be careful about your assumptions about time and space. If you want to talk about the cause of the universe, you should be careful with ideas like "before" and "after", since these concepts may or may not exist independently of the universe. Furthermore, in these matters, I think it is irrelevant whether Relativity is in fact true. Relativity is just a heads-up to philosophers to be careful with hidden assumptions. Ideally, philosophers would realize this without science's help, but whatever it takes.
*For the record, the equation for the interval is (ΔS)2 = (Δx)2 - (cΔt)2
In general, I feel the answer is that, no, physics does not tell us much about metaphysics. Furthermore, people who try to connect physics and metaphysics are often engaged in gross abuse of the science. Much more often, physics only helps us realize how much we don't know about metaphysics.
I've already tried to explain Special Relativity (Explained: 1, 2, 3), so I'm going to use it as an example to demonstrate my point.
First off, Relativity is not even related to Moral Relativism, or indeed any sort of subjectivist philosophy. They have nothing to do with each other. Yes, Relativity suggests that different observers can have different perceptions of time and space. But "observer" is a technical term that ultimately has no connection to humans, much less human ethical theory. Similarly, the details of time and space have little to do with ethics. If I say that time and space depend on your frame of reference, "frame of reference" is a technical term that depends on your velocity, not your point of view. People seem to think that Relativity tells us, "It all depends on your point of view," but the more accurate statement is, "It all depends on your direction and magnitude of motion." I guess that just doesn't have the same ring to it.
Another problem with the idea is that Special Relativity doesn't say everything is relative. Previous to Special Relativity, we used what we retrospectively call Galilean Relativity. In Galilean Relativity, the distance between two objects, and the time between two events would always remain the same, no matter your frame of reference. Time (Δt) and distance (Δx) are what we call "invariants". In Special Relativity, there is an invariant that combines space and time: what we call the "interval".* That means that though space and time are relative, space-time, taken as a whole, is not. Changing reference frames is analogous to rotating a keyboard (only you're actually rotating space-time). You may have changed the positions of the keys, but the shape of the keyboard stays the same. You may have changed space and time, but some things about space-time never change. For example, the speed of light always remains the same.
What Relativity does tell us is that our intuition of time and space can be incorrect. Our common experiences bias us towards thinking that time is absolute and independent of space, but that's not necessarily the case. Therefore, if you want to philosophize, you should be careful about your assumptions about time and space. If you want to talk about the cause of the universe, you should be careful with ideas like "before" and "after", since these concepts may or may not exist independently of the universe. Furthermore, in these matters, I think it is irrelevant whether Relativity is in fact true. Relativity is just a heads-up to philosophers to be careful with hidden assumptions. Ideally, philosophers would realize this without science's help, but whatever it takes.
*For the record, the equation for the interval is (ΔS)2 = (Δx)2 - (cΔt)2
Thursday, January 17, 2008
Ask a question!
Why's it so quiet? Does everyone agree with absolutely everything I say? I find that unlikely and undesirable.
So can I ask for comments? Let's start here. Use this thread to ask me any question! Or you can just say hi or something.
So can I ask for comments? Let's start here. Use this thread to ask me any question! Or you can just say hi or something.
Wednesday, January 16, 2008
How to recursively divide atheists
A satirical introduction to atheist divisions
We start with the divide between atheism and religion. Atheists think there is no god. People with religion disagree. Simple enough, right?
Well, things are really not so simple. See, there are two types of atheists. Most people like to divide atheists into "good" atheists and "bad" atheists. The problem with this is that people disagree on which is which! Nevertheless, it is clear that there is a real divide. To describe it objectively, one kind of atheist prioritizes being friendly, while the other side prioritizes being outspoken. The latter group is variously described as the "new atheists", the "militant atheists", the "atheist fundamentalists", the "angry atheists", the "outspoken atheists", or the "uppity atheists". The former group is mostly referred to as either the "friendly atheists" or the "appeaser atheists". Is it obvious who uses which labels?
The difference between these two groups has little to do with their opinion of god, and everything to do with their opinion of those who believe in god. How should we behave towards religious people? Should we slap them around the face and tell them they're delusional? Or should we hold hands, and sing? You must choose one, or so I'm told.
So now we have not two, but three sides in the debate. We could also split religious people in the same way, resulting in no less than four sides.
But wait, there's more! We can pick any of these sides, and further split it into two. For example, take the "friendly atheists". They agree on god, and they agree on how to behave towards religious people, but do they all agree on how to behave towards the "militant atheists"? There are those who rebuke the militant atheists, and those who accept them as partners in activism. Are those militant atheists popularizing the cause, or is their shrill tone alienating everyone?
As a second example, take the "outspoken atheists". They agree on god, and they agree on how to behave towards religious people, but do they all agree on how to behave towards the "appeaser atheists"? Are they putting friendly faces on the cause, or are they just appeasing the religious, much like Neville Chamberlain did with Hitler?
And so, there are not two, but four kinds of atheists.
But this is, so far, an oversimplification of the reality. We can further divide each of these kinds of atheists into two more, each of which can be further divided. For example, take the friendly atheists who rebuke the outspoken atheists. Do they also rebuke the friendly atheists who accept the outspoken atheists? Do they go on to rebuke those who accept those who accept the outspoken atheists? Do the friendly atheists who accept the outspoken atheists choose to accept those who reject the the outspoken atheists? Do they also accept those who reject those who reject the outspoken atheists? All of these questions are of utmost importance!
So as you can see, we can easily generate an infinite number of positions to choose from. You must choose one, or so I'm told. How can you not be satisfied by the infinite? It has every nuance that you could possibly want.
We start with the divide between atheism and religion. Atheists think there is no god. People with religion disagree. Simple enough, right?
Well, things are really not so simple. See, there are two types of atheists. Most people like to divide atheists into "good" atheists and "bad" atheists. The problem with this is that people disagree on which is which! Nevertheless, it is clear that there is a real divide. To describe it objectively, one kind of atheist prioritizes being friendly, while the other side prioritizes being outspoken. The latter group is variously described as the "new atheists", the "militant atheists", the "atheist fundamentalists", the "angry atheists", the "outspoken atheists", or the "uppity atheists". The former group is mostly referred to as either the "friendly atheists" or the "appeaser atheists". Is it obvious who uses which labels?
The difference between these two groups has little to do with their opinion of god, and everything to do with their opinion of those who believe in god. How should we behave towards religious people? Should we slap them around the face and tell them they're delusional? Or should we hold hands, and sing? You must choose one, or so I'm told.
So now we have not two, but three sides in the debate. We could also split religious people in the same way, resulting in no less than four sides.
But wait, there's more! We can pick any of these sides, and further split it into two. For example, take the "friendly atheists". They agree on god, and they agree on how to behave towards religious people, but do they all agree on how to behave towards the "militant atheists"? There are those who rebuke the militant atheists, and those who accept them as partners in activism. Are those militant atheists popularizing the cause, or is their shrill tone alienating everyone?
As a second example, take the "outspoken atheists". They agree on god, and they agree on how to behave towards religious people, but do they all agree on how to behave towards the "appeaser atheists"? Are they putting friendly faces on the cause, or are they just appeasing the religious, much like Neville Chamberlain did with Hitler?
And so, there are not two, but four kinds of atheists.
But this is, so far, an oversimplification of the reality. We can further divide each of these kinds of atheists into two more, each of which can be further divided. For example, take the friendly atheists who rebuke the outspoken atheists. Do they also rebuke the friendly atheists who accept the outspoken atheists? Do they go on to rebuke those who accept those who accept the outspoken atheists? Do the friendly atheists who accept the outspoken atheists choose to accept those who reject the the outspoken atheists? Do they also accept those who reject those who reject the outspoken atheists? All of these questions are of utmost importance!
So as you can see, we can easily generate an infinite number of positions to choose from. You must choose one, or so I'm told. How can you not be satisfied by the infinite? It has every nuance that you could possibly want.
Monday, January 14, 2008
Occam's Razor: Useful is better
See my previous post on Occam's Razor, which described the interpretation I see most often. This post describes my preferred interpretation (which may or may not be a common interpretation).
A scientific hypothesis is a way of explaining a phenomenon. But the purpose isn't just to answer the question "why?" A useful hypothesis makes predictions. Why does the sun rise every morning? Because the Earth rotates. The reason this answer is important is not because it tells us about ultimate "why"s. The reason that it's important is that it makes predictions. For example, we can predict an equatorial bulge. We can predict the height of a geosynchronous orbit.
There can be lots of hypotheses to explain any one phenomenon. The way we decide between them is that we compare the predictions they make. We find an experiment under which hypothesis A predicts X, and hypothesis B predicts Y. If we observe X, we prove A (provided that we didn't forget a hypothesis C that also predicts X).
So what happens when we have two hypotheses that always make the same predictions? This occurs occasionally in physics. For example, there is an alternative hypothesis to "The Earth rotates". Perhaps the entire universe revolves around us. Under General Relativity, you can consider a rotating reference frame by changing around a few laws. Though it's not obvious without studying General Relativity, this hypothesis makes the exact same predictions as the hypothesis that the Earth rotates. Therefore, we can never choose one of these hypotheses over the other.
So why is it that we say the Earth rotates, and not that the universe rotates around us? It is because of Occam's Razor. Occam's Razor states that given two hypotheses with identical predictions, we should use the one that's easier to use. Neither hypothesis is more true than the other, but one is definitely more useful. If we wanted to send a satellite into orbit, we must choose one of the hypotheses to make our calculations. The calculations are much simpler if we choose the hypothesis that the Earth rotates. Physics is complicated enough without our help. Note that the most "useful" hypothesis may depend on the situation. For example, I doubt that when you commute, you take into account that your destination is slowly rotating around the Earth.
All of this was based on the premise that the only purpose of explaining things was to make predictions. But I lied--this is not always the case. Sometimes, due to basic human curiosity, we really are interested in ultimate "why"s. What if you think our "ultimate purpose" hinges on a question? For example, perhaps you think that the universe rotating around us means our planet is special. Well, Occam's Razor does not necessarily apply in this case, since usefulness is not a concern. You are absolutely free to choose whichever makes you happiest. And whenever you need to make predictions, you can temporarily switch to the simpler hypothesis.
But this raises a question. If two hypotheses are indistinguishable, why should either of them make you happier than the other?
A scientific hypothesis is a way of explaining a phenomenon. But the purpose isn't just to answer the question "why?" A useful hypothesis makes predictions. Why does the sun rise every morning? Because the Earth rotates. The reason this answer is important is not because it tells us about ultimate "why"s. The reason that it's important is that it makes predictions. For example, we can predict an equatorial bulge. We can predict the height of a geosynchronous orbit.
There can be lots of hypotheses to explain any one phenomenon. The way we decide between them is that we compare the predictions they make. We find an experiment under which hypothesis A predicts X, and hypothesis B predicts Y. If we observe X, we prove A (provided that we didn't forget a hypothesis C that also predicts X).
So what happens when we have two hypotheses that always make the same predictions? This occurs occasionally in physics. For example, there is an alternative hypothesis to "The Earth rotates". Perhaps the entire universe revolves around us. Under General Relativity, you can consider a rotating reference frame by changing around a few laws. Though it's not obvious without studying General Relativity, this hypothesis makes the exact same predictions as the hypothesis that the Earth rotates. Therefore, we can never choose one of these hypotheses over the other.
So why is it that we say the Earth rotates, and not that the universe rotates around us? It is because of Occam's Razor. Occam's Razor states that given two hypotheses with identical predictions, we should use the one that's easier to use. Neither hypothesis is more true than the other, but one is definitely more useful. If we wanted to send a satellite into orbit, we must choose one of the hypotheses to make our calculations. The calculations are much simpler if we choose the hypothesis that the Earth rotates. Physics is complicated enough without our help. Note that the most "useful" hypothesis may depend on the situation. For example, I doubt that when you commute, you take into account that your destination is slowly rotating around the Earth.
All of this was based on the premise that the only purpose of explaining things was to make predictions. But I lied--this is not always the case. Sometimes, due to basic human curiosity, we really are interested in ultimate "why"s. What if you think our "ultimate purpose" hinges on a question? For example, perhaps you think that the universe rotating around us means our planet is special. Well, Occam's Razor does not necessarily apply in this case, since usefulness is not a concern. You are absolutely free to choose whichever makes you happiest. And whenever you need to make predictions, you can temporarily switch to the simpler hypothesis.
But this raises a question. If two hypotheses are indistinguishable, why should either of them make you happier than the other?
Saturday, January 12, 2008
I revisit church
I attended a large religious gathering hosted by the Inter-Varsity Christian Fellowship. My motivation for doing so was really just to accompany a friend, but I also think it a good topic for discussion. I mean, I'm practically doing the same thing as Hemant Mehta, only on a much smaller scale.
Of course, the difference between me and Hemant is that I'm an ex-Catholic, not an ex-Jainist. I've had previous experience with Catholic mass, not so long ago, in fact. I have never liked church. I found it extremely boring. This was exacerbated by my selective hearing, which cannot reliably parse boring stuff, especially when it is spoken in a large echoing church. I've never liked the music either. I am fully appreciative of the fact that most people like music, but I tend not to. When I grew older, I became slightly better at parsing the homilies (aka sermons), but this usually involved thinking, "That's not necessarily true..." and then losing track of the homily again. I was often bitter about how this ritual was endorsed by God.
I've since heard that non-Catholic services are much more interesting and lively. I'm fairly sure that I, personally, still wouldn't like it, given my dislike of music and of overly enthusiastic groups. Oh, and I guess the religion thing, too.
I am close friends with many of the Inter-Varsity members. I sat with them in the front row, center. The service was very similar to my previous experiences. The music, though not the same as in the past, was still not to my taste (it can't be helped, really). The preacher was a much better speaker than the ones in memory, and I was able to parse his speech. But I still essentially disagreed with the sermon (more on that below).
Among the differences was that at a few points in time, people spoke with their neighbors. Though this left me in embarrassed silence, I view this as a positive aspect overall. Contrast the Catholic mass, in which everyone only exchanges handshakes and says "peace be with you." In fact, I'd far prefer it if we just socialized the whole time instead of doing the religious stuff.
The topic of the sermon was doubt. It started out by mentioning the story about Mother Teresa's crisis of faith. This is a very contentious issue among atheists. Led by Christopher Hitchens, some think this means Mother Teresa "ceased to believe". On the flip side, I once asked emerging church pastor Mike Clawson (who hangs around friendlyatheist.com) what the deal was. He answered that it is "apophatic theology", the idea that people can continue to believe what has already been proven to them, even when there is a lack of immediate results. It is based on the idea that God does not always appear in the form that people expect.
I think Hitchens is mostly wrong. I'm more inclined to agree with Mike's view of the situation. I would still criticize apophatic theology for its implicit premise that the doubts are not correct... but I don't think this criticism isn't going anywhere.
So the sermon basically echoed Mike Clawson's apophatic theology. There was a... um... delightful story about how Elijah burned 50 prophets of Baal. He's running from his crimes, and needs help from God. God comes to him in an unexpected way, as a small whisper in the wind. Well, it's unexpected to Elijah, but it's exactly the way I would have expected. It sounds exactly as if Elijah is mistaking his own thoughts for God's. Of course, the preacher ignored my private thoughts on the matter. He went on to conclude that we should trust God, and be obedient to Him, "even if it doesn't make any sense." *sigh*
Now the part that I did enjoy was catching up with a few friends afterwards.
Of course, the difference between me and Hemant is that I'm an ex-Catholic, not an ex-Jainist. I've had previous experience with Catholic mass, not so long ago, in fact. I have never liked church. I found it extremely boring. This was exacerbated by my selective hearing, which cannot reliably parse boring stuff, especially when it is spoken in a large echoing church. I've never liked the music either. I am fully appreciative of the fact that most people like music, but I tend not to. When I grew older, I became slightly better at parsing the homilies (aka sermons), but this usually involved thinking, "That's not necessarily true..." and then losing track of the homily again. I was often bitter about how this ritual was endorsed by God.
I've since heard that non-Catholic services are much more interesting and lively. I'm fairly sure that I, personally, still wouldn't like it, given my dislike of music and of overly enthusiastic groups. Oh, and I guess the religion thing, too.
I am close friends with many of the Inter-Varsity members. I sat with them in the front row, center. The service was very similar to my previous experiences. The music, though not the same as in the past, was still not to my taste (it can't be helped, really). The preacher was a much better speaker than the ones in memory, and I was able to parse his speech. But I still essentially disagreed with the sermon (more on that below).
Among the differences was that at a few points in time, people spoke with their neighbors. Though this left me in embarrassed silence, I view this as a positive aspect overall. Contrast the Catholic mass, in which everyone only exchanges handshakes and says "peace be with you." In fact, I'd far prefer it if we just socialized the whole time instead of doing the religious stuff.
The topic of the sermon was doubt. It started out by mentioning the story about Mother Teresa's crisis of faith. This is a very contentious issue among atheists. Led by Christopher Hitchens, some think this means Mother Teresa "ceased to believe". On the flip side, I once asked emerging church pastor Mike Clawson (who hangs around friendlyatheist.com) what the deal was. He answered that it is "apophatic theology", the idea that people can continue to believe what has already been proven to them, even when there is a lack of immediate results. It is based on the idea that God does not always appear in the form that people expect.
I think Hitchens is mostly wrong. I'm more inclined to agree with Mike's view of the situation. I would still criticize apophatic theology for its implicit premise that the doubts are not correct... but I don't think this criticism isn't going anywhere.
So the sermon basically echoed Mike Clawson's apophatic theology. There was a... um... delightful story about how Elijah burned 50 prophets of Baal. He's running from his crimes, and needs help from God. God comes to him in an unexpected way, as a small whisper in the wind. Well, it's unexpected to Elijah, but it's exactly the way I would have expected. It sounds exactly as if Elijah is mistaking his own thoughts for God's. Of course, the preacher ignored my private thoughts on the matter. He went on to conclude that we should trust God, and be obedient to Him, "even if it doesn't make any sense." *sigh*
Now the part that I did enjoy was catching up with a few friends afterwards.
Friday, January 11, 2008
Logical consistency quiz
Check this link out.
Battleground God: a quiz that doesn't tell you if you're right, but does tell you if your beliefs are logically consistent. Logical contradictions are fun.
The Philosophers' Magazine has a bunch other interesting-looking games/quizzes.
via Friendly Atheist
Battleground God: a quiz that doesn't tell you if you're right, but does tell you if your beliefs are logically consistent. Logical contradictions are fun.
The Philosophers' Magazine has a bunch other interesting-looking games/quizzes.
via Friendly Atheist
Thursday, January 10, 2008
I attend a skeptical meeting
So I attended for the first time a meeting for the campus skeptical/secular/atheist group. I will be brief, because I don't care to detail my personal life on the internet, much less talk about other people's lives. Some members of the group are potentially reading this.
First impression: The members are... what's the opposite of down-to-earth? This is coming from a guy who talks to the internet about things that are utterly disconnected from real life. Retrospectively, Nica Lalli was down-to-earth. She would talk a lot about New York and the weather. These people, on the other hand...
I came wondering what exactly people would do at such a meeting, but apparently they have lots to do. They talk and talk and talk. About everything. From science to politics, and the nerdy to the irreverent. It's like the internet all over again.
It was also highly disorganized. If conversations were particles, I would describe the meeting as being in entropic equilibrium. This is probably the fault of the president, who has been perpetually absent for the last few months.
Anyways, I met some pretty cool and unique people. Freethinkers are so darn individualistic.
First impression: The members are... what's the opposite of down-to-earth? This is coming from a guy who talks to the internet about things that are utterly disconnected from real life. Retrospectively, Nica Lalli was down-to-earth. She would talk a lot about New York and the weather. These people, on the other hand...
I came wondering what exactly people would do at such a meeting, but apparently they have lots to do. They talk and talk and talk. About everything. From science to politics, and the nerdy to the irreverent. It's like the internet all over again.
It was also highly disorganized. If conversations were particles, I would describe the meeting as being in entropic equilibrium. This is probably the fault of the president, who has been perpetually absent for the last few months.
Anyways, I met some pretty cool and unique people. Freethinkers are so darn individualistic.
Tuesday, January 8, 2008
The Golden Compass movie review
Earlier, I wrote spoiler reviews of The Golden Compass and the rest of His Dark Materials. I expected to leave it at that, since I'm not really into movies. But long story short, I ended up seeing the movie. So I feel I should write a review.
So, overall, not so great. It's like the Harry Potter movies in that they're glossing over a very complicated storyline, inevitably resulting in quite a few plot holes that would be unexplained had you not read the book. Unlike the Harry Potter movies, most people have not read the books. You might gather that I didn't particularly like the Harry Potter movies, and you'd gather correctly. For example, there is a scene where Lord Asriel gets captured while in the North. The next time we see him, he's in a cabin trying to find a way between parallel universes. I don't remember the book well enough to be able to explain this discontinuity.
The whole thing felt a rushed. The scenes seemed to be tossed together in a random order, with little connection between them. It was difficult to keep track of the many characters. The anti-authority theme seemed tacked-on and disconnected from the actual plot. The worst of it was that there was no ending to the movie. Well, I expected this, since the book was the same way. The characters spent the last five minutes explaining what they were going to do, and then it ended. I'm not saying I can think of a better way to have done it, but the end result just isn't so good.
You will be further disappointed to hear that it is unlikely that they will actually make the sequel to this movie. The making of a sequel depended on the financial success of the first movie. This movie was not very successful. But then again, Hollywood seems awfully fond of making poor sequels, so you never know. I'm not going to lament the lack of a sequel when they make movies so poorly.
As for the anti-religious themes (since that was the focus of my previous reviews), there is not much. Well, the Magisterium is very clearly a fictional form of the Church--you can tell that just from the costumes. It comes off as a little anti-clerical, but this is nothing new in fiction. Seriously, there was about as much anti-clericalism in Happy Feet. This movie was not worth boycotting. Nor was it worth all the hype it got in the blogosphere.
So, overall, not so great. It's like the Harry Potter movies in that they're glossing over a very complicated storyline, inevitably resulting in quite a few plot holes that would be unexplained had you not read the book. Unlike the Harry Potter movies, most people have not read the books. You might gather that I didn't particularly like the Harry Potter movies, and you'd gather correctly. For example, there is a scene where Lord Asriel gets captured while in the North. The next time we see him, he's in a cabin trying to find a way between parallel universes. I don't remember the book well enough to be able to explain this discontinuity.
The whole thing felt a rushed. The scenes seemed to be tossed together in a random order, with little connection between them. It was difficult to keep track of the many characters. The anti-authority theme seemed tacked-on and disconnected from the actual plot. The worst of it was that there was no ending to the movie. Well, I expected this, since the book was the same way. The characters spent the last five minutes explaining what they were going to do, and then it ended. I'm not saying I can think of a better way to have done it, but the end result just isn't so good.
You will be further disappointed to hear that it is unlikely that they will actually make the sequel to this movie. The making of a sequel depended on the financial success of the first movie. This movie was not very successful. But then again, Hollywood seems awfully fond of making poor sequels, so you never know. I'm not going to lament the lack of a sequel when they make movies so poorly.
As for the anti-religious themes (since that was the focus of my previous reviews), there is not much. Well, the Magisterium is very clearly a fictional form of the Church--you can tell that just from the costumes. It comes off as a little anti-clerical, but this is nothing new in fiction. Seriously, there was about as much anti-clericalism in Happy Feet. This movie was not worth boycotting. Nor was it worth all the hype it got in the blogosphere.
Polarized glasses solution
See the puzzle first
Polarized lenses can come in all directions, not just vertical and horizontal. For example, you can rotate a vertical filter 45 degrees, and get a diagonally polarized lens. For the 3D glasses to work, it is not necessary that the two lenses be horizontally and vertically polarized. They could also both be diagonally polarized. The difference between these two cases is best demonstrated with some illustrations.
Click to see picture
In this drawing, I represented the polarized lenses with lines indicating the orientation of the polarization. The left side represents the case in which the lenses are horizontally and vertically polarized. The right side represents the case in which the lenses are diagonally polarized. The glasses on the bottom are the ones you're wearing, and the ones on top are the ones your neighbor is wearing.
So let's say you close your right eye. In the case on the left, you can see your neighbor's left eye (which is on your right). In the case on the right, you can see your neighbor's right eye. Based on my description in my puzzle, you can conclude that the glasses are diagonally polarized, despite my suggestions otherwise.
Polarized lenses can come in all directions, not just vertical and horizontal. For example, you can rotate a vertical filter 45 degrees, and get a diagonally polarized lens. For the 3D glasses to work, it is not necessary that the two lenses be horizontally and vertically polarized. They could also both be diagonally polarized. The difference between these two cases is best demonstrated with some illustrations.
Click to see picture
In this drawing, I represented the polarized lenses with lines indicating the orientation of the polarization. The left side represents the case in which the lenses are horizontally and vertically polarized. The right side represents the case in which the lenses are diagonally polarized. The glasses on the bottom are the ones you're wearing, and the ones on top are the ones your neighbor is wearing.
So let's say you close your right eye. In the case on the left, you can see your neighbor's left eye (which is on your right). In the case on the right, you can see your neighbor's right eye. Based on my description in my puzzle, you can conclude that the glasses are diagonally polarized, despite my suggestions otherwise.
Sunday, January 6, 2008
Occam's Razor
Occam's Razor is often considered to be one of the major tenets of skepticism. It has many forms and interpretations, ranging from "Keep it simple, stupid" to "Entities should not be multiplied beyond necessity". The problem is that Occam's Razor can be difficult to justify (depending on which interpretation you use).
The most common interpretation I see is that Occam's Razor is a rule of thumb that states, "The simplest explanation is the most likely one". This is useful against all kinds of conspiracy theories and pseudosciences. Which is a simpler explanation: physicists have to this date missed a fifth fundamental force that somehow acts only upon human brains, or that parapsychology studies occasionally have methodological flaws? Which is simpler: that our incompetent government succeeded in organizing a vast conspiracy to fabricate 9/11, or that our incompetent government failed to stop some terrorists?
But is it really true that the simplest explanation is most likely? It's not a logical contradiction to say otherwise. And what constitutes a "simple" explanation anyways?
One way to justify it is through empirical observation. We observe that simpler explanations are more likely to be successful than more complicated explanations. I'm not exactly sure how you would systematically test this fact, but in any case it's only a rule of thumb. On the other hand, I could point out various counterexamples. Confining myself to physics, I think Quantum Mechanics is not at all simple. Physicists are awfully fond of talking about how simple our fundamental laws are, but in the same breath they declare how counterintuitive Quantum Mechanics is. I don't think it can be both.
Or perhaps I not using the correct definition of "simple". Usually, in the context of Occam's razor, people define "simple" to mean involving the fewest entities ("entities" is not particularly well-defined). Furthermore, Occam's razor is not meant to trump empirical evidence. If there is evidence of many entities, we should posit these entities, but no more. Hence, "entities should not be multiplied beyond necessity". By this measure, Quantum Mechanics is definitely the simplest possible explanation of all the evidence. (An aside: The Many Worlds interpretation is sometimes said to violate Occam's Razor, since it has infinite parallel universes, but arguably, it only has one entity, the wavefunction of the multiverse.)
I think the empirical evidence suffices to justify this interpretation of Occam's Razor. Just keep in mind that it is only a rule of thumb, and it is known a posteriori, not a priori. Personally, I would be extremely careful to use Occam's Razor, and first try other kinds of arguments. Lastly, if you want to apply this to metaphysics, empirical evidence does not cover this region, and you will have to find other justification. As far as I can tell, there is no other justification, aside from the fact that simpler theories are more useful to humans. But the most "useful" theory isn't necessarily the true one, is it?
I wrote on a different interpretation of Occam's Razor here.
The most common interpretation I see is that Occam's Razor is a rule of thumb that states, "The simplest explanation is the most likely one". This is useful against all kinds of conspiracy theories and pseudosciences. Which is a simpler explanation: physicists have to this date missed a fifth fundamental force that somehow acts only upon human brains, or that parapsychology studies occasionally have methodological flaws? Which is simpler: that our incompetent government succeeded in organizing a vast conspiracy to fabricate 9/11, or that our incompetent government failed to stop some terrorists?
But is it really true that the simplest explanation is most likely? It's not a logical contradiction to say otherwise. And what constitutes a "simple" explanation anyways?
One way to justify it is through empirical observation. We observe that simpler explanations are more likely to be successful than more complicated explanations. I'm not exactly sure how you would systematically test this fact, but in any case it's only a rule of thumb. On the other hand, I could point out various counterexamples. Confining myself to physics, I think Quantum Mechanics is not at all simple. Physicists are awfully fond of talking about how simple our fundamental laws are, but in the same breath they declare how counterintuitive Quantum Mechanics is. I don't think it can be both.
Or perhaps I not using the correct definition of "simple". Usually, in the context of Occam's razor, people define "simple" to mean involving the fewest entities ("entities" is not particularly well-defined). Furthermore, Occam's razor is not meant to trump empirical evidence. If there is evidence of many entities, we should posit these entities, but no more. Hence, "entities should not be multiplied beyond necessity". By this measure, Quantum Mechanics is definitely the simplest possible explanation of all the evidence. (An aside: The Many Worlds interpretation is sometimes said to violate Occam's Razor, since it has infinite parallel universes, but arguably, it only has one entity, the wavefunction of the multiverse.)
I think the empirical evidence suffices to justify this interpretation of Occam's Razor. Just keep in mind that it is only a rule of thumb, and it is known a posteriori, not a priori. Personally, I would be extremely careful to use Occam's Razor, and first try other kinds of arguments. Lastly, if you want to apply this to metaphysics, empirical evidence does not cover this region, and you will have to find other justification. As far as I can tell, there is no other justification, aside from the fact that simpler theories are more useful to humans. But the most "useful" theory isn't necessarily the true one, is it?
I wrote on a different interpretation of Occam's Razor here.
Friday, January 4, 2008
Polarized glasses
Difficulty: 4 of 10
I've already said that I've written puzzles before. Here's one of the easier ones.
This one requires a bit of background on how 3D movies work. Two images are projected on the screen, each using a different polarization of light. You are given polarized glasses where each lens has a different polarization. Each eye sees one of the two images, creating the illusion of 3D. A vertically polarized lens filters out all horizontally polarized light. If you turn that lens 90 degrees, it becomes horizontally polarized, and will filter out all vertically polarized light. If you put a horizontally polarized lens on top of a vertically polarized lens, no light can come through.
Let's say you're watching a 3D movie. Everyone is wearing an identical pair of polarized glasses. You find that if you close your right eye and look at your neighbor, you can no longer see his left eye.
Wait, that's wrong! Are his glasses backwards?
What is the most likely explanation? [This is based on a true story, and nobody's glasses were backwards.]
Can't figure it out? See my explanation of the solution.
I've already said that I've written puzzles before. Here's one of the easier ones.
This one requires a bit of background on how 3D movies work. Two images are projected on the screen, each using a different polarization of light. You are given polarized glasses where each lens has a different polarization. Each eye sees one of the two images, creating the illusion of 3D. A vertically polarized lens filters out all horizontally polarized light. If you turn that lens 90 degrees, it becomes horizontally polarized, and will filter out all vertically polarized light. If you put a horizontally polarized lens on top of a vertically polarized lens, no light can come through.
Let's say you're watching a 3D movie. Everyone is wearing an identical pair of polarized glasses. You find that if you close your right eye and look at your neighbor, you can no longer see his left eye.
Wait, that's wrong! Are his glasses backwards?
What is the most likely explanation? [This is based on a true story, and nobody's glasses were backwards.]
Can't figure it out? See my explanation of the solution.
Thursday, January 3, 2008
Skeptic's Circle #77
Skeptic's Circle #77: The Overmedicalized Edition is up at WhiteCoat Underground. It's filled with great stuff.
Wednesday, January 2, 2008
"Visa God" silliness
A reader sent me this article from The Wall Street Journal.
If you ever wondered why so many skeptics are atheists, this one of the reasons why. Superstition and religion blend seamlessly into each other. How is the belief that prayer will lead to visas any different from the belief that you can see remote objects if you try real hard? Both are scientifically verifiable. You might say that modern theology is actually much more sophisticated than all that, and that it's just hiding in ivory towers, and I'd concede that. But I could have been fooled--on the surface it all looks the same.
Hoping to capitalize on all the activity, technical colleges sprouted up in the city's outskirts near Mr. Gopala Krishna's temple. Students started trickling by on their way home from school; many complained about their failed attempts to secure U.S. visas. That gave the priest an idea to sell the students on the deity by giving him a new persona, "Visa God." Mr. Gopala Krishna counseled the students in English, then told them to walk around the temple 11 times to get their wish. "I used to say, 'Go, this time you'll get it,'" he recalls.In brief: It's really hard to get a U.S. visa, applications are chosen through a random number generator, and now there's a popular temple somewhere in India where people pray to a Visa God. This is prayer in its silliest form. It's comparable to praying for rain.
If you ever wondered why so many skeptics are atheists, this one of the reasons why. Superstition and religion blend seamlessly into each other. How is the belief that prayer will lead to visas any different from the belief that you can see remote objects if you try real hard? Both are scientifically verifiable. You might say that modern theology is actually much more sophisticated than all that, and that it's just hiding in ivory towers, and I'd concede that. But I could have been fooled--on the surface it all looks the same.
Mr. Babu of the Indus Entrepreneurs says the appeal of the Visa God boils down to the following: "Even if you're not religious, you say, 'Why not? I can just go and spend a few minutes and get a visa,'" he says.This is a form of Pascal's wager (which basically says that you lose nothing by believing, and might lose everything if you don't believe). Mr. Babu offers an excellent reductio ad absurdum against Pascal's wager. If you accept Pascal's wager, why don't you start praying to win the lottery or something? He doesn't lose much, aside from time, energy, and dignity, and if he gets a visa as a result, it's all worth it, right?
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