Solution to red-eyed monks

See the original puzzle

Cuddly Teddy Fish was the first person to solve.  Hir explanation was so good and/or I am so lazy, that I'm just going to copy it.

If there is only one monk with red eyes, then he sees all the others are brown-eyed, so he must be the red-eyed one. He kills himself the first night.

If there are two monks with red eyes, then each sees one monk with red eyes and reasons that if this other monk is the only monk with red eyes, he will kill himself the first night. Neither monk kills himself the first night, so they each reason that they must have red eyes too. Both kill themselves the second night.

If there are three, each expects the other two to commit suicide the second night. This doesn't happen, so each deducts that he must be a third, and the suicides happen the third night. Extends to four, five, etc.

If the suicides happened n midnights after the tourist's remark, then there are n monks with red eyes.

What I always found mind-blowing about this puzzle is that if there are multiple red-eyed monks, then they already know from the beginning that there is at least one red-eyed monk.  The tourist didn't really tell them anything new.

But the tourist did convey a key piece of information.  Because of the tourist, all the monks know that all the monks know that all the monks know that all the monks know [etc. etc.] that there is at least one red-eyed monk.

(By the way, in the last website update, I added some javascript to make spoiler links more inconvenient to use.  Now, whenever you follow a link from the puzzle to the solution, there will be a prompt asking you to confirm.)

Greta Christina was right!

Last weekend, I attended the Western Regional LGBTQIA College Conference.  At the risk of having queer topics temporarily dominate my blog, I'd like to say a bit about what happened.  There were a lot of interesting things going on, but one issue really sticks out in my mind.  There was a bit of tension, because there were not enough workshops focusing on the issues of queer people of color

Greta Christina, who is one of my favorite people, wrote earlier about what the atheist movement can learn from the gay movement.  The point she emphasizes most is that we should be more inclusive of women and people of color.  The LGBT movement got this one wrong early on, and the problem has perpetuated itself to this day.

I saw this message played out in the conference.  The organizers of the conference, of course, have nothing but the best of intentions.  But they can't force people to make more workshops for queer people of color.  They can only host whatever workshops they get.  As the pieces fell, they got only two workshops dealing directly with issues of race.*  As the pieces fell, these workshops were scheduled for the same time slot.

*On the plus side, there were a lot of workshops dealing with transgender issues.  Kudos for that.

It's not a matter of actively doing anything wrong.  It's a matter of not actively working to fix the problem.  They should have actively searched for workshops dealing with race, and actively tried to reduce such schedule conflicts.  But it seems like the issue of race was not even on the radar for the organizers, until the conference had already started.  They scrambled to reschedule the workshops so that people could attend both.  At least they were both very good.

I knew that the LGBT movement had some internal conflict about race (mostly from Greta Christina), but I hadn't realized how big it was until now.  I believe UCLA gave me a skewed perspective.  The queer organizations at UCLA are relatively diverse.  There are several subgroups for different ethnicities.  There was a time when I thought this was strange, since conventional wisdom holds that segregation is always bad.  But I can clearly see that the subgroups are effective at increasing diversity.  Different groups are able to focus on different issues, so that everyone can find a group which is relevant to them.  There is also a lot of cross-participation between the groups too, so it's not nearly as segregated as it might seem.

Let's talk about the organization I run, the Bruin Alliance of Skeptics & Secularists.  I have to admit that we have a diversity problem.  We have women, and we have ethnic minorities, but we don't have nearly as many of them as I would like.  Furthermore, all the officers are men, and most of them are white.  These are officers that I picked.  In my defense, I pick officers on the basis of who wants to get actively involved, and as the pieces fell, they were mostly white men.  At least I can say that they're not all heterosexual.

Let's also look at the larger atheist and skeptical movements.  As the pieces fell, all of the biggest leaders are white heterosexual men.  Richard Dawkins, Sam Harris, Christopher Hitchens, Daniel Dennet, PZ Myers, Michael Shermer, James Randi, Phil Plait, etc.  You really have to know your skeptical celebrities before you can name any exceptions.  And whose fault is this?  It's hard to say, since leaders are "selected" through a complicated and mysterious process.

But regardless of the source of the problem, it is a problem nonetheless, one which requires a solution.  Talking about the cause of the problem is only useful insofar as it helps us find a solution.  And perhaps some of the best solutions are those which are effective regardless of cause.

Anyways, I am seriously inspired to bring up this topic at BASS.

Privileged priors and God

On Less Wrong, someone thought up a new kind of fallacy, called "privileging the hypothesis".

Suppose that the police in Largeville, a town with a million inhabitants, are investigating a murder in which there are few or no clues - the victim was stabbed to death in an alley, and there are no fingerprints and no witnesses.

Then, one of the detectives says, "Well... we have no idea who did it... no particular evidence singling out any of the million people in this city... but let's consider the possibility that this murder was committed by Mortimer Q. Snodgrass, who lives at 128 Ordinary Ln."

I would describe this fallacy as "questionable choice of prior probabilities".

Prior probabilities are something you need to consider if you wish to compare hypotheses with Bayesian statistics.  The prior probability of a hypothesis is the probability you assign before you consider the relevant evidence.  Prior probabilities are fundamentally arbitrary.  It's supposed to indicate your personal degree of belief.  Therefore, you can pick whatever numbers you like, and so can I.

And yet, some choices of prior probabilities are just more reasonable than others.  In the example of Largeville, we can reasonably say that there is a prior probability of one in a million that Mortimer Q. Snodgrass is the murderer.  Or perhaps we'd choose a higher probability, because we want to exclude young children.

But the detective has a much less reasonable choice of prior probabilities.  By simply pointing Mortimer out, the detective has biased our investigation significantly.  Because we have trouble conceptualizing numbers as small as one in a million, we can't help but overestimate the probability that Mortimer is the murderer.  The detective has wrongly privileged the hypothesis that Mortimer is the murderer.

For fun, here's a gratuitously controversial example of "privileging the hypothesis": God.  Specifically, let us consider the cosmological argument for God (ie God was required for the universe to exist).

If we accept the cosmological argument, then we can conclude that something ("the first cause") allowed for the universe to exist.  We can also conclude (depending on which kind of cosmological argument we're using) that the first cause is eternal, non-contingent, and so forth.  But there's not really anything that requires the first cause to be a god, much less God with a capital G.

I propose that the first cause, if it exists, can be all sorts of things.  The vast majority of those things are not deities, indeed the vast majority don't even have consciousness or intentionality.  But we still know it as the cosmological argument for God.  The hypothesis that the first cause is God is a wrongly privileged hypothesis.

Furthermore, I discourage the use of "god" when it does not refer to any of the gods of major religions.  When we talk about a god, it could be all sorts of things.  But most religious people instantly think of their own god.  By simply using the same word, "god", we inadvertently privilege the hypothesis that the god in question is the god of a major religion.

(via The Thinker)

Some website changes

I finally did it!  I switched up my blog's design!  Tell me what you think!

I've also switched back to embedded comment editors.  Last time I did this, some people had problems.  If you have any problems commenting, please e-mail me at skepticsplay a-t gmail d-o-t com.

I have not created a banner yet, but I did put a placeholder banner so it isn't completely obvious that I'm using a default template.  I am still planning to make a real banner, but knowing me I'll never get around to it.

I also have a few other changes in mind, but we shall see.

Dreams of a site redesign

My blog's current design is boring and I've been wanting to change it for years. I've just been so lazy. Dear readers, please help motivate me.

But I don't have the technical knowledge for it. I'd have to just choose one of the boring blogger templates. I'm thinking of using one with smaller text-width, but then it takes more scrolling to get through the same amount of text, and some images may be cut off.

I also want to design a banner, but I have little confidence in my own aesthetic judgment. At one point, I was thinking of having "Skeptic's Play" written on line paper, surrounded by math/physics/puzzle doodles, but this idea seems lame to me now. Any suggestions?

I also wanted to add something on the sidebar like the Scarlet Letter from the Out Campaign, except for asexuals. Another one for queers too. I may not blog about queer topics all the time, but I still want to represent. But what's a good image to use? What do you think of these asexual symbols?

On the left is an ace. In the middle is a half-filled heart. On the right is the AVEN logo. Another accepted asexual symbol is a slice of cake, but the story behind that is so ridiculous I don't know if I want to use it.

And I suppose a good queer logo would be a rainbow flag. That sound good?

Asexuals: going science-free?

As a member of the reality-based community, I put a high value on science. And so, when I was questioning my sexual identity, I was slightly bothered by the lack of scientific support for the conclusions I was making. This is especially true of something like asexuality. I feel like the existing research is sufficient to support the existence of asexuality, but it couldn't possibly say anything about all the details discussed in my presentation or in the asexual community at large.

But perhaps I was the only one bothered by this. After all, people form their political opinions without constantly referring to scientific evidence. How could we do otherwise? But I feel it is pretty lame to simply say, "science can't know everything." Even if it's obvious, I want a real reason, not just an empty cliche.

Luckily, it's quite easy to think up several real reasons.

1. We are facing a lack of evidence, not contrary evidence. The reason there is so little science on asexuality is not because we've looked around and found nothing. It's because there are some serious methodological difficulties in studying human sexuality, especially that of such a small minority.
   
   Furthermore, there is not enough motivation to conduct these studies. It will remain that way unless the asexual movement pushes for it. The movement must precede the science; there is no other way.
   
   
2. Most claims are about human experience. It's true that a skeptic like me tends to devalue personal experience as evidence. There are statistical biases which render anecdotes unreliable. There are biases which cause us to see patterns where there are none. Altered states of consciousness reflect the reality inside our brain, not the reality outside our brain.
   
   But sexual orientation is different. We are not using personal experience to make claims about outside reality. It is using personal experience to make claims about personal experience. When I observe that I don't find women attractive, I am offering this evidence to prove that I don't find women attractive. I would go on further to say that this experience will likely continue in my life. These claims are not so outrageous that I need to cite scientific sources to back me up.
   
   
3. Some of the most important "claims" are not claims, but obvious value judgments. The issue of sexual orientation is not just about the qualities and characteristics of queer people. The more important message is "these people deserve respect." This is based on the broader premise that everyone deserves respect. However you arrive at this conclusion, I hope it does not hinge on just a few scientific studies.
   

And that's just off the top of my head. I'm sure there are more.

Of course, we still need some way to distinguish between true and false claims. We can't accept everything that's ever said in the asexual community. At least some of those claims will contradict each other. At least a few of them are nonsense, like the idea that asexuality is evolution's response to overpopulation. A little critical thinking and a healthy dose of agnosticism goes a long way.

For example, I take with a grain of salt anything that's said about the prevalence of asexuals or of any of their characteristics. There was a small AVEN survey in 2008 in which 71% of respondents were female and 54% were not religious, but I don't take this to be representative of asexuals in general. If I'm not going to trust a seriously conducted poll, I'm also not going to trust an anecdote as evidence of prevalence. I may make some tentative conclusions on the matter, but I treat them as questionable at best.

I'm also very skeptical of any claims about causes. Causal relationships are hard enough to prove even when the science is there to back you up.

A weekend for holidays

It's two days late, but Happy Darwin day! Darwin was born on February 12, 201 years ago. In previous years, I've prepared essays for Darwin Day, but I didn't have time this year on account of I had to write a lab report. In any case, there is a limitation on my knowledge of Darwin and evolutionary biology.

Did I forget any other important holidays? Oh! It's also Chinese New Year. Gung Hey Fat Choi.

This is the year of the tiger. As the internet tells me, that means that all people born this year will have the unusual characteristic of being sometimes generous, and sometimes selfish. They also tend to be incompatible with people born in the year of the sheep. If that sounds totally like you, your age must be a multiple of 12. Either that or it isn't. Astrology isn't perfect, see, so you should forget about any misses.

We're eating gyoza! Yum.

Skeptical sightseeing on Bruin Walk

Some time ago, the Secular Student Alliance released this advertisement.



I gotta disagree with one part of the video; members of secular student groups aren't exactly the most normal people you'll ever meet.

But the portrayal of the other student groups rings true. On a university campus, you can meet all sorts of groups and individuals with unusual beliefs. At UCLA, all these people appear on Bruin Walk, alongside the fraternities, ethnic groups, and groups for political causes. Most UCLA students miss the strange groups, because they're too busy rushing through Bruin Walk, trying to avoid fliers. But one of the great things about being in a skeptical group is that I learn to recognize the different groups, and learn a little something about each of them. It makes Bruin Walk a lot more fun.

Here's a list of some of the groups I see, in no particular order. One should not assume that I am antagonistic to all these groups.

"You're Going to Hell" sign-holders: They hold large signs saying who's going to hell and why, with appropriate Bible citations. I'm fairly sure that these people are not in a coherent group, but are individual missionaries sent from who-knows-where to evangelize at college campuses. I've never heard a single student speak sympathetically about them. I haven't seen any lately, so maybe they collectively realized how ineffective they were? Nah, that couldn't be it.

9/11 Truthers: They believe 9/11 was an inside job. They don't actually show up on campus except on rare special occasions. My friend likes to go up to these guys and ask them what they're doing to free Khalid Sheikh Mohammed.

Jehovah's Witnesses: This group tables nearly every single day. Jehovah's Witnesses are known for not celebrating holidays and rejecting blood transfusions. They're a bit cultish in that they discourage interaction with outsiders, and "disfellowship" anyone who leaves (cutting off all contact). On the plus side, they have been historically very important in defending separation of church and state.

The Latter Day Saints: AKA the Mormons. I've actually never spoken to the ones on campus, but I do know a bit about Mormonism in general. They believe Jesus came to the Americas shortly after his resurrection. They're comparable to the Jehovah's Witnesses in that leaving the religion will kill your social life.

LaRouche PAC: This non-student group is a cult of personality around Lyndon LaRouche. They're best known for their image of Obama with a Hitler mustache. They oppose the British Empire. Their favorite arguments are "the guy who came up with that idea was an asshole", and breaking Godwin's Law. No, they're even more bizarre than they sound.

The Muslim Student Alliance: These guys show up on afternoons to persuade people to submit to Allah. I find that Muslim apologetics is much classier than Christian apologetics, though it tends to be long-winded and just as ineffective. I've heard of some bad things going on in the group (eg anti-semitism), but I take that with a grain of salt.

LOGIC: LOGIC is the Objectivist club, the only other student group on campus which is explicitly secularist. Objectivism is the philosophy of Ayn Rand, and it's politically libertarian. I forget what the name stood for, but the G is greed and the C is capitalism.

The "Religion is for the Weak" guy: He is a Lutheran minister! I think he believes everyone is weak, and that's why everyone needs religion. I heard he also believes that people can choose to follow God after they die, which I guess is a more pleasant way to imagine the afterlife.

Revolutionary Communist Party: Yes, this is actually a political party. If I were to summarize their position, it would be very liberal economics achieved by means of revolution. The Communists are very sympathetic towards our group, because they're anti-religious, but our group is less sympathetic towards them.

Campus Crusade for Christ: They're just one of many, many Christian student groups on campus. The three major ones are Campus Crusade for Christ, Grace on Campus, and Inter-Varsity Bruin Christian Fellowship. Campus Crusade and Grace on Campus are very conservative Christian groups, but this is not necessarily true of individuals within the group. Inter-Varsity skews liberal, and seems to be filled with International Development Studies majors.

The Universal Philosophical Genius: He's a homeless guy who occasionally appears in the plaza and yells out incoherent stuff about philosophy and physics to no one in particular. One time I saw him doing this as little kids on field trips were walking by. I just feel sorry for this guy.

Hare Krishnas: This Hindu sect will set up a carpet on the grass, chant and play music. They also believe that the moon landing was a hoax, because it contradicts Vedic astrology. They're also very very old earth creationists. I actually haven't seen them since last year. Too bad, they provided some nice atmosphere.

One thing you might notice is that most of these groups are religious in nature. Take that how you will.

The red-eyed monks

Time for more classic puzzles!

There is an island whose only inhabitants are perfectly logical monks with strange practices. Every monk has either red eyes or brown eyes. Red eyes are considered a curse, and any monk who discovers that he has red eyes must kill himself next time it is midnight.

However, the monks do not have any way to discover if they have red eyes. There are no reflective surfaces on the island. While monks can see each other's eyes, they have taken a vow of silence and are not allowed to communicate with each other.

One day, a tourist came by and loudly noted that at least one monk on the island had red eyes. At first, all the monks just silently regarded this fact, but many nights later there were a bunch of suicides. What happened and how?

Bonus question: How do the writers of these puzzles come up with such disturbing situations?

See the solution

Solution to Coloring a Donut

See the original problem

Solution (Spoiler alert!)

Graphics are made with Mathematica. Some of the map is hidden, since it's 3-D, but you may assume that nothing unusual is going on in the back.

If you thought that the donut was too easy, you should try creating a map on a mobius strip that requires at least six colors.

Mobius solution (Spoiler alert!)

Identical particles in Quantum Mechanics

It's been a while since I last discussed Quantum Mechanics. Let's do some more!

One of the aspects of Quantum Mechanics is the existence of identical particles. Suppose I'm holding a photon in my right hand, and a photon in my left hand. I can't physically hold a photon in my hand, of course, but consider it as an abstract example that I can illustrate with pretty pictures.


These two photons are identical. They are exactly alike in every respect. And I do mean every respect. Furthermore, this has profound physical consequences. By profound, I mean that you wouldn't be here if it weren't for identical particles.

Now, I could start talking about the mystical oneness and sameness discovered by scientists in the 20th century, but that would be quite meaningless. There is in fact some meaning I intend to convey here. I say that the photons are "identical" because if you switch photon A and photon B, nothing will change.


But as shown above, it sure seems like something does change when we switch the photons. Namely, before the switch, photon A is in my left hand, and photon B is in my right hand. After the switch, photon A is in my right hand, and photon B is in my left hand. Arguably, this is a very similar situation, but I said that the particles are identical in every respect, identical in a deep quantum mechanical sense.

Therefore, it is not the case that photon A is in my left hand while photon B is in my right hand. Instead, we have a mixed quantum state, with both photons in both hands. Being in a mixed state means adding or subtracting the wavefunctions of two or more states.


Recall that addition is commutative (ie x+y = y+x). And that's how switching the two photons leaves us with the exact same quantum state that we started with.

Okay, so that's nice, you say, but what physical consequence does that have? In this case, there is no consequence whatsoever, because the photons in my two hands are too far apart. But imagine that the photons were very close together, so that their wavefunctions were overlapping. Then we'd have some constructive interference in the overlap.

More impressively, some kinds of particles will have destructive interference. Let's say that instead of photons, we had electrons in our two hands. The two electrons are identical in every respect. But unlike photons, if we switch two electrons, one thing does change. That is, after switching, the wavefunction will be the negative of what it was before. Therefore, the quantum state of the two electrons will have subtraction instead of addition.


Aside: I am representing photons with wavy things, and electrons with fuzzy circles, but the intelligent reader will realize that these are just artistic representations with little basis in reality.

Now imagine that the two electrons weren't in two different hands, but were both in the exact same spot, with the exact same momentum and spin and everything. Then the wavefunction would be something like this:


But I just took a wavefunction and subtracted it from itself. That's just zero! A wavefunction of zero is not possible. Therefore, it is not possible for the two electrons to occupy the same state.

Consequences? To start, this is why atoms have electrons in a complex orbital structure. If the electrons weren't identical, then they would all fall to the lowest orbital around the nucleus. Chemistry would be very different, and you can just forget about biology. But because they're identical, electrons cannot all occupy into the same state. Instead, electrons are forced into higher energy states around the atom, with the highest energy electrons doing all the chemical reactions.

A more astronomical consequence: White dwarfs. White dwarfs are small stars that are held up by so-called electron degeneracy pressure. The electrons can't compress into a smaller volume, because that would require them to fill up the higher energy states. The gravitational force is not enough to supply this energy. However, if the star accumulates enough mass, perhaps from a nearby star, it reaches the Chandrasekhar limit, where the gravitational force is strong enough to supply the extra energy. Upon reaching the Chandrasekhar limit, the white dwarf will collapse, causing a supernova.

Neutron stars are very similar, except they're held up by neutron degeneracy pressure.

Neutrons, like electrons, will interfere destructively with each other. Particles which interfere destructively (like electrons) are called fermions. Particles which interfere constructively (like photons) are called bosons. Fermions include electrons, neutrons and protons. Bosons include photons, gravitons, and certain atomic nuclei, like Helium-4.

Identical particles are all around us. They exhibit weird and important properties that have no analogue in classical mechanics. This is why quantum mechanics matters.