Tuesday, October 23, 2007

Let's see you argue with this

Sometimes an argument occurs to you that's just so ridiculous you have to share. But that's not today. Today I have a very serious point to make, on the very serious subject of abortion.

Now, many pro-lifers claim that life begins at conception, and that the child is a legitimate human at that point. What is it that makes them human? Well, if they stay out of religion, they'll argue about continuity of being, presence of human cells, and so on (if you have another argument, feel free to share that).

So, hypothetical question for any pro-lifers around here: Zombies. Okay, I should probably give you an actual question, I guess. Do zombies qualify as living humans? Now, while there's debate on whether zombies are human, they're by definition dead. If they weren't dead, they wouldn't be zombies. So, zombies are not overall living humans.

But what makes a fetus so different from a zombie? Zombies are connected to humans through a continuity of being, they're made of human cells, and even have higher intelligence and a more human form than a fetus. If zombies are dead, what is it about fetuses that makes them more alive than zombies?

Proceed with your information binge...

Thursday, October 18, 2007

Skeptic's Circle #71: Solutions, part 1

For those of you still hanging around and trying to solve the problems I posed you in the last Skeptic's Circle, I thought I'd do you the favor of compiling some of the solutions that have been posted. So far, I'm just going to give solutions to the problems that someone has solved in the comments, so anyone who wants to can still work on the as-yet unsolved problems. If those don't get solved in a while, I'll post the solutions for them as well.

If you still want to solve them on your own, don't read on. Also, note that for parsimony, I'm not going to be repeating the problems here. Go back here if you need a refresher.

Personalized Perfume Peril

Flip over 48 disks, and then separate those 48 into one pile, with the other 52 in the other pile.

Creative Cake Capers

As yet unsolved, at least here. This problem has been posted with solutions elsewhere on the internet.

Popping Placebo Pills

Take out one pill from the first jar, two from the second, three from the third, four from the fourth, and five (or zero would work too) from the fifth, and weight them. The weight should be the expected weight of 15 placebo pills + x grams, where x corresponds to the number of pills you took out of the jar which has the real pills.

Perilous Peace Problems

Push the cork into the bottle, somehow destroy the cork while making sure any remnants fall into the bottle, melt a hole in the bottle, or simply ignore the whole problem as it's more likely there is no poison gas and it's instead the pill that's poisoned.

Crazed Canting Christians

As yet unsolved here. One little hint: If you make a certain observation about the problem, it becomes trivial math to find the solution.

Hidden Handbook Hassle

Skeptico puts the book in his safe, and his lock on it. He sends the safe to his friend, who puts his lock on it as well, and then returns it. Skeptico removes his lock and sends his safe back. His friend removes his lock and takes out the handbook.

Weird Water Woo

Tilt the glass to the side until the water just reaches the rim. If the water at the bottom also meets the edge there, it's half full. If it's above the edge, you have more than half; below, less than half. If you accidentally spill the water, you now have less than half.

Screwy Scarfe's Secrets

Referring to the guys by the time it takes them to cross:

1 and 2 cross (2 minutes)
1 returns (1 minute)
4 and 8 cross (8 minutes)
2 returns (2 minutes)
1 and 2 cross (2 minutes)

Total time: 15 minutes. Most people end up with some solution that results in 16 minutes, but it's not optimal.

Poor Poisoned Pinheads

Number all the bottles in binary, from 0000000001 to 1101101010 (which corresponds to 874. On the first day, give each of Buzz's captives a number from 1 to 5. Have each of them take a sip from each bottle that has a 1 in its binary digit corresponding to their number. For each captive that gets amnesia the next day, write a 1 in that digit, and a zero for captives who didn't get amnesia. The second day, do the same thing with the 6th through 10th digits. Once all the digits are written down, you'll have uniquely identified the poisoned bottle. At this point, make them all drink from it and throw them out on the street so they won't be able to tell anyone what you did.

What Wifi Woo?

As yet unsolved here. The best solution given can do it in 4 total trips, but it's possible to do it in only 2.

Manic Motor Mythbusting

Use the following program:

Move 100m forward (label: START)
Move 100m forward
Move 100m backward
Skip next command unless a parachute is nearby
Move 100m forward (label: SPEEDUP)

Paddling Pooch Problem

As yet unsolved here.

Action/Adventure Akusai

Choose to play first, and place your first disk at the center of the table. After this, match each of your opponents moves with a symmetric move across the table from him. He'll run out of moves first.

Great Galileo's Ghost

I'll just quote the solutions from my comments here. Figuring out which is which is trivial, as you just have to ask questions you know the answer to, and keep repeating to sort out who's answering randomly. First, from Miller:

For the Galileo puzzle, you can ask the following compound question to voip out lying clones:

Is the following true: You will answer this with "yes" or (inclusive) you are the real Galileo.

Similarly, the following will voip truth-telling clones.

Is the following true: You will answer this with "no" or you are the real Galileo.

Alternating between these two questions will eventually voip a clone with the random curse.

From Simon, a single-shot question:

"Is it the case that you are a clone and that you will either answer this question truthfully with a 'no' or falsely with a 'yes'?"

My original answer to this last part was the question: "Is the statement, 'You are a clone and this statement is false,' true?"

Super-Scammer Secrets

As yet unsolved completely. There are many ways you could decrease the amount of information found on a single slide, but the true puzzle is to figure out a way that whichever two slides are found, absolutely zero information is passed on.

For a hint, imagine if the puzzle were to instead use two slides, and either alone would carry no information. The following solution would work in this case: Pixelate the presentation, and make sure the pixels are quite large and easily distinguishable. Generate one transparency that's completely random, with each pixel being randomly either transparent or 50% opaque. Then, for the second sheet, for the places where the message is spelled out, choose either transparent or 50% opaque as necessary to make the pixel result in 50% opaque. For places where the message isn't, match the pixel to the one on the other slide. The result will be the message appearing in grey text on a mixed black and white background.

Note that this is possibly the most difficult problem here. Though it's been posed on the internet, I haven't found any solutions posted. I have solved it myself, however, so don't worry.

Harebrained Hat Help

Solution by RodeoBob:

Got the Hats puzzle solved. It does, however, depend on everyone being an expert at logic, and everyone following the same game plan...

The color of the wearer's hat is the same color as the smallest group of colored hats he or she can see, and they must make their guess (and leave the circle!) at the first opportunity allowed.

To make it clearer, let's break the process up into 5-minute rounds. (at the end of each 'round', the announcement comes on asking folks to announce the color of their hat)

In the first round, anyone who can only see one hat of a specific color is wearing that color hat. (we know there must be at least two, right?)

In the second round, anyone who can see only two hats of a given color is wearing that color. (we know that there must be three of each color now, since any color that were only present on two heads should have left last round...)

The puzzle only works if everyone is looking, and if everyone leaves at the right time. If somebody falls asleep, or isn't paying attention, or loses count and misses a round, the whole thing falls apart.

Singular Sword Slashes

From Rick Taylor in the comments:

In the singular sword slashes, none of the prisoners were killed.

They all got together and agreed as follows. Whoever was last in line would call out his own hat based on the parity of red hats he saw before him. If he saw an even number of red hats, he'd call his red; if he saw an odd number red hats, he'd call his blue. That man might die, but the next in line, seeing the hats in front of him and knowing the parity of red hats including his own could deduce his hat color. The man in front of him, now knowing both the color of the hat behind him and the parity of all the hats besides his own could deduce his own, and so on to the front of the line. The executioner, hearing this and seeing he could not avoid sparing all but the last in line, arranged the hats to ensure at least he was killed, even though the 99 others were spared, and that was that.

Only it wasn't. All one hundred silently reasoned that the executioner would have to place an even number of red hats in order to kill the last one in line. And so they abandoned their plan and used that information to save them all from last to first.

The truly delicious part of that last solution is that even if we assume the executioner anticipated they would change their strategy to trick him (no reason to as he isn't part of the mensa cult) and put an odd number of red hats to on them, the last man in line would die, but the 99 remaining would still live, even using the wrong information. So there's no reason for them not to try!

Ending Erroneous Expectations

From Edward in the comments:

We can answer the pirates problem using induction, of sorts.

Consider the situation with 5 pirates. If it ever gets down to two pirates, the senior one can simply award all the money to himself and vote for it. With three pirates, the senior one has to convince one other pirate to vote for his plan. The cheapest way of doing this is to award the junior pirate 1 coin and keep 99. Then with four pirates, the senior one only has to convince one other pirate to join him. If it gets down to three, the middle one can't expect to make anything, so he can be bought with 1 coin. With five pirates, the senior pirate needs two others to join him. He can do this by giving one coin to each of the 3rd and 5th most senior pirates, since they'll get nothing if he dies. He would keep the other 98 coins to himself.

Now consider six pirates and only one coin. As before, with only two pirates, the senior pirate can award all money to himself. With three, the senior pirate needs to award the one coin to the junior pirate. With four, the senior pirate can award the coin to either of the two pirates immediately below him. With five pirates, the senior pirate need to convince two pirates to join him, which is impossible. Therefore the second most senior pirate will die if it gets to him, so he will vote for absolutely any plan the most senior pirate proposes. The most senior pirate can then avoid death by awarding the coin to the most junior pirate.

That's it for now, so go give those unsolved problems another try if you think you're up for it!

Proceed with your information binge...

Tuesday, October 16, 2007

Something for nothing and your universe for free

One argument I keep running into that is supposedly evidence for God (sometimes a generic god, sometimes a specific one) is that the universe began, therefore it must have been created. Sometimes it's more elaborate than this, sometimes not. In the cases where it's just this simple, it's effectively a God of the gaps argument. Since that type of argument has been dismantled repeatedly, I'm going to focus on the more elaborate versions today.

The most common elaboration to this argument is that the creation of the universe violates conservation of energy. "It's a well-known fact of science that you can't get something from nothing," they say. Interestingly, it seems that the people who say this sort of thing rarely have any real background in physics, much less a background in theoretical physics or cosmology. Before making big assumptions like this, wouldn't it make sense to check with someone who knows what they're talking about in this area to see if they could explain it?

Now, if only we had a cosmologist on hand... Wait a second, I'm a cosmologist! Well, I guess I'd better try to make some sense of these problems then. So, to the claims that the creation of the universe violates conservation of energy, my response can be summed up in two simple retorts: "Says who?" and "Even if so, so what?" Allow me to elaborate.

The first catch is that we don't know for sure that the creation of the universe actually does violate conservation of energy. First, let's keep to known science, and use an example taking place within our own universe. Let's say that somehow, a massive particle was created. Since mass = energy, this took up energy to create it. Now, what could have happened to allow this creation? A few possibilities:

1. Some physical process took place which resulted in an excess of energy. This extra energy was converted into this particle.
2. Even a vacuum doesn't have zero energy. It's possible that this particle borrowed energy from the vacuum in order to form (possibly along with its antiparticle if it has other properties such as charge which need to be conserved).
3. This particle was created alongside a mirro version of itself which has negative mass, resulting in a net change of zero energy. Note that we've never observed negative mass particles, but our current laws of physics don't bar them from existing.

So, let's expand to the creation of our universe. It turns out that for each of these, there's a nice parallel for the creation of the universe as well:

1. Some physical process took place outside our universe which resulted in an excess of energy. This extra energy was converted into our universe.
2. Whatever medium exists outside our universe might not necessarily have zero energy. It's possible that the creation of our universe simply borrowed some energy from this medium. A parallel anti-universe might also exist to balance quantities which must be conserved.
3. Our universe was created alongside a negative energy version of itself, so the net change in energy is zero.

There's also one more explanation which works for our universe, but not for the particle example:

4. Our universe has a net energy of zero. It is possible that the mysterious phenomenon we've termed "Dark energy" actually has negative energy, and this balances out the positive energy all of the mass in the universe provides. A little catch is that there's likely much more dark energy in the universe than all the other mass, so we'd actually be at an excess if this were true. That's little problem though, as it could easily have just been radiated away or whatever outside our universe.

So there you have it, four possible reasons why the creation of our universe might not violate conservation of energy. But even going into all that isn't really necessary. The catch is, violating conservation of energy isn't necessarily a problem when it comes to the creation of the universe. The reason for this is a bit complicated, but a simple version is as follows: Conservation of energy is an observation we've made which always seems to hold within our universe. We have no evidence that it holds outside our universe, or even that any of our laws of physics are the same out there. Therefore, we don't have reason to believe it must hold at the point of creation.

Now, for the more complicated explanation. We actually do have one explanation for why energy (and other properties, for that matter) is conserved. The reasoning is complicated, so I won't go into it here, but the key point is that it relies on what are known as symmetries. In the physics world, a symmetry is more than simply being able to mirror something and have it be the same. What it means here is that we could move the whole frame of reference in some way, and all the physics would remain the same.

There are three big symmetries of this type you'll know of. There's translational symmetry, which means if you move a foot to the right for instance, physics stays the same. There's rotation symmetry, which means whichever way you turn, the physics is the same. And there's temporal symmetry, which means that physics stays the same over time. There are also some others you probably haven't heard of it you haven't take college physics, such as gauge symmetry, but you don't need to worry about those here.

The important point about this is that there's a law of physics which states that for every symmetry, there must be some conserved quantity. This is completely unintuitive, but it's provable. Not easily provable, and most people reading this probably wouldn't understand the proof in any case, but it is provable, so just trust me on this. When we apply this law, we get the following conservations from the following symmetries:

-Translational symmetry gives us conservation of momentum.
-Rotational symmetry gives us conservation of angular momentum.
-Temporal symmetry gives us conservation of energy.
-Gauge symmetry gives us conservation of charge.

The important one for our purposes is the third: Temporal symmetry gives us conservation of energy. What happens if we no longer have temporal symmetry? Well, we can no longer guarantee conservation of energy. Now, think back to the beginning of the universe. At this point, all of the universe is compressed to a single, zero-dimensional point. Are the laws of physics the same here? Not at all. Temporal symmetry must be broken at this point, so we have no reason to believe that conservation of energy must apply. The instant after it, we start to have temporal symmetry, so whatever energy we start with we're stuck with, but there's no way to say what this might be.

So there you have it: a cosmologist's perspective on conservation of energy at the beginning of the universe. We don't know that the beginning of the universe violates conservation of energy at all. Even if it does, this isn't necessarily a problem. Even if all this is a problem, it's still at best a God of the gaps argument, and that's really no reason to believe at all.

Proceed with your information binge...

Friday, October 12, 2007

The Streisand Effect

The Society of Homeopaths really should do their research before trying to censor something on the internet. Then again, homeopaths and actual research aren't exactly the best of friends, so it's not surprising they've never heard of the Streisand Effect. Basically, it's a trend on the internet that trying to censor some material just generates more publicity and makes the material more widely available. This is why you now see many bloggers - myself now included - reposting Le Canard Noir's post, "The Gentle Art of Homeopathic Killing." Check out Respectful Insolence for a bit more on the story.

So, I now present to you:

The Gentle Art of Homeopathic Killing

by Le Canard Noir

The Society of Homeopaths (SoH) are a shambles and a bad joke. It is now over a year since Sense about Science, Simon Singh and the BBC Newsnight programme exposed how it is common practice for high street homeopaths to tell customers that their magic pills can prevent malaria. The Society of Homeopaths have done diddly-squat to stamp out this dangerous practice apart from issue a few ambiguously weasel-worded press statements.

The SoH has a code of practice, but my feeling is that this is just a smokescreen and is widely flouted and that the Society do not care about this. If this is true, then the code of practice is nothing more than a thin veneer used to give authority and credibility to its deluded members. It does nothing more than fool the public into thinking they are dealing with a regulated professional.

As a quick test, I picked a random homeopath with a web site from the SoH register to see if they flouted a couple of important rules:

• Advertising shall not contain claims of superiority.
• No advertising may be used which expressly or implicitly claims to cure named diseases.

72: To avoid making claims (whether explicit or implied; orally or in writing) implying cure of any named disease.

The homeopath I picked on is called Julia Wilson and runs a practice from the Leicestershire town of Market Harborough. What I found rather shocked and angered me.

Straight away, we find that Julia M Wilson LCHE, RSHom specialises in asthma and works at a clinic that says,

Many illnesses and disease can be successfully treated using homeopathy, including arthritis, asthma, digestive disorders, emotional and behavioural difficulties, headaches, infertility, skin and sleep problems.

Well, there are a number of named diseases there to start off. She also gives a leaflet that advertises her asthma clinic. The advertising leaflet says,

Conventional medicine is at a loss when it comes to understanding the origin of allergies. ... The best that medical research can do is try to keep the symptoms under control. Homeopathy is different, it seeks to address the triggers for asthma and eczema. It is a safe, drug free approach that helps alleviate the flaring of skin and tightening of lungs...

Now, despite the usual homeopathic contradiction of claiming to treat causes not symptoms and then in the next breath saying it can alleviate symptoms, the advert is clearly in breach of the above rule 47 on advertising as it implicitly claims superiority over real medicine and names a disease.

Asthma is estimated to be responsible for 1,500 deaths and 74,000 emergency hospital admissions in the UK each year. It is not a trivial illness that sugar pills ought to be anywhere near. The Cochrane Review says the following about the evidence for asthma and homeopathy,

The review of trials found that the type of homeopathy varied between the studies, that the study designs used in the trials were varied and that no strong evidence existed that usual forms of homeopathy for asthma are effective.

This is not a surprise given that homeopathy is just a ritualised placebo. Hopefully, most parents attending this clinic will have the good sense to go to a real accident and emergency unit in the event of a severe attack and consult their GP about real management of the illness. I would hope that Julia does little harm here.

However, a little more research on her site reveals much more serious concerns. She says on her site that 'she worked in Kenya teaching homeopathy at a college in Nairobi and supporting graduates to set up their own clinics'. Now, we have seen what homeopaths do in Kenya before. It is not treating a little stress and the odd headache. Free from strong UK legislation, these missionary homeopaths make the boldest claims about the deadliest diseases.

A bit of web research shows where Julia was working (picture above). The Abha Light Foundation is a registered NGO in Kenya. It takes mobile homeopathy clinics through the slums of Nairobi and surrounding villages. Its stated aim is to,

introduce Homeopathy and natural medicines as a method of managing HIV/AIDS, TB and malaria in Kenya.

I must admit, I had to pause for breath after reading that. The clinic sells its own homeopathic remedies for 'treating' various lethal diseases. Its MalariaX potion,

is a homeopathic preparation for prevention of malaria and treatment of malaria. Suitable for children. For prevention. Only 1 pill each week before entering, during and after leaving malaria risk areas. For treatment. Take 1 pill every 1-3 hours during a malaria attack.

This is nothing short of being totally outrageous. It is a murderous delusion. David Colquhoun has been writing about this wicked scam recently and it is well worth following his blog on the issue.

Let's remind ourselves what one of the most senior and respected homeopaths in the UK, Dr Peter Fisher of the London Homeopathic Hospital, has to say on this matter.

there is absolutely no reason to think that homeopathy works to prevent malaria and you won't find that in any textbook or journal of homeopathy so people will get malaria, people may even die of malaria if they follow this advice.

Malaria is a huge killer in Kenya. It is the biggest killer of children under five. The problem is so huge that the reintroduction of DDT is considered as a proven way of reducing deaths. Magic sugar pills and water drops will do nothing. Many of the poorest in Kenya cannot afford real anti-malaria medicine, but offering them insane nonsense as a substitute will not help anyone.

Ironically, the WHO has issued a press release today on cheap ways of reducing child and adult mortality due to malaria. Their trials, conducted in Kenya, of using cheap mosquito nets soaked in insecticide have reduced child deaths by 44% over two years. It says that issuing these nets be the 'immediate priority' to governments with a malaria problem. No mention of homeopathy. These results were arrived at by careful trials and observation. Science. We now know that nets work. A lifesaving net costs $5. A bottle of useless homeopathic crap costs $4.50. Both are large amounts for a poor Kenyan, but is their life really worth the 50c saving?

I am sure we are going to hear the usual homeopath bleat that this is just a campaign by Big Pharma to discredit unpatentable homeopathic remedies. Are we to add to the conspiracy Big Net manufacturers too?

It amazes me that to add to all the list of ills and injustices that our rich nations impose on the poor of the world, we have to add the widespread export of our bourgeois and lethal healing fantasies. To make a strong point: if we can introduce laws that allow the arrest of sex tourists on their return to the UK, can we not charge people who travel to Africa to indulge their dangerous healing delusions?

At the very least, we could expect the Society of Homeopaths to try to stamp out this wicked practice? Could we?

Proceed with your information binge...

Thursday, October 11, 2007

Skeptic's Circle #71

Welcome one, welcome all, to the 71st edition of the Skeptic's Circle. The theme for this week is logic. Logic puzzles to be precise. After all, logic is one of the best razors against irrational thinking, and like any razor it needs to be periodically sharpened. So, for that purpose I've prepared some logic puzzles for you all to work through, each one based on a post submitted.

I've sorted the puzzles by a rough estimate of their difficulty, though the ones each person will find easiest will likely differ. Feel free to discuss the puzzles in the comments, including guesses as to the answers (though if you've heard one before, don't spoil the fun for others). Just be warned that if you go reading the comments, you might run across an answer or two that's already been guessed.

I've also prepared a "Just the links" version if you're short on time or logic, so feel free to take advantage of that.

The next Skeptic's Circle will be hosted at The Quackometer Blog. Check over there for contact information to submit for next week's. So long, and happy puzzle-solving!

Proceed with your information binge...

Skeptic's Circle #71: Hard

Following are the hard problems for this Skeptic's Circle. Math isn't as much a requirement as for the medium problems, but you'll have to compensate with a ton of advanced logic.

Great Galileo's Ghost

Cranks have always loved to compare themselves to Galileo. Sick of this, one day Greta Christina decided to set them straight once and for all. To do this, she decided to go on a fictional journey to the afterlife to find Galileo himself so he could explain to them why they're acting like idiots. However, when she reached the afterlife, she ran into a little problem.

It seems that one day, Galileo accidentally touched a noodly appendage he shouldn't have, and ended up with a couple clones. On top of this, the three are cursed to always stay together and that if any yes-or-no question is posed to one of the three, they all must answer it. Any other type of question will be ignored by all three. Each of the clones plus the original has a specific curse on them, but it's unknown who has which curse. One of the curses requires the bearer to tell the truth to any question, another curse requires the bearer to lie in response to any question. The third curse causes the bearer to randomly choose between telling the truth and lying before answering each question.

Each of the Galileos knows whether it's the original or a clone, but without knowing which bears which curse, it would be tricky to figure it out. Is there a questioning procedure that would work here?

Now, Greta can't go back to the real world with three mixed-up possible Galileos, but fortunately, there's a way to break the curses. If any of them is ever faced with a question they can't answer (for instance, they're bound to tell the truth for this question, but the question has no truthful answer that doesn't result in a paradox), they'll go "Voip!" and vanish (so sayeth the FSM). If the two clones both vanish, the original Galileo will be freed from all the curses on him. However, he could vanish too if he's asked a question he can't answer, and if he does, it's game over. Is there a way to target out the two clones and make them vanish while keeping Galileo safe?

If you can accomplish that, one further challenge: Can you make both clones vanish with a single question, even if you haven't previously figured out which one is the real Galileo?

Super-Scammer Secrets

Lord Runolfr recently got a couple of e-mails from scammers, raising my suspicions that something big was afoot behind the scenes. I called up a few contacts, did some research, hired a few James Bond-alikes, and here's what I've figured out:

There's some evil mastermind behind the whole plan, and he's about as supervillanous as they come. This of course means that he wants to capture one of my James Bond-alikes and subject him to an intricately detailed explanation of his evil plan before killing him in a creative way. Apparently, the way he's decided to go about this revelation is through an overhead transparencies with the key points of his evil plan (you'd think he'd have better technology than my high school, but he's out to make money, so he saves it where he can).

Now of course, he's wary of this transparency falling into the wrong hands, so he's come up with a plan to keep things safe. He's figured out some method to spread the information across multiple sheets, arranging it so that if we get a hold of any two, we'll still have no idea what he's planning. So, what we need to figure out now is some possible ways he might have done this, so if we manage to get our hands on more than two, we'll know how to read them (if it's not immediately obvious). What are some possible things he could do? Remember that he's out to save money, so splitting it up to have a single word on each slide or something huge like that doesn't seem too likely.

Harebrained Hat Help

Orac reports that the University of Maryland's Shock Trauma center has gone to the dark side, citing how Reiki therapy is now being used to "help" patients. Well, I did some digging of my own, and it turns out this isn't the craziest thing they're doing. They've got something even dumber going on, called "Colored Hat Therapy." Here's how it works:

A bunch of patients are seated in a circle, and a hat is placed on each one's head. They don't know the color of their own hat, but they can see everyone else's hat. There are many colors of hats, but each color present shows up on at least two hats. The patients sit in the room for a while, and every couple of minutes an announcement comes on the PA system, asking anyone who's figured out the color of their own hat to announce it and then leave the room. The theory goes that the magical hat energy must have seeped into their brain, and they're now cured.

Of course, most of the time it doesn't work so well, and people guess incorrectly about their hat color, miss their chance to get it and never figure it out, or get screwed up by inferring wrong things from other people's mistakes. However, one day, purely by chance, everyone brought into the room was an expert at logic puzzles, and they all managed to figure out the colors of their hats. How did they do this?

(Aside: When one of these experts left the room, a nurse noticed that the wound he was suffering from hadn't magically healed, and this therapy was quickly abandoned.)

Singular Sword Slashes

Martin Rundkvist recently uncovered a unique 16th century sword, and he was wondering how many lives it might have taken. Well, I did a little Tardis travel archeology of my own, and I managed to come pretty close to getting the answer before I was discovered and had to flee ran out of funding.

It turns out this sword was used in a ceremonial mass execution. 100 condemned prisoners were brought out and given one last chance at life. They were all stood up in a line and had a hat put on their head, colored either red or blue. No one knew the color of their own hat, but they could see the color of every hat in front of them. If they guessed correctly, they were spared, but if they guessed incorrectly, they were killed on the spot. This particular sword was used for the killings, and it was so fast and efficient that none of the prisoners in front would be able to hear a sound from the death, and so would have no idea if the guess was correct (though they would be able to hear the guess).

Unfortunately, I didn't see the actual procedure, but I did learn two things that might give us a clue as to what happened: First, the prisoners were given a chance to discuss a plan amongst themselves before the ceremony and decide on it. However, the executioner was listening in and would likely set up the hats to thwart the plan as best as possible. The second thing I learned is that these prisoners were all condemned to death for being part of a "dangerous cult" - which was actually more along the lines of Mensa. So, these are pretty smart people, and we could trust them to come up with a pretty good plan.

Putting this all together, what probably happened during the ceremony, and how many lives did the sword take?

Ending Erroneous Expectations

The Sexy Secularist writes in about how he was able to persuade his mother against recommending the atrocious woo film What the (Bleep) Do We Know?. You see, personally, I know that the whole Law of Attraction thing is bull. Why? Because I was expecting at least one post sent in would have some tenuous connection to pirates and allow me to bring you this classic puzzle. But nope, no pirates. Well, screw you guys, I'm doing pirates anyways!

A crew of 5 logic pirates comes upon a treasure of 100 gold coins. According to the rules of the logic pirates, to distribute the loot the most senior pirate must first propose a plan, and then they'll all vote on it. If at least half agree with the plan, they'll go with it. If not, the most senior pirate has to walk the plank, and then the next most senior pirate has a chance to propose a plan. This continues until a plan is accepted.

Each pirate is perfectly logical and has the following priorities they will strictly pursue: First, they don't want to die. Second, they want to get as much money as possible. If everything else is equal, they'd rather see more of their seniors walk the plank.

So, what plan can the most senior pirate of this group of 5 propose that will get him the most coins? Figured that out? Now, try the situation with 6 pirates and only one coin; what happens there?

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Skeptic's Circle #71: Medium

Following are the medium-difficulty problems for this Skeptic's Circle. Some math skills may be useful here.

Poor Poisoned Pinheads

You just knew one of these days the Moon Hoaxers would push Buzz Aldrin too far, and they finally have. This one started with a post at Space Files that showed a clip of Buzz explaining that the "UFOs" seen during the Apollo 11 flight had actually been identified. Well, a group of five hoaxers really didn't like this, and so they tried to take Buzz out of the picture.

They prepared a special poison which would cause retrograde amnesia in the person to consume it. It's extremely potent, and you'd have to dilute it to homeopathic portions to make it safe, but it takes a day to kick in. They sneaked into Buzz's wine cellar (Didn't know he had one? Probably because I'm just making it up), and went about spiking his bottles. However, they'd only managed to spike a single bottle before Buzz found them. In the ensuing chaos, Buzz managed to catch them all, tie them up, and get them to spill the beans on their plan, but he lost track of which bottle they'd spiked.

At this point, Buzz is so pissed off that he cares more about figuring out which bottle was spiked than whether he might inflict amnesia on his new prisoners. His cellar has a total of 874 wine bottles in it he has to check. With his five prisoners and one day for the poison to take effect, what's the shortest time it might take him to figure out which is the poisoned bottle, and how can he do it in this time?

What Wifi Woo?

Sandy Shwarc reports that there's been some scare over the ill effects of all the elctromagnetic radiation going through the air, but I'm not buying it. Personally, I think this is all just an excuse to avoid having to work. Confused? Let me explain.

Take the new Ultra-Mega-Awesome Wifi tower built the other day. It had 1000 power cords going from the bottom to the top, and not one of them was initially hooked up to anything. Worse, they're all tangled in the middle so it's impossible to figure out which bottoms of wires correspond to which tops.

Now, some poor shmuck has to go and sort them all out, and the only tools he's given are a battery and a lightbulb. They somehow expect him to to hook up the battery at the bottom to a couple of wires, then go to the top and see which wires he can connect the lightbulb to to sort them out. Maybe he could pull a few tricks like tying some wires together at the bottom or top to make long wires, but it's still going to take him quite some time.

With that job ahead of him, you can see why he'd want to believe it shouldn't be done. Maybe if we could help him out and figure out the most efficient way to solve this problem, he'll be a bit more likely to accept Wifi. The tower's pretty tall and the only way up is by stairs, so he'd probably appreciate most if we could help minimize the number of trips he has to take, regardless of how much work he has to do at the top or bottom. How can we do this, and what is the minimum number of ascents and descents required?

Manic Motor Mythbusting

Paddy K recently demolished some myths about the efficacy of so-called "green" cars, and now that he's done with that, he wants to actually demolish the cars. To do that, he's sent them to - who else? - the Mythbusters team. Now, they can't simply destroy the cars, they have to do it in an interesting way. Here's what they've set up:

Two cars are set up with a robot controller each, and this robot will have some programmed instructions. The two cars will be airlifted and dropped at a random point on a very long line marked out in the desert. Both cars will be initially facing north along the line, but we don't know which one will be in front of the other. Once they hit the ground, their parachutes will detach and remain where they landed. After this, the robots will take control of the cars and start driving according to their programming.

Now, there are a lot of fancy things that could be done in programming them, but Adam has decided to give Jamie a challenge. The first restriction is that both robots must use the same instructions. The second restriction is the the instructions are limited to the following commands:

Move 100m forward
Move 100m backward
Skip next command unless a parachute is nearby
Go to [label] (any line may be labeled for this purpose, and as many labels as necessary may be used. This line means the robot's "mind" will go to the instruction at this label and start working forward from there.)

How can the robots be programmed to guarantee a collision? Try to use as few lines of code as possible.

Paddling Pooch Problem

Well, Bronze Dog has done it again. He went and pointed out that made a completely unfounded accusation that the way many fundies practice is akin to the devil worship atheists and D&D players have been accused of. Now, they're accusing him of being a devil (as a talking dog made out of bronze, he's definitely not normal, but I don't see many mentions of devils like this in the Bible).

In the hot pursuit, eventually Bronze Dog found himself paddling in the middle of a circular lake, with a fundie waiting on shore for him. This fundie can run about four times as fast as Bronze Dog can swim, though fortunately he never learned how to swim and won't enter the water. If Bronze Dog can make it to land, and the fundie isn't waiting right at the shor for him, he should have no problem outrunning him.

The fundie isn't going to listen to anything Bronze Dog might say, so tricking him is out of the question. Bronze Dog is pretty fit and can paddle for quite a while, but he'll still likely run out of energy before the fundie gives up, so he's going to have to do something. Assuming the fundie makes his best effort to catch Bronze Dog, what can Bronze Dog do to guarantee he'll be able to get to shore safely?

Action/Adventure Akusai

Akusai recently "psychically" predicted a phone-call from his long estranged cousin. After hearing that his father had gotten this call, he decided to go out and surprise this cousin with a visit. Well, things didn't go quite as planned on his journey, and, long story short, he found himself at the mercy of a deranged hermit.

This hermit offered to play Akusai in a game, with his freedom at stake. The game is played on a circular table, and the players take turns laying circular disks down at any location on the table. If a player can't lay down a disk anywhere without overlapping a disk that has already been placed, they lose. The hermit gives Akusai the choice of playing first or second. Which should he choose, and what strategy should he use in the game?

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Skeptic's Circle #71: Easy

Following are the easy problems for this Skeptic's Circle.

Personalized Perfume Peril

Bad has been captured by perfume manufacturers he recently angered. They're utterly convinced that their personalized perfume works, so they've arranged an elaborate puzzle to force Bad to admit this as well. They've thrown him into a dark room, in which 100 disks of perfume samples are placed. Each disk has a different scent on each side, taken from "completely different" people. The sides are color-coded red and blue for easy counting later, but it's too dim in the room for Bad's eyes to be able to make out the colors. Bad's task is to sort the disks into two piles, each with the same number of red sides facing up. If he succeeds, he'll be set free, but if he fails, he'll be shot. He'll also be shot if he tries anything "clever" such as balancing disks on their edges or throwing them out the window.

Bad knows that the task is hopeless, so he pleads with his captors to give him a hint, just one little hint. Eventually, one of them takes pity on him and gives him the following hint: In the initial set-up, 48 of the disks are placed with the red side facing up. With this information, is it possible for Bad to come up with a plan to separate the disks into two piles with the same number of red sides facing up? If so, how?

Creative Cake Capers

Christian of Med Journal Watch has been attempting to combat rumors that overweight women should lose weight when they get pregnant. In his quest to inform women that this isn't always going to be the case, he's stumbled upon one particularly tricky customer.

This particular woman has quite a sweet tooth, and figures that since she should expect to lose some weight, she can afford to binge a little. She's got a nice big rectangular cake which she plans to eat, but Christian is able to convince her down to only consuming half of it. However, when they get out the cake they find that her husband has already cut out a rectangular slice from it. The woman wants half of the full cake, but she settles on half of the remainder.

The woman knows that each slice takes away a small amount of the cake and so she won't let him use more than one. She also won't settle for anything less than half the cake, but Christian wants to make sure she gets no more than half. So, the problem is, how can Christian cut the cake perfectly in half with a single cut?

And no, making a big horizontal slice through the center of the cake isn't an option, as the cake has icing on the top and thus isn't symmetric in that direction.

Popping Placebo Pills

After a recent article by Mark Hoofnagle on the diagnosis of Chronic Lyme Disease, an enterprising researcher decided to conduct a placebo-controlled study to see if there was any benefit to the use of the antibiotics typically prescribed for treatment of it. During the conduction of this experiment, the grad student assigned to sort out the bottles of pills (some placebos, some real) ran across a problem when the record sheet was smudged and she couldn't identify whether five of the bottles had the placebos or real pills. Counting up the identified bottles, she figures out that one of the bottles should have real pills, while the rest should be placebos.

She does some quick research and figures out that the easiest way to tell apart the pills is by weight. The real pills weigh 1 gram more than the placebos, so a few comparative weighings should be able to sort them out. However, when she gets to the lab to weigh them, she finds that a lab class is going on and there's a huge line-up to use the scale. The pills need to be in before the class is over, so she'll have to put up with it. Asking the instructor for permission to step in, he relents, but allows her only the time to perform one weighing. Is it possible for her to sort out which of the bottles contains the real pills with only one weighing? If so, how?

Perilous Peace Problems

The Factician recently dismantled some biased thinking which led to the bizarre conclusion that peacetime is more dangerous than war, and for his trouble, he received a mysterious package in the mail one day. Opening it, he finds a corked wine bottle with a pill inside of it and a note. The note reads:

So, you think you're a smart guy pointing out accidental deaths, huh? Well, here's the situation: When you opened this box, a specially-prepared poison was released into the air. The pill in the bottle is the antidote for it, but I've got a little challenge for such a smart guy. I want to see if you can get the pill out of the bottle without removing the cork or breaking the bottle. If you do either of those things, I can't guarantee you won't have an "accidental" death of your own.

The Factician suspects they're just bluffing about the whole thing, but he decides to go ahead with it anyways, as he's already come up with the solution. What does he do?

Crazed Canting Christians

Romeo Vitelli tells us a story of some strange convulsing women, which is apparently a miracle. Personally, I'd chalk up curing something like this to be more miraculous, but I guess that just goes to show I don't have faith.

Anyways, it seems that a group of 20 of these women decided that it if their strange behavior led to their death, they'd go straight to heaven. So, they set up a weird ritual suicide type of thing, where the 20 of them get out on a 100-meter long raft in the middle of the ocean, each randomly selecting a direction to face and a starting point from marks laid out every meter (the first a meter from one end, up to one a meter from the other end).

At a cue to start, each woman starts convulsing forward at 0.1 m/s. If she bumps into another woman, both will immediately turn around and start walking in the other direction. They'll keep walking until they inevitably all fall off one end and (hopefully) meet their end. If the woman are miraculously set up in the right configuration, what's the maximum time it might take for all of them to fall off the raft?

Hidden Handbook Hassle

After a perilous journey into the land of the woos, Skeptico managed to escape with the Woo Handbook. However, he's now on the run from woos who want it back, and he needs to pass off the book to a fellow skeptic. He's under close observation, so he won't be able to make personal contact with this other skeptic, but they've arranged a plan to get the hand-off to take place. The plan was to have them both lodge at the same hotel, and during the night, hire one of the employees there to pass it off.

But they ran into a problem with this plan, as it turns out that everyone that works at this particular hotel is a rabid kleptomaniac and would steal anything in their hands before passing it off to another guest. Each room did come equipped with a small portable safe though, and these are equipped with tracking devices to make sure no guests would run off with them. It also fortunately means that the employees wouldn't run off with them, so the trick is to transport the handbook within a safe.

Of course, there's still a catch. The safes are closed through a clasp, which a padlock can be put on to steal it shut. The padlocks can only be unlocked with keys found in the hotel rooms and safely wired down, and each key is unique to each lock. So even if the handbook were passed off in a locked safe, Skeptico's friend would have no way to unlock it. Is there any way to solve this problem without either Skeptico or his friend leaving their room and thus risking being caught by a rabid woo?

Weird Water Woo

PalMD recently made a post discussing hydrogen peroxide woo, and, true to the nature of events these two weeks, has been kidnapped by a crazed woo and forced to solve a logic puzzle if he wishes to live. He's locked in an empty room and given a glass that's around half full of water. His task is to determine precisely whether the glass is half full, less than half full, or more than half full. There are a few ways to do this, but some of them are pretty tricky and inaccurate if you don't have a very steady hand. What are some good methods?

Screwy Scarfe's Secrets

The guys at Holford Watch recently exposed Chistopher Scarfe as the fraud he is. Unfortunately, they didn't realize that Scarfe is also an insane supervillain, and they were promptly captured and imprisoned in his mountain fortress. They managed to escape from the fortress (Scarfe forgot to lock the cell door), but on the way out they came across a rickety bridge they'll need to cross.

It's night, and they only have one flashlight among them which anyone crossing the bridge will need. The bridge is unable to support more than two people at any time, so they'll have to make multiple trips to get everyone across, passing off the flashlight as necessary. The guys each incurred various injuries in the escape, so they're all able to move at different rates. One guy is pretty much uninjured and could make it across the bridge in two minute. Another of them is a marathon runner and could easily do it in a single minute. A third stepped on some caltrops on the way out, and it will take him four minutes to cross. The fourth had his leg broken in a fight with a guard dog, and it'll take him eight minutes to cross (if there aren't actually four guys behind this blog, pretend there are). Of course, if two are crossing together, they have to cross at the speed of the slower person.

Scarfe's hot on their tails, so they want to get across the bridge as quickly as possible. How can this be done, and how long will it take them?

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Wednesday, October 10, 2007

Skeptic's Circle #71: Quick Links Version

Here ya go, all the links for this Skeptic's Circle in one small place, for those of you too intellectually lazy (or time-deprived) to work on a few logic puzzles.

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Monday, October 08, 2007

Deadline Update

Well, it looks like I'm not going to have any conflicts with hosting, so I'm going to extend the deadline for Skeptic's Circle submissions to Wednesday at midnight GMT. Even if you miss that, don't worry too much, I'll still slip in a link for ya.

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