Monday, June 29, 2009

Near the speed of light

What happens when we travel near the speed of light?

Let's say you're traveling at 99.5% the speed of light. That's 299792458 meters per second, or 185351 miles per second. You're heading straight towards Proxima Centauri, the nearest star besides the Sun. Proxima Centauri is about 4 light years away, meaning that it takes a beam of light four years to get from here to there. 4 light years is about 2.3 x 1013 miles.

Large numbers, eh?

It might seem as if you would get to Proxima Centauri in about 4 years. After all, you're practically like a beam of light yourself now. But things are not so simple when we get close to the speed of light. To continue with our calculations, we will need something known as the Lorentz factor. The Lorentz factor is just some number, symbolized with (the letter gamma).
= 1/sqrt( 1 - (v/c)2)
v is the velocity, and c is the speed of light. In our example, is approximately equal to 10.

One of the things that happens when you travel near the speed of light, is that all distances in the direction of travel get shortened by a factor of . The Earth will seem like a squashed spheroid to you. It will also seem as if Proxima Centauri is not 4 lightyears away, but 0.4 lightyears away. So you will get there in 0.4 years without ever breaking the speed limit set by Relativity!

I would be on Earth, watching you. I would see you arrive at Proxima Centauri 8 years later. From my perspective, it took you 4 years to get there, and 4 more years for your signal to return to me. Let's say that you decided to return home, and sent a message to me saying so. It would take the message 4 years to get to me, and you will appear about one week later, since you travel at nearly the same speed as your own message.

By the time you returned, about 8 years would have passed on Earth. From your perspective, the entire trip only took 0.8 years. From your perspective, Earth has skipped ahead in time by about 7.2 years. From my perspective, it seems like you hardly aged over that long trip.

Let's say that you're about 100 kg (220 lb). Once you start moving near the speed of light, your mass increases by a factor of , so you will appear to be 1000 kg. Since your mass increased by 900 kg, guess how much energy it required to mobilize you? That's right, E=mc2. In your case, this will be 8.1 x 1019 Joules, or about twenty thousand megatons. And that's just you by yourself. If you're in some kind a space ship, the space ship might carry about a million more megatons of energy. You would probably make quite an explosion if you hit one of Proxima Centauri's planets, if it has any. Not that we were planning to do anything like that.

You and your spaceship will appear to be flattened by a factor of . You will seem as flat as a pancake. You will probably look quite absurd, a massive, flying, pancaked person. What's more, your colors would be all shifted. When you're flying away, you will be redshifted by about a factor of 20. Basically, I will only see what little ultraviolet light you emit. But when you're flying towards me, you will be blueshifted by a factor of 20. Much of that infrared light which you normally radiate will now be blueshifted into visible light and x-rays. I'm not sure what color you would appear, but I estimate about the color of a star of 6,000 degrees, like the sun--a yellowish white.

You, while on your journey, will see something even more exciting. Everything behind you will be redshifted by a factor of 20. You would see the extreme ultraviolet range. In the ultraviolet range, most stars will seem much dimmer, except for the hotter ones, including white dwarfs. If you look in front of you, light is blueshifted by a factor of 20, so you will see part of the middle infrared spectrum. You can see giant dust clouds and nebula in this range. Some of these dust clouds are where stars will form. And as you swing your head around, looking from front to back, you will see all the ranges between middle infrared and extreme ultraviolet. I'm sure it would be quite an experience.

Thursday, June 25, 2009

Falsifiability and having it both ways

Long time readers might have figured out that I have it in for Karl Popper's philosophy of falsifiability. I don't believe Popper gave an accurate description of how science works, nor how science should work. I think Popper's philosophy is at best a clunkier version of induction, and at worst, simply wrong. It is also prone to abuse and/or misunderstanding.

However, I will say that there is more than just a grain of truth to it. At the heart of the philosophy of falsifiability is the recognition a particular logical fallacy. I am not sure if this fallacy has a common name, but I will call it "having it both ways".

Take the following illustrative real-life example (via Phil Plait). Patricia Putt, a claimed psychic applied for the James Randi's Million Dollar Paranormal Challenge. In this challenge, Putt and the testers agreed on an experiment which would be able to test her ability to "read" people. In the experiment, Putt read ten women and wrote down descriptions of each of them. Each of the women was asked to choose the description out of the ten which fit her best. If five of the women picked out the correct description, Putt would move on to the final testing.

As it happened, none of the women picked out the correct description. At a later time, Putt decided that this meant she had actually gotten 10 out of 10, since each of the women had picked out one of her descriptions. Nevermind that each of the women were asked to pick out a description, and that none of them picked out the correct one.

There are only two possible results to this experiment:
(1) Most of the women pick the correct description.
(2) Few or none of the women pick the correct description.

If (1) had occurred, then that would be evidence in favor of Putt's psychic abilities. Not absolute evidence, mind you, since it could also happen by chance. But it would be evidence enough that we would want to investigate it further. However, what actually occurred was (2); none of the women chose correctly. Putt claims that this is nonetheless evidence in favor of her psychic abilities. But she can't have it both ways! We might say that one possible result is evidence for psychic ability, or that another possible result is evidence for psychic ability, but we cannot say that all possible results would be evidence for psychic ability.

If all possible results of an experiment have the same conclusion, then there would hardly be any need to perform the experiment in the first place. Even before the experiment occurs, we know that either (1) or (2) will occur. According to Putt, either way, this means the experiment comes out in her favor. But then, what is the point of the experiment? Can we really call it experimental evidence if we think it is unnecessary to ever actually perform the experiment?

The bottom line is that if you want to entertain the possibility of evidence for something, you must also entertain the possibility of evidence against it. You can't have one without the other.

I propose that this fallacy doesn't just make for bad science, it makes for bad reasoning, period.

Monday, June 22, 2009

Summertime is the only time I ever get any real book-reading done. I may be a bit busy this summer, but I won't let that stop me. In fact, I read a book already.

I read Kurt Vonnegut's Cat's Cradle. I've never read Kurt Vonnegut before and I wanted to try it. I would describe the book as very dark, and deeply ironic. Not funny, but deeply ironic. We meet character after character, and we watch how their personalities clash with the reality around them. I enjoyed it. (I'm pretty sure, though, that ice-nine couldn't possibly exist. Sure, there does exist chocolate-six, but that's just delicious, and won't destroy the planet at all. So we can rest easy, knowing that there is no such doomsday scenario.)

What books are you reading this summer?

Next on the list is Slaughterhouse-Five. After that, I don't know. Any recommendations? I want to stick to fiction, on account of I already read plenty of non-fiction in non-book form. I also tend to like books which are funny.

Friday, June 19, 2009

Minesweeper puzzle

I trust most of you have seen minesweeper before? If not, then this puzzle will go right over your head.

Where should you click in order to maximize your chances of winning?

In case you didn't know, the number 4 in the upper left represents the number of unmarked mines remaining.

See the solution

Wednesday, June 17, 2009

See the original puzzle

I created a bunch of pictures in Mathematica to illustrate the process of turning the torus inside out.

If you look carefully at the pictures, you'll see that the rings remain linked throughout. And yet, at the end, the red ring is on the inside and the blue ring is on the outside. The resolution to this paradox is that the rings have switched places!

Update: Another intermediate step (hopefully this makes it a little clearer)

Monday, June 15, 2009

Is SETI falsifiable?

Overheard in a conversation:
"I don't believe that SETI is science because it is unfalsifiable. If we don't find any aliens, they can simply say that we haven't searched for long enough."

SETI is the Search for Extra-Terrestrial Intelligence. It is a science program which looks at radio waves from space in order to search for signals from alien civilizations. The idea is simple. There are a tremendously large amount of stars out there. Some of those stars have planets, and some of those planets are capable of holding life. Some of those life-friendly planets actually have life, and some of them have intelligent life with civilizations, and some of those civilizations send out radio signals. We know that this must be true, because we already have one example: us. The question is, are there any such civilizations (besides us) close enough that we can see them?

However, some critics (as seen above) say that SETI is not science, because it is unfalsifiable. I disagree. SETI is science, and it is falsifiable.

Falsifiability is an idea created by philosopher of science Karl Popper. According to Popper, it is one of the things which distinguishes science from non-science. If we have a scientific hypothesis, then there must exist some experiment which might produce results to disprove that hypothesis. For example, the statement "All swans are white" could theoretically be disproven if we found a black swan.

The hypothesis "There are intelligent alien civilizations (besides us) which send out radio signals" does not seem to be similarly falsifiable. What observation could we possibly make that would falsify this hypothesis? Theoretically, we could look at every single bit of space throughout the entire universe and find no such civilization. But this is not a remotely realistic experiment. So SETI is unfalsifiable and not science.

But what happens if we restate SETI's hypothesis: "There are no intelligent alien civilizations (besides us) which send out radio signals". Now, this hypothesis can be falsified! We could theoretically make an observation which disproves the hypothesis. All we need to do is find a radio signal from an alien civilization. So now SETI is science.

So how about that? We state SETI's hypothesis one way and it's not science. We state SETI's hypothesis another way and it is science. This is absurd! Either we've misunderstood Popper's idea of "falsifiability", or it was never a very good idea in the first place (I would say both).

In any case, I've misstated SETI's central hypothesis. SETI does not tell us whether there are alien civilizations out there. Rather, it only tells us whether there are any nearby. This, in turn, tells us something about the frequency of such alien civilizations. Are there so many alien civilizations that everyone has at least one in their own backyard? Or are they so sparse that you'd have to go to the next galaxy to find another one? There are a ton of different estimates for the density of extraterrestrial civilizations. Personally, I agree with the more pessimistic estimates.

But of course, I would first defer to the evidence. If we want to distinguish between a universe where extraterrestrial civilizations are common, and a universe where they are sparse, then we have to look at a small sample of the universe and count the number of extraterrestrial civilizations. That's what SETI is doing. And since SETI hasn't found anything yet, the sparse hypothesis is looking more and more attractive.

We never really disprove the idea that alien civilizations are common. Maybe we're just unlucky. Or maybe the aliens are transmitting signals at the wrong frequencies, or none at all. Or their signals are to weak to reach us. Of course, few things are flatly disproven in science. Usually, they become less and less likely (or more and more likely) as we slowly accumulate evidence.

Saturday, June 13, 2009

Some of my readers are puzzle enthusiasts, correct? You should register for the 2009 US Google Puzzle Championship. The championship occurs on Saturday, June 20, from 1:00-3:30 PM EDT. You must register before this Thursday, June 18.

You take the test from home. You just print out all the puzzles, solve them on paper, and then submit your answers online. Typical puzzles include Sudoku, Arrow ring, Battleships, and all sorts of other "grid" puzzles. But there's also a "spot the difference" puzzle every year. You can look at last year's test to get a better idea.

My tips: Try the practice test first. Use colored pencils. Don't expect to win. I never get close. Do it just for fun.

Tell us if you're participating!

Thursday, June 11, 2009

A conversation

When I was hanging out on campus, I met a guy, henceforth referred to as Alex. He was just walking by, and a mutual friend pulled him over. We were introduced and we started talking.

Because of the location of my hangout point (next to the BASS table), it didn't take long for the topic to turn to religion. Alex quickly realized that I was an atheist, and was curious about it. He was interested in the extent of my knowledge of Christianity and the Bible. One question he asked was, what did I think was the central message of the Bible?

I said I think there are a lot of different things which different Christians hold to be the central message. I have ideas as to what different Christians believe, but I would not dare to guess what he, Alex, thought of as the central message, because I would almost certainly get it wrong.

Mind you, I am a lot less articulate in person than I am in writing (and I also now have the benefit of hindsight). As waffly as I might sound now, I probably sounded worse when I was talking to Alex. Nonetheless, he was consistently polite, and seemed to understand where I was getting at before I got to it.

Another guy, henceforth referred to as Eddie, came up to the table. Eddie told Alex that he thought the debate on religion too often focuses on the extremes. For instance, the most outspoken atheists tend to focus on the most extreme forms of religion, like the Creationists. I quickly pointed out that this is to some extent justified, since the most extreme forms of religion are the ones which disproportionately cause the most problems, and thus deserve the most criticism.

Eddie responded that he didn't think the extremists were the source of the problem, but rather, stupid people were the problem, to put it bluntly. Stupid people will remain stupid whether they are religious or not. But I disagreed with this too. In my experience with skepticism, people who believe weird or harmful things are not necessarily stupid at all. Most of them are ordinary people, and some are highly intelligent.

At this point, Eddie asked Alex what he believed. To Eddie's surprise and mine, Alex believed that the Bible's account of creation was true. That is, he believed in a young Earth of six thousand years. After this, I kept quiet, because I could not think of a better demonstration of my point than to let them continue their own conversation.

Tuesday, June 9, 2009

Gödel's ontological argument, step by step

Update 2015: I wrote a new series on ontological arguments.

By request, I am going to explain Gödel's ontological argument step by step, for your reference. Here's how it will work. I am following the symbolic logic proof shown on the Wikipedia article.* In the first section, I will explain everything in English. In the second section, I will write out the proof symbolically, expanding out steps as much as I feel necessary.

*Please note that there are several different variations of Gö
del's ontological argument with different sets of axioms and different steps. C. G. Small has another explanation, using a different variation of Gödel's argument.

Section 1: English

All capital letters represent any given property. All small letters represent objects. I use the word "negative" to merely mean non-positive.
• Entailment: V "entails" W if and only if in all possible worlds, all objects with property V also have property W. Note that if in all possible worlds, there is not a single object with property V, then V automatically entails W.

• Axiom 1: If Z entails Y, and if Z is positive, then Y is also positive.

• Axiom 2: For all properties Z, either Z is positive or not-Z is positive, but not both.

• Theorem 1: If a property Q is positive, then in some possible world there exists an object with property Q.
• Suppose that Q is positive, and that there is not any possible world where there exists an object with property Q.
• Then in all possible worlds, there are no objects with property Q.
• Therefore Q entails any given property. Q entails R and Q entails not-R.
• Therefore R and not-R are both positive. This contradicts Axiom 2.

• God-like: An object is "god-like" if and only if the object has every property which is positive. Note that a god-like object cannot have any negative properties. If a god-like object had negative property V, then it would fail to have the positive property not-V.

• Axiom 3: The property of being god-like is a positive property.

• Theorem 2: In some possible world, there exists an object which is god-like.
• Since god-like is a positive property, Theorem 1 states that in some possible world there exists an object with the god-like property.

• Essence: Property V is an "essence" of x if and only if the following conditions hold:
• The object x has the property V.
• If x has any property U, then V entails U.

• Axiom 4: If a property is positive, then it is positive in all possible worlds.

• Theorem 3: If an object x is god-like, then the god-like property is the essence of x.
• Suppose x has any property Q. x cannot have any negative properties, so Q must be positive.
• Therefore, in all possible worlds, Q is a positive property.
• Therefore, in all possible worlds, any god-like object must have property Q.
• Therefore the god-like property entails Q.

• Necessary existence: Object x is "necessarily existing" if and only if the following condition holds: For any property V, if V is an essence of x, then in all possible worlds there exists an object with property V.

• Axiom 5: Necessary existence is a positive property.

• Theorem 4: In all possible worlds, there exists a god-like object.
• We know that in some possible world, there exists a god-like object.
• Since necessary existence is a positive property in all possible worlds, that god-like object must be necessarily existing.
• That object has the god-like property as its essence.
• By the definition of necessary existence, there must, in all possible worlds, exist an object which has the god-like property.

• Corrolary 1: If there are two god-like objects, then they cannot have any properties which are different.
• Suppose we have two god-like objects, and some property Q which applies to one object, but not the other.
• Since god-like objects cannot have negative properties, Q must be positive.
• Similarly, not-Q must be positive. This contradicts Axiom 2.
Section 2: Symbolic Logic

P represents the property of being "positive". G represents the property of being "god-like". NE represents the property of necessary existence. All other capital letters represent any given property. All small letters represent objects. The letters "ess" represent "is the essence of".

[Update April 2015: I finally converted all these equations to LaTeX. Hope that makes it more readable! Javascript must be enabled.]
• Axiom 1: $\{P(Z) \wedge \square\forall x[Z(x) \Rightarrow Y(x)]\} \Rightarrow P(Y)$

• Axiom 2: $P(\lnot Z) \Leftrightarrow \lnot P(Z)$

• Theorem 1: $P(Q) \Rightarrow \Diamond \exists x[Q(x)]$
• Suppose $P(Q) \wedge \lnot \Diamond \exists x[Q(x)]$
• $\square\forall x[\lnot Q(x)]$
• $\square\forall x[Q(x) \Rightarrow \lnot R(x)]$
• $P(\lnot R)$ (By Axiom 1)
• $\lnot P(R)$ (By Axiom 2)
• $\square\forall x[Q(x) \Rightarrow R(x)]$
• $P(R)$ (By Axiom 1)
• $\lnot P(R) \wedge P(R)$ (Contradiction)

• Definition of G: $G(x) \Leftrightarrow \forall V[P(V) \Rightarrow V(x)]$

• Axiom 3: $P(G)$

• Theorem 2: $\Diamond \exists x[G(x)]$
• Proof: Combine Axiom 3 and Theorem 1

• Definition of ess: $V~ess~x \Leftrightarrow V(x) \wedge \forall U\{U(x) \Rightarrow \square\forall y[V(y) \Rightarrow U(y)]\}$

• Axiom 4: $P(Z) \Rightarrow \square P(Z)$

• Theorem 3: $G(x) \Rightarrow G~ess~x$
• Proof: Suppose $G(x) \wedge Q(x)$
• $P(\lnot Q) \Rightarrow \lnot Q(x)$ (By definition of G)
• $Q(x) \Rightarrow \lnot P(\lnot Q)$
• $\lnot P(\lnot Q)$
• $P(Q)$ (By Axiom 2)
• $\square P(Q)$ (By Axiom 4)
• Suppose (for contradiction) that $\lnot \square\forall y[G(y) \Rightarrow Q(y)]$
• $\Diamond \exists y[G(y) \wedge \lnot Q(y)]$
• $\Diamond \exists y[[P(Q) \Rightarrow Q(y)] \wedge \lnot Q(y)]$ (By definition of G)
• $\Diamond \exists y[\lnot P(Q)]$
• $\Diamond \lnot P(Q)$
• $\lnot \square P(Q)$
• $\square P(Q) \wedge \lnot \square P(Q)$ (contradiction)
• $\forall Q\{ Q(x) \Rightarrow \square\forall y[G(y) \Rightarrow Q(y)] \}$
• $G~ess~x$ (By definition of ess)

• Definition of NE: $NE(x) \Leftrightarrow \forall V[V~ess~x \Rightarrow \square \exists y V(y)]$

• Axiom 5: $P(NE)$

• Theorem 4: $\square \exists x G(x)$
• Proof:
• $\Diamond \exists y[G(y)]$ (Theorem 2)
• $\square P(NE)$ (By Axiom 4)
• $\Diamond \exists y[G(y) \wedge NE(y)]$ (By definition of G)
• $\Diamond \exists y[G(y) \wedge ( G~ess~y \Rightarrow \square \exists x G(x) )]$ (By definition of NE)
• $\Diamond \exists y[G~ess~y \wedge ( G~ess~y \Rightarrow \square \exists x G(x) )]$ (By Theorem 3)
• $\Diamond \exists y[\square \exists x G(x) ]$
• $\Diamond \square \exists x G(x)$
• Lemma: $\Diamond \square S \Rightarrow \square S$ for any statement S
• $\Diamond \lnot S \Rightarrow \square\Diamond \lnot S$ (an axiom of modal logic)
• $\lnot \square\Diamond \lnot S \Rightarrow \lnot \Diamond \lnot S$
• $\Diamond \square S \Rightarrow \square S$
• $\square \exists x G(x)$

• Corrolary 1: $G(x) \wedge G(y) \Rightarrow \forall Q[Q(x) \Leftrightarrow Q(y)]$
• Suppose $G(x) \wedge G(y) \wedge \exists Q[ Q(x) \wedge \lnot Q(y) ]$
• $P(\lnot Q) \Rightarrow \lnot Q(x)$ (By definition of G)
• $\lnot P(\lnot Q)$
• $P(Q)$ (By Axiom 2)
• $P(Q) \Rightarrow Q(y)$ (By definition of G)
• $\lnot P(Q)$
• $\lnot P(Q) \wedge P(Q)$ (Contradiction)
Questions, corrections welcome.

I realize that in the comments, it's hard to use symbols which don't appear on a keyboard. The following symbols will be understood:
~ or $\lnot$ is "not"
[] or $\square$ is "in all possible worlds" or "it is necessary that"
<> or $\Diamond$ is "in some possible world" or "it is possible that"
=> or $\Rightarrow$ is "if ..., then..."
<=> or $\Leftrightarrow$ is "if and only if"
^ or $\wedge$ is "and"
v or $\vee$ is "or"
E or $\exists$ is "there exists"
A or $\forall$ is "for every" or "for all"

Friday, June 5, 2009

So I have a friend, henceforth referred to as Joe the Skeptic, who likes to talk to the LaRouchebags and other crazy people on campus. It's like a hobby for him.

"LaRouchebags" is our name for the LaRouche movement, a cult of personality around economist and philosopher Lyndon LaRouche. They are a very cryptic and bizarre political movement. If I were to pick an overarching theme, I'd say that it is their opposition to the British Empire. You know, as if we were still fighting the American Revolution.

And because Isaac Newton was British, he couldn't possibly deserve the credit which is given to him. He is a Babylonian witch, and may not have even existed. They believe all of Newton's laws of motion were stolen from Kepler's laws of planetary motion. As a physics student, they would say I'm part of the cult of Newton.

I think these guys prey on college dropouts.

At a previous point in time, Joe the Skeptic had given the LaRouchebags a simple physics problem. The problem involved frictional force. He asked them to solve it through use of Kepler's laws alone, without reference to Newton's laws. Of course, this is impossible, since Kepler's laws only refer to planetary orbits, and say nothing about non-orbital motion. But wouldn't you know, the LaRouchebags never admit it (and never solve the problem either).

The other day, I accompanied Joe the Skeptic on one of his ventures to speak with the LaRouchians. He asked one if he ever solved that physics problem he gave them. Yes, he said, he had e-mailed him the answer. Joe says he never got that e-mail. So the LaRouche guy starts talking about pre-Newtonian concepts of force. Allegedly, such-and-such scientist had decided that F=mv. And then later, another scientist decided that F=mv2. So when Newton came up with F=ma, that was nothing new. He just changed a "v" to an "a".

So, I said, Newton changed a wrong equation to a correct one? Doesn't that deserve credit? No, he says. All he did is change a letter. It doesn't matter whether you call it "v" or "a".

So my friends and I started telling him how ridiculous this is. The units aren't correct. "v" and "a" represent completely different concepts. No, they're not measured the same way. Would you say that Einstein simply took the equation E = mv2/2, dropped the 1/2, and changed the "v" to a "c" to make his famous equation E=mc2?

After a bit more of this, the guy Godwinned us all. See, it's people like us that allow this to happen. He points down to the sign on his table, which has a picture of Obama with a Hitler mustache. See, Hitler approves of Obama's health care policies. And if there's one thing we don't like about Hitler, it's his health care policies. Also, all of us are liberals, and liberals can't be scientists!

And then he said he wanted us to go away. He didn't want to talk to us anymore. Joe the Skeptic told me that this was the first time he had seen them ask anyone to go away.

Oh, the stories! Supposedly, many years ago, the LaRouchebags had a formal debate with the campus Objectivist club. Guess who won?

Wednesday, June 3, 2009

Plug: Faith Meets Doubt

"Faith Meets Doubt"

This was a student discussion panel held at UCLA with two Christians, two Muslims, and two atheists. It occurred two weeks ago, and I finally got around to writing up a summary of the discussion. It's fairly lengthy. A few samples:
According to Tim, if you live under Sharia law, stealing is punished by cutting off the thief’s hand. This is a just punishment, because you are under Sharia law. Likewise, we are part of God’s system, so God’s justice must be just. Under God’s justice, God used an innocent man to forgive everyone’s sins.

If we study past societies, we find that they always have a higher figure, though they often have different characteristics. To understand the details of this higher figure, it is best to ask God himself. Nader then pointed to the Koran as a book without contradictions, and some scientifically confirmable facts.

[Andrew, an atheist] commented that in the story of Abraham, the first question that should be asked is “Am I being deceived?” He noted that when the Jim Jones cult committed mass suicide, no angel came in to save them, as they saved Abraham’s son.
Looks like fun, eh? Go read the whole thing, and feel free to disagree with any panelists and verify their facts.

[Is it just me, or have I had a glut of religiously related posts lately? I will not apologize for this.]

Monday, June 1, 2009

ReligiousTolerance: biased by Scientology?

I heard a rumor on the internets that the website religioustolerance.org is run by Scientologists. Oh no!

I mean, if it were true, that would be rather disappointing. I've cited them myself a few times. They have all sorts of useful fact sheets. Would I have to retract these citations? I have never cited them on any Scientology-related topic, but I did once cite them on recovered memory therapy. Given Scientologists' negative views of psychology, this may have been an unwise move.

But wait, hold on! First we must consider two questions. Is religioustolerance.org (henceforth referred to as OCRT, the Ontario Consultants on Religious Tolerance) in fact linked to Scientology? Are they a reliable source of information?

See, the Church of Scientology has a history of rather deceptive practices. For instance, they had a hostile takeover of the Cult Awareness Network in 1996. And there was also Operation Snow White in the 1970s, where they infiltrated the government to purge certain documents about L. Ron Hubbard. I'm not going to go on about it, but if you look around, you'll find that the Church of Scientology has a lot of front organizations that you would not expect. They also tend to criticize their opponents as being religiously intolerant. If you ask me, having a negative view of a religion is not quite the same thing as intolerance.

But what evidence do we have that OCRT has any connection to Scientology? I found one good source which explained all the relevant evidence: the Scientology Critical Information Directory. Apparently, the main criticism is in their treatment of the articles on Scientology itself. Supposedly, the articles used to contain a small amount of critical information in them, but they were changed in late 2006 to be entirely positive towards Scientology (often copying text directly from Scientology publications). The previous versions have disappeared off the internet, so this is unfortunately unverifiable.

What is verifiable, is that many of the articles were written or coauthored by Al Buttnor, who is a spokesperson for the Church of Scientology. If you look around the Scientology section, you'll find that most of the articles are credited to him.

Now, let's go to the OCRT website to see what they say about themselves. They claim to be a group of 5 volunteers, none of whom are Scientologists. Because these volunteers are not named, I do not know if Al Buttnor is considered to be one of them, or if he's just some outside contributor. They do refer to accusations that they are closet Scientologists, but they do not actually address any of the arguments. Instead, they address some argument I've never seen:
The person who accused us of being members of the Church of Scientology noted that we used the same unusual date notation as did L. Ron Hubbard. Actually date notations in year-month-day order (such as 2000-JAN-25) are fairly common outside of the U.S.; they are clear and unambiguous, and easy for computers to sort.
This is not very reassuring to me. In fact, it is the opposite of reassuring. Who is this unlinked critic? Why don't they address any of the actual criticisms which are being made, like the co-authorship of Al Buttnor? They seem to openly state all the other criticisms which they receive, why not this one?

That said, the evidence is disappointing, to say the least. There are plenty of alternative explanations for their failure to address criticism. Maybe they just didn't consider it worth addressing.

The next question is, are they a reliable source of information? Regardless of whether they have any Scientologists in the background, I think the answer is about the same. When it comes to information which is unflattering to the Church of Scientology, they do not provide reliable information. They provide hardly information at all.

When it comes to most other things, they seem reliable. Of course, it's hard to tell. Since they mostly list lots of facts, and clearly cite their sources, there is not much room for them to do anything horribly wrong. At worst, they could be committing the sin of omission. They could be omitting certain facts, making it look like one side has much more evidence than the other.

I suppose the lesson is that it's best to look at multiple sources to avoid possible omissions. Because otherwise, you never know whether they're omitting anything or not. This is true whether Scientology is involved or not. Everyone has their biases.

But in practice, I'm probably too lazy to do any of that (the nicer way of putting it is "energy efficient"). Pending further evidence of bias, I tentatively retract none of my citations to OCRT.