Currencies + alcohol = Profit?!

[Note: I'm starting to think that putting difficulty ratings at the beginning of each puzzle was a mistake--so I'm not going to do it this time!]

U.S.A. and Canada were having an argument. I know! How could possibly be unhappy with the U.S.? But that's what happened in this hypothetical. Tempers flared, and before we knew it, each country took action on the other. Previously, the U.S. and Canadian currency had been on equal terms: one dollar to a dollar. But then the U.S. made it law that every Canadian dollar is now only worth ninety cents in U.S. currency. Canada made it law that every U.S. dollar is now only worth ninety cents in Canadian currency.

Charlie, ever the opportunist, found a way to profit from this. He lives near the border, where there are two bars, one on either side. In the bar in the U.S., he uses a U.S. 10 dollar bill to buy a 1 dollar drink, and receives 10 Canadian dollars of change. He walks across the border to the other bar, and buys a 1 dollar drink with his 10 Canadian dollars. He receives 10 U.S. dollars change. He crosses the border again back to the U.S. bar to buy another drink. This process is repeated until he is drunk silly.

Charlie is obviously profiting from this situation. But who is losing?

This is an open-ended problem, so I will not have a separate solution post like I usually do.

Planned Parenthood and racism?

Abortion! It's not really a can of worms I want to open.*

But here's a video that accuses Planned Parenthood (hereafter referred to as PP) of racism. Hurry up and watch it before PP's legal threats convince YouTube to take it off the net.



I'm having trouble finding many articles on the internet that refute the claim that PP is racist. This could be because: a) PP does not pay enough attention to their critics b) I'm not looking hard enough, or c) anyone but the most naive blogger can see that PP is obviously racist. The best I could find was a biography of PP founder Margaret Sanger. I can't comment on the biography's accuracy.

*sigh* I guess I'll come to PP's defense. Don't expect it to happen again.

First, a few minor points:

1. The callers, I believe, are actors that are simply pretending to be racists. Are such people truly representative of PP's supporters? After all, the PP representative did say, "This is the first time that I've had a donor call and make this kind of request." Of course, right afterwards, she said "so I'm excited", which is difficult to interpret favorably.
   
   
2. The video could be a hoax. I hate to assume any bad intentions on the part of the video-makers, but hoaxes do happen.
   
   
3. The newsletter that created the video, The Advocate, quote mines** Margaret Sanger as saying "We do not want word to go out that we want to exterminate the Negro population." It sounds like she's organizing a conspiracy, but the original context indicates otherwise. Quote mining greatly harms The Advocate's credibility.

And one last major point:

I think it is entirely uncontroversial to say that PP is pro-choice as opposed to pro-life. Since they are pro-choice, they think that legalizing abortion is good for communities overall. So how does making abortions available to black communities indicate racism? Perhaps some racists have tried donating to them. More disturbingly, perhaps they have accepted these donations. But from their pro-choice perspective, it is not racist to make abortions available to black communities. From the pro-life perspective, they may inadvertently be harming the black community, but that's certainly not their intention.

I feel like I'm pointing out the obvious here. Am I simply the only one who's too dense to see some glaring fact right under my nose?

I suspect this is the result of a debate in which the two sides mostly ignore each other. Are pro-lifers not able to acknowledge that maybe, just maybe, some people think that legalized abortions are overall good for society?

Similarly, shouldn't PP be acknowledging that this call occurred, instead of making legal threats? They have the right to choose legal action, but their use of this right makes them look bad.

*I mean it when I say I don't want to open this can of worms. I would prefer if you confine comments to things relating to the accusation of racism against PP, rather than the pro-life/pro-choice debate.
**Quote mining is the practice of taking quotes out of their original context in order to distort, and sometimes completely change, their original meaning.

The mountain theologians

For the scientist who has lived by faith in the power of reason, the story ends like a bad dream. He has scaled the mountains of ignorance; he is about to conquer the highest peak; as he pulls himself over the final rock, he is greeted by a band of theologians who have been sitting there for centuries.

-Robert Jastrow, God and the Astronomers

After staying a while to share some stories with the theologians, the scientist begins to explore the surrounding area. Soon he realizes that the mountain goes much higher, but the path is poorly marked and obscured in fog. He points it out to the theologians, but they cannot see the markings.

"How did you get this far?"

"God guided us here."

"Can God guide you further?"

They cannot agree amongst themselves. Some declare they are already at the peak. Others speculate that there is no peak, and thus no reason to continue. Still others say, "Yes, God will guide us," and begin to wander in the direction pointed out by the scientist, to become forever obscured in the mist.

The scientist prepares to leave, bringing only a few theologians with him. He slowly continues to scale the mountain, meticulously checking every rock, and occasionally backtracking for days at a time.

Those would not be the last theologians he would pass by.

[Incidentally, Robert Jastrow died shortly before I wrote this, but I didn't hear about it until afterwards.]

Coin sliding solution

See the original puzzle

This puzzle can be solved in 4 steps.

1. Slide coin 4 next to 5 and 6.
2. Slide coin 2 next to 4 and 5.
3. Slide coin 5 next to 1 and 3.
4. Slide coin 1 next to 2 and 5.

Alternate solution:

1. Slide coin 2 next to 4 and 5.
2. Slide coin 3 next to 5 and 6.
3. Slide coin 5 next to 1 and 4.
4. Slide coin 1 next to 5 and 6.
   

Null Physics, non-physics

The other day, I was browsing Discover magazine. I’m not a big fan of Discover. I’m all for popularization of science, but I’m for good popularization.

Anyways, I came across this ad for a book called Our Undiscovered Universe. The ad has “crackpot" written all over it. It starts by decrying the state of modern physics, especially String Theory, the Big Bang Theory, and the Standard Model. It goes on to say that this book, and its theory of Null Physics will fix this, because it’s willing to ask ultimate why questions. And then we get a glimpse of the claims in the book.

Energy is a three-dimensional substance, and its most basic unit is time-distance².

...
Seriously?!
Is he trying to outdo the E=mc³ claim that the Autodynamics fools make? Uh, the units for energy are [kg m²/s²], not [s m²]. (Didn't he know?) The units are not even close to working out. In what sense is he talking about the same thing? Perhaps he’s saying that there’s some conversion factor between the units. But then it wouldn’t be energy, it would be energy times a conversion factor. Additional hint: energy is not a “substance” unless you’re a woo.

The underlying problem with this ad is the entire idea of publishing a book with your new theory, and then advertising it in a popular science magazine. The correct method to start a scientific revolution is not to publish a book for the general public. You publish in a peer-reviewed a science journal first. Otherwise, how do we distinguish you from the crackpots? We don’t, that’s how.

The author, Terry Witt, said the following in the JREF forums.

Unfortunately, self-published physics books are invariably the product of uniformed [sic], and in many cases, positively deranged individuals. Just as unfortunately, peer-reviewed journals strenuously reject ideas contrary to the reigning paradigms. So rather than fight the battle a little bit at a time, I decided to wait until I had some convincing results and published the results of my work from 1978 to 2004 all at once. So far it’s gone well with the individuals who actually read the book, but after reading Lee Smolin’s new book, “The Trouble With Physics” I fear I might be tilting at windmills with regard to the theoretical physics community.

Beep-beep-beep-beep! My crackpot alarm just went off. He apparently spent 25 years working on this, and never previously let it stand up to scrutiny. I highly doubt that Lee Smolin or Peter Woit would approve of bypassing the physics community. They're real physicists, you know? Terry Witt knew BIG SCIENCE would reject his ideas, and not because his ideas are wrong. You just know he’ll be paranoid that his critics are all tools of string theory.

One other question; does JREF have an "official" stance on the status of string theory as a viable science, or is it just a variety of opinions?

Right on cue! And this is not an isolated example. He repeatedly asked each of the forum users what they thought of string theory.

If that made you hungry for more head-banging, you'll be interested to know he has a website. The author doesn't really seem to have the qualifications for this. None of the reviews are by physicists. There are a few selected excerpts, and it looks like nonsense.

Totality is the simultaneous product of infinite smallness and infinite largeness, exhibiting their combined dimensional content. Infinite smallness lies external to the dimensions of infinite largeness. It is the only way the two can coexist as equivalent paths to nonexistence. What this means is that the space of our universe is the boundary surface of its own totality:

He makes a bunch of unconfirmed, and perhaps already falsified predictions. I am not impressed. Unsupported claims are a dime a dozen.

To be fair, it is obvious that Terry Witt has some knowledge of physics, perhaps more than me (Any other physicists want to jump in?). But what he doesn’t seem to have knowledge of is science, critical thinking, and how not to look like a crackpot. He would rather appear “positively deranged” than ask for other scientists’ input. A good theory must stand on its own merit. It does not require spending thousands of dollars on advertisements to shout out to the easily mislead Discover readership. Of course, for a crackpot theory, there's no other way.

Update: There's also a little discussion about this on the BAUT forum.

Update 2: Ben Monreal has a full review of Our Undiscovered Universe, and Blake Stacey has further comments.

Quantum Mechanics: The double slit experiment

See previous post: Particles and Waves

The Set-up

The double slit experiment is one of the most famous physics experiments of all time. It demonstrates that light has properties of both particles and waves.

Here's the set up. We point a laser at a plate. The plate has two slits in it. The light goes through the slits and hits a screen in the back. This results is what's known as an interference pattern. It looks like this:


When I first saw this, I thought, why are there so many bars? Shouldn't there only be two bars, one for each slit? To understand why the interference pattern appears, we have to understand two properties of waves.

Two Properties of Waves

The first important wave property is diffraction. Diffraction allows waves to move around obstacles. When you shout out, "Dinner time!" the whole family can hear you regardless of whether you have a direct line of sight to them. This is because sound can travel around corners, through doorways, and into people's ears. Whenever a wave goes through a doorway or a slit, the wave spreads out in all directions on the other side.

In a way, diffraction is the opposite of what we expect from particles. When we shoot a particle through a slit, we expect it to follow a very narrow path on the other side. The smaller the slit, the narrower the path will be. But when we shoot a wave through a slit, it will spread out in all directions on the other side. The smaller the slit, the more it will spread out. So when we shoot light through a slit, it's not going to just make a single spot on the screen, but will go in all directions.

The second important property of light is interference. If two identical waves go through each other, then their intersection will look like the sum of the two waves. Recall that all waves are fluctuations in something. A typical wave quickly alternates between a fluctuation up and a fluctuation down. That's why, in the above drawing, we represent the wave with alternating black and white lines. The black lines represent upward fluctuations and the white lines represent downward fluctuations.

If two intersecting waves both happen to be fluctuating up, then the sum will be a fluctuation up with twice the amplitude. This is called constructive interference. If one is fluctuating up while the other is fluctuating downwards, they will cancel each other out. This is called destructive interference.

Return to the Double Slit Experiment

Now that we have an idea of how waves behave, we can now predict the results of the double slit experiment. Some of the light will go through slit 1, and some through slit 2. After going through the slit the light will spread out in all directions. The light that went through slit 1 will interfere with the light that went through slit 2.
How can we tell from the diagram where the light will interfere constructively and destructively? Well, the light interferes constructively whenever both waves fluctuate up in the same place and time. The light interferes destructively when the waves are fluctuating in opposite directions at the same time. To make this clearer, I've shown the locations of constructive (red lines) and destructive interference (blue lines) in the picture below.
The result? We only see the spots where the light interferes constructively, and not destructively. Therefore, we will see alternating light and dark bars--the interference pattern.

The Particle Properties Emerge

The fact that we see an interference pattern is proof that light is a wave, right? But what about the proof that light is a particle? It had been shown by Einstein that light comes in little separate packets, called photons. What happens if we send one photon through the double slit? According to our previous analysis, the interference pattern requires that the wave go through both slits at the same time and interfere. But if we just have one photon, it can only go through one slit. After all, it can only hit one spot on the screen behind the slits.

But when this experiment is performed the interference pattern does appear. Each photon, of course, hits only one random spot on the screen. But if we shoot, one by one, a whole bunch of photons, then the sum of their landing points forms an interference pattern. That is, a photon is much more likely to land in a spot where there is constructive interference. The only way this can happen is if the photon is traveling through both slits at once and interfering with itself!

The conclusion is that light shares properties with particles and waves. Which of the two is it? Neither, of course.

Next page: The Quantum Measurement Problem. This is where Quantum Mechanics gets weird!

Random links

Cosmic Variance: The physics of psychics - You don't need to perform parapsychology experiments to know that telekinesis is extremely unlikely. We've already tested for the physics that would be involved.

Cectic: Footsteps - I've come to really like Cectic. This particular comic pokes fun at the famous footprints poem.

Look, it's Jesus! - Quick, give him a Turing test! (via Skepchick)

Intrinsically Knotted - A new blog about math, art, atheism, etc.! I'll toss a few (very few) readers that way, because I happen to like it.

"The Games Skeptics Play"

I tried googling my blog's title, and look what I found. I'm the first hit, of course. The other hits, unlike me, use "play" in a negative sense. There's a letter called "Do Skeptics Play Fair?" but that looked boring. More interesting was the second hit, an essay called "The Games Skeptics Play" on a website called Ex-Atheist.com.

A. S. A. Jones first takes a moment to distinguish "anti-Christian intellectuals" and "ordinary skeptics". He defines anti-Christian intellectuals to be those who will ignore opposing arguments because they have an axe to grind. Ordinary skeptics are those who will acknowledge sensible arguments when they see them. His criticisms are directed at the anti-Christian intellectuals, whom he will refer to (for the sake of simplicity) as "skeptics".

"Skeptics", he claims, know how to manipulate an audience, generate an uneven psychological playing field, and use specious arguments. He gives an example of a professor named "Mr. Owl" who gives a rather poor argument involving justice and mercy. I'd call straw-man, but apparently Mr. Owl is based on a real person.

Now, obviously, I call myself a skeptic, but I'm not sure that we really mean the same thing here. I fully realize that when most people talk about "skeptics", they're using some sort of negative definition that doesn't exactly match the positive definition used by the skeptical movement. Jones even said so himself that he is only using the word "skeptics" for simplicity's sake. Nevertheless, I will treat the argument as if he is talking about the skeptical movement, if only so I can have an excuse to talk about it.

His portrayal of skeptics does not quite match what I know about the skeptical movement. Here are some discrepancies:

1. The distinction between "good skeptics" and "bad skeptics" sounds similar to the distinction I might make between skeptics and denialists. But I wouldn't make the distinction on the basis of attitude (being angry does not make you wrong). I would make the distinction based on the types of arguments they use and their respect for science.
   
2. He appears to be describing spoken debate. It is in fact a common sentiment among skeptics that spoken debate should be avoided. For one thing, it's difficult to cite scientific papers on the spot. I much prefer written debate, and not the sort you find on the typical internet forum either.
   
3. He ignores the fact that skeptics, at least in principle, go out of their way to avoid fallacious arguments, not use them. Being able to recognize logical fallacies is a standard skeptical topic. Sagan's Baloney Detection Kit is considered classic skeptical literature.
4. He seems to use "skepticism" and "atheism" interchangeably. They are related, but not equivalent. There is a reason my blog isn't called "Atheist's Play". As a matter of fact, you can be a skeptic and a theist simultaneously (at least in my opinion). I might even call Jones a skeptical theist, though he is free to disagree with this assessment.
   

One thing of note is that in Jones' reconversion story, he says he used to be a nihilist. I'm not going to dispute that fact, but I will point out that this sets him apart from most atheists I see these days. I've written against nihilism myself. Being a nihilist atheist disqualifies him from representing the typical atheist. Therefore, the whole sympathetic "I was once an atheist" angle mostly fails.

Look at this quote:

What is the best way to witness to an atheist? Live your Christianity, don't debate it.

I greatly appreciate and respect this attitude. But I don't think it would be particularly effective as apologetics, since the existence of friendly Christians is only contradictory to the most nihilistic of atheist philosophies. Oh well, who says witnessing has to be about apologetics anyways?

Michael Shermer's Mind of the Market

I attended a talk by Michael Shermer. Shermer is the founder of the Skeptic's Society and Skeptic Magazine. He also writes the skeptic column for Scientific American. I should also point out his talk on TED on Why people believe strange things. I am a member of the Skeptic's Society (which really just means I subscribe to their magazine), and a big fan of Shermer. I got a signature and photo!

There were also some 9/11 truthers, who apparently follow Shermer's tours to protest. The 9/11 truthers, if you didn't know, are the people who think 9/11 was a conspiracy of the US government. They were ... interesting. Not really. Truthers are boring. All their questions were excuses to rant about 9/11. Moving on...

The subject of the talk was Shermer's new book, The Mind of the Market. I haven't actually read this book, so my understanding of it is based only on this talk. The central theme of the book is a comparison between evolution and economics. Neither require any sort of intelligent designer or central organization. Natural selection is parallel to the invisible hand. Given the similarities, it is rather curious why the conservatives who support free market economy tend to be the same people who reject the idea of natural selection. On the flip side, many liberals understand the process of evolution, and yet reject that a similar process could operate in economics.

Now, I have some reservations about relating skepticism to anything explicitly partisan. We can't have skepticism be too closely associated with either political party, lest it lose all credibility. For another thing, based on my perceptions, skeptics are not in fact skewed in either direction. Skeptics are split more or less equally among liberals and libertarians (with a minority of conservatives). As a liberal-libertarian, it's in my interest that it stays that way.

But I understand where Shermer is coming from. The same biases that cause people to believe in pseudoscience are also at work when people think about politics. Skepticism is a good thing, so why shouldn't its application to politics be a good thing? Furthermore, you can't (and shouldn't) disallow skeptics from having political opinions. I think politics is worth discussing, as long as it remains a discussion, not a fight for the skeptical identity.

Back to the talk. Shermer pointed out two parallel myths in evolution and in economics. It's often said that evolution is "Nature, red in tooth and claw," and it's all about competition between individuals. Well, not all the time. Evolution often promotes altruistic behavior. Your neighbor shares much of your DNA, so loving your neighbor is an adaptation (skipping over important details). The parallel myth in economics is that free market capitalism is all about greed and competition. Not really. It's the Googles ("Don't be evil") of the world that succeed, not the Enrons.

Now, Shermer presumably takes this analogy between evolution and economics to its full potential in his book. Not having read it, I wonder how he answers the following concern. Evolution and economics is simply an analogy, and not necessarily a perfect analogy. The biggest difference I see is that in evolution, you only have to show that natural selection works. In economics, you have to show that the invisible hand not only works, but is the best possible way for it to work. If you asked me, it is not the best way, but instead an approximation of the best way, and the one least prone to error. But why can't some careful modification result in improvements? My first thoughts are about things like the environment, education, and science, where the goods are important, but somewhat intangible. Oh, but I'm no economics expert.

Coin sliding

Difficulty: 3 of 10

Here's a simple puzzle that you can do yourself with just six identical coins. All you have to do is move around the coins, starting with a triangle and ending with a hexagon.

Easy, right? But don't start yet! I have to tell you the rules:

1. Slide one coin at a time.
2. Keep the coin flat on the table at all times. Do not push or move any other coins.
3. When you've finished sliding a coin, that coin must be touching at least two other coins.
4. Finish in the least possible number of moves.
   

For example: For your first move, you can place coin 2 next to 3 and 6. After you have done this you cannot move coin 3 because this would either require pushing other coins or picking up the coin off the table.

The first person to solve it gets a cupcake and six coins! (This blogger is not responsible for providing aforementioned cupcake or coins.)

Update: The solution is now available. Cupcakes are not.

Darwin: A really cool guy

Today is Darwin Day. Charles Darwin was born on Feb. 12 1809, making this his 199th birthday.

For the moment, let's put aside all thoughts of the current cultural battles over evolution. Instead, I'm going to talk about the man. My main source material is Voyage of the Beagle and Origin of Species which are available online.

Darwin was a really cool guy. I'd even say he's better than Newton or Einstein. Coming from a physics guy, that's quite a compliment! Seriously though, Newton is known for being antisocial, and Einstein is known for stubbornly rejecting Quantum Mechanics (the other physics revolution around the same time as Relativity). But when I look at Darwin, I see a model scientist.

Voyage of the Beagle

The most well-known part of Darwin's life was his voyage on the Beagle. He went on the voyage to accompany Captain FitzRoy, since it was improper for the captain to socialize with his insubordinates. But Darwin took this opportunity to do all sorts of adventuring. And did Darwin have adventures! Darwin had a habit of not only observing nature, but interacting with it, and forming new theories about it. Who can forget that time he hit an idle fox with his geologic hammer?¹ Or the time he discovered a new species of ostrich (which was named after him) only after having eaten it?² Oh, and the Galapagos lizards!

...when [the lizard is] frightened it will not enter the water. Hence it is easy to drive these lizards down to any little point overhanging the sea, where they will sooner allow a person to catch hold of their tails than jump into the water.
...
I threw one several times as far as I could, into a deep pool left by the retiring tide; but it invariably returned in a direct line to the spot where I stood.³

Darwin's lizard-tossing ways stemmed from his child-like curiosity about nature, along with his scientific search for explanations. This is why Darwin is cool.

Much of Darwin's voyage also involved interacting with the indigenous people. Since this is from a less enlightened time, the characterizations are quite painful. Darwin observed the "savage" peoples almost as if they were animals. However, he was anti-slavery, and we see glimmers of enlightenment as in the below example.

I was crossing a ferry with a negro, who was uncommonly stupid. In endeavouring to make him understand, I talked loud, and made signs, in doing which I passed my hand near his face. He, I suppose, thought I was in a passion, and was going to strike him; for instantly, with a frightened look and half-shut eyes, he dropped his hands. I shall never forget my feelings of surprise, disgust, and shame, at seeing a great powerful man afraid even to ward off a blow, directed, as he thought, at his face. This man had been trained to a degradation lower than the slavery of the most helpless animal.⁴

The Origin of Species

Perhaps influenced by his voyage, Darwin later came across the idea of natural selection. But he delayed publishing his work because he was acutely aware of the controversy that it would provoke. Instead, he spent years and years accumulating more evidence to make his case stronger. Truly, this is how a scientist reacts to controversy: by collecting evidence! Darwin was actually very afraid of the controversy that would ensue, and delayed publication for twenty years. Only when a friend, Alfred Russel Wallace, had come across the same idea, did Darwin choose to publish.

Origin of Species is actually very well written. Well, admittedly, it's a little dense, mostly because Darwin is always putting in phrases like "seems to me," "perhaps might," and "quite conceivable." This is the language of someone who wants to avoid overstating his case. Darwin very clearly states all the observations and reasoning he has in favor of his theory, as well as all the flaws, and his responses to these flaws. Darwin was, of course, wrong on many points (hilarious examples: flatfish trying to twist their eyes⁵, stags with one antler⁶, fish traveling by whirlwinds⁷), but such a large scientific theory could scarcely have had a better start.

Oh, and he's poetic too! Below is the famous passage at the end of his book.

It is interesting to contemplate a tangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent upon each other in so complex a manner, have all been produced by laws acting around us.
...
There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone circling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being evolved.⁸

Happy Darwin Day!

And check out this awesome artwork, thanks to Travis Morgan.
And more artwork? From cpurrin.
And there are other people talking about Darwin Day too! Click on the picture below.

I encourage you to find the passages I refer to!
1. VotB Ch 13
2. VotB Ch 5
3. VotB Ch 17
4. VotB Ch 2
5. OoS Ch 7
6. OoS Ch 5
7. Oos Ch 13
8. OoS Ch 15

Play of the mind

Check out this quote I found. This is exactly what I was thinking of when I thought up my blog's title (in the spur of the moment).

The widespread distrust of intellectuals in America reflects a tendency to depreciate their playfulness and distrust their piety. Ours is a society in which every form of play seems to be accepted by the majority except the play of the mind.

-Richard Hofstadter

Taken from the LA Times.

Quantum Mechanics: particles or waves?

Quantum Mechanics! It's everyone's favorite physics topic, outside of cosmology. Few people understand it, and no one understands it fully. I am admittedly a little reluctant to get into this topic because I've only had an introduction to quantum mechanics so far in my formal education. Well, I at least understand it better than your average science journalist (though I'm probably worse at explaining it).

Most every explanation of Quantum Mechanics starts with a question. Is light a particle or wave?

particle


wave

How could scientists possibly be confused about this? Well, both particles and waves transmit energy and information between here and there. A particle is simply a point that moves from here to there. A wave is a disturbance that transfers from here to there through a medium (at least, we used to think it required a medium). In the above example, the ocean is a medium for an ocean wave. The ocean wave is a fluctuation in water level that transfers between this patch of water and that patch of water. It does not require that the water itself move from here to there.

Particles and waves behave very differently. Particles have a definite position and come in whole-number quantities. Waves do not have a specific position, and may come in any quantity. Waves can move around obstacles. Waves have a property called frequency, which is a measure of how quickly it fluctuates up and down. Waves can interfere with each other such that a fluctuation up and a fluctuation down cancel each other out. There are many more differences, since the mathematics that govern particles and waves are completely distinct.

Though particles and waves are completely different, it is not immediately obvious which one describes light. Historically, scientists just couldn't figure it out. Pythagoras thought light was a particle, Aristotle thought it was a wave. Newton thought it was a particle, Young thought it was a wave. Cocktail Party Physics probably gives a better treatment of the history than I could.

In the early 20th century, there was very good evidence on both sides. Maxwell's equations predicted the existence of electromagnetic waves that behave just like light. Einstein used the photoelectric effect to show that light comes in discrete quantities (this is, by the way, how he got his Nobel Prize). Physicists had long assumed that light is one or the other, so the ambivalence of evidence was confusing to them.

The culmination of the debate was a single experiment that simultaneously showed that light had properties of both particles and waves. This experiment was called the double slit experiment... and is explained on the next page.

An argument against unprovable gods

This argument takes several premises, any one of which you may disagree with.

1. Science cannot possibly support the existence or non-existence of God.
2. Science can support any hypothesis over another if they make different predictions.
3. Occam's Razor: Given two hypotheses with identical predictions, we should always use the one that's easier to use.
4. The hypothesis that God doesn't exist is easier to use than the hypothesis that God does exist.
   
5. We should not believe in a hypothesis that we never should use.
   

Conclusion: We should not believe that God exists. (I think the reasoning is clear.)

Now, this is a deductive argument, meaning that it absolutely must follow from its premises. But such an argument is only as strong as its premises, and these are some questionable premises. Below, I discuss them one by one.

1. This premise is not my claim, but something I hear other people claim. I actually disagree with it. Note that here, "science" is used in the very wide sense of any process that can be used to choose between hypotheses.
2. If two hypotheses make different predictions, we can devise an experiment that will allow us to observe one prediction or the other. But in actuality, this premise is false. Perhaps the only possible experiment is impractical. For example, miracles are difficult or impossible to test in practice, since they are by definition non-reproducible events.
3. This is a very specific interpretation of Occam's Razor, as explained and justified in a previous post.
4. Let's just say that when I walk around, I don't even bother considering what effect an omnipresent but inactive god would have on my daily activities. If I did consider it, then I would simply end up reaching the same conclusions with more effort. If you're reaching different conclusions, you've either contradicted the first premise, or have demonstrated how confusing it can be to use the hypothesis that god exists.
   
5. I suspect this premise will get the most disagreement. Just because one hypothesis is simpler doesn't mean it's true, right? But the whole idea is that it doesn't matter whether it's true. A world in which it is true is indistinguishable from a world in which it is false. You can therefore believe what you want. Believing in an unusable hypothesis is a poor choice. Therefore, it is best to be agnostic or atheist with respect to this unprovable god.
   

I follow the same line of thought whenever I hear about "questions that science can't answer".

So, any disagreements?

Critique of the Political Compass

How many people have seen The Political Compass? Even if you haven't seen this website, perhaps you've heard of the two-axis political spectrum. The idea is that politics is much more complicated than "left" and "right". In particular, there is a third political position that is somewhat popular--libertarianism. Libertarians tend to agree with the left when it comes to social issues, and with the right when it comes to economic issues. If we confine ourselves to "left" and "right", however will the libertarians distinguish themselves from the rest of the rabble?

So the primary criticism I see of the two-dimensional spectrum is that it has a libertarian bias. I think it's true that there is an underlying libertarian motivation. Of course, that doesn't make them wrong. Libertarians obviously disagree with both left and right, so why shouldn't they posit a two-dimensional spectrum? This may bias the quiz they create, in that they have questions that clearly fit into either the "social" or "economic" category, but if it helps to distinguish liberals from conservatives from libertarians, I don't see what the problem is. Of course, I waver around (0,-5) (liberal/libertarian), so maybe I'm just part of the evil libertarian agenda.

One thing that I am critical of, though, is how they've placed all the presidential candidates on the spectrum. Notice anything? Everyone's in the upper-right (conservative) quadrant! I'm in-between the lower two quadrants--so obviously I should be voting for Kucinich (if he had a chance), right? And I definitely shouldn't have voted for Obama. Well, I'm skeptical...

It's rather well-known that the US is on average much further to the right than the rest of the world. The US has a conservative bias (gasp!). Actually, it's probably more correct to say that the rest of the world has a liberal bias (gasp!). After all, the US is obviously more important the rest of the world combined (just based on our military spending).

But why is it that the entire selection is far to the right, compared to me? I don't regularly look at politics and think "Damn, why is everyone so far right?" Even Edwards is too far to the left for me. Why does the test disagree so much with my political intuition? I call shenanigans!

Now, I'm just speculating, but I think it has to do with the difference in how they test me, and how they test the candidates. To test me, I just gave a mostly emotional response to a bunch of politically slanted statements. To test the candidates, they say, "We've relied on reports, parliamentary records, ... and actions that spoke louder than words." I think there is a systematic bias in one or both of these tests that makes it impossible to compare their results.

In particular, there is a bias in the test I took. I am not a politician, and all my political opinions are rather half-baked. I just have a general idea of "We should let people be free. A free market is good, but that doesn't mean you can't improve upon it." If you asked me how much taxes we should pay, I would have no clue because I'm not even sure how much we pay now. I have no quantitative opinions on the matter. All the questions on the quiz ask me to react to some qualitative opinions. I respond in the general direction that I think society should go relative to where it is now. Therefore, I think the quiz only tells me where I am relative to my surrounding society. If I became a politician, and they put me through their rigorous (ha!) testing process, I'd probably score midway between Obama and Ron Paul.

That places me nearest to Hillary. But I don't really like Hillary. Or Ron Paul for that matter. Go figure. The moral: don't base your vote on internet quizzes.

Billiards balls solution

See the original puzzle, "The infinite bag of billiards balls".

I feel kind of bad because nobody is actually solving the puzzles that I post. At least, no one but lurkers. Are they too hard, or not interesting enough? Oh, well, I understand that not everyone's into solving puzzles. Well, the solution to this one should be interesting, even if few people are interested in solving the puzzle themselves.

This puzzle is what Wikipedia calls the "Balls and Vase Problem". The paradox is that there are two ways to analyze the problem, each giving different results. On the one hand, every single ball that is put in the bag is eventually taken out. So the bag should be left empty. On the other hand, after the nth step there are 9n balls left in the bag. So as the number n reaches infinity, the number of balls in the bag should also reach infinity. So which is it, zero or infinity?

Well, there is a flaw in one of these approaches, the one that says there are 9n balls after the nth step. How do we prove that there are 9n balls at each step? We use induction. First, we show that it is true for n=1. Then we show if it is true for n=1, it must also be true for n=2, n=3, n=4, and so on. The problem is that induction only works for finite numbers. No matter how many times you increment n, n will never be infinite. It is a mistake to assume that the formula 9n holds true even when n is infinite.

Here is another example of the same mistake. Try to catch where it goes wrong.

1 is a finite number.
If n is a finite number, then n+1 is a finite number.
Therefore, all natural numbers are finite.
Therefore, infinity is finite.

With that out of the way, we can focus on the other approach.

Without some specific information, the resolution to the puzzle is indeterminate. If you put in an infinite number of balls, and take out an infinite number of balls, we might be left with zero, infinity, or even something like twenty-two. However, a definitive answer can be found if we know exactly which balls we remove. For example, if we put in all natural numbers (1, 2, 3, ...) and take out all natural numbers, we're left with nothing. If we instead take out all positive even numbers (2, 4, 6, ...), then we're left with the odd numbers, which is an infinite set.

So you probably can see where this is going. In the main problem, we put in all the natural numbers, and then remove all natural numbers. Therefore, we're left with nothing. In variation 1, we put in all natural numbers, and then remove all numbers that are divisible by 10. We're still left with all the numbers that are not divisible by 10, which is an infinite set.

Variation 2 is the most interesting of all. If you're philosophically inclined, maybe it will provoke questions about how we label objects, and how this relates to their true identity. But I'm not going to dwell on it. In this problem, we are obviously left with an infinite number of balls, since we have not removed a single one. But can you name a single number that is left over? The resolution is that there is not a single finite number left over, but there are many infinite numbers. More specifically, each billiards ball will have an infinite number of zeros in its label. We will have an infinite number of these in the bag.

So, are you tired of thinking about the infinite yet?

The two obstacles to changing the world

Have you ever listened to motivational speeches? Read inspirational material? These sort of works are meant to inspire action, whether to change your self, or to change the world. How do these works actually inspire action? Well, they tell you that you should get to it, and get to it now, because you have the power and, damn it, this stuff is important! (Obviously, I'd be a very poor motivational speaker.)

Inspirational and motivational material is meant to overcome what I will call the second obstacle to changing the world. We all want to help the less fortunate. We all want to preserve the environment. We all want to cure human disease. But wanting does not translate to action. Sometimes, it's difficult to actually bring yourself to help these causes. It's tempting to ignore the homeless, to toss recyclables in the trash (and yes, I'm as guilty as the rest of you). After all, a single person can only have a negligible effect on the world, so are these things really worth the attention and effort?

As I understand it, this was the whole point of The Lord of the Rings. In the trilogy, Frodo knows that he must bring the one ring to the top of Mt Doom, and toss it into the fires. His path is clear. But actually walking that path is long and difficult.

This brings me to the first obstacle to changing the world. Unlike Frodo, our paths are not always clear. I mean, we don't exactly have a based-on-Jesus Gandalf character to tell us what we must do (unless you count Jesus himself). It is impossible to distinguish temptation from reasonable doubts unless you try thinking about it. Furthermore, even if a goal is obviously worthwhile, there are usually several methods to achieve that goal.

For example, take the goal of helping the poor. Most everyone shares this goal. But there is more than one way to attain it. There is a debate between two methods, known as charity and social justice. Charity seeks to meet the immediate needs of the poor. Social Justice seeks to change the system in order to eventually decrease poverty or lessen its impact on people. Obviously, there need not be a dichotomy between the two methods, but there is still the question of how effective they are. How much should we invest in one relative to the other? The answer to this question usually divides along political lines, with the liberals supporting social justice, and the conservatives supporting charity.

In summary, the first obstacle to changing the world is making a decision. The second obstacle is acting it out. Occasionally, these two are in conflict. On the one hand, we must decide carefully, and on the other hand, we cannot be indecisive.

When there is a conflict, motivational speakers would have you believe that those who hesitate are just cynics and skeptics. As a self-identified skeptic, I can say that there is some degree of truth in this. It is true that I hesitate. That's because I emphasize overcoming the first obstacle. People can be easily mistaken about the correct path. So caution is advised. I've spent too much time reading opinion articles and blogs to think that everyone agrees on goals and the proper means to achieve them. Who, if anyone, is correct? Which actions should we take, and not take?

Does it really make me a cynic when I hesitate? I actually think of myself as an idealist. Case in point, a cynic would have been compelled to point out that not everyone wants to preserve the environment. I tend to assume everyone is essentially good-natured. But I realize that even the well-intentioned will disagree on what to do.

But I'm not here just to give an anti-motivational speech. The solutions to the two obstacles are not always in conflict. You can, for example, support education. Education fulfills a variety of societal needs and helps people better choose society's direction. You can participate in the public debate. Debate helps us make decisions and promotes public awareness and action. And you can vote, making you both a participant in the public debate and an agent of real change.

Of course, I'm probably not one to speak. Here I have a blog that covers controversial topics, but avoids politics. It's so easy to just talk, but the actual doing takes more work...