I used to think Santa was a myth

'Tis the season for anecdotes...

I didn't ever take Santa very seriously when I was younger.  Or at least, not as far as I can recall.  And I thought that no one else took Santa seriously either.

I mean, kids believing in Santa, that's just something that happens in the movies, right?  There are countless movies depicting little kids who believe in Santa Claus.  They'll write letters to Santa.  They'll wait excitedly at the stairs for Santa to come, deliver presents, and eat the cookies and milk.  Kids believe in all these elaborate legends and rituals, sometimes even in the face of disbelief from their parents or older kids.

Of course, in these movies, Santa also happens to be real.  But Santa isn't real.  So why should belief in Santa be real?  For me, belief in Santa was all part of the mythos, along with the elves, reindeer, and red suit.

But some time ago, my dad told me that he and my mother made a conscious decision not to emphasize Santa Claus.  (They also made a decision not to emphasize heaven and hell, but that's another story.)  The reason?  Apparently, one of my uncles had a very negative experience with Santa.  One year, he found out Santa wasn't real, and he broke down crying.  He had a huge tantrum, and IIRC, also questioned the existence of God.

And then the next year, he forgot that Santa wasn't real.  And then he found out again and had another tantrum.

So it turns out that my childhood experience was not identical to other people's childhood experiences.  And plenty of kids really do believe in Santa, as well as the Tooth Fairy.  In a study I found, about 70% of 3-year-olds believe in Santa, as opposed to 78% who believe in the garbage man.  83% of 5-year-olds believe in Santa, and a third of 9-year-olds believe in Santa.

This just boggles my mind.  Next you'll tell me that kids actually write letters to Santa (what does the post office even do with them?), actually leave out cookies and milk on Christmas Eve (don't they go bad?), and parents actually dress up as Santa to fool their children.  This entails a much greater societal investment into the legend than I previously thought.

And what a bizarre legend it is.  Often, it's about the conflict between the believing children and disbelieving adults.  And as the narrative goes, it's the children who are in the right for believing.  Why??  Why is belief for its own sake a value?  It's one thing to claim that it has some value for child psychological development, but I hardly think that the legend has caught the public imagination because of psychological research.

I used to believe we lived in a world where children only believed in Santa in the stories.  That world made much more sense, but now I know that is not the world we live in.  I guess I learned a valuable lesson in critical thinking.

Interlude: God is infinite

This is a continuation of "A few things wrong about the cosmological argument," an ongoing series. This will be a lighter post.

In William Lane Craig's formulation of the Kalam Cosmological argument, he argues that infinities cannot exist, therefore the universe began, therefore God exists.

But... surely God is infinite?  You know... actually infinite.

This seems like such a jarring inconsistency in the argument.  I give William Lane Craig more credit than that, and I'm sure he has a functional response somewhere.  Let's just pretend that I've put in the effort to find his response, and that I've been suitably convinced that of all the problems with the cosmological argument, this is not one of them.  *wink*

As many of you know I went to a Catholic high school.  It wasn't so bad.  Actually a really good high school, run by Jesuits.  But yes, it was a religious education.  Morning prayers.  Religiously infused mission statement.  Monthly services.  Retreats.  A few teachers who were Jesuits.  I was Catholic at the time, so I didn't mind. Except for the monthly services.  Mass is boring!

I also took some religious classes, learning about the Bible, social justice, and apologetics.  They didn't call it apologetics, but that's what it was.  The teacher for that class was pretty good.  He had a flair for the dramatic and comedic.  He used lots of creative teaching techniques, and frequently showed videos.  From a high schooler's perspective, showing videos in class was like the best thing ever.

I think he was a fan of William Lane Craig.  When I later encountered Lane Craig's arguments, they seemed utterly familiar to me.  I consider them to be classic apologetic arguments, though this is perhaps only my perception.  "Classic" is just whatever I learned about in high school.

Along the same lines, I also believe that one of the "classic" understandings of God is The Infinite.  God isn't merely infinite, God is The Infinite.  You can't possibly comprehend God with your finite mind!  That would be like trying to comprehend the integers, or quantum field theory!  (Silly physicists...)

I took all this stuff with just a grain of salt, but he said one thing that really bothered me.  Paraphrased from memory fragments:

God is defined as The Infinite.  Suppose there were two gods.  Then there would be two infinites.  But there can only be one infinity, because all infinities are overlapping and identical.  Therefore, there can only be one God.

Arrrgh!  I mean, I don't mind arguing for a single God.  Whatever.  But man, that is some bad math!  The set of even numbers and the set of odd numbers are both infinite but they don't overlap!  Also, neither odd nor even numbers are identical to God.  This got me to thinking along other lines, like what is God's cardinality?  Does God's power set have greater cardinality than God?

This series on the cosmological argument is in about the same spirit.  I don't particularly care if people argue for the existence of God.  I definitely don't care if people argue about whether God is single or multiple.  At least, I don't care in the abstract.  But sometimes I see these arguments, and wow!  Bad math, bad physics, bad argumental form.  If someone argues that we're justified in believing an invisible conscious being that can only touch us in our "hearts", that's okay on some level.  (Well, no, it's ridiculous.)  But when you start talking bad math?  Blasphemy!

A few people have accused me of hiding behind lots of complicated logic, math, and physics.  It's all an attempt to dazzle people in to agreeing with me.  But that's not the point.  The point is to trick you all into reading about logic, math, and physics, when you just wanted a refutation of the cosmological argument.  Ha!  Ha ha ha!

...
Tune in next time for more of...

"A few things wrong about the cosmological argument"
1. Actual and potential infinities
2. Actual infinities in physics
3. What is real?
4. The "absurdity" of Hilbert's Hotel
5. Interlude: God is infinite
6. Forming Infinity, one by one 
7. Uncertain beginnings
8. Entropy: The unsolved problem
9. Kalam as an inductive argument
10. Getting from First Cause to God  

The "absurdity" of Hilbert's Hotel

This is a continuation of "A few things wrong about the cosmological argument," an ongoing series.  Today we will discuss William Lane Craig's treatment of Hilbert's Hotel.  I will assume you are familiar with Hilbert's Infinite Hotel; if not, you can read William Lane Craig, me, or any other source on the internet.

William Lane Craig (WLC) thinks Hilbert's Infinite Hotel is absurd.  If Hilbert's Hotel is full, then you can add or remove people and it will still have the same number of guests.  Absurd!

Can anyone sincerely believe that such a hotel could exist in reality? These sorts of absurdities illustrate the impossibility of the existence of an actually infinite number of things.

This is an argument from absurdity, which has the following form:

A implies B.
Both me and my opponents agree that B is obviously false.
Therefore we should agree that A is false.

There is nothing wrong with an argument from absurdity if it is done correctly.  But it is not done correctly.  I can agree that Hilbert's Hotel is absurd.  But not all infinities are necessarily absurd.  We can have infinities without specifically having an infinite hotel.  Hilbert's Hotel is absurd because we will never have the resources, the manpower to create such a hotel.  We don't have the people to fill it, the means to maintain it.

Of course, WLC thinks there is a more abstract property of Hilbert's Hotel which is absurd.  Specifically, he claims it is absurd that you can add or remove things, and still have the same number of things.  I do not think this is absurd.  The argument from absurdity relies on my agreement at this point, but I do not agree.

(An aside: WLC makes a technical error here.  We do not say that there is the "same number" of things, we say that the two sets of things have the "same cardinality".  Neither set has a well-defined "number" of things, since both sets are infinite.  There is a reason we use technical terms like "cardinality", and it is to avoid making mistakes by accidentally applying intuition where it does not apply.  WLC may have simply wanted to avoid technical jargon...)

WLC cites a couple people who objected, like me, that infinities are not absurd.  His basic response is, "It looks pretty absurd to me."  "Nuh uh."  "Yeah too."  We seem to be at an impasse.  If you're keeping track, that means WLC lost, since he is the one presenting the argument, and he has failed to convince.  But let's stop keeping track, and focus on resolving the impasse.

An anecdote: I first learned about infinite sets in high school.  This was back in the day, when the internet was still a novelty to me, and I wasn't smart enough to use a pseudonym.  I used to exchange puzzles with people and argue about mathematics.  In one of these arguments, someone told me to read about infinite set theory.  It was crazy!  Infinite sets blew my mind.  But by the time I got to college, they became intuitive and familiar, like a favorite old joke.  Non-math people think that when math people get together, they make jokes about pi and squares.  In my experience, they make jokes about infinite sets.  And yet, the set of untold jokes about infinite sets remains as big as ever.

I contend that infinities are not "absurd" in the sense of "obviously false".  Rather, infinities are only counter-intuitive (and only at first).  Infinite set theory is well-established in mathematics.  Due to some complications*, it is impossible for me to simply prove that set theory is consistent.  But we think that set theory is consistent for the same reason we think arithmetic is consistent, and I don't see WLC waving his arms incredulously at arithmetic.

*See Godel's second incompleteness theorem.

This is a point that clearly needs a response, so WLC has already responded to it.

Hence, one could grant that in the conceptual realm of mathematics one can, given certain conventions and axioms, speak consistently about infinite sets of numbers, but this in no way implies that an actually infinite number of things is really possible.

WLC distinguishes between "logical" possibility and "real or factual" possibility.  Unfortunately, this places infinite sets in a very odd place.  What kind of absurdity is this, that is too absurd for the real world, but not absurd enough for mathematics?  And for what kind of "real" is it too absurd for?  Lastly, if there are different degrees of absurdity, how do we know which degree it is?

There is no way to answer these questions, because "absurdity" is an intuitive idea.  Either we think something sounds absurd or it doesn't.  Intuition doesn't whisper in our ear, "It is absurd in reality, but not mathematics.  Also, 'reality' is a category that includes past events, but not future events, and it excludes inconvenient counterexamples."  Anyways, my intuition never says anything like that to me.

Put it this way.  If WLC didn't know anything about what mathematicians said, he would have guessed infinite sets were bad math.  And then when he finds out that it's good math, what is the appropriate response?  WLC's response is to say that infinite sets are still absurd, just not in mathematics.  I think the proper response is to revise what we previously thought was absurd.

I must say one last thing, as a physicist.  WLC thinks absurdity is a good argument against a physical theory?  Even when said absurdity is mathematically consistent?  I question his knowledge of modern physics.

"A few things wrong about the cosmological argument"
1. Actual and potential infinities
2. Actual infinities in physics
3. What is real?
4. The "absurdity" of Hilbert's Hotel
5. Interlude: God is infinite 
6. Forming Infinity, one by one 
7. Uncertain beginnings
8. Entropy: The unsolved problem  
9. Kalam as an inductive argument
10. Getting from First Cause to God  

Electrons, gaps, and pseudogaps

I want to give you a bit of flavor of what I've been researching this semester.  Problem 1: It is confidential information (there are scientific competitors). Problem 2: It is incomprehensible.

So I'm not going to talk about my research.  I'm going to talk about a few of the broad ideas in cutting edge research into high temperature superconductors.  The point is not really to teach you about high temperature superconductors (which is hardly useful information if you're not studying superconductors), but so you get the idea of what it looks like.

So.  Superconductors.  Below a certain temperature "Tc", superconductors conduct electricity perfectly, with no resistance.  This property has obvious practical value, but unfortunately all known superconductors have a very low Tc.  Even the so-called "high Tc superconductors" discovered in 1986 still have a Tc of about -140 Celsius. 

We understand how low Tc superconductors work.  The problem was solved in 1957, and the solution is called BCS theory.  BCS theory provides a way for electrons to attract each other (despite being opposite charge), and the electron pairs form a Bose-Einstein condensate.  The condensate of electron pairs is what makes a superconductor.  High Tc superconductors also have condensed electron pairs, but BCS theory doesn't work, and no one knows why the electrons attract each other.

There are two major classes of high Tc superconductors, the cuprates and the iron-based superconductors.*  Iron-based superconductors are currently a hot topic because they were just discovered in 2008.  But I study cuprates.  In particular, I spend most of my time on a material called Bi-2212, which is one of the most highly studied superconductors.  I am not sure why it gets so much study, but I would guess that it is because it is cheap, easy to study, and (somewhat self-referentially) has been studied enough that it allows for an ever higher tower of knowledge.

*There are other high Tc superconductors, but I will not speak of them.

I study Bi-2212 using a technique called ARPES.  In concept, ARPES is simple: shine light on the material, and look at the ejected electrons.  In particular, we look at the direction that the ejected electrons go, and the energy.  If we graph the energy of the electrons (vertical axis) vs the angle (horizontal axes), we get something like this:

From Ronning et al, Science 1998.  Figure cropped for clarity.  I marked the Fermi Surface in blue.  Don't worry about what a quasiparticle is.

Experimental physics being what it is, we don't really see that whole picture there.  We see tiny slices of it at a time.  If I showed you some real data, it would be unrecognizable.

The way the electrons work, there are a bunch of quantum states for them to fill.  The quantum states act like slots, and only one electron fits in each slot.  The electrons only fill slots up to a certain energy, but there are more empty slots above that energy.  The most interesting physics happens where the filled slots meet the empty slots, what's called the Fermi Surface.  In fact, this is where the electron pairs live.

Long story short, when we look at the Fermi Surface of a superconductor, there is a small energy gap between the filled and empty slots.  This gap in energy represents the energy required to pull the attractive electrons pairs apart.  The fascinating thing about cuprate superconductors, is that the gap is not the same size everywhere on the Fermi Surface.

Also from Ronning et al.  The size of the gap has been greatly exaggerated.

Yes, in fact, there are even points on the Fermi Surface where there is no gap at all!  These points are called nodes. It would seem that at these nodes, there is no superconductivity happening.  This is very different from conventional superconductors, which have gaps everywhere on the Fermi Surface.

And what about iron-based superconductors?  Iron-based superconductors also have gaps everywhere, just like conventional superconductors.   But it's not quite the same!  We have reason to think that there are nodes in iron-based superconductors, but they cannot be seen directly because they are between Fermi Surfaces, rather than on the Fermi Surfaces.  Of course, this is not a settled matter...

When you raise the temperature of a superconductor, the superconductivity disappears, and so does the gap.  But the cuprates do something funny.  The gap remains even at high temperatures, when the material is not a superconductor.  Or at least, part of the gap does.

 From Lee et al, Nature 2007.  Figure cropped for clarity.  The horizontal axis is the position in the Fermi Surface; the vertical axis is the size of the gap.  The blue and green lines are at superconducting temperatures; the red line is above superconducting temperature.

The gap that remains when the material is no longer superconducting is called the "pseudogap".  It's a silly name, since the gap is real.  But is the gap there because of incipient superconductivity?  Or is it an unrelated property of the material?

Check out the date of that paper.  2007.  Scientists are still arguing over the pseudogap.  I've seen several talks about it, talks which disagree with each other.

So, that's what superconductivity research looks like.  Or at least, that's one very small part of it.

Same-sex PDA: reactions

My boyfriend and I are sorta into PDA.  What can I say, I like hugging and kissing and holding hands, and I don't mind doing it in public.  I think he likes showing me off too.

As you would expect, PDA between two men often gets weird reactions.  This is true even in San Francisco.  I started collecting a few of these reactions, but I stopped after the novelty wore off.  Here they are.

Woman on train: How old are you?
Me: I'm 22.
Woman: You look 16.  I was going to tell you that you shouldn't hold your son that way.
Woman leaves train.

That one offended my boyfriend.

Man on street: Let go.
Man: Let go.
Man: Let go.
Some minutes pass as he repeats himself.
Man: Stop doing that.  Come on!
etc.

I thought this guy was especially weird because he was walking half a block in front of us, and trying to talk to us.

Female reveler at street fair: Oh, they're so cute!
She hugs us as her friend takes a picture.

It's funny that she treated us as a novelty, but I guess if we didn't secretly enjoy this sort of thing, we wouldn't be doing PDA.

We're locked out of my BF's apartment, waiting for the landlady.
Man walks up to us: Father, son?
BF: No.
Me: *ignore*
Man pesters us for a while, talking nonsense.  I get the impression that he's trying to proposition us, but it's unclear.  My BF thought he was trying to sell us drugs.
Man: You're not open-minded enough to try black.  (The man is black.)  Look, he's open-minded enough. (He gestures at me.)
Me: *roll eyes*
Eventually he leaves and the landlady arrives.

This guy helped me appreciate how awkward women feel when being propositioned in elevators.

Guy on the bus, just as he exits: Faggots... Out in public.

I wanna look at this ironically and laugh about it, but having the real experience is just disturbing.

Relativism and the gelato guy

Remember the Gelato guy?  A few weeks ago at Skepticon 4, the owner of a gelateria posted a sign that said, "Skepticon is NOT welcomed to my Christian Business”.  The owner took it down fairly quickly, and posted an apology.  In most of the atheist blogs that I pay attention to, people responded very positively to the apology.

That’s exactly the type of response we want from people who may not agree with us. I don’t know what more we could ask from a Christian. I forgive him. Hell, next time I’m in Springfield, I might even buy some gelato from him.
--Hemant Mehta

The notable exception was PZ Myers, who made a big deal about rejecting the apology:

GelatoGuy lives in one of the most religious countries on earth, in a particularly intensely religious part of that country, and in a moment of smug self-righteousness, felt he could openly discriminate against people who do not respect his beliefs. And now he thinks he can walk away, forgiven, and return to his blithe happy Christian pocket universe, just by saying a few words.

Someone asked PZ, "Just out of curiosity, what would the guy have to do to be forgiven?"  PZ responds, "Nothing. Make an example of him; don't give bigots an out."

I basically don't care about Gelato guy, and I forget which state he's in.  But I point this out as a recent example of judging people based on their context, as I discussed in my previous post on cultural relativism.

On an objective measure, I don't think Gelato guy's actions are "positive".  I would prefer that businesses don't discriminate in the first place, rather than discriminating and then apologizing for it afterwards.

On the other hand, we intuitively judge people based on what they can be reasonably expected to do.  We feel the need to give a person an "out".  If we simply condemn people no matter what they do, our condemnations will fail to encourage better behavior.  Gelato guy is just going to throw up his hands, because there is no way he can earn PZ's forgiveness.

On the other other hand, who is the audience for our condemnation?  Is it the Gelato guy, or is it blog-reading atheists?  If the audience is blog-reading atheists, condemnation is useful after all, because atheists can be expected to behave better.  As I understand it, this is PZ Myers' goal, to make a statement to atheists, not to Gelato guy.  His statement is that atheists should have higher standards, and I sympathize a lot with this message.

On the other other hand, I basically don't care about Gelato guy.

On cultural relativism

Here's a good example of what you might derogatorily call cultural relativism. Coming from Biblical scholars, no less.

In a chapter of The Bible Now, Friedman and Dolansky argue that the Bible's seeming unambiguous condemnations of homosexuality can be ignored, even if you accept the Bible's moral authority.  According to a review by Adam Kirsch, this is one of the arguments they make:

Turning from ancient Israel to Assyria, Egypt, and Greece, Friedman and Dolansky observe that these other Near Eastern societies generally had nothing against homosexual acts as such. They reserved their odium for the passive partner in anal sex, the man who was penetrated.
...
Why, then, does Leviticus, uniquely among ancient Near Eastern law codes, prescribe death for both partners in homosexual acts? Friedman and Dolansky argue, quoting another Bible scholar, that it is because Leviticus “emphasizes the equality of all. It does not have the class distinctions that are in the other cultures’ laws.”

This is a remarkable performance. Before you know it, a law that unambiguously prescribes death for gay men has been turned into an example of latent egalitarianism.

It's not altogether clear to me that killing both men is better than killing just one of them, but let's put that aside.  I wish to discuss the question of whether the surrounding culture can make the authors of Leviticus more morally praiseworthy.

As I understand it, cultural relativism is not so much a distinct philosophy, as a term that you use to denigrate philosophies you don't like.  But of course, we all know the stereotype of cultural relativism.  "Cultures all have different moral guidelines, and we should judge people from the perspective of the culture they come from."  Well, what if this culture thinks it is morally correct to apply its own moral guidelines to other cultures, huh?

However, I think there is a grain of wisdom in even the strawiest of cultural relativist strawmen.  Allow me illustrate it with faux mathematical graphs.

Suppose that there are a variety of actions we can make, and some are morally preferred to others.  Let's invent a number "x" which says how strongly a particular action is preferred.  A higher value of x corresponds to a greater moral good.

But even though we may prefer x=3 to x=2 to x=1 to x=0, it is hard to express different gradations of moral approval.  For the most part, we either express praise, or condemnation, or indifference.   So when express judgement, we have to translate this potentially continuous variable x to a discrete value.  Here are a few ways to do the translation, though there are many more:

I was too lazy to bust out Mathematica for this one

But depending on what culture a person is from, they may have a different range of actions available to them.  Either people from that culture believe that a certain range of actions is "reasonable", or the culture punishes people who go outside that range.  For example, the authors of the Leviticus could have chosen to express more or less condemnation of homosexuality, but it would be extremely unlikely for them to express anything approaching an enlightened view.

In other words, the authors of Leviticus had various values of x available to them, but all of these available values are very low in my view.

If I were to express praise and condemnation according to method 2, this wouldn't be very effective.  No matter what action the ancient people take, I condemn them, so they have no incentive to do better.  But if I express praise and condemnation according to method 1, praise is within reach for them!  Perhaps this will cause them to change their actions.

And that's why we may want to look at the surrounding culture before issuing judgments about the people in it.

But there's a problem here.  The authors of Leviticus aren't listening to my moral praise.  They're dead!  The only people listening to my moral judgments are people in my culture.  Therefore, I'm sticking to method 2.  That means universal condemnation of the authors of Leviticus and their surrounding culture.

(via Evolutionblog)

Science vs Acne

I have pretty bad back acne.  No, I will not show you photos.  This is not that kind of blog.

I don't really care about my acne.  I've shown it scientifically!  In the past when I've tried acne medication, my conclusion was that I don't have the motivation to apply the medication on a regular basis, and that medication applied on an irregular basis is ineffective.

But I have new motivation.  I have what I'm worried is another abscess.  After how painful it was last time, I'm taking someone's suggestion that I apply hot packs to kill the bacteria before it grows big.  As long as I'm boiling this water, I might as well kill some acne!

Of course, I'm not actually going to do any science.  I am participating in what has been called the "coffeeshop fallacy" (via The Thinker).  I like the idea of doing science, but I'm not actually willing to put in the effort.  I'm a PhD student, and I have real science to occupy my time!  So what I'm actually going to do here is an affectionate parody of science, whatever amuses me.

The hot pack idea comes from Brian Dunning.  He cites a study which says you can treat acne by applying 120 farenheit for three minutes twice a day.  There's no way I will use such stringent protocols.  Brian suggested using a laptop power adapter, but I'm going to use a rag with a bit of boiling water poured on it.  I can use the extra boiling water for tea!

The other day I had some Yogi tea called "skin detox".  On the label, it said:

Goodness should become human nature because it is real nature

This so that I can credit the tea later if I get rid of the acne.

I'm taking another idea from XKCD:



On one side of my back, I'll apply the hot pack.  On the other side, I may just try some acne medication.  Then I will ask my boyfriend to say which side looks better, without telling him which is which.  Actually, I will probably use really shoddy blinding, and he'll find out which side is which.  But he will appreciate the excuse for me to be topless.

And my excuse for writing about the experiment before it's done is to avoid reporting bias.  As you know, scientists are less likely to report negative results than positive ones, which can lead to systematic errors.  Therefore, if I never write about this again, you may assume that the results were negative, or that I lost all motivation.