Power sets and the Chef Paradox

The Chef Paradox

Suppose that there is a chef.  The chef cooks for all people who do not cook for themselves.  But he does not cook for anyone who cooks for themself.  Does the cook cook for himself?

If he cooks for himself, then he must not cook for himself.  If he does not cook for himself, then he must cook for himself.  It's a paradox.  The solution to the paradox is simple: the chef does not exist.  We were wrong to suppose that he did.

Normally, this is called the Barber Paradox (or Russell's paradox) because it's about the barber who shaves all men who do not shave themselves.  But I decided to use a chef instead.  I hope I don't get any hate mail for this.

The Chef paradox will reappear again, you'll see.

The power set

Let's say we have a set of three elements, {a, b, c}.  Call this set S.  We can define the power set of S, abbreviated P(S).  P(S) is the set of all possible subsets of S.  Here's the list of all elements in P(S):

{}
{a}
{b}
{c}
{a,b}
{a,c}
{b,c}
{a,b,c}

P(S) has eight elements in it, while S has only three.  Clearly P(S) is bigger than S.

There's a simple way to think of power sets in terms of chefs.  Suppose we have three chefs a, b, and c.  The chefs cook for each other.  For example, chef a might cook for a and b.  Chef b might cook for a and c.  Chef c might cook for no one at all.

a → {a,b}
b → {a,c}
c → {}

By stating which chef cooks for whom, I've just matched each element in S to an element in P(S).  So if S is the set of chefs, then each element in P(S) is a possible list of chefs that a chef could cook for.

But what if S is an infinite set?  Clearly P(S) will also be an infinite set.  But now that we've discussed that some infinite cardinalities are larger than others, we should consider the possibility that P(S) has a larger cardinality than S.  We will find that P(S) is indeed larger than S.  To prove it, we will first assume that P(S) and S have the same cardinality, and then show that this leads to a contradiction.

Assume that P(S) and S have the same cardinality.  This means that the elements in S can be matched exactly one to one to the elements in P(S).  Using the chef analogy:  Each element of P(S) is a list of chefs.  For every list in P(S), there exists a chef who cooks for exactly those people on the list.

Consider the list of all chefs who do not cook for themselves.  As I just said, there must be some chef who cooks for exactly the people on this list.  Therefore, there is a chef who cooks for those who do not cook for themselves.

As previously explained, such a chef is impossible.  So we have to backtrack to see where we made an incorrect assumption.  The incorrect assumption was that P(S) and S have the same cardinality.  This is not the case.  P(S) is always larger than S, no matter what S is.

An aside: If S is the set of positive integers, then P(S) has the same cardinality as the real numbers.  So this is another proof that there are more real numbers than positive integers.

The larger implications

We can take the power set of any set.  Any set.  That means that no matter what infinite set we choose, there is always a bigger set.

Why not take the power set of a power set?  P(P(S)) must be bigger than P(S), which must be bigger than S.  We can continue to take power sets and build a sequence of progressively bigger sets.

S
P(S)
P(P(S))
P³(S)
P⁴(S)
P⁵(S)
...

In fact, we can build a set that's even bigger than every set in the sequence!  Just join together all the sets in the sequence and call it Q.  (ETA: I'm not sure if this is allowable by set theory rules, so perhaps it was an error.)  Q is bigger than P^N(S), because Q contains all the elements in P^N+1(S), which is bigger than P^N(S).  However, Q is still not as big as P(Q) or P(P(Q)) and so on.  There's basically no end to the infinite cardinalities we can make.

The series on infinite sets:
Hilbert's Hotel
Doubling the Sphere
Larger infinities and the Diagonal Proof  
Power sets and the Chef Paradox
The unmeasurable set

Michio Kaku and Deepak Chopra

Some people have asked me what I think about Michio Kaku, the string theorist who popularizes physics and futurism.  His last book, Physics of the Impossible: A Scientific Exploration Into the World of Phasers, Force Fields, Teleportation, and Time Travel, discusses three classes of "impossible" technologies.  Class I impossibilities may become possible within a century or two.  Class II impossibilities may become possible in thousands or millions of years.  Class III impossibilities will never become possible unless there is some fundamental shift in our understanding of physics.

I think Michio Kaku and I have very different philosophies about popularizing science.  Kaku likes to reach for the amazing and sensational potentials of the world.  I like to bring things down to earth, grounding them in simple concepts.  Or something like that.  Clearly there are differences even if I cannot articulate them.

But that doesn't mean we have to clash!  I would probably agree with Michio Kaku on most of his futurist predictions, at least when properly translated.  Allow XKCD to do the translating.

Michio Kaku says that class I impossibilities may come in a century or so.  The translation is "It has not been conclusively proven impossible."  I totally agree!  See, no clashing.

But recently, Uncertain Principles pointed out an interview of Michio Kaku by Deepak Chopra.  If there is a time to clash, now is it.  Let me pull out a bunch of the worst quotes.

DC [Deepak Chopra]: What the basis for your book is, that if it does not violate the laws of mathematics or physics then it is in the realm of possibility, really?
MK [Michio Kaku]: That's right. If it's not forbidden by the laws of physics, it's mandatory.

This is an example of type 2 technobabble.  It's true that there is a principle in physics that states, "If it's not forbidden, then it's mandatory," but this is really not the right context for it.  The correct context is particle physics, because all possible particle interactions will mathematically contribute to the result.  Of course, some interactions contribute more than others, and most interactions are just impossible.  But don't let that get you down on life, because this only relates to the context of particle physics.

MK: Right. Think about this: if you were to push a button and the force field has knowledge of how to construct walls and floors and sidewalks, with a push of a button you could create an entire city.

If I had an infinite lever and an immovable place to stand on, then we could move the world around.  It's all a matter of getting the technical details sorted out. (That's a Terry Pratchett reference btw.)

DC: Is our conversation affecting something in another galaxy right now?
MK: In principle. What we're talking about right is affecting another galaxy far, far beyond the Milky Way Galaxy. Now when the Big Bang took place we think that most of the matter probably was vibrating in unison.

I guess if we take a strict Many Worlds Interpretation, I suppose it is true "in principle" that things here are correlated with things in other galaxies.  But this is very misleading.  Really, it will be a mix of correlations, anti-correlations, and everything in between, which is to say that on average there is no correlation at all.  This is the very important principle of quantum decoherence.

MK: We actually demonstrated it right on TV cameras. We went to the University of Maryland outside Baltimore and we showed an atom being teleported right across the room. You can actually see two chambers, an atom in one being zapped across the room.

Chad explained why this is misleading over at Uncertain Principles.  One major error is that there is already an atom in each chamber.  Quantum teleportation only transfers a quantum state from one atom to another, not the atoms themselves.  Also, the atoms were very carefully prepared by experimenters, not by the Big Bang.

This post is longer than I expected, so I should insert another visual.

DC: Every cell is instantly correlated with every cell. A human body can think thoughts, play a piano, kill germs, remove toxins, make a baby all at once.
...
To my mind the human body is an example or for that matter a leaf for any biological, of quantum entanglement. Everything is correlated with everything instantly. What would you say to that?

MK: Yes, things are entangled so in some sense messages can travel faster than light instantaneously, however the messages that go faster than light are random messages. You can't send Morse code or information through these things and sometimes we de-cohere from matter so that we can no longer communicate with other forms of matter.

This time, it's Deepak Chopra who is saying something deeply silly, and Kaku just lets most of it go.

Chopra is proposing that correlations between different parts of our body is caused by quantum entanglement.  I'm no expert, but I thought it was caused by electrical signals moving along neurons.  It certainly is not instant, it's just instant for all practical purposes.  It is not faster than light, so no quantum entanglement is necessary.  And as Kaku points out, if it were faster than light, then only random messages would be communicated.

DC: But let's come back to a biological system. That's not random, that's very coherent, you know this biological system or a system like say when you have morphogenesis and differentiation, when a cell divides, keeps dividing so that you know in first year applications it has become the hundred trillion cells which is more than all the stars in the Milky Way Galaxy. That requires some kind of non-local correlation to my mind, theoretically.
MK: Well these non-local correlations are going to be extremely important in the next few decades coming from the computer realm of things.

Auuggh, no!  Michio Kaku just conceded that the biological correlations are non-local (ie faster than light).  They aren't!  That's why the messages can be non-random, as Chopra observes.

DC: To me a rose is rainbows and sunshine, earth, water, and wind, air, and the infinite void and the Big Bang all rolled into one.
MK: Mmm hmm. And Einstein was wrong in this one. We measured this every day in the laboratory. That electrons can dance in between multiple states and then the question is why can't I dance between multiple states?

If someone says, "a rose is rainbows and sunshine," the correct answer is "No it isn't," no matter what kind of dance the electrons are doing.

Michio Kaku also said something very silly about how quantum mechanics might prove the existence of an omniscient being, but I'll leave that one for another post.  (ETA: It is done)

I agree with Chad, someone ought to be ashamed for this interview.

Colds and causality

Over the past two weeks, I had a bit of a cold.  At various points I was coughing, I had a sore throat, I had a stuffed nose, my sinuses hurt, I was tired, and so on.  I'm better now.  If I were still living on campus I probably wouldn't have done anything about it except maybe take some dayquil or something.  But since I'm home right now, my parents are giving me the usual treatment.

My mom has been giving me some traditional medicine consisting of tea and honey.  It's some sort of special tea that tastes like licorice, and some kind of special honey that is supposedly good for colds.  I'm not sure I believe that, but I like tea and honey anyway.  The honey is sweet and dissolves well in tea.  The tea is a bit too much licorice for my taste, but it's good too.

My friend who is in nursing said that if it makes me happier, it probably boosts my immune system.  But if that is the mechanism at work, then surely any kind of tea and honey would do.  I'd probably prefer chamomile tea, and it could be a cheaper honey.  Or I could do without any honey at all, because I like dark and bitter tea, which may or may not be a metaphor for my soul.

My dad, who has a somewhat different philosophy about medicine, bought me some Nyquil.

The conversations between my mom and dad on the subject of my cold were probably hilarious.  But you, my readers, will never know, since I'm not in the habit of publishing private conversations on the internet.

This is all to say that I'm not that highly principled when it comes to taking medicine.  Maybe it's because I'm apathetic about my health.  Or because it's not that expensive and I'm not paying for it myself.  Or maybe it's because, when it comes down to it, I'm don't personally know of any scientific research that says Nyquil probably works better than these particular kinds of traditional medicine.

I am somewhat more principled when it comes to attributing causes.

My mother would like to credit my recovery to the tea and honey.   The thing is, colds usually go away on their own with time and rest.  This cold has been slowly declining over the past two weeks since before I started drinking the tea.  I'm just going to keep drinking the tea until it goes away entirely, at which point my mother will credit the tea.

The reasoning goes that I drank special tea with special honey, and now I'm better.  The reasoning applies equally well to any other number of ordinary things I did in the past two weeks.  Seriously, how else would we expect it to happen?  Would I drink the tea after I get better?  Would I just never get better?

Causality is one of the most difficult things to prove.  Without getting too philosophical about it, causality means that if I change factor A (ie drinking tea) independently of anything else, then factor B (ie recovery from the cold) will be different.  To even begin to prove causality, I need two data points, one where I drink tea and one where I don't.  And since a lot of random factors are involved, we actually need a lot more than two data points in order to average out the results.

Furthermore, the tea drinking factor really does need to be independent of anything else.  If the tea is always accompanied by Nyquil, that will completely compromise the evidence.  More subtly, if the tea is always accompanied by my belief that I am drinking special tea that will help me, then this too will compromise the evidence.  That's why we need placebo-controlled studies, to separate out the effects of treatment from the effects of believing in the treatment.  If only the belief suffices, I might as well be drinking chamomile tea.

I'll say it again: causality is extremely difficult to prove.  In the face of this difficulty, all I have is one data point.  One measly data point.  I'll take the tea because I like tea, but I refuse to interpret the "results" as evidence of anything whatsoever.  Same goes for the Nyquil.

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

Larger infinities and the diagonal proof

It's time to continue my probably never-ending series on infinite sets.

A brief review (see here)

Consider Hilbert's Hotel, which has an infinite number of rooms, one for each positive integer (1, 2, 3, ...).  If we take the set of all rooms in Hillbert's Hotel, we can assign that set a "cardinality" which is sort of like the number of objects in the set.  However, a cardinality doesn't have to be a number; it can be infinite.  Two sets of objects have equal cardinality if they can be shuffled around and matched one to one.  For example, if we take all the guests from two infinite hotels, we can shuffle them around and fit them in one infinite hotel.  Therefore, we can say one hotel has the same cardinality as two hotels.

The question is, "Can we build a hotel which has greater cardinality than Hilbert's Hotel?  Is there a 'larger' infinity?"

Unfortunately, I'm going to have to drop the hotel analogy, because it will become cumbersome before long.

The Diagonal Proof

Let's consider the set of real numbers between 0 and 1.  That includes both the rational and irrational numbers.  Each number can be expressed as an infinite decimal expansion.

Examples:
1/2 = 0.50000000...
1/3 = 0.33333333...
π - 3 = 0.14159265...

Some of these numbers (ie the rational numbers) repeat themselves, while others (ie the irrational numbers) never repeat themselves.

Now let's compare the set of real numbers between 0 and 1 to the set of positive integers (1, 2, 3, ...).  Do these sets have the same cardinality?  They both have infinite cardinality, so why not?  Maybe there's a way to shuffle the positive integers and match them one to one with the real numbers.  Why don't we just try it and find out?

1 → 0.50000000... = 1/2
2 → 0.33333333... = 1/3
3 → 0.14159265... = π-3
4 → 0.70710678... = sqrt(1/2)
5 → 0.69314718... = ln(2)
6 → 0.71428571... = 5/7
...

It looks like I still have a long ways to go before I hit every single real number between 0 and 1, but who's to say that it can't happen?  Crazier things have happened in mathematics.  But it turns out that this particular task is impossible.  Let me show you one number that we will never hit.

First, take the first digit of the first number, the second digit of the second number, the third digit of the third number, and so on.

1 → 0.50000000... = 1/2
2 → 0.33333333... = 1/3
3 → 0.14159265... = π-3
4 → 0.70710678... = sqrt(1/2)
5 → 0.69314718... = ln(2)
6 → 0.71428571... = 5/7
...
Result: 0.531145...

Now, take each digit, and add one to it.  If it's a 5, change it to a 6.  If it's a 9, change it to a 0.

Result: 0.642256...

This number will never get hit.  It can't be hit by the first number because the first digit doesn't match.  It can't be hit by the second number because the second digit doesn't match.  It can't be hit by the Nth number because the Nth digit doesn't match.  This is Georg Cantor's so-called Diagonal Proof.

No matter how we shuffle around the numbers, I will always be able to construct such a number that will never get hit.  In conclusion, the set of real numbers will always be larger than the set of integers.  We say that the real numbers has a larger cardinality than the set of positive integers.*

A digression on the Continuum Hypothesis

The Continuum Hypothesis states that there is no set which has cardinality greater than the positive integers and lesser than the real numbers.  It was conjectured by Georg Cantor in 1877, but he had no proof.

We still have no proof of the Continuum Hypothesis, but now we know why.  Mathematicians have proven that the Continuum Hypothesis is impossible to prove or disprove without taking new assumptions.  If you have trouble wrapping your head around that, rest assured that you are not alone.

*Incidentally, the set of rational numbers has the same cardinality as the set of positive integers.  The set of irrational numbers has the same cardinality as the set of real numbers.

Next time: Power sets and the Barber paradox!

The series on infinite sets:
Hilbert's Hotel
Doubling the Sphere
Larger infinities and the Diagonal Proof
Power sets and the Chef Paradox  
The unmeasurable set 

Man gives savings to church

 In New Zealand, there's a recent news story about a partial paraplegic who gave most (all?) of his savings to a church.

A Napier church took at least $20,000 in donations from a disabled rest home resident with head injuries and rejected pleas not to take the last of his life savings.
...
Mr Abraham, 54, was a partial tetraplegic with head injuries, after being hit by a car in 1986, Ms Dever [his rest home manager] said.

"He's got no family or next-of-kin on our list, and they've taken everything from him. It is unethical, immoral and I believe un-Christian.

"He used to have a nest egg but now he has no life savings. He believes if he doesn't give it to them, he won't go to heaven."
...
"I said most people would think that accepting huge amounts from someone with nothing is wrong," Ms Dever said. "I tried to reason with [the church pastor] and asked him to give the money back but he wouldn't."

Ms Dever may be right, but we shouldn't be asking, "What would most people do?"  We should be asking, "What would Jesus do?"

Jesus would cheer the man on.

As he looked up, Jesus saw the rich putting their gifts into the temple treasury. He also saw a poor widow put in two very small copper coins. "I tell you the truth," he said, "this poor widow has put in more than all the others. All these people gave their gifts out of their wealth; but she out of her poverty put in all she had to live on."

(Luke 21:1-4)

And here, I thought that charity was about spreading the wealth, not concentrating it.  Apparently, it's really about hurting yourself as much as possible.  New Testament morality is... strange.

(Via Friendly Atheist)

News update: It seems the church pastor tried to get Mr. Abraham to sign a document clearing the church of any wrongdoing, but the rest home stopped him.  Later, the church decided to return the donations to Mr. Abraham, though it looks like they can't stop him from donating money anonymously.

Linking rings with scissors

It's time for some hands-on puzzling!

Here are the rules:
1. Start with a long rectangular strip of paper.
2. Tape the two ends of the strip together.
3. Using only scissors, and no more tape, cut the paper into two rings.
4. The end result must be two simply linked rings.

"Simply linked" means that it should be no more complicated than this:

How do you do it?

See solution

Removing squares solution

See the original puzzle


Click for a solution

The solution proves that you can do it by removing nine matches.  We can prove that it is impossible to do any better.

Before we remove any matches, there are sixteen 1x1 squares.  For each one, we need to remove one of its four sides.  If we remove one of the inside matches, then we can remove two of the sixteen squares.  So we can get all of the 1x1 squares by removing eight matches.  However, we also need to remove one of the outside matches to get rid of the 4x4 square.  Therefore, we need at least nine matches.

On Catholic confirmation

On FriendlyAtheist.com, people regularly ask Richard Wade for advice on their religion-related conflicts.  The last question came from a 13-year-old atheist whose parents want her to get confirmed.

The idea behind confirmation (and I'm speaking exclusively of Catholic confirmation) is that it gives people a chance to affirm their own faith.  After all, babies, when they're baptized, can hardly affirm their own faith.  So Catholics need another initiation ceremony for older people, usually teenagers.  Many other religions have ceremonies and rituals fulfilling a similar purpose.

When I was a Catholic teenager, I refused to get confirmed on principle.  It wasn't that I had stopped believing by then.  I simply didn't consider myself particularly religious, and figured I could get confirmed later if that ever changed.  My parents wanted me to get confirmed but I insisted that it should be my choice lest we defeat the entire point of confirmation.

But now I see confirmation for what it really is.  Confirmation is there to give the illusion of choice.  Many religious people like to think that their own religion is not merely an accident of birth, but something they personally chose.  But the illusion falls apart when you look at the experiences of people who try to choose something different.

(From the comments at Friendly Atheist)

I agreed to Confirmation on the contigency that I never attend youth group or Bible study ever again or Mass after turning 18. My parents reluctantly agreed. When we had our meeting with the coordinator, I told her I was an atheist only being confirmed to appease my parents, and she really didn’t care. She took no offense at my lip service or coercion, nor did she try one last time to convert me.

I’m and atheist but i went through confirmation because as a boyscout i needed a religious leader to sign off that I’m religious.

I was confirmed in 8th grade. What I remember of it was mostly sitting through the classes, with the promise that the classes were leading up to this, and once it’s over, I wouldn’t have to go to the classes anymore. An appealing prospect to me, so I went through with it.

The morning of the day I was supposed to get confirmed arrived, and when I said I didn’t want to go she just broke down in tears crying about her failure as a mother. I went to the ceremony because of that, and haven’t been to a church except for funerals or weddings since.

On the other hand, when I myself refused to get confirmed, my parents simply let me go without too much fuss.  So perhaps there is still hope for the principle of the thing.

An additional note: according to Catholic Canon law, Catholics must be confirmed before they marry "if they can do so without serious inconvenience."  From what I hear, the confirmation requirement is only enforced by the pastor who marries the couple, and many pastors don't enforce it.  But still, I'm sure many people get confirmed just because they want to get married in the church.  I find myself wondering how meaningful confirmation really is when people get confirmed just because they want a particular kind of marriage ceremony.

Happily, that will never be an issue for me, because I think it's safe to say I will never get a Catholic marriage ceremony anyway.

Why the definition of orientation is confusing

Definitions, Plural

On rare occasion, I've said confusing things about sexual orientation, nearly implying that it is a choice.  And of course it isn't a choice.  But there is a complication that confuses many people: Sexual orientation has multiple definitions.

Take, for instance the word "gay".  "Gay" can have any number of definitions, but I will simplify it to these three:

1. Desire definition: A gay person is someone who is attracted to members of the same sex but not the opposite sex.
   
2. Behavior definition: A gay person is someone who forms romantic and/or sexual relationships with members of the same sex but not the opposite sex.
   
3. Identity definition: A gay person is someone who identifies as gay.

Similarly, all sexual orientations can be defined in these three ways, or in some combination of the three.

The Real, the Useful, and the Really Useful

In some sense, the desire definition is the "real deal", and the other two definitions are just proxies.  Behavior and identity are far too contingent, and can be changed by mere circumstance.  The desire definition, on the other hand, encapsulates something essential about the group, and gets to the heart of what's really going on.

However, I hesitate to go too far in assuming that the desire definition is the "real deal" in all its aspects.  For instance, I believe that "attraction" is actually a whole set of distinct phenomena, and we simply categorize them together because it is useful to do so.  As an analogy, take the word "weather".  Weather describes a whole set of distinct phenomena including wind, rain, and temperature, but we find it useful to put them all in the same section of the newspaper.  But perhaps it could have been different; we could have put temperature in one section, with another section for cloud cover and stargazing.  Similarly, "attraction" could be divided up in any number of ways, or even joined with other essential qualities.  But we divide it up the way we do because that is the most useful to most people.

In conclusion, the desire definition is not entirely about what is "real" but also about what is useful.  And once we admit that usefulness is important, we must take the other definitions seriously, because they are also very useful.

The behavior definition is most obviously useful for some medical issues.  For example, if we're studying the role of gay men in the spread of HIV, the only important issue is who they have sex with.  It clearly doesn't matter if they identify as hetero, or if they have no attraction to men.  A related issue is the ban on gay blood donors.  The ban actually applies to "men who have sex with men", not to gay people, because they want to make it explicit that only behavior matters.

I think the behavior definition is also useful on a personal level.  By the desire definition, I'm in a gray area, so I could spend quite some time describing the details of orientation.  But at some level, many of the details are unimportant, and the only important question is, am I "available" for a same-sex relationship?  Interested guys need to know.  (The answer is yes.)  This is not a question about desire, but about my future behavior.

The identity definition is perhaps the most useful in everyday situations.  If someone says that they're gay, that's what you go by.  For one thing, you want to be respectful of people's wishes.  A person's identity is determined by a particular combination of behavior and desire; you do not get to decide what that combination should be, they do.  Furthermore, it is very presumptuous to think that you know a person's orientation better than they know themselves.  When it comes to individuals, self-identity is one of the most reliable indicators of sexuality.  (In large groups, it is less reliable because there are systematic biases affecting self-identity.)

But the identity definition confuses people because it is rarely explicitly stated as a definition.  This is probably because when you state it as a definition, it sounds really silly.  A gay person is someone who says they're gay.  But why do they say they're gay?  The identity definition is not meant to be a stand-alone definition, but it is still very prevalent and useful.

A Matter of Choice

The question of whether sexual orientation is a choice is a highly politicized one.  By the desire definition, sexual orientation is not a choice, but by the other two definitions, it is a choice.  So it is not surprising that different political groups choose to emphasize different definitions.

I think the desire definition is the most relevant one in determining whether sexual orientation is a choice.  The desire is the primary cause of both the behavior and identity.  We cannot go any further down the causal chain, because the cause of the desire is too obscure.

At the same time, I also assert the right for people to choose their behavior and identity.  I think in most situations, it's advisable to choose behavior and identity that align with desire.  But it's not an absolute moral obligation.  Also, it's not always possible, since the underlying desire tends to be more nuanced than our range of choices for identity labels and behavior.

Some groups, such as the Catholics, are okay with gay people, but not okay with gay behavior.  The Catholic Church correctly understands the distinction between what is chosen and what is not chosen, and applies their understanding to their rules.  And yet, I still consider their rules morally backwards.  It just goes to show that conceptual understanding is not enough.

Definitions of Asexuality

Since my expertise is in asexuality, I should comment on how the different definitions apply to asexuality.

When the asexual community was younger, certain leaders decided to emphasize the difference between asexuality and celibacy.  If you rarely or never experience sexual attraction to others, then you are asexual.  If you don't have sex with anyone, then you are celibate.  I believe this was a very shrewd political move, because it clearly distinguished between the desire and behavior definitions by giving them different words entirely.

There is a great danger that the behavior definition could erase asexuality.  After all, lots of people are perpetually single.  Lots of asexuals are in relationships, both sexual and nonsexual.  There's not any particular behavior which clearly corresponds to asexuality.  So if we used the behavior definition of sexual orientation, it's not clear where asexuality would fit in, if anywhere.  (Similar concerns affect bisexuality, causing bisexual erasure.)

Therefore, the behavior definition is strongly discouraged.  But it's still occasionally used sparingly in combination with the desire definition.

The identity definition, of course, is used all the time.

It's much less clear which definition is used for romantic orientation among asexuals.  There's a lot of disagreement about whether an "aromantic" is someone who never experiences romantic attraction to people, or someone who just doesn't ever pursue relationships.  It's essentially a dispute between the desire and behavior definitions of romantic orientation.

Many asexuals intuitively understand that the desire definition of romantic orientation is the best.  But at the same time, the behavior definition is obviously very useful.  A lot of asexuals say that they have romantic attraction, but avoid relationships altogether.  Clearly, the fact that they avoid relationships is just as important, if not more important than the presence of romantic attraction.

To make things more complicated, the desire definition of romantic orientation is not clearly "real".  There are all sorts of different things that people classify as romantic attraction, and it's not clear that they belong in the same category.  There is a significant minority in the community that doesn't identify by any romantic orientation.

Given the lack of consensus on definitions, the identity definition tends to prevail.  

(Some ideas in this post were inspired by Kenji Yoshino on bisexual erasure, via Asexual Explorations)

Goodbye, BASS

This entire past year, I was the president of the Bruin Alliance of Skeptics and Secularists, a student group at UCLA.  By now, I'm already done.  I've passed it on to the next president, told him what to do and everything.  I feel a mix of sadness and relief.  In all likelihood, I will never lead a skeptical or atheist organization again.

Being president wasn't really that much work, but it was a lot of stress.  Most of the time, I just came up with objectives and made other people do the work.  But what little work I did made me feel like I had no clue what I was doing.  No one gave me any training.  I attended no leadership workshops.  All I knew for sure was that many other student orgs run much more smoothly than ours.  I'm sure every organization looks smoother when you're not running it, but I'm still convinced that BASS could be doing much better.

I felt like I wasn't ambitious enough.  But at the same time I felt I couldn't be ambitious.  There were many ideas I turned down from the start, because I felt that student motivation was a precious resource, not to be wasted.  I would tell people, "That could be good, but if I tell my officers to set it up, will they ever follow through?  If they do follow through, will anyone participate?"  Many of the ideas I pursued were flops, so I was always pessimistic.

As for benefits... I got a lot of leadership experience.  At least, I think I did.  Most of the concrete things I learned were uselessly specific, like the fact that in some of the rooms at UCLA, the projectors will randomly stop working unless you pay them $109 ahead of time.

That came out a lot more depressing than I meant it to.  I need to say something more cheerful, or I'll discourage the future president.

I really liked the activist cred that the job gave me.  Once I tell someone that I run a skeptical group, they instantly know that this is not a new topic to me.  A lot of people get uncomfortable talking about beliefs, especially personal beliefs.  If I was ever uncomfortable talking about this stuff, then I've long gotten over it, even offline.

Also, basically everyone knows who I am.  I'm one of the "popular" kids, as depicted in countless Disney channel shows, except not even remotely similar.

And when we had successes, they were very satisfying.  I think the biggest successes were our response to Ray Comfort, the Westboro Baptist Church, and hosting Hemant Mehta.  Pretty much every time I've ever blogged about BASS, it was related to some success.  So, you know, keep the selection bias in mind.

With any luck, this will appear in the yearbook. (click for bigger version)

  

Another success not yet mentioned is that I made sure to train next year's officers.  I don't know everything about running a group, but it is my hope that the leaders of BASS will start to accumulate knowledge each year, rather than having to start at the beginning every time.  I think BASS has a bright future.

Goodbye, UCLA

I have an announcement to make.  I am graduating from UCLA!  Woooo!  Graduation!

This means that I'm leaving many things behind.  I'm leaving the Bruin Alliance of Skeptics and Secularist.  I'm leaving whatever queer student groups I was involved in.  I'm leaving symphonic band.  I'm leaving friends.  I'm leaving Los Angeles altogether.

Next year, I'm going to grad school in physics.  Where, you ask?  Berkeley!  Tentatively, I want to study condensed matter theory, but it's not fixed at this point.

I want to get involved in student groups again at Berkeley, but you know what they say about grad students dropping extracurriculars to focus on their career.  We'll see.

Experts in skepticism

Several months ago, I proposed that a court of law is another "way of knowing" just like science.  I was going to start a series of posts comparing law to science and skepticism, but I got distracted, as usual.  But I never forget a topic idea that I don't want to forget (ie I write them down).

There are two great things about law as a method to determine truth.  The first is that law is practical, not philosophical.  A court of law never has to worry about silly questions like, "How do we know we aren't brains in a vat?"  Time is money, so courts don't waste it on that.  What a relief!

The second great thing is that law must have explicit rules regarding all the little components of an evidence-based debate.

One of those components is the expert.  In law, an expert witness is basically anyone who has special knowledge which allows them to draw inferences that the average juror cannot.  Law sets the bar rather low for an expert; you only need to be above average in a particular area.

Expert witnesses are necessary because not everyone has the necessary information to make every decision in the practical world.  You might say, just gather the necessary information, but often there's so much necessary information that it would be too time-consuming (and thus money-consuming) to gather it all.  The worst part is that you may end up thinking you have sufficient information to draw the correct conclusion when you don't really.  The solution: experts.

I think a lot of skeptics don't like to rely to experts very much.  Why rely on someone else when you can be independent?  If you rely on someone else's knowledge, you have no way of knowing if they're wrong.  If you rely on someone else, you risk committing the argument from authority.

But perhaps we just need to get over it.  Experts are a necessary part of many debates.  They are on our side.  Skeptics are frequently framed as the group of people who dare to question authority, but I don't put to much stock in such narratives because we could just as easily be framed as the defenders of experts.

But if we always rely on experts, what's left for the lay skeptic to do, aside from knowing what the experts say?  In fact, there's still plenty of reasoning to be done.  There are lots of things that the pseudoscientific fringes say that are not directly covered by scientists. Usually, it's because it's too silly, and scientists don't want to waste time on it.  For example, when Creationists claim that evolution contradicts the second law of thermodynamics, that's just too stupid and doesn't deserve a penny of research funding.  When a ghosthunter claims to be able to find ghosts, obviously very few scientists are interested in testing that.

Other times, it's because the scientists are trained as scientists, not trained to counter the many rhetorical and political strategies of pseudoscience.  For instance, not every scientist knows the best way to respond to fear-mongering about cell phone radiation damaging our brains.  They just know how to test the idea, but apparently this isn't enough, since the negative results have not significantly dampened speculations.  This is the skeptic's area of expertise, because we are familiar with the behavior of pseudoscientific movements and organizations, and with the many ways that people are mislead.

(This post was partly influenced by Daniel Loxton's thoughts on skepticism's relation to science.)

Pseudoscientific technobabble

One of the common strategies of pseudoscience is to use technical language in order to sound more scientific.  It serves the same function as technobabble in science fiction: it makes people sound like they know what they're talking about when they don't.

In my presentation "Quantum Mechanics for the skeptic", some of the audience asked how to tell the difference between technobabble and real scientific language.  But there's a problem in asking me for help.  The method I use and the method they use are necessarily different.  I can easily tell the difference myself because I study physics and know the scientific language.  But they are lay people who may never study physics.

In the presentation, I showed this video as an exercise in spotting quantum nonsense.



Let me describe a bit how this video looks to someone who knows the scientific language.  Lynn Mctaggart plainly uses a lot of technobabble.  I might put the technobabble into three categories which sometimes blend into each other.

1. Words that aren't really used by physicists.  Usually, these words appear to be derived from some real concept in physics, but she's garbled it so much that she doesn't recognize that the words she uses mean something completely different from the original words.
   
   Examples: connected, sea of light, separateness, potential life, nether region, beings of light, vibrating energy, sea of energy, memory bank
   
   
2. Words that are used by physicists, but don't mean what she thinks they mean.  Sometimes she mixes in true facts, but often in really misleading ways.
   
   Examples: energy, field, zero point field, Copenhagen interpretation, observation, nonlocality, photons, ground state energy, information, waves
   
   
3. Technical words that are just tossed around for no apparent reason.  The words are just there to provide an aura of science.
   
   Examples: DNA, frequency, constructionists (?), vacuum, hologram, magnetic resonance imaging, geomagnetic storm

But the layman can't see any of this.  To the layman, Lynn McTaggart looks vaguely suspicious, but, hey, physicists say pretty crazy things too.

The rule of thumb I would suggest is "Physics language, when properly used, does not say things about moral or social issues."  You can't go from physics to sociology without first passing by chemistry, biology, and psychology.

For example, at the beginning of the video, Lynn says we're all connected, and starts talking about wars and the "mine is bigger than yours" mentality.  You automatically know she's talking nonsense because even if "we're all connected" were a true statement in physics, it could not possibly mean that we're connected in a psychological, social, or moral sense.

Really, she's just using the physics as a metaphor.  She even says so herself at one point.  We determine the laws of physics based on experiment, not based on which ones give the best metaphors.

Even if a physicist uses technical words in this way, I would regard it with suspicion.  Physicists like to make social commentary just as much as the next person, after all, but they don't have any special insight into social issues that the layperson doesn't.  I think most physicists would actually appreciate it if you can distinguish between their authoritative statements on physics and non-authoritative statements on social issues.

But this rule of thumb is not sufficient.  For example, if someone tries to sell you a bracelet that interacts with your bioenergetic fields to keep you healthy... well, that's pseudoscientific technobabble right there.  But no social commentary is necessary to sell you a bracelet.  What other rules of thumb can the layperson use?

Or must the layperson accept that they cannot always spot pseudoscience on their own?  Gee, I sure hope this isn't the answer... that would require humility.  Surely, we can find a better answer than that.