Thursday, September 30, 2010

Interview: Sexual Dysfunction and Asexuality

How do you distinguish between people who have sexual dysfunctions, and people who, by orientation, don't experience sexual attraction?  As each of these two groups asserts their own existence, do they need to deny the existence of the other group?

Back in June, there was a lot of discussion about Flibanserin, a proposed drug meant to treat women with hypoactive sexual desire disorder.  Critics complained that the drug was marginally effective, and that the subsequent marketing campaign would generate unreasonable distress among women about low desire.  However, there are also people who might want the drug--are we marginalizing them?  (Flibanserin was eventually rejected by the FDA.)

On this topic, there is an interview on Shades of Gray with someone who has Female Sexual Dysfunction, and blogs about it from a feminist perspective.  Go read it if you're interested.

I consider this to be an... er... advanced topic in feminism and queerness, but you can handle that, right?  I'm drawing attention to the interview because I was one of the ones who pushed for it (I even wrote some of the questions).

Wednesday, September 29, 2010

Earthquake predictions: not likely!

So there's some website, called Quake Prediction, claiming that there is large chance that a large (6.5-7.0) earthquake will hit Los Angeles, and then another in San Francisco in the next few days.
Oct 05: 05%
Oct 04: 14%
Oct 03: 42%
Oct 02: 72%
Oct 01: 97%
Sep 30: 98%
Sep 29: 90%

Oct 05: 74%
Oct 04: 66%
Oct 03: 51%
Oct 02: 27%
Oct 01: 10%
Sep 30: 05%
Sep 29: 05%
The predictions above were taken from the website on September 29, 3:30 PM PDT (with links removed).  I note the time, because who knows how often the website changes.

I'm slightly confused by those numbers, because there seems to be some very bad math going on.  If there is a 90%+ chance of earthquakes on Sep 29, 30, and Oct 1, does that mean that there is at least a 70% chance of three earthquakes?  Someone doesn't understand probability... but let's ignore that for a moment.

There are many reasons to be very suspicious of this.  The first is that a lot of research has gone into forecasting earthquakes, but no one can achieve anything anywhere near this accuracy.  We don't expect there to suddenly be a breakthrough where we can start predicting earthquakes within a few days.  And if there is a breakthrough, we don't expect it to come from some standalone person with a poorly constructed website.  In fact, this is more what we would expect if there were some crank who just thought he could predict earthquakes.

Moreover, how does he know his predictions are that accurate?  The best and easiest way to know is by looking at past predictions and seeing how they aligned with reality.  Has he done this?  If he has, then why isn't it published?  Why isn't it all over the news?

In fact, I did find this guy in the news.  They called him the Quake Quack.  Note the date of the article: April 12.  It's talking about a prediction he made for a large (5.0-6.5) Southern California earthquake on April 12-14.  I don't remember that one ever happening, do you?

In fact, if you look back on QuakePrediction's twitter archives, you find that it's just littered with predictions that never happened.  He predicted a 5.0-6.5 earthquake on September 25, a 4.0-5.5 on September 14th, a 4.5-5.5 in September 6-7, and so on.  You can check these against the list of significant earthquakes on the US Geological Survey, and nothing matches.

It's a marvel how someone can be so confident when a cursory glance reveals that the predictions have nowhere near the claimed success rate.  Seriously, that kind of self-confidence is a Life Skill, but one that has been hopelessly misdirected.  A more cynical suggestion is that he's just throwing around lots of predictions just so he can brag about it when he eventually gets one right.

I was thinking of doing a more systematic analysis of the twitter archives, comparing his successful prediction rate to that of chance*, but then I remembered I have better things to do.  I was going to suggest that someone else do it, but then it occurred to me that if I have better things to do, you probably do too.

*Experimental note: Measuring the chance success rate is very simple.  Just take each prediction, and pretend he really made the prediction for a day N weeks later/earlier.  Try for many values of N and see if his success rate is significantly higher for N=0.

As a final note, this stuff is not harmless.  Here's a story from What's the Harm? on how a quake rumor disrupted a town.

Tuesday, September 28, 2010

The internet makes us all bad people

I've just deleted and closed all comments in my previous post.  Someone was claiming to be someone they were not.  Details will not be discussed.

But this is not the only blogging adventure I've ever had, so I'll tell you a different story.

This one occurred off site.  Someone linked to one of my old physics posts.  Whenever someone does that, I'm flattered, but sometimes I question their judgment of sources.  This is a blog, after all.  Until recently, it was all just written by some physics undergraduate.  It's good for an informal physics explanation, but there are many uses which are inappropriate.

In this case, the person, a blogger, linked to my post to demonstrate that those crazy Physicists are just trying to bullshit us.  How can my explanation possibly account for observation X?!  So I left a comment on his blog saying that professional physicists actually have a much more precise theory than could be contained in my post.  In this framework, observation X is trivially explained by Y.

He conceded the point, but reiterated that Physicists are all bullshit because they can't explain Z.  Well, Z is also trivially explained, but I'm not going to waste my time.  I've browsed through his blog and I can see that there is clearly too much crap to correct it all.  He's trying to propose some grand theory of electromagnetism that doesn't contain relativity, but does contain lots of references to the visions in the Book of Ezekiel.  So I basically told him that I wasn't his personal physics tutor.

I also remember having a troll on this blog a long time ago.  He was arguing about how I was being really offensive to Christians, even though he himself wasn't Christian.  I think in context, I was just talking about how Christians aren't monolithic.  I've said a lot more offensive things than that!  He wouldn't know offensive if it slapped him in the face.

Anyways, this troll spent half the time insulting me.  I never got angry though, because I just couldn't take him seriously.  I just calmly shot down all his arguments as he got increasingly hysterical.  He also kept making food analogies, as if he was hungry or something.  The high point was when he started making empty threats--in rhyme!

Yeah, I just can't take trolls seriously.  Sometimes I wonder if this is a problem, if I should take them more seriously.  The thing is, I have a really slow temper, and I tend to project this onto everyone else.  So when someone gets angry, I tend to underestimate it.  I just find the insults funny, and I can't imagine that anyone should be upset by them.

But not everyone seems to react the same way.  I seem to recall that the aforementioned troll was also insulting my other readers, some of whom got a bit riled up.  I think he called one of them gay.  When I read that, I thought, "He's calling someone gay, on my blog?  How quaint!"  But maybe someone was actually upset by that?  I don't know.

I've always been lax about comment moderation, and this will continue.  I think it is both acceptable and inevitable that people get angry on the internet.  But my tendency is to let it go too far, simply because I can't see why anyone would get upset.  I make no promises, but if any of you regular readers ever have any complaints, let me know.

Friday, September 24, 2010

Asexuality is queer

This has nothing to do with skepticism,* but for some time I've wanted to write about the relationship between asexuals and the queer community.  This topic is close to my heart, because I live in that intersection.  I openly identify as gay and asexual (or more precisely, between the two).  Clearly, it's in my interest that these groups get along and be allies to each other.  But I also think that these groups should be together because they advance each others' causes.

*Note that my blog has always included topics of little relevance to skepticism, since the beginning.

The queer ideal is to be radically inclusive of all gender and sexual minorities.  This does not just mean gay, lesbian, bisexual, and transgender.  This means pansexual, intersex, polyamory, fetishism, questioning, fluidity, asexual, and the intersection of all these minorities with gender, ethnicity, disability, social class, and anything else you can imagine.  The queer ideal is to destroy all the false binaries and societal norms that unduly disadvantage these minorities.  That's the impossible dream.

Asexuals belong in that dream, but not just because asexuals are a sexual minority.  Nor is it because asexuals physically overlap with those other minorities, though there is indeed a large overlap.

A breakdown of the community on the Asexual Visibility and Education Network.  Some caution is advised, since this is based only on two internet surveys, but we're not going to have much better data than this for a long time.  "Romantic orientation" tells us which gender(s), if any, the asexual is inclined to form romantic relationships with.  "Assigned" refers to the gender (male or female) assigned at birth.  "Cis" means having the same gender identity as the gender assigned at birth.

Asexuality belongs in the impossible dream because it challenges many of our deeply held assumptions about sexuality and relationships.  It challenges the assumption that sex and romance always go together.  We all sort of knew that already, in the back of our minds, but there is no clearer demonstration than the existence of people who experience romantic feelings, but not sexual desire.  And clearly nonsexual relationships are not any more "pure"; this is just how people are, and it has nothing to do with virtue.

Asexuality challenges us to seriously talk about fluidity.  People often assume that asexuals are just "late bloomers" or they haven't met the "right person".  These people have a very naive view of fluidity, as if everyone is constantly changing, but changing in specific directions conforming to specific norms.  Many asexuals don't change, but a few do.  And that's okay, because people can identify as something without having to commit permanently with absolute certainty.  The best we can do is provide a space where people are allowed to question themselves, and where new self-discoveries are accepted, even celebrated.  Fluidity is not betrayal, after all.

Asexuality challenges the assumption that romantic and sexual relationships are the ultimate form of interpersonal relationship and success.  If that's the case, why do people get on just fine without them?  Sexual relationships are seen as the best and only source of intimacy in our lives, but in fact there are other sources.  We have our friends, and our communities, and we can make new relationships which are uncategorizable as either friends or romantic partners.  The same way gay people opened up new possibilities for sexual relationships, asexuals have the power to open up new possibilities for nonsexual relationships.

Sadly, the impossible dream is not here, and asexuals know it.  The asexual community is split between the people who want to be part of queer, and the people who don't (clearly I am radically in favor of the former).  When you ask people in the latter group why, they give three reasons.  The first reason is that they are not gay, and thus do not belong in the gay community.  I think this is sad, because it indicates that the queer community is doing so poorly at its goal of radical inclusiveness, that people don't even recognize it as anything more than a group for gay people.

The second reason is that they feel that we need separate spaces.  This objection is just based on a simple misunderstanding.  I am not advocating that we dissolve our separate communities and merge into an amorphous whole.  I am advocating that we all be allies and friends, that we fight for each other's causes, and we make our respective spaces safe for each other.

The third reason people give is that they tried to join a queer group, but it didn't turn out well.  Many asexuals, when they first discover the concept, initially assume that the place to go is the queer community.  And then when they get there, they find that some queer groups are no more accepting than anyone else.  Sometimes they are sex-positive in the most naive way.  Often they're just ignorant about it, occasionally willfully ignorant.

A more difficult problem is the focus of such groups.  They focus a lot on sex.  And that's great until it comes at the exclusion of everything else.  When that's all there is, I feel there's a lack of imagination.

And in case this all seems hopeless, let me just say: I am typing this from a queer space right this moment.  I am sitting in an LGBT themed house, where I often get food and internet.  I like it here a lot.  I recognize that the reason I can be happy in queer spaces is due a fortunate series of circumstances.  But some of these circumstances are no accident!  It's an accident that I am privileged enough to be able to go to university, but it's not an accident that university queer groups are so successful at being radically inclusive.  This is the result of an intentional and sustained effort.  Let's keep it up!

Monday, September 20, 2010

Evolution and the 2nd Law

A common Creationist argument is to say that evolution by natural selection violates the Second Law of thermodynamics.  The Second Law of thermodynamics says that entropy increases over time.  Entropy is a quantitative measure of disorder.  So Creationists point to the complexity and order of life and say, "How is that consistent with natural law?"

There are any number of responses to this question, first beginning with the fact that Earth is not a closed system.  That is, the Earth has contact with a very large source of energy, the sun.  The Second Law only says that the total system (that is, the sun and the earth) will increase in entropy.  It's entirely possible for part of the system to decrease in entropy if it's offset by a larger increase in entropy elsewhere.

Creationists sometimes respond by saying, "Even if it's possible, is it really plausible?"  Absolutely!  Whenever energy gets transferred from a high temperature object to a low temperature object, this causes an increase in entropy.  So whenever the sun radiates energy onto the earth, entropy increases.  The sun radiates a lot of energy.  Transferring energy from hot to cold objects is how most processes do work (that is, they provide free energy with no entropy attached).  Engines work this way, for instance.

If you look at the total power from the sun, it turns out that one year's worth of power provides enough work to rearrange all the molecules in the Earth's biomass from a completely disordered state to a completely ordered state.  Given the long time that the sun has been powering the Earth, and given that all the molecules biomass are not even close to being completely ordered, evolution doesn't seem at all unreasonable.

Another response is that entropy is not exactly the same thing as disorder.  "Entropy is disorder" may be helpful when you first encounter the concept, but entropy is more precise than that.  Entropy is a measure of the number of different ways a system could be, and yet still look the same from the big picture.  When we look at the sun, we can tell certain things about it, like its temperature, size, and mass.  But the thing is, the sun is composed of 1057 particles or so, and they're all moving very fast in an unknown direction.  There are a whole lot of ways those 1057 particles could be configured, and yet the Sun would still appear the same temperature, size, and mass. So the sun has a huge amount of entropy.

I bring up this very large number of 1057 particles to convey the fact that disorder on the atomic scale is far more important to entropy than disorder on a macroscopic scale. Consider cars.  Our car system is highly ordered.  All the cars need to be in the exact right places so that they obey traffic laws, don't crash, and can take their passengers exactly where they want to go.  There are about 800 million cars the world.  But how many molecules are there in a single gallon of gasoline?  Somewhere around 1023, 14 orders of magnitude larger.

And now consider DNA.  Human DNA has about 200 million base pairs, each of which has only four possibilities: A, C, G, or T.  The amount of entropy involved in having the right letters is trivial compared to the entropy involved in a simple chemical reaction, like the combustion of gasoline.  It's nothing compared to the entropy involved in the radiation from the sun.

A third response is that the Creationist argument has a very limited view of what is possible within the confines of the Second Law.  To see examples of processes that are consistent with the Second Law, look around you.  Everything you see was created by the Second Law.

The Second Law is why things fall down and stay down.  It's why evaporated water goes up into the sky and forms clouds.  It's why ice cream gets warm and melts when you leave it out.  It's why freezers can be so much colder than their surroundings.  It's why when you break a clay bowl, it stays broken.  It's why, when you smoosh two pieces of wet clay together, they become one.  It's why mountains erode into nothingness, but also why mountains form in the first place.

The point is that even if the Second Law favors one result under certain conditions, it can reverse the result under other conditions.  Creatures tend to die and decay, but under other conditions, they get born.  Sure, evolution involves some reduction in entropy (however trivial compared to the entropy of a typical chemical reaction).  But every step of the way, organisms are dying and decaying.  Every step of the way, organisms are consuming food, leaving more disordered waste products.  These waste products ultimately get converted back to food with the help of photosynthesis (remember the sun?).

The process of evolution leaves plenty of disorder to go around.

I was curious, so I checked to see if this argument was on Answers in Genesis' list of "Arguments we don't use".  It is not.

Saturday, September 18, 2010

Physics preconceptions

One of the interesting things about teaching introductory physics students is the weird mistakes they make.

For instance, many people come to class with the preconception that acceleration goes in the same direction as velocity.  You define velocity, and you define acceleration, and they see that they're different.

Then you draw a graph of position vs time and ask which way it's accelerating.  "That way," they say, and they point in the direction of velocity.  "So... the velocity is increasing in this direction over time?"  Confused stares.  Mumbled answers.  The answer is clearly "no," but doesn't that contradict their previous answer?

Later, we do a simple hands-on lab, with a cart on a track.  We tilt the track.  If we push up the cart and let it go, which way is it accelerating as it goes up?  Which way is it accelerating when it stops at the top?  And when it comes down again?  It's clearly changing direction... right, Mr. Miller?

When the track is flat, I ask them to show how they pushed the cart to give it positive acceleration.  They give a short and sharp push and let it roll freely.  See, acceleration!

After all this has been corrected, I ask them why it is we think acceleration is in the same direction as velocity.  Nobody knows.  I say, "I don't know either; I study physics, not psychology."

It's hard for me to sympathize, because I don't remember ever making this kind of mistake.  Maybe I just don't remember it.  But I sure didn't make the mistake repeatedly, having to relearn the same lesson every time the context changes just a little.

In my pedagogy class, we are learning a bit about the cognitive psychology of the naive conceptions brought in by introductory physics students.  We are learning what they are, where they come from, and most importantly, how to deal with them as teachers.

Don't expect me to blog much about this psychology stuff.  I'm quite aware that we only really scrape the surface, to practical ends.

But I will say that this sounds an awful lot like skepticism.  Skepticism is all about the strange things people believe, where they come from, and how to deal with them.  Skepticism is a lot like teaching.

The difference is that the subjects of skepticism are often hostile to it, and skeptics are not in any position of authority.  Come to think of it, this is a really huge difference.  As a physicist would say, this can't be modeled as a small perturbation.  Maybe skepticism is nothing like teaching after all.

Thursday, September 16, 2010

New asexual flag

Perhaps you've noticed that on the margins, I replaced this triangle symbol...

... with a new symbol.

This is was declared to be the flag for asexuality about a month ago.  Even though it's new, I'm throwing my support behind it.  It's not universally accepted, but I'm not going to dwell on that issue because it is boring.

However, I should take a moment to comment on the meaning and history of the symbols.

The inverted triangle symbolizes the spectrum of sexualities.  The top of the triangle represents heterosexuality and homosexuality, and everything inbetween.  The lower corner represents asexuality.  The gradient represents "gray-As" like me, who are, in various ways, between asexuality and sexuality.  However, it is widely recognized that the model is incomplete because it does not include romantic orientation, and it relies on the gender binary.  But then, you wouldn't really expect to have a simple symbol that is also a complete model of sexuality.

The triangle dates back to around 2003, near the time that AVEN was founded in 2001.  It tends to be strongly associated with AVEN specifically, to the point that it's sometimes called the AVEN triangle.

The asexual flag, as I said, is about a month old.  Some efforts were made to let all parts of the asexual community have a say on the flag, rather than just English-speaking AVEN.  But AVEN dominates the asexual community so much that I think of those efforts as more symbolic than effective.  In any case, it's nice to have a decent universal symbol for once.

(Yes, I am aware of the irony that the image on my blog's margin links to AVEN.  But then, the Scarlet Letter links to Richard Dawkins even though I consider it a universal symbol of atheism and not a symbol of Richard Dawkins.)

The colors have specific meanings.  As in the AVEN triangle, black is for asexuals, gray is for gray-As, and white is for sexuals.  Purple stands for community.

The stripe pattern is reminiscent of the Rainbow Flag, as well as flags of various subgroups, like bisexuals and transgendered folks.  I think of this as a point in favor the flag.

Monday, September 13, 2010

Current work: teaching

My brief research project ended a few weeks ago, and now I'm doing something completely different.  I'm teaching!  I am leading two sections of the introductory physics course for non-physics majors.  It's a class filled with pre-meds.

Pre-meds are really competitive about grades, to the point that they'll argue over a fraction of a point on homework, or sabotage classmates.  They'll complain if you try to teach them something that isn't on the test.  They prefer to memorize as much as possible so that they never have to think about the subject in front of them.

At least, that is their reputation.  They're really not that bad.

I think it's a relatively easy class to teach.  Each section meets for four hours a week, so they're plenty of time.  It's actually kind of ridiculous how much time people spend in this class.  It's a pretty easy class too, at least for me if not the students.  It helps that I can solve any problem in this class on the spot if I need to.  It also helps that we have worksheets prepared for the entire semester.  There's a simple standard template for every section: let the students do their worksheets in groups, and go around checking on them.

Oh, and homework grading is automated.  I haven't done any grading yet.

I find that I'm not too bad at teaching either.  I'm pretty confident.  My presentation is clear and engaging.  I can improvise lessons whenever a teachable moment pops up.

I make mistakes too.  Not physics mistakes, but teaching mistakes.  For example, if I don't explain something quite as clearly as I could have.  Or I use more or less time than I expected.  Or I don't organize the section in quite the optimal manner.   But these mistakes are hard to correct because it's difficult to judge whether an explanation is good or if a section is well-organized.

One skill that has been unexpectedly handy is my ability to write problems.  I have been writing puzzles since high school, but I never considered it a useful skill.  But whenever the worksheets are too boring, too easy, or too short, I can write my own problems just like that.  I can make them as challenging as I need them.  Let's just say that the students never have a shortage of exercises.

Friday, September 10, 2010

Responsibility and causality

Previously, I've talked about causality from a scientific perspective, but causality is also very important in ethics.  Specifically, causation tells us something about who we hold morally responsible for various outcomes.

For example, let's say that I borrow a friend's laptop and it breaks.  Should I be held morally responsible for breaking the laptop?  It depends on whether my handling of the laptop caused it to break.

Case 1: My handling of the laptop caused it to break.  That is to say, it would not have broken if I had not mishandled it.  Therefore, since prefer our laptops in working condition, my mishandling should be discouraged.  That is to say, I should be held morally responsible for the mishandling.

Case 2: My handling of the laptop did not cause it to break.  That is to say, it would have broken anyway.  Discouraging my treatment of the laptop is pointless because the results could not have been prevented.  So I shouldn't be held morally responsible.

"I didn't do it, honest!"

In this context, causality just means that the results wouldn't have happened if not for the actions.  Moral responsibility means that the actions should be encouraged or discouraged.  We intuitively understand that causality is a necessary condition for moral responsibility, because there is little point in encouraging or discouraging actions that have no bearing on the results.

On the other hand, causality is not a sufficient condition to establish moral responsibility.  Most obviously, the laws of nature are what cause earthquakes, hurricanes, and other natural disasters, but we don't hold them responsible for anything.  This is because the laws of nature are not human and don't respond to encouragement or discouragement.

But even when all parties are human, this is still true.  Consider a general scenario where Alice performs action X.  Bob, in response, performs action Y.  Y results in negative consequences.  Both actions caused the result, in the sense that if either action had been avoided then the consequences would have been avoided.  But should Alice or Bob be held morally responsible?

This is an outcome table for our scenario.  It's assumed that Alice and Bob have some motivation for acting the way they do, and are inconvenienced if they don't do it.  Depending on the precise situation, this inconvenience could be great or small.

If both parties are being coerced with threats of violence, then the "inconveniences" are quite large, and we couldn't hold them morally responsible.  If both parties are just being lazy, we might hold them both morally responsible.  For example, if Alice is a lab safety supervisor, and Bob is a lab worker, then we expect Alice to inspect the lab conditions and for Bob to be prepared for any hazards.  Safety is more important than laziness.

But sometimes, one party is much more inconvenienced than the other.  Unsurprisingly, the first example that comes to mind is queer-related.  If Alice goes out in public with her girlfriend, or if she is MTF and goes out in public presenting as female, then this might cause Bob to harass her.  But it's a pretty major inconvenience for Alice to never show herself in public, and not a big inconvenience for Bob to stop harassing people.  So Bob should be given all the moral responsibility.  Alice may recognize the chain of causality, and may choose to be more discrete, but she is not morally obligated to do so.

On the flip side, it could be Alice who holds all the responsibility.  For example, Alice could be someone who advertises healing touch therapy with false claims, and Bob could be a customer.  Certainly Bob bears some responsibility for investigating the validity of the services he pays for, but Alice is far more responsible because she is lying.

Come to think of it, in the above scenario, Alice has the greater inconvenience, because she's missing out on a lot of money that she could have conned from people.  Perhaps it's better to measure it by inconvenience to society in general rather than inconvenience to Alice or Bob specifically.  Or maybe there are other factors I'm not considering.  Point to ponder.

In general, this is a very difficult ethical dilemma, finding out who is morally responsible.  For many situations, there are social conventions for who is expected to step aside.  Sometimes, these conventions are neither good nor bad, it's just that society has to pick one or the other (like the convention that all cars drive on the right side of the road).  Other times the conventions are bad, but they're hard to change without some intermediate negative consequences.  Ethics is hard.

(This post came to mind when I read something on The Thinker.  I have no comment on the specific example he uses.)

Other posts in this mini-series:
Colds and Causality
Women and Causality
Responsibility and Causality
Nature/nurture and Causality
Physics and Causality 
Math and Causality 

Wednesday, September 8, 2010

What is temperature?

In an earlier post, I wanted to explain temperature, but I think this deserves its own post.  Temperature is complicated.  It's clearly defined at the beginning of any class on thermodynamics or statistical mechanics, but I think that this definition will leave a popular audience cold (no pun intended).
Even if you understand everything about this equation (T is temperature, S is entropy, and E is energy), you would be hard-pressed to find the connection between this definition and our perceptions of "hot" and "cold".

So I'm going to explain it in the other direction, starting with hot and cold, and then working our way back to this definition.

Building a definition of temperature

I think we all intuitively understand that if we put a hot object and a cold object together, the hot object gets cooler and cool object gets hotter.  This represents an exchange of energy between the two objects.  The energy flows from the hotter object to the cooler object.  Eventually, the two objects will reach the same temperature.

But this is not the same as saying that the two objects reach the same energy.  If hot steam comes out of a teapot, the steam clearly doesn't have as much energy as the entire earth's atmosphere, yet energy will still flow from the steam to the atmosphere as the steam cools down.  It might seem like you could correct for this by considering the density of energy rather than the total energy, but this approach will also ultimately fail.

But we can definitely say one thing about temperature.  The higher the temperature of an object, the more "willing" it is to give up its energy.  The lower the temperature, the more "willing" it is to accept energy.

I want to point out a characteristic of this process that may not seem strange at first, but is.  The process of energy flowing from hot objects to cold objects cannot be reversed.  If we recorded the process, and played the recording backwards, it wouldn't make any sense.  The hot object would get hotter, and the cool object would get cooler.

This is strange because pretty much every law of physics works the same way forwards in time and backwards in time.  But there's one notable exception, the Second Law of Thermodynamics.  The Second Law states that entropy increases with time (and therefore decreases if you play time backwards).  So if a process occurs forwards, but not backwards, that means it must involve an increase entropy.  We'll get to the precise meaning of "entropy" later, but for now you just need to know it increases over time.

The exchange of energy between hot and cold objects represents a redistribution of energy to where it will contribute the most entropy.  In a cold object, a little energy goes a long way to increasing the entropy.  In a hot object, it takes a lot of energy to increase the entropy just a bit.  So in order to maximize entropy, it makes sense move energy from the hotter object to the cooler object.

Typically, the dependence of entropy on energy looks something like the blue curve below.  Note that the more energy you have, the less quickly entropy increases.  This produces a temperature which increases with energy (in purple).

However, there's no logical contradiction in having a system where the temperature decreases as the energy increases.  Nor is there logical contradiction in having a negative temperature.  But it just doesn't happen in stable systems.

What is Entropy?

Let's talk briefly about entropy (but not too long).  Entropy is usually described as a measure of disorder.  But a more precisely, entropy is a measure of how many different ways a system can be, and yet still look the same from the big picture.

For example, from the big picture, a broken egg is a broken egg.  But there are a lot of ways an egg can be broken, a lot of ways the cracks can go, and a lot of ways the shell can be scattered around.  On the other hand, there is basically one way for an egg to be intact.  So we could say that a broken egg has higher entropy than an intact egg.

But the egg is just a toy example.  Here's a more realistic one: I can look at a gas from the big picture and measure its temperature and volume and pressure.  But I can't see the motion of every individual particle.  There are a lot of different ways the particles could be moving around, and yet they'd still look the same to me.  So we can say that the gas has entropy.

Usually, the more energy a system has, the more ways there are to allocate that energy among all the little particles.  And therefore it has more entropy.

The second law of thermodynamics is based on the idea that every possible state of a system is more or less equally likely.  Therefore, from the big picture, high entropy states are more likely.

The Boltzmann Factor

Let's look at an individual particle in a gas.  The more energy this particle has, the less is left over for the rest of the gas.  The less energy the gas has, the less entropy it has.  More precisely, if you divide the cost in energy by the temperature, then you will find the cost in entropy.  The more entropy it costs, the less likely it is to occur.

But if a gas has a very high temperature, then it doesn't cost much entropy for our particle to be energetic.  So the higher the temperature, the more likely it is for a particle to have high energies.

This relationship is described in Boltzmann's Factor:

p is the probability that a single particle is in a state with energy E.  T is the temperature.  k is just a constant to make the units right.  The equation says that p exponentially decreases as E/kT.

So another way to understand temperature is as a measure of the spread in energy.  The higher the temperature, the greater the variance in energy held by each particle.  The lower the temperature, the more the particles are confined to low energies.

So now you can see that temperature is closely associated with the random energy held by individual particles in a system.  But temperature is not the same as energy.

Monday, September 6, 2010

Parachuting robots

Two identical robots living in flatland parachute from the sky.  Each one falls somewhere an on infinite number line.  They each leave their parachutes on the ground and start walking around.

For some reason, this puzzle brings to mind an image of a para-bomb, from one of the Super Mario Brothers games.

When each robot lands, it executes a program that tells it when to go left or right and under what conditions.  Each robot has an identical program.  Neither robot can tell which direction the other robot is just by looking. The goal is to have these two robots meet.

Write a program that will make this happen.  You don't need to know any programming, just write it in English or pseudocode.

See the solution

Friday, September 3, 2010

Solution to Parity Puzzles

See the original puzzles

Puzzle #1: See image

If we color the shape in a checkerboard pattern, then each domino must cover exactly one blue square and one green square. The problem? There are 23 green squares and 25 blue squares. Therefore it's impossible.

Puzzle #2: See Image

Here, we imagine that the entire plane is tiled with a checkerboard pattern like shown in the above image. Each N tetromino covers an odd number of green squares. So an odd number of N tetrominoes covers an odd number of green squares. But each O tetromino covers an even number of green squares. Therefore it's impossible to find a shape that can be tiled by an odd number of N tetrominoes or an odd number of O tetrominoes.

Similar proofs can be constructed for any pair of tetrominoes.  But I leave this as an exercise to the reader.

Reader Secret Squirrel proposed another proof that was a little more complex.  I summarize it here:
  1. Each N tetromino is either vertically or horizontally oriented.  So out of an odd number of N tetrominoes there must either be an odd number of vertical tetrominoes or an odd number of horizontal tetrominoes.
  2. Let's say that there are an odd number of horizontal N tetrominoes (if not, then rotate the plane 90 degrees).  Consider the number of squares covered in each column, and consider whether this number is odd or even in each column.  Each horizontal N tetromino contributes an "unpaired" square to two columns (and vertical tetrominoes contribute nothing).  It's impossible to pair up all the unpaired squares with an odd number of tetrominoes.
  3. If we build a shape with O tetrominoes, each column must have an even number of squares covered.  Therefore, we can't build the same shape with O tetrominoes.
On some reflection, you might see that Secret Squirrel's solution is the same as mine.  Consider this image. If we just consider the horizontally oriented N tetrominoes, then each covers an odd number of green squares.  This is equivalent to step 2 above.  However, we're ignoring the vertical tetrominoes, so we also need to add on a pattern of horizontal stripes.  The horizontal and vertical stripes add up to a checkerboard pattern.

I think this is a case of polished vs unpolished proof.  When you first figure out how to prove a proposition, it's often clunky and difficult.  But from there you can remove the scaffolding and polish it.  But you would never think of the polished proof at first.  When I first formulated a proof, it didn't look much like looks now.

Sometimes this is a problem with math and physics textbooks.  They only present the most polished proofs, leaving it a mystery how anyone ever thought them up.  I sure felt this way all the time in abstract algebra.

Wednesday, September 1, 2010

Temperature, pressure, and kinetic energy

Reader Barefoot Bum asks:
If temperature and pressure are both the kinetic energy of the molecules, how are they different?
The short answer is that temperature, pressure, and kinetic energy are three different things.  But most of the time, as one increases, the other two also increase.  As one decreases, so do the other two.

This relationship is contained in the famous ideal gas law:
p is pressure, V is volume, n is the amount of gas, T is temperature, and R is a constant to make the units right.

So given a constant amount of gas in a container of constant volume, the pressure is proportional to temperature.

Somewhat less well-known is the Equipartition Theorem:
U represents the total energy.  In an ideal gas, all the energy is kinetic energy.  f just represents a number (e.g. 3 or 5) which depends on the type of gas.

So given a constant amount of gas, the kinetic energy is also proportional to temperature.

But the ideal gas law and the equipartition theorem do not define temperature, pressure, or kinetic energy.  Each one has its separate definition, and the relationships between them must be derived from other principles.  Therefore, it makes sense to say that there are some situations where the relationships between the three are less clear-cut.  As it says in the name, the ideal gas law is an idealized model of gases, and it may not hold true if there are further complicating factors.  For example, if the gas is so dense that it condenses into liquid nitrogen, then the ideal gas law is obviously not going to hold.

In the longer explanation, I would have to actually explain what these three things are.  In order from simplest to most difficult.

Kinetic energy is a measure of how much energy is in the motion of the molecules.  If the molecules are moving around, or if they are spinning, or if they are vibrating, this all contributes to the kinetic energy.  Note that kinetic energy is not exactly equivalent to motion.  If a single atom of mass m is moving with speed v, the contribution to kinetic energy is:
It's sort of an odd definition, and it's not obvious why v needs to be squared.  But long story short, the kinetic energy must be defined this peculiar way so that energy is conserved.  That is, the total energy in a system remains constant as long as there is no input or output.  There are similar equations defining the kinetic energy of rotation and vibration.  Just sum up all the different kinds of kinetic energy among all the billions of billions of molecules, and you've got the total kinetic energy.

Pressure is the amount of force that a gas exerts on the walls surrounding it, divided by the area of the wall.  Pressure is caused by molecules physically bumping into the walls.  Faster molecules will not only bump into the walls more often, but also exert more force on the walls when they do bump into them.  So clearly, the greater the kinetic energy, the faster the molecules are moving, and the more pressure the gas exerts on the walls.

But obviously some kinds of kinetic energy are not going to contribute to pressure at all.  If the molecules are rotating or vibrating, for instance, that doesn't make them bump harder into walls at all.  If the molecules are moving parallel to the walls, that doesn't contribute to pressure either.  The only reason we can say that the kinetic energy is proportional to pressure is because the kinetic energy naturally distributes itself evenly among all the different subtypes of kinetic energy, provided that you divide up the subtypes the right way.  In the equipartition theorem, f represents the number of different subtypes of energy.

An interesting aside is that one of the earliest lines of evidence for quantum mechanics came from this framework.  At high temperatures, the kinetic energy of air gets distributed among motion, rotation, and vibration.  But at room temperature, a greater fraction of the kinetic energy is in motion, because the molecules don't vibrate.  Ultimately the explanation came from quantum mechanics, which says that there are discrete energy levels of vibration.  Only at higher temperatures is there sufficient kinetic energy to overcome the jump between the first and second energy levels of vibration.

The last concept that needs explaining is temperature.  Ehh... Temperature will take much longer to explain, so I'll leave it for next time.  It's a strange thing, of the three concepts, temperature is the most tangible.  You can literally touch and feel temperature.  But it's the hardest to physically define.  In contrast, kinetic energy is simple to define in terms of mass and speed, but has more abstract significance.

Update: The next part about temperature is here.