Precession of the Earth

The earth rotates. It has an angular momentum in the direction from the south pole to the north pole. This axis of rotation, as I explained earlier, is tilted slightly, and this is what causes seasons. The axis of rotation, in fact, does not always tilt in the same direction. This direction moves slowly around in a circle every 25,800 years. This circular motion is called precession. First, I'll explain why it precesses, and then the implications of precession.

Why does the Earth precess?

First, see precession explained

There are two components of precession. First, there's some angular momentum, and second, there's some torque. The angular momentum of the earth is obvious: it spins, about once a day. The source of the torque is less obvious.

It comes from the Earth's equatorial bulge. The bulge is caused by the fact that at the equator, the surface of the earth moves much faster. When an object rotates quickly, what we call the centrifugal force pulls outward on the object. The earth doesn't rotate quickly enough to fling people out into space, but it does weaken gravity very slightly (by less than 1%). This causes the ground near the equator to be further from the center of the earth, making the equatorial bulge.

Because of the equatorial bulge, there is more mass on the earth's equator. The sun and moon both pull on this extra mass. They pull the equator towards the ecliptic plane. If the earth weren't rotating but still had a bulge, then it would be pulled until there was no axial tilt. However, since the earth is spinning, it causes precession instead. The axial tilt doesn't disappear, but instead moves around in circles, just like a wobbling gyroscope.

What are the effects of the Earth's precession?

Because the angular momentum changes direction, "north" changes direction. The north star is just some lucky star that happens to be directly north at the moment. However, over thousands of years, the direction north changes such that the north star is no longer north. There are several other stars that are "north stars" at different times in the precession cycle.

If you think of it from the star's point of view, the star used to point north, but then the world moved. But the world will come around again, eventually giving the star another moment. Perhaps this is symbolic of something?

There is another effect: a difference between the "sidereal year" and the "tropical year". A sidereal year is the amount of time it takes for the earth to complete a full orbit. A tropical year is the amount of time it takes to complete four seasons. The precession of the earth causes the axial tilt to rotate around in a circle every 25,800 years. The direction of the tilt relative to the direction to the sun causes seasons. That means that for every 25,800 sidereal years, there will be an extra four seasons. 25800 sidereal years equals about 25801 tropical years.

New Years and Astrology

Our calendar uses tropical years, not sidereal years, because it is more convenient to farmers, among other people. The end result is that when we celebrate the new year, we are not celebrating a complete orbit of the earth, back to the location at the beginning of the year. We're celebrating a rather arbitrary time marker. But that's ok. I can still wish you a Happy New Year!

I should also note that the positions of stars go by sidereal years, not tropical years. Since we've been using tropical years to count the last 2 millennia, the usual dates for astrological signs are actually off by about a month. Also, there's a new astrological sign in the northern hemisphere. Of course, most people never know this, probably because astrology is equally ineffective either way.

Should skeptics trust science?

There's a discussion going on at Aardvarchaeology and Respectful Insolence about skepticism and scientific consensus. Should skeptics always side with the scientific consensus? Martin and Orac agree that we should, provided that there is a sufficiently unambiguous consensus. I agree, though I would add the further qualification that this rule does not always apply to experts in their own fields. Perhaps a better qualification (as one commenter suggested) is that the scientific consensus is only the default position of skeptics.

Why would we think this? Isn't it characteristically anti-skeptical to unquestioningly accept authority, scientific or otherwise?

Let's first look at which sorts of people are "skeptical" of the scientific consensus. There's Global Warming deniers, Intelligent Design proponents, racists, parapsychology proponents, alternative medicine proponents, the antivaccinationists, and relativity deniers. Orac also offers an example from social science: Holocaust denial. If you deny accepted science, you're in the company of the biggest opponents of skepticism. On the other hand, we might also include major scientific revolutionaries like Einstein, Galileo, and Darwin. However, in all these cases, the revolutionaries were all experts in their fields, they started from the default position that the consensus is correct, and the scientific consensus soon came to agree with them.

Relying on scientific authority is not the same as the fallacy of "argument from authority". The reason that argument from authority is fallacious is because an argument is an argument regardless of who says it. It doesn't matter if the person who makes the argument is an average Joe, a scientific expert, or the president--our acceptance or rejection of the argument ought to rest on the argument's merits, not the person's authority. However, scientific authority is different, because whenever scientists agree on a claim or argument, there is always some evidence backing them up, even if the general public cannot see it or understand it. Scientific authority comes from the fact that scientists have a much better grasp of the entire field of evidence then the public could ever hope to attain.

So what is a science layman to do? Should they accept the scientific consensus, or should they avoid taking any position (leaving that up to the scientists)? I think that some people like to avoid taking any position because there is a fear of being wrong. But I would argue that it is equally wrong to take the neutral position if one of the sides is the clear winner. For example, I know very little about Global Warming aside from a lecture about Milankovitch cycles and a lecture about carbon dioxide sources and sinks. I would be wise to avoid debating the topic, but wouldn't it be wrong to avoid voting with Global Warming in mind? Just because I don't understand it does not make it less supported by evidence, or less important.

One last thing worth noting is that this doesn't mean we shouldn't question science. Questioning is often a good way to learn.

Precession explained

Forget precession for a moment. First, it's rotation explained!

When you rotate a three dimensional object, it always rotates around an imaginary line that we call the "axis of rotation". If the object we rotate is a wheel, then the axis of rotation goes through the axel. If you roll a spherical ball on the ground, the axis of rotation is perpendicular to the ball's path, and goes through the ball's center.

Well, if we want to know how "hard" it is to stop the object, then we need to find a certain value called "angular momentum". The angular momentum of any bit of matter is equal to its distance from the axis of rotation, times the mass, times how quickly it goes around the axis of rotation. Of course, your typical object is not a "bit" of matter, but an infinite number of bits of matter. To find the total angular momentum, we just sum up the angular momentum of all the little bits.

The problem with this simplistic view is that it ignores that objects can spin in many directions. To specify the direction of rotation, we say that the angular momentum goes in the same direction as the axis of rotation. If you look in the direction of angular momentum, the object will always appear to be rotating clockwise. If you rotate a standard screw, it moves in the direction of angular momentum.

Now, precession explained!

What is precession? Precession is when the axis of rotation itself spins. For example, when a gyroscope wobbles, its axis of rotation is first tilted north, then east, then south, and west. Its axis of rotation continues to change directions, moving around in a circle. It is important to remember that the axis of rotation is not in itself a physical object, so we would not expect it to spin unless there was some cool physics afoot. There is.

Angular momentum is just like regular motion: it does not change unless something pushes the object. In physics terms, we apply a force to the object. But force alone does not change angular momentum. For example, let's say we have a balance scale.

If we push straight down on the yellow circle, the two arms are not going to start rotating. However, if we push down on one of the arms, it will start moving. The further from the center we push, the less force it takes to move the scale.

The rate at which the angular momentum changes is equal to a value called "torque". Torque is equal to the amount of force times the distance from the axis of rotation. The reason it is easier to push the scale when further from the center is that it takes a smaller amount of force to create the same amount of torque. Torque, just like angular momentum, has a direction. If you apply torque, it will cause an object to change its angular momentum in the same direction as the torque you applied.

Now that we know about torque, let's look at a simple wheel with an axel. One end of the axel is hanging from a string. Excuse my poor art.
In case it isn't clear, the wheel is rotating in the direction of the arrow in the middle, and the string is applying a force in the direction of the arrow on the left. The angular momentum of this wheel goes to the right.

Which way does the torque go? Well, if the wheel weren't spinning, then it would simply fall so that the axel is vertical. This fall would cause the wheel to spin clockwise from our point of view. Therefore, the torque is going into the page (forward, in the direction we are looking). This causes the angular momentum to move into the page.

However, once the angular momentum starts going into the page, the entire wheel turns. The direction of the torque has also turned, and is now facing left. The more the wheel turns, the more the direction of the torque turns. As a result, the angular momentum will perpetually go around in circles, chasing after the torque. And that's what causes precession.

Now, all of this is difficult to understand, except by resorting to math (yes, we were doing math, albeit simplified math). I can conceptually visualize special relativity, and the fourth dimension, but precession? That's hard. I believe that is the sentiment behind this comic strip from xkcd.


Next time: Precession as applied to Earth!

Fractal Christmas Tree

Merry Christmas!
This is a fractal generated by a program written by yours truly. I like to show off. It would take a while to explain how I created this, but suffice it to say that it involves using Newton's method of approximating roots, as applied to the function f(x) = log(x²) over the complex plane.

Actually, since this tree was created using a mathematical process invented by Isaac Newton, perhaps it would more appropriately be called a Newtonmas tree. See, Sir Isaac Newton, unlike Jesus, was actually born on December 25th under the Julian Calendar. As a result, some people with a bad case of hero worship like to talk about "Newtonmas". Of course, the Newtonmas tree is usually an apple tree.

Dispatches from the War on Christmas

I know what you're thinking. You're thinking, "I want to know what the Enemy is doing this year to destroy Christmas, but I can't scan the atheist blogosphere myself lest the Devil tempt me! If only I had some sort of spy." Well... *ahem* ...I've been collecting a few, uh, links, if you know what I mean.

PZ Myers and his pharynguloid minions have been celebrating "squidmas." Then he turns around and wishes us a Jolly Christmas. It's an evil conspiracy against all of us vertebrates!

The Pastafarians want to return to the true meaning of Chrifsmas. You know... His Noodliness. Yes, Virginia, He exists.

According to C. L. Hanson, the true meaning of Christmas isn't about consumerism or religion. Read "The Grinch and the True Meaning of Christmas" to find out what she says.

Richard Wade tries to be a nice atheist this Christmas. Hilarity ensues! The "humbug" Christmas lights are so cute.

This isn't from the blogosphere, but I really like this Wonderella webcomic. Is it a Christmas or a Holiday tree? Let's ask it!

No More Mr. Nice Guy tells us that the War on Christmas is a myth. But he can't fool us. We all know he's trying to kill Jesus.

If you look at Google Trends (via Cosmic Variance), interest in Science dips around Christmas time! Ironically, so does interest in Religion. It seems that the only victor of the War on Christmas is Shopping. But you already knew that?

Merry Christmas! Happy Holidays!

BMJ spoofs

From Language Log...
The British Medical Journal has a bunch of spoof articles around this time of year. Much of the media seems unable to tell the difference between science and joke science. I am reminded of the Sokal affair.

Axial Tilt: The Reason for the Season

[Added 2012: this picture does not belong to me, but the source website went defunct at some point]

 

This picture has been going around the blogosphere. Forget discussions about how this fits into the "War on Christmas"--instead, I'm going to use this opportunity to explain the basic science of seasons.

The Earth moves around the Sun in a roughly circular orbit. The plane that includes Earth's orbit is called the ecliptic plane. While the earth is orbiting around the sun, it is also spinning around itself. When it is spinning, exactly two points on the surface, known as the north and south poles, do not move. The imaginary line going through the two poles is called the axis of rotation.

Seasons are caused by the fact that the axis of rotation is not perpendicular to the ecliptic plane. If they were perpendicular, the Earth's spin and orbit would go in the exact same directions. Instead, they are off by 23.5 degrees. The axis of rotation is tilted towards the sun during summer and away from the sun during winter. Why is the Earth apparently tilted in different directions at different times of year? It is in fact tilted in the same direction all year, it's just that the direction towards the sun changes throughout the year.

[Image from Timezone.com]

The day when the axis of rotation is tilted furthest away from the sun is called the winter solstice. This year, the winter solstice is December 22. The day when the axis is tilted closest towards the sun is called the summer solstice, which is somewhere around June 21 or 22.

[Image from Penn State University - I'm not sure what's up with the smiley faces.]

The reason axial tilt causes seasons is twofold.

First, the power from the sun is not evenly distributed on the Earth's surface. If you look at the above picture, there is about an equal amount of power between each of the yellow lines. However, towards the top and bottom of the Earth, that same amount of power is spread over a larger area of Earth. Therefore, the power per unit area is smaller closer to the poles, and larger at the equator. The power peaks at the Tropic of Capricorn during the winter solstice and at the Tropic of Cancer during the summer solstice.

Second, the length of the day grows shorter in winter, and longer in summer. In the above picture, you might notice that most of the tropic of cancer is in the dark. This indicates a shorter day. Also note that the entire arctic circle is completely in the dark. This indicates that it is perpetually nighttime. During the summer solstice, the arctic circle is in perpetual daylight. If you stand at the north pole, there is exactly one night and one day every year.

Both the length of the day and amount of power from the sun affect the temperature and climate. Around December, the northern hemisphere has shorter days and less power from the sun. However, the southern hemisphere has longer days, and more power from the sun. The southern hemisphere has summer at the same time that we in the northern hemisphere have winter. And vice versa. The southern hemisphere, I imagine, doesn't get many white Christmases.

Now, some people mistakenly think that the reason for the season is the distance from the sun. The Earth's orbit is not exactly circular, meaning that there are times of year when the Earth is closer to the sun, and times when it is further from the sun. This does have a very small effect on the climate, but it is not nearly as large as the effect of axial tilt. In fact, the day when the Earth is furthest from the sun (called the aphelion) is around July 7--in the middle of the northern hemisphere's summer. The Earth is closest to the sun (this point is called the perihelion) around January 3.

So there you have it--third grade science, as explained by me. Next time, I'll talk about more advanced stuff like precession or something.

I see contemporary art

Quite a while ago, I visited a local art museum. I have a better appreciation for these things after I took an art history class in the summer. However, I only studied modern art, which refers to a period from around 1770 to 1940. The most interesting part of the museum for me was the contemporary (post-modern?) art exhibit. I don't understand what is up with art these days (after WWII). What is up with it?

There was some pretty cool stuff, like a creepy car sculpture. And there were also the stereotypical minimalist stuff like a blank canvas, an empty room, a glass cube. And then there's everything in-between. For example, there was a black canvas with a white rectangle in the middle, but upon closer inspection the rectangle was a detailed drawing of a house.

I think the minimalist stuff is what gives modern art a bad name in the public's mind. I'm inclined to agree with the critics. I mean, maybe the first time, it was novel and all. But there are only so many blank canvases you can see before they all look the same--just one. Unless you think it has some value outside of novelty, it's more or less worthless.

Oh! But here I am talking about it, which means that it must be good art! In my mind, this argument only really discredits its own premise. "Good" art does not mean "promoting discussion". Besides, if you think about it, this is just a very brief discussion of an entire category of artworks.

One thing that's good about minimalist art is that after thinking, "This is art?", my next thought is, "I should be an artist!" Behold! I call it The Net.
Forget rectangles! Hypercube net silhouettes are the new deal, because I, an artist, said so! And it's not "ms paint", it's my personal style! This piece is a perfect blend of minimalism, technology, and four-dimensional geometry. Did I mention that you have to see 261 of these "paintings" before you've seen them all?

Bonus points if you can identify the hypercube net in question. In fact, I'd be impressed if anyone had any clue what I'm talking about.

Blind coin-sorting solution

A few days after posing a puzzle to you, I begin to tire of your complaints of hunger. "Oh fine!" I say. "I'll tell you the answer."

Taking your blindfold, I place it around my own head. Your eyes slowly adjust to the light. "Observe!" I say. I divide the pennies into two groups, one of which has five pennies. I flip over every single penny among the group of five. You suddenly realize that each group is showing equal numbers of tails. When I had isolated a group of five pennies, a certain number X of those would be showing tails, and there would be 5-X showing tails in the other group. Once I flip over all the pennies in the group of five, there would be 5-X pennies that were tails-up. Therefore, no matter how I divided it up, there would always end up the same number of tails in each group.

You exclaim, "I could have figured that out!" I applaud your confidence and offer to show you another "party trick". After a brief pause, you say, "Oh! I've got a call. (It's on vibrate.)" You fumble around and pull out your phone. "Really? I'll be right there!" Closing the phone, you say to me, "Sorry, I've got to go," and then you run off. I smile, and then carefully count my pennies.

Humanist Symposium #12

The Humanist Symposium #12 is up at Evanescent. It includes my post "Meaning without God".

A few highlights:
"If You Weren't an Atheist, What Would You Be?" Greta Christina's writing is always engaging.
"In Pursuit of Happiness" I am happy to see libertarian views represented in this carnival. Humanism always seems so far left, as often as they deny it.
"Critical Values" A brief criticism of moral relativism at Philosophy, et cetera.

A simple Ontological argument

Today I will be considering a simple Ontological proof of God. Ontological arguments are basically attempts to prove God through concepts alone, without any real-world evidence. This particular variant has been fully discredited in modern times (and this is not just my atheist bias talking). This isn't so much an attempt to argue about God as it is an exercise in reasoning.

The Ontological proof is in three steps.

1. Definition: "God" is the greatest being imaginable.
2. Premise: It is greater to necessarily exist than to not necessarily exist.
3. Conclusion: God necessarily exists.

There is a very simple counterargument using what's called reductio ad absurdum. We show that if ontological argument works, various absurd results must also follow. Take the following example:

1. Definition: "Drod" is the greatest video game imaginable.
2. Premise: It is greater to necessarily exist than to not necessarily exist.
3. Conclusion: Drod necessarily exists.

Similarly, I could argue that the greatest sandwich exists, the greatest dad exists, and the greatest island exists. I do not even need to confine myself to objects of the form of "the greatest [blank] imaginable", nor do I have to assume any premises. Take the following:

1. Definition: The "IPU" is an invisible pink unicorn that necessarily exists.
2. Conclusion: the IPU necessarily exists.

I could continue to use this argument to prove the existence of anything, as long as I define it to necessarily exist. That is absurd. Unfortunately, while the reductio ad absurdum tells us that the ontological argument cannot possibly work, it does not tell us exactly where it goes wrong.

In my opinion, the central question of this argument is this: what sort of control do you have over objects when you define them? Normally, when I define something, I have full control over its properties. If I define a triangle to be a polygon with three sides, these properties must be true. There is no triangle with more than three sides, because if an object has more than three sides, it cannot be a triangle.

Why can't I do the same with the property "necessarily existing"? Let's try the same argument I tried with the triangle. "There is no God that doesn't necessarily exist, because if an object doesn't necessarily exist, it cannot be God." Aha! The argument with the triangle only proves that if there is a triangle, then it has three sides. Similarly, this argument only shows that if God exists, then God must necessarily exist. The Ontological Argument basically assumes what it is trying to prove. We fully control the properties of an object that we define, but we cannot control whether there is an instance of the object in the real world. (Some philosophers go on to say that existence cannot be a property of an object, but that distinction is irrelevant for now.)

In the spirit of critical-thinking fun, I shall attempt a similar argument going in the other direction. This isn't a serious argument, just what passes for humor in my mind. Any refutations?

1. Definition: "God" is the greatest being imaginable.
2. Premise: A being would be greater if its existence could be proven with the Ontological Argument.
3. Premise: The Ontological Argument is impossible.
4. Conclusion: God is impossible.
   

Argument from fiction

After reviewing The Golden Compass and His Dark Materials, it's time for me to express my reservations about taking fiction too seriously. I hereby declare a new logical fallacy called "argument from fiction."

Dinosaur Comics offers the best demonstration. Try mousing over the comic too. (Man, I'm such a sucker for these webcomics...)


It's common for writers to want to teach some sort of moral lesson (TVTropes has a list of these). How do you do it? Well one way is by having a character obey or disobey that lesson, and then punish or reward them based on your ideology The Truth™. This isn't the only way, but it does occur in countless fables, children's TV shows, and even in Jesus' parables. What's the problem here?

The problem is that even though the fictional character was rewarded for doing good and punished for doing bad, how do we know a real character would get the same results? If it were a true story, we could at least point to the ending as empirical evidence (though, as an anecdote, it would suffer severely from selection bias). But since it's fiction, the evidence is fictional. As moving and inspirational the story might be, it is a poor way to prove anything about the real world.

On the other hand, perhaps the story makes a very convincing case that it could be real. For example, take the thought experiments performed by Albert Einstein. He created fictional stories of things moving near the speed of light, and from this was able to prove deep truths about space-time. What's the difference between Einstein's thought experiments and regular old science fiction novels?

I think that in general, the difference is only by degree. Some stories are simply more believable than others. For example, I find it highly improbable that Utahraptor will win the lottery, and much more believable that the boy who cried wolf would be ignored after lying so much. But you can't just say it's believable. You do not want your arguments to even resemble, "I believe it, therefore it's true." (What if it's only believable because you hope it's true?) You have to give reasoned arguments for why the outcome of the story would also be the outcome of a real situation. And if you already had reasoned arguments, what need is there for a story, except as a tool to generate interest and understanding?

On second thought, that sounds pretty useful...

Moral: Be cautious when deriving real life lessons from fiction. Instead, we should value fictional works for what they are--stories that can be provocative, inspirational, and entertaining.

Blind coin-sorting

Difficulty: 4 of 10

I pull out a stack of pennies. I use pennies because I don't trust you. Last time, you stole a quarter. I know you did! I counted. You wonder where I got a stack of pennies, and what kind of person still carries around such worthless things. But before you can ask, I produce an ugly green and blue handkerchief and say, "Blindfold yourself." While you blink incredulously at me, I explain: "It's in the name of Reason!" I make sure to capitalize "Reason" as I speak. "Or Fun. Or Whatever Else it is that you like."

After some more incredulous blinking, you finally tie the handkerchief around your head. It smells faintly of skepticism. You hear the clatter of a stack of pennies being scattered on the table. I say, reassuringly, "Preliminary tests suggest that this is a fun 'party trick,' as they call it." I make quote motions with my fingers as I say "party trick," but you can't see them, which is why I need to type out what I'm doing. You wonder why it is that you are performing the party trick and not I.

I boldly declare, "There are five tails showing among the pennies on the table! Your task is to sort all of the pennies into two groups, each group showing an equal number of tails!"

I ignore your incredulous blinking, almost as if I could not see through your blindfold. After a bit of hesitation, you pick up a penny, and try to feel whether it is heads or tails. "No!" I shout, surprisingly close to your ears. "There is an easier way, without tricks! Think!" You start to mumble that you feel uncomfortable, but I cut you off with another, "Think!" I go on to reassure you, "If you can't figure it out, don't worry. You'll only be doomed to blindly flip and sort coins until I post the solution in a few days."

<blatant genre switch>
Are you unable to solve the puzzle? Turn to page 2.
Do you solve the puzzle? Turn to the comments section and choose your own adventure.
</blatant genre switch>

Cosmic Variance on dark energy

Cosmic Variance explains some of the more confusing details of dark energy.

I know at least one of my readers likes to jump ahead to this complicated stuff, so there you go.

While I'm at it, I might as well link their Arrow of Time FAQ.

Science is social

For reasons that will remain unexplained, I've been watching a Japanese show about a physicist who solves crimes using his amazing physicist abilities. The physicist sometimes fulfills the scientist stereotype, and sometimes subverts it. For example, in one episode, another protagonist tells him that he is more interested in numbers than people. Later, the physicist explains that scientists have a dull life (what!?) and seldom meet people, but are not anti-social.

I appreciate the effort to humanize scientists, but the characterization is still false, at least in my experience. I've found that scientists in fact meet lots of people. We basically deal with information and knowledge, so we must perpetually be in contact with other people. I only do a small amount of research, but I still need to meet once a week. The rest of the week, I make-do with lots of e-mails.

Secondly, scientists do not spend most of their time in a dim lab repeating the same experiment over and over. Relatively little time is spent in lab--much more time is spent analyzing the results of experiments than actually performing them. In fact, scientists get to travel a lot. They often go to science conferences, which are all over the world. My professor goes to several of these a year. He also travels to see nearly every solar eclipse, and travels to set up or check on magnetometers, which are placed all over the world. Indeed, traveling is so important to science that it is a force for peace between nations. Go science!

Anti-religious themes in His Dark Materials

This is the second half of my discussion of the trilogy His Dark Materials.
See my post on The Golden Compass.

I do not want to put off anyone from reading this trilogy. The last two books, The Subtle Knife and The Amber Spyglass, are much less subtle than The Golden Compass, but the trilogy remains highly imaginative, enjoyable regardless of what you think of religion. I mean, I don't even completely agree with them myself. Also, I would like to put to rest a popular misconception about these books. No, they do not kill God. If you didn't know that, I recommend skipping my spoilers and reading the trilogy instead.

Spoiler Alert for the His Dark Materials trilogy

The Church adopts a much more sinister quality as compared to the first book. For example, one character performs "preemptive penance," which absolves him of future sins, allowing him to be an assassin. It also turns out that the Church is simply a pawn of the Authority, who controls churches in all the parallel worlds. The Authority, by the way, is not God, but the oldest angel, who had claimed to be God. The Authority is senile, and actually lets another angel, Metatron, rule for him. Metatron is a tyrant dictator, and the biggest antagonist of the series. I can't help but think that Authority and Metatron are supposed to be symbolic of moderate and extremist religion respectively, for their story echoes the common freethinker sentiment that moderates "enable" extremists.

You often hear that Pullman killed God in this trilogy, but that's completely false. Technically, they only killed Metatron, the Regent of an angel that falsely claims to be God. I totally missed it when I read it, but apparently the Authority also died. He died unspectacularly, simply dissipating in the wind. The missability of the Authority's death is Pullman's way of belittling the fraud.

After defeating Metatron, Pullman sets up what he calls the "Republic of Heaven" as opposed to the "Kingdom of Heaven." Pullman is not destroying heaven, but improving upon it. Pullman seems to think that religion has unfairly monopolized heaven, spirituality, and whatnot. He thinks religion, just like the Authority, is a fraud claiming to be divine. The stories strongly suggest that there is something truly divine, but Church is not it.

In my opinion, the real God in this trilogy is Dust itself. Pullman adds a lot more creatures, each of which is not only interesting in its own right, but is also designed to further describe Dust. Spectres are evil creatures that eat Dust, leaving pure apathy in their wake. Angels are beings made of condensed Dust, but not blessed with material bodies (more rebuttal to C. S. Lewis' "hatred of the physical world"). [Interestingly, Pullman inserted a gay angel couple, which I'm sure upsets many conservative Christians.] The Mulefa are creatures that evolved to roll on wheels (a detailed explanation followed). When the Mulefa found a way to access Dust, they became conscious and gained a permanent collective memory. Yes, Dust pretty much makes up all that is good in the world.

The anti-religious themes don't stop there. In their adventures, Lyra ends up destroying the afterlife, which it turns out was hardly paradise. It's a not-so-subtle attempt to argue that the materialist view of the afterlife is actually better. Later, Lyra reenacts the Adam and Eve story and then... There was more blatant allegory, but I forget the rest.

But like the first book, there's a lot more to the themes than just regular old anti-religion. For example, there is one character from our world who discovers Dust not through theology, but through particle physics. She finds what she calls "Shadow Particles" (aka Dust) that seem to hang out only around humans and human-designed objects. It acts as if it were conscious. However, her discoveries are so unbelievable that she loses funding. If this book is critical of religion, it's critical of science as well. It asks us, could science ever prove God?

So I've been calling all these themes "anti-religious", but is that what they are really? Are they anti-religious, anti-dogma, anti-Christian, anti-God, or what? I would say The Golden Compass is mostly anti-dogma (which is only anti-Christian if you think Christianity is all about dogma), but these books are arguably much stronger. Before, the Church was just misguided, and would justify evil acts with close-minded ideals. Now, the entire belief system of the church turns out to be a sham. It's still anti-dogmatic, but it also suggestively connects dogma and nearly all of organized religion.

Whether that means that Christians are justified in boycotting the movie... well, I'll let the reader decide that one.

Anti-religious themes in The Golden Compass

(Note: no spoiler alert yet)

On December 7, The Golden Compass movie is coming out. The atheist blogosphere has seriously been abuzz about this for months. Why? Because The Golden Compass, first in the trilogy called His Dark Materials, is *gasp* anti-Christian! Or so the many boycotting groups say. See, the author, Philip Pullman is *gasp* an atheist, and hates Christianity, The Chronicles of Narnia, and probably babies too. Never mind that the movie will dilute all such themes into nothingness--it will end up boosting book sales! I could probably insert an analogy to homeopathy in there.

These worries do have some foundation. Take a look at some of these Philip Pullman quotes.

So I'm caught between the words 'atheistic' and 'agnostic'. I've got no evidence whatever for believing in a God. But I know that all the things I do know are very small compared with the things that I don't know. So maybe there is a God out there. All I know is that if there is, he hasn't shown himself on earth.

When you look at organized religion of whatever sort – whether it's Christianity in all its variants, or whether it's Islam or some forms of extreme Hinduism – wherever you see organized religion and priesthoods and power, you see cruelty and tyranny and repression. It's almost a universal law.

I didn't read the whole of Narnia as a boy: I read The Voyage of the Dawn Treader, and felt slightly queasy, as if I were being pressured to agree to something I wasn't sure of.

Narnia has always seemed to me to be marked by a hatred of the physical world.

What I say to people who criticize me for attacking their religion... is simply this: what qualities in human beings does the story celebrate and what qualities does it condemn? And an honest reading of the story would have to admit that the qualities that the stories celebrates and praises are those of love, kindness, tolerance, courage, open-heartedness, and the qualities that the stories condemns are: cruelty, intolerance, zealotry, fanaticism... well, who could quarrel with that?

I don't know anything about the movie, but I do know about the books. As it happens, I read the entire trilogy just last year. I highly recommend the first book, The Golden Compass. It has a tremendous amount of depth, a terrific plot, and makes for great reading even for adults. The other two books, I didn't like as much, since they sacrificed plot quality for stronger themes, but they're still good too.

Let's dive into the details of what might be considered anti-religious about the first book. If you don't want to read spoilers, the conclusion is that the major theme is not so much anti-religious as it is anti-dogmatic. Also, this is just one of many themes, most of which do not directly touch on religion.

Spoiler Alert for The Golden Compass

The Golden Compass occurs in a parallel world. In this world, theology and science are one and the same. The main political power is the Church (also called the Magisterium), which is actually composed of a bunch of rivaling groups. The Church is portrayed as a sort of corrupt organization that tends to suppress "heretical" research. The message here isn't so much anti-religious as it is anti-dogma. After all, in this world, theology plays the role of science, providing technology for the world. It's not that theology is wrong, it's that their rigid beliefs become a barrier to progress.

But I don't think the characterization of the Church is the real meat of what's anti-religious in this book. The biggest theme in this book is all about growing up. Pullman is using this as a rebuttal to Chronicles of Narnia, which in his mind, seems to glorify children and demonize growing up. In particular, Pullman was unhappy about a certain part of Narnia in which one of the characters became "too keen on being grown up" (she was interested in lipstick, boys, etc), and essentially lost salvation. Also, at the end, the children died, as if C. S. Lewis wanted them to forever stay innocent rather than have them grow up to do good in the world as adults. Pullman thought this was just terrible, as if C. S. Lewis hated the physical world (see quote above).

In the world of The Golden Compass, there is a precise moment when children suddenly become grownups--when their daemons (souls, in the form of talking animals) can no longer shapeshift, and settle on a single animal form. To Lyra, the protagonist, this seems scary at first, since she likes her daemon to be able to shapeshift. But it turns out that growing up is a good thing.

When they grow up, a kind of particle called "Dust" gravitates towards them. Dust is basically (spoiler alert!) original sin, or at least the Church thinks so. In their version of Adam and Eve, the daemons of Adam and Eve stopped changing shape after they ate from the Tree of Knowledge. The Church mostly tries to suppress all knowledge of Dust. However, one part of the Church, headed by the charismatic and deceptive Mrs. Coulter, tries to actually do something about Dust. She kidnaps children, and brings them to a facility where they are severed from their daemons (which is like severing their souls). If the children even survive, they do indeed lose Dust, but also develop a mindless, apathetic quality.

Pullman clearly considers original sin a good thing. It is the knowledge of good and evil. It confers a higher level of consciousness, a freedom of choice, and a feeling of love. It's what allows armored polar bears to talk, think, and be all-around awesome. But again, this theme is more anti-dogma than it is anti-religion. Pullman's complaint about religion is that in its misguided quest for purity, it tends to reject knowledge, freedom, and love.

It seems strange to me that so many people have a problem with this. Are they pro-dogma? They're overreacting. You don't see me complaining about the whole thing with the souls.

I'd also like to mention that there are a ton of other themes that aren't anti-religious in this book. The story has a picaresque structure, in which Lyra travels place to place, learning new things at every step. Also, practically every detail in the world is used as a metaphor of some sort; daemons are but one example. For more details, you'll have to read the book. (Reading spoilers before reading the book? tsk tsk...)

I wrote more, but it went on too long. See Anti-religious themes in His Dark Materials (there will be more spoilers).

Sitemeter installed

The nosy among you might notice that I switched out statcounter for sitemeter. In between, I had briefly tried Google Analytics, but it wasn't capable of blocking my own visits, which totally killed it for me. Statcounter was cool, but it had a 500 log limit. Hopefully, sitemeter won't have any problems.

Getting statistics was definitely the most enlightening and addicting part of starting a blog. I feel like Zeno, obsessively checking visitors' referring links. I thought at first that I'd be happy with an F-list blog with maybe one visit a week, but no! I want more power! Mwahaha!

But once I get onto the C-list B-list, I'll be satisfied. Right.

The speed of electricity

I mentioned yesterday that in a normal wire (copper, 1 mm diameter), a current of 10 amps corresponds to an average electron velocity of about 3.3*10^-5 meters per second. To compare, I'd guess that the velocity from thermal energy is around 10³ meters per second (within a factor of 10 or so). The only reason the thermal energy doesn't come into play is because it makes the electrons move in random directions, both forwards and backwards. All but the tiniest amount of velocity gets canceled out. The reason the number must be so tiny is that when there are around 10²³ of these electrons moving around, a tiny average velocity corresponds to a large overall current.

Even though the electrons move slowly, it is also correct to say that electric current itself travels at the speed of light. If I plug in a lamp, I don't have to wait for an individual electron to slowly crawl through the wire before it lights up. All the electrons in the wire start to move nearly instantaneously. When you plug a wire in, a small electric field appears, pushing the electrons forward. The electrons themselves may not move fast, but the electric field is carried through the entire wire by electromagnetic waves--another word for light. Therefore, electric current travels at the speed of light. (Or close to it anyways. When we talk about the "speed of light" we actually mean the speed of light in a vacuum. Light moves slower when not in a vacuum.)

This post is in response to a question from a reader. Ask and you shall receive. Also, correct my math, because I regularly make mistakes.

Relativity + Electrostatics = Magnetism

[Update: Given the popularity of this post, I made a clearer rewrite.]

There is another dramatic success of Special Relativity that is virtually unknown among laymen. Special Relativity is what causes magnetism.

First, what is the electrostatic force, and what is the magnetic force?

The electrostatic force is what causes opposite charges to attract, and like charges to repel. Electrons, negatively charged, tend to stick to protons, positively charged. Two protons would repel each other, as would two electrons. On a macroscopic scale, the electrostatic force is what causes static electricity, in which an object accumulates an excess or shortage of electrons. It also causes lightning, which is basically static electricity on an even larger scale.

The magnetic force acts upon moving charges. If I've got an electric current, where the electrons are moving forward in a wire, the current creates a magnetic field. If I place two of these wires next to each other with the currents going in the same direction, they will attract. If the currents go in opposite directions, the wires repel. What we call magnets are materials with permanent circular currents on an atomic scale. The north pole of a magnet has currents going counter-clockwise, and the south pole has currents going clockwise. The north and south poles attract because when they are placed together, the currents go in the same direction.

The magnetic and electric forces interact and affect each other, but it is not clear why. Why should currents in the same direction attract? The wires, after all, have no net charge. There are just as many electrons as protons in each wire. So it can't be that the electric force is somehow sneaking in, disguised, right?

There is, in fact, a paradox associated with magnetism. Magnetic forces only act upon moving charges. But if we consider a moving particle's reference frame, the particle always has zero speed relative to itself. Therefore, from the particle's reference frame, it cannot be affected by magnetic forces. These forces shouldn't be disappearing just because our reference frame is different!

Let's consider a specific case: two wires with current going in the same direction. Wires, along with most everyday objects, consist of equal numbers of protons and electrons. If a wire has electric current going through it, that means that the protons are remaining still while the electrons are moving in one direction along the wire. The electrons, in fact, are moving at a large range of speeds, but for simplicity's sake I will assume that they are all moving at one constant speed.

Let's consider the wires with Relativity in mind. Of course, from the protons' motionless frame of reference, the wire is electrically neutral. But what happens if we consider the frame of reference of a moving electron? From the electron's point of view, the other wire contains a bunch of motionless electrons and a bunch of backwards-moving protons. Since the electrons and protons are moving relative to each other, we must take into account Lorentz contraction. If you don't recall, Lorentz contraction makes all distances in the direction of motion smaller. Lorentz contraction causes the protons to be closer together, more densely packed. As a result, the other wire has an overall positive charge, creating an electrostatic force. The electron will be attracted by this force.

So from my point of view, standing still, the wires attract because of magnetic forces. From the electron's point of view, they attract because electric forces. Both of us are correct, much in the same way that we would both be correct in thinking the other's clock ticks slower than our own. The resolution to the paradox is that electrostatic and magnetic forces transform into each other as we change reference frames. It turns out that magnetism is necessary for Special Relativity and electrostatics to make any sense together.

What's interesting about this is that it occurs at extremely low velocities. I did a bit of math, and I found that if we have 10 amps (a quantity of current) going through a copper wire of diameter 1mm, then the average velocity of electrons is 9.4*10^-5 [edit: corrected math] 3.3*10^-5 meters per second. That doesn't even begin to approach the speed of light (3*10⁸ meters per second). And yet, if you place two of these wires next to each other, there will actually be a measurable magnetic force. Not a significant force (about the weight of a paperclip per foot of wire), but not negligible either. We rely on this force for electric motors, generators, and countless other applications.

Usually, when you learn Special Relativity, teachers are quick to say that it is entirely ignorable at everyday speeds. But it turns out that even at microscopic speeds, Relativity does no less than power the modern age.

Puzzle difficulty

I've decided add a difficulty rating to all my puzzle posts. It is on a scale from 1 to 10, where difficulty 1 means it is more of a demonstration than a challenge, and difficulty 10 means it would stump puzzlers greater than me. Most of the puzzles I've done so far are on the easy end of the scale. I'll probably keep it that way until they get a bigger response. If you disagree with any of the ratings, feel free to say so.

Oh, and I am not oblivious to the fact that most people do not like puzzles. Lurkers! You cannot hide from me. I know you've been skipping over my puzzle posts. I've had enough experience with puzzling to know that most people simply don't care about this stuff, and refuse to even think about it. Unless I devote my entire blog to puzzling (not likely!), I will forever have readers that skip over the puzzle stuff.

On the other hand, people apparently perform many google searches for these puzzles (the brick puzzle in particular). I suspect that they're just looking for solutions so they don't have to think about it anymore.

I know this has been proven to be a futile effort, but I'd like to ask my readers a question. Do puzzles bore you? Is there any kind of puzzle that interests you? I am curious.

Meaning without God

An all-too-common complaint about atheism is that it leaves a life without meaning. This is trivially false—you don’t have to meet many atheists before finding that most have found profound meaning in their lives. It is troubling to me that some people think that God is the only possible meaning of life. Even more troubling is the thought that some atheists might agree. Life does have meaning, and it is important!

The uncaring universe

We are alone in an uncaring universe. On the cosmic scale, we are even less than a pale blue dot, since, outside of a tiny region in just one of the billions of galaxies, we are too small to see. Our lives are much too short to see much more than a snapshot in the cosmic, geological, and evolutionary timescales. There is no consciousness hiding behind the cosmos, no greater being to love us. The universe had no purpose in mind when it created us, indeed it has no mind at all.

But just because the universe is uncaring doesn’t mean we have to be. We may be invisible from just a few light-years away, but we’re not a few light-years away—we’re right here. Our lives may be too short to see the universe unfold, but it is not too short to have plenty of experiences that are meaningful to us. There is no reason to identify with the universe’s apathy—we are not the universe. Unlike the universe, we have a mind and purpose.

Finding purpose

When I say we have a purpose, I don't mean that there is an absolute purpose handed to us from above. We create our own purpose. This is true whether you believe in God or not. If God exists, you must still choose: is your purpose to do God's will, or to rebel against his will? The choice may be obvious, but it is you who chooses, not God. And that is not the only choice you make. Do you want to see the world? Help others? Develop talents? Better society? Make friendships? For the atheist, these choices remain the same. The only difference is that instead of choosing whether to do God's will, you choose whether to do good. This choice is equally obvious. After all, the only reason that doing God's will is obvious is because "God's will" is just a stand-in for what's good.

Zero sum

In the endgame, the Earth will burn up. Whatever good or bad humanity did would only cause an unnoticeable, irrelevant difference in the chemical make-up of the Earth. The universe will steadily continue on towards its death. Our souls will have long disappeared with our bodies rather than travel to any sort of afterlife realm. There is nothing to look forward to in the distant future. But why should we look so far in the future? If nothing that far in the future matters, then our only choice is to care about the present and near future. The present—your life, right now—is important. And since we care about others as well, this is reason to care about what happens to humanity after our own deaths.

Caring for others

If there is no afterlife in the end, what is the incentive to help others at our own expense? Well, if you're acquainted with game theory, you know that helping others often results in your own benefit in the long run. If you're acquainted with the theory of evolution, you know that social creatures like ourselves adapt by coming to want to help others. If you're acquainted with friendship, you know that helping others is its own reward. My preferred reason is because helping others is, well, helpful to others. It's not for me, it's for them. Aren't they reason enough?

On the lighter side, it's a juxtaposition of Dawkins and dinosaurs, as presented by Dinosaur Comics! Enjoy life!

"Outside of the box" solutions

Nine/Twelve/Sixteen Dots puzzles

Twelve Dots solution

Pause. You still have a chance to solve the Sixteen Dots puzzle.

Sixteen Dots solution

Observation shortens the universe's life?

A reader showed me a recent article in the Telegraph: Mankind 'shortening the universe's life'. As a resident "physicist" of the blogosphere, I feel obligated to comment. My warning is that the science here is quantum mechanics, and I have not yet received a full formal education about the theory. I may or may not know what I am talking about. For a real physicist's comment, I refer you to Rob Knop, Chad Orzel, or Pamela (Edit: also, John Baez). Another warning is that I usually try to "work my way up" to complicated science like this by explaining the background first, but there will be none of that this time. We're heading into deep waters!

The article is based on a paper in New Scientist. I haven't read the paper, and probably wouldn't understand it, so I can't say whether the Telegraph has over-sensationalized it or if it was New Scientist itself. But the article states that we may be shortening the universe's life expectancy (which is still many billions of years) simply by making astronomical observations of dark energy. Hmm, well... making wild claims might impress the Telegraph, but it just makes me more skeptical.

The first thing I thought was, "Life expectancy?" Last I checked, cosmologists think the universe extends infinitely into the future. The article explains that dark energy, which (allegedly) caused the Big Bang, and currently accelerates the expansion of the universe, may at any point in time cause another Big Bang of sorts. "Any point in time", of course, means that it has a very small chance to occur over any given billion-year period. That sounds pretty iffy to me, where "iffy" means "legitimate, but not well-established". Actually, I suspect this hypothesis is the main topic of the New Scientist paper.

The reason that observing dark matter might affect the age of the universe is because of something called the Quantum Zeno Effect. Perhaps I will fully explain this in the distant future (Cosmic Variance already has), but I'll just summarize for now. The Quantum Zeno Effect is a way of affecting quantum states by making multiple measurements. Each measurement "collapses the wavefunction", which means the quantum state has changed. With enough of these measurements, you can change the quantum state to something completely different from what it would have been otherwise. This is not to be confused with the "observer effect" in which the act of shooting photons at what you want to see changes it. This is a genuine, tested quantum effect that requires no physical contact of any sort. Yes, it is very strange.

I'm not sure of the details, but supposedly observing dark energy may "reset" its quantum state such that the universe's life expectancy shortens. But the problem with this is that it assumes a specific interpretation of quantum mechanics. That is, it assumes that wavefunctions collapse only when humans observe them. See, there are lots of interpretations of quantum mechanics, most of which are mathematically (if not philosophically) equivalent. So if you've got some theory, it should work under all interpretations or none of them. The fact that this theory relies on one specific interpretation makes it suspect in my admittedly uneducated eyes. All the interpretations must come out the same, or you're doing something wrong.

In the unlikely scenario that their idea is correct, I think they are mistaken if they think that quantum state should reset only when scientists try to measure dark energy. I think the wavefunctions collapse as soon as you look into the sky, regardless of whether you decide to do some mathematical calculations afterwards to find how much dark energy there is. For that matter, I think that there is not even any need to look at the sky. If the photons from the sky hit my desk, then merely looking at my desk is an indirect observation of dark energy. Does looking at my desk shorten the lifespan of the universe? I doubt it.

The second half of the article talks about an unrelated story in which a previous measurement of mass turned out to be wrong by a certain amount. I don't know much about that, but it sounds completely legitimate. However, there is a misleading segue between the two stories. This is not a case of measurements changing the universe, just a case of human errors changing measurements.

CotG #79 and Humanist Symposium

Two carnivals are up today. The Carnival of the Godless is up at the Sexy Secularist, and the Humanist Symposium is up at The Greenbelt. The Carnival of the Godless includes my article Negative ≠ Bad.

It occurs to me that it is not immediately obvious to everyone what exactly a carnival is. A blogging carnival is where someone collects all the best blog postings on a particular topic and puts them together in one big carnival post. In other words, lots of bloggers like me submit their best posts to the carnival host, and the host makes one big post linking to all of the submissions. There are three main carnivals around my subject area: the Skeptic's Circle, about skepticism; the Carnival of the Godless, about godlessness; and the Humanist Symposium, which is specifically about the positive aspects of godlessness. Each occurs every two or three weeks with a different blogger as the host.

Blogging carnivals are a great way to:

1. read the best posts on a topic from the past few weeks from all over the blogosphere.
   
2. find new blogs worth reading.
3. accumulate readers (from the perspective of a young and ambitious/narcissistic blogger).

Of course, I can't just steal eyeballs without allowing other blogs the same opportunity. It's just common blogging etiquette to link back to others. In conclusion, go read the carnivals!

Outside of the box

Difficulty: 4 of 10

The Infamous Brick Puzzle seems to be a favorite among googlers. With that thought, I present another classic puzzle that involves drawing lines without lifting your pencil. The Nine Dots puzzle is one of the most well-known puzzles ever. It is the origin of the phrase "Think outside of the box".
Without lifting your pencil, draw four straight lines such that they go through all nine dots (which, by the way, represent infinitesimally small points). This puzzle is just too famous, so presumably everyone already knows the solution? If not, I will never spoil it for you--I insist that you solve it for yourself! (But of course, I can't stop you from googling "Nine Dots puzzle".)

So once you've found the solution to the classic, there's still more! I give you two more variations: The Twelve Dots puzzle and the Sixteen Dots puzzle.

Without lifting your pencil, draw five straight lines through all twelve dots. You must complete a loop, ending where you started. Cross each dot no more than once.
The Sixteen Dots puzzle is identical to the Twelve Dots puzzle, only you must draw six lines.

If anyone wants to post a solution in the comments, I suggest listing the coordinates of where you're starting and ending the lines (since it would be difficult to post pictures). Just let the lower left point be the origin or something.

Solutions

Negative ≠ Bad

One of the complaints against atheism, as well as skepticism, is that "it's all so negative!"

Let's break up the complaint into it's two components. First, the complaint states that atheism and skepticism are completely negative. This is not true. Skepticism goes hand in hand with science, which is hardly negative. Atheism often accompanies a ton of positive views (usually including science), though the particular positive views may vary from person to person.

The second component of the complaint is often implicit: "...and negative things are bad."

This is an excellent example of the equivocation fallacy. The equivocation fallacy is when you switch around the meanings of words. For example, let's say I use astronomy to show that stars are gigantic balls of hot gas. I go on to say, "Therefore, Tom Cruise is full of hot air." I've just switched around two meanings of "star"--those things we see in the sky, and those things we see on the screen. I also switched around different meanings of "hot air". In this fictional case with stars, I would probably fool no one with my reasoning, but in practice it is much harder to catch.

The word "Negative" has two meanings. In the first part of the complaint, it means focusing on criticizing claims rather than making new ones. A "negative claim" states what is false rather than what is true. In the second part of the complaint, "negative" means "bad". Just because these two meanings can be signified with the same word doesn't mean we should confuse the two. It's possible that the two meanings are equivalent, but you have to argue that fact.

So why might negative be bad?

1. Negative claims practically advertise the things they criticize.
2. Negative claims lead to disrespect.
   
3. With what will people replace their previous beliefs?
   
4. Negative claims can't unite anyone.
   

My rebuttals...

1. There is something to be said about prioritizing claims that have wide acceptance. If we're criticizing a claim that is virtually unknown, then yes, maybe it is a little counterproductive. But religion and pseudoscience are hardly unknown.
   
2. Sure, if a few people have their own self-worth all tied up with their beliefs, maybe it is disrespectful. But such people have already set themselves up for a fall, and deserve a dose of disillusionment. For everyone else, it is actually quite easy to respect the person while disagreeing with them. I do it all the time.
   
3. Positive and negative claims are not mutually exclusive. You can criticize other claims while simultaneously putting forward better ones. But even without our help, it is a mistake to think that people will systematically replace their old beliefs with something worse.
   
4. On the contrary, I think that negative claims often unite many more people. For example, "Atheist" is a largely negative label that only really says what people don't believe. But if you consider more positive labels like "Secular humanist" or "Objectivist", you've just split atheists into a bunch of smaller groups. These groups might be tighter knit, but at the cost of size. So which do you want: a group that loosely unites many people, or a group that tightly unites only a few people? Bad question. We can have both kinds of groups, and both play important roles. So there is no reason to outright reject negativity as a basis for uniting people.

Really, negative claims are something we need. If we could only make new claims without criticizing old ones, we would be left with a mess. In the spirit of making positive and negative claims simultaneously, I'd like to replace the old claim "negative is bad" with a new one: "Negative is good!"

Skeptic's Circle #74

Skeptic's Circle #74 is up at Med Journal Watch. It includes my post on the 10% myth. Have fun.

And happy Thanksgiving! For those who don't celebrate, then, umm... happy Thursday!

"Science makes leap of Faith"

An anonymous reader pointed to me an article in The Daily Breeze called Science makes leap of faith. Time for a bit of fisking, yes?

The article is talking about Nobel winning James Watson's recent racist comments. I seem to recall that the ScienceBlogs were chatting about this (exampes: PZ, Zuska). In brief, James Watson has made it clear that he's a dangerous fool (and misogynist!).

Some quotes from the article:

Why is Watson quelled in pursuing his theory that "There is no firm reason to anticipate that the intellectual capacities of peoples geographically separated in their evolution should prove to have evolved identically"?

Yes there is. The timescale is too short. They are not completely isolated. The environments are not significantly different. And if I recall, the usual racial "divisions" often don't match the populations that were actually genetically isolated.

Why all the outrage? All the epithets? All the accusations of racism? All the canceled lectures?

Maybe because he's wrong and he's spreading particularly harmful misinformation.

Since I'm not an evolutionist, I need not stick my feet in the muddy waters of this emotionally charged issue - the Bible asserts that all men (regardless of DNA structure) are made in the image of God, and that's enough for me.

I get the feeling that "DNA structure" constitutes the totality of this writer's scientific knowledge.

[Naturalists] are generally so quick to point out how Copernicus, Galileo and Darwin took rank against the tide of their day and how we are all better off for it.

Galileo Fallacy

Watson is seeking to live this maxim ["No Heaven. No Hell. Just Science."] out to its logical conclusion and what a mess!
All this reveals the vacuum formed with the efforts to oust an ultimate and absolute immaterial being - I think the common term is "God" - from any venue in life.

What?! Is this, like, surrealist performance art? Because all I see are non sequiturs.

The scientific community's cannibalization of Watson demonstrates that they have a system of ethics that trumps their academics. But their unwillingness to acknowledge an ultimate and supreme source of ethics naturally results in their divided house where Watson currently sits surrounded by vacancy signs.

He is assuming that Watson's comments are academically sound, which they're not. So, garbage in, garbage out, right? But is it just me, or is there more garbage coming out than going in? Let's break this down. He says that there is confusion because scientists are putting ideologies before truth. But it's not the ideology-before-truth thing that's the problem. The problem is that they're going by their own separate ideologies rather than the one supreme ideology (aka Jesus). Oooookay. Someone has not thought this through very clearly.

Replacing the 10% myth

It's often said that we only use 10% of our brains. The other 90% is, of course, filled with penguins. I've got proof, in fictional form!

She passed the time quietly in a world of her own in which she was surrounded as far as the eye could see with old cabin trunks full of past memories in which she rummaged with great curiosity, and sometimes bewilderment. Or, at least, about a tenth of the cabin trunks were full of vivid, and often painful or uncomfortable memories of her past life; the other nine-tenths were full of penguins, which surprised her.

-Douglas Adams, The Long Dark Teatime of the Soul

So in case anyone didn't already know, this is a myth. It's not true that we only use 10% of our brains, nor is it true that only 10% is active at any one point, nor is it true that we understand, or are conscious of only 10%. When I googled the words "10 percent" and "brain" I didn't find a single credulous article until the third page. So I think saying more on this myth is just overkill. Instead, I'll go off on a tangent about how skeptics deal with truth.

Anyways, I think the reason the 10% myth persisted for so long is that people like the point it is meant to make. "Everyone has a lot of hidden potential," is the message. Who are we skeptics to take away from that? It's certainly difficult to think of a case where the 10% myth would actually harm anyone. Well, the myth is occasionally used to justify drug use or belief in "psychics" (aka con artists), but for the moment, let's ignore those possibilities. If it's not hurting anyone, and if people actually find meaning in this myth, why burst their bubbles? Isn't this a slippery slope in which skeptics will start to reject all of life's little lessons and become bitter-hearted cynics?

Not really, no. But I do think we should reject life's little lessons when it turns out they're wrong. If the only way to justify a life lesson is through lies, well then maybe that lesson is wrong. If it requires pseudoscience to inspire people to do something, then maybe people shouldn't be inspired. If people need a myth to find meaning, that meaning might be false. False meaning can still motivate people, but who in the world wants to be motivated by lies?

So is it true that all people have hidden potential? I think so. But it's not because we only use 10% of our brains. Surely, we can think of a good reason without resorting to myths. It is because when we see great men and women, we realize they are not so different from us. That wasn't so hard, was it?

I can't keep this up

I've been sustaining a steady update schedule of once per day, but I don't think I'll be able to maintain it forever. I can't be like PZ who keeps an average of 6 or 7 posts a day (no exaggeration!), or the Friendly Atheist, who averages about 3. Part of it is that this is mostly original writing, and I don't get a ton of e-mail asking me to comment on this or that news story. (Again, I will not make public an e-mail address unless there is enough demand for one.)

I am a student with other uses for my time, so I'd like to slow down the schedule. Let's try once every two days. I might also take my Thanksgiving holiday. If you're really bored, I suggest looking at my sidebar links. There's my blogroll (on which only awesome blogs are allowed), the ever-nifty atheist blogroll, and some other stuff.

In other news, I am now googlable. I'm on the first page of a search of "tangent time" (even without quotes). It's so awesome.

Moving goalposts

As I said before, I think it's important that we not blindly apply logical fallacies as if they were infallible. Well the "moving goalposts" fallacy is one that I think should not be considered a fallacy at all, though for different reasons from the previous examples. Most skeptics would disagree with me, so I'll argue my point.

The "moving goalposts" fallacy starts out when, in a debate between Alice and Bob*, Alice sets a "goalpost" for Bob. Alice says, "If you can do X, you will have proven me wrong." Bob proceeds to do X. Alice seems to forget what she had previously said, and now says, "If you can do Y, I will eat my words." Bob proceeds to do Y. Alice again seems to forget, and now says, "If you can do Z, I will put my foot in my mouth." Bob becomes frustrated and gives up.

The idea behind this fallacy is that even though Bob has disproven Alice's claim twice, Alice does not recognize that she has lost. If action X does in fact disprove Alice's claim, and if Alice does not change her claim, then, yes, Alice is in the wrong. She is also in the wrong if she merely changes the name of her claim, or otherwise equivocates what she really thinks. She is doing the rhetorical equivalent of sticking her fingers in her ears and singing loudly, "I know I'm right and you're wrong because I haven't heard any evidence!"

But I think that in practice, this is not what usually happens. In practice, Alice changes her position. Her change in position may have been very slight, and implicit, but it is a change nonetheless. Perhaps she has decided that X does not in fact disprove her original claim. Other times, Alice may change her original claim slightly to accommodate the evidence from X. I do not see why changing one's own position should be considered in itself fallacious.

However frustrated Bob may be, he must provide a new argument against Alice's new claim. Either that, or Bob may point out that his previous arguments still apply to Alice's new claim. There are innumerable wrong positions Alice could take. Must Bob counter every single one that Alice decides to take? Yes, at least if Bob wants to convince Alice. Perhaps he can think up an argument that counters all possible positions Alice could take.

I think what people really find frustrating about moving goalposts is that they want their opponent to definitively lose. Bob wants Alice to publicly admit complete defeat. But instead of admitting defeat, Alice merely decides to replace her old claim with a new, slightly different one. But I would say that the desire for a clear surrender is an emotional one. In a way, Alice has admitted defeat by discarding her old position. She just hasn't done it loudly or theatrically. They seem to fantasize about their opponents saying, "I was a fool, and you are wise." Take what you can get, I say. The real goal of debate isn't victory, it's truth.

Rather than just talking about Alice and Bob, allow me to substitute a real life example. Many people think of "Intelligent Design" as being Creationism with a moved goalpost. Well, I think that means you can't always use the same arguments against the two. On the one hand, you could argue against both ID and Creationism by pointing out that Evolution is really one of the best established theories in all of science. On the other hand, you couldn't argue against ID by pointing out evidence of a 4.6 billion year history, because (as far as I know) ID already accepts the age of Earth. ID has a ton of problems, but it's still a slight step above Creationism. I just don't see the goalpost-moving as being in itself fallacious. Are people not allowed to change their minds, to improve their own positions?

Well, I guess in this case it's reasonable to want a definitive loss, but that's only because ID isn't so much a real debate as it is a silly PR machine.

*In case it isn't clear, Alice and Bob are just two names I am using to represent any two people in a debate. Physicists seem to be fond of using these two particular names in thought experiments, so I will do the same.

Special Relativity Part 3: Mass-energy

Part 0: More historical background
Part 1: The problem
Part 2: Space-Time

One of the results of SR is that velocities do not add. If one rocket is going to my right at 3/4 the speed of light, and another is going to my left at 3/4 the speed of light, these two speeds to not sum to 3/2 the speed of light. Instead, each rocket observes the other to be going at 24/25 the speed of light. The equation for the relativistic "sum" of two speeds is as follows:

(v₁ + v_2)/(1 + v₁v₂/c²)
...where v₁ and v₂ are the two speeds, and c is the speed of light

The derivation of this equation unfortunately relies on math that I skipped, so you'll have to take my word for it. It basically arises from the equations that fully describe lorentz contraction and time dilation. One thing to note is that if either v₁ or v₂ is equal to c, then the relativistic sum is equal to c. That means that no matter how fast an observer is moving, light will still travel at speed c. Einstein originally set out to explain why light is always observed to move at speed c, and now we've done it.

Also note that if v₁ and v₂ are both less than c, their relativistic sum will be less than c. So no matter how much you try, you can never push an object above speed c. In fact, what happens, is that the closer its speed is to c, the harder and harder it becomes to increase its speed. That means that Newton's second law (Force equals mass times acceleration) is wrong. At high speeds, it takes greater force for a smaller amount of acceleration. In some sense, the mass of the object increases when it speeds up. Specifically, the "relativistic mass" of the object increases. Usually when physicists talk about mass, by default they refer to "rest mass" (the mass of an object when it isn't moving) rather than the relativistic mass. The rest mass stays constant during acceleration.

Whenever you apply force to a moving object, you are transferring energy. You are also changing the object's relativistic mass. With a bit of calculus, we can conclude that energy is relativistic mass multiplied by a factor of c². That's where we get the equation E=mc².

Technically, the famous equation is incorrect. The correct form is E=ɣmc², since these days, relativistic mass is written as ɣm. The letter m represents the rest mass of the object, though in Einstein's time, it was used to represent the relativistic mass, thus the source of this confusion. The number ɣ (represented by the letter gamma) is called the Lorentz factor, and it turns up in the equations for Lorentz contraction and time dilation. For the interested reader, ɣ=1/sqrt(1-v²/c²).

For a non-moving object, ɣ=1, but when the object's speed approaches light, ɣ approaches infinity. That means that E=mc² is only true for an object that is not moving. In order to push an object to the speed of light, it would require an infinite amount of energy, and the object would gain an infinite amount of mass. Along with time-travel, this is why the speed of light is the ultimate speed limit. (However, this does not disprove the existence of tachyons, which, in theory, already start out faster than light, so that there is no need to push them through the light-speed barrier.)

I don't think most people realize the implications of this equation, so I want to expound upon them. Most people have heard that this is how atom bombs work. When an atom bomb explodes, the nuclei of Uranium atoms split apart. The way they split is such that the total mass decreases. Because c² is such a large number, a small difference in mass results in a huge amount of energy. The same basic idea is behind hydrogen bombs, and nuclear power plants.

What most people don't realize is that mass-energy equivalence is true of all energy. If you use energy to heat up an object, it becomes a tiny bit heavier. This should not be surprising, since the temperature of an object tells you how fast the individual particles are moving, and I've already said that objects moving at higher speeds become more massive. But more surprising is that if you compress a spring, giving it potential energy, it becomes heavier. If you snap your fingers, you become slightly lighter, since a small amount of energy is released through the snapping sound.

Mind you, none of these mass differences come in large enough quantities that we would ever notice them, and they would be completely swamped by other effects. But mass-energy equivalence also gives protons and neutrons the vast majority of their mass. Without it, atoms would be too light, the force of gravity would be less effective, and we probably wouldn't exist. It is by the grace of Special Relativity (along with a ton of other cool physics) that we're all here.

This concludes my series on Special Relativity, though I may still talk about it, and go off on other tangents. If you've got any questions, ask, and I could write more to explain the answers.