Here's a little case study from last week.
"Brown Student Misidentified as Boston Bomber Found Dead in River", in Gawker.
The headline leads us to believe that someone thought the student (Sunil Tripathi) was one of the Boston bombers, and took it upon themselves to kill him.
The real story is that Sunil Tripathi had been missing for a month, and had likely commit suicide before the Boston bombings even occurred. It seems that Redditors accused him of being one of the bombers, and harassed his family, until the police finally identified the real bombers. At that point, the Reddit general manager apologized for Reddit's role. Later, his body was found in the river, where it was so decomposed that they needed to identify him by dental records.
In short, the Redditors in question weren't guilty of inciting violence, they were just guilty of harassing a bereaved family.
Here are a few more examples:
"Student, Sunil Tripathi, wrongly tied to Boston bombings found dead"
"Social media stigma can last a lifetime or, in Sunil Tripathi's case, end in tragedy"
It seems that it is not the articles themselves that are misleading, just the headlines. However, the blame does not lie entirely with the headline writers. When I searched for "Sunil Tripathi", most headlines were fine. But when I looked at Facebook, only the articles with misleading headlines were linked. For shame.
Monday, April 29, 2013
Wednesday, April 24, 2013
Math and causality
I was reflecting on my old mini-series on causality (from 2010??), and I thought I'd conclude it with a recap of sorts. But in this recap, I offer a reinterpretation of what I've written--with mathematics.
I am not a serious philosopher. My discussions on causality are in the category of "personal musings", a tool for me to talk about other things that interest me. They aren't really informed by a dialogue with previous philosophical writings or anything. However, what they are informed by is a mathematical method of thinking. I may not have explained it in mathematical terms, but I was certainly thinking in them.
It's just part of my education, as a physicist. I see everything in mathematical terms, because that's the best way to understand physics. When I've explained physics in the past, I generally avoid math because it scares people. But when I'm talking to math people, physics is just so much easier to explain. It goes something like this:
"Could you explain String Theory? What's this about 11 dimensions?"
"Well, you're familiar with N-dimensional differential manifolds, right?"
"Yeah"
"It's like that, with N=11"
"Oooooh"
"And you can decompose it into a Cartesian product of space-time and a 7-dimensional compact manifold."
etc.
Math people: soooo cool.
Causation is easy to think of in mathematical terms. Causation is a derivative of results with respect to prior conditions. If the prior conditions are changed, then how much do the results change?
As I pointed out in Colds and causality, experimentally, we can't really measure derivatives. So instead we take multiple data points and infer the derivative. Usually there are a lot of random factors, so instead of looking at the results of individual data points, we look at the expected results.
In Women and causality I pointed out other complications with the definition as derivative. The derivative of a function varies from point to point. So causal relations may depend on current conditions.
Furthermore, results are not just a function of one variable. They are functions of many variables. I identify causation with the partial derivative with respect to one of the variables. But this definition is ambiguous unless we specify what the other variables are. For example, if I transform (u,v) to (u,w), this may change the partial derivative with respect to u, even though the value of u was unchanged.
In Nature/nurture and causality, I talked about another limitation of the derivative concept of causality. If we want to compare the relative effect of two causes (for example, the effect of nature and nurture on human behavior), it seems easy enough to just take the derivative with respect to each of those variables. However, the two variables have different units, and thus cannot be compared! The typical solution is to consider the quantity
where f is the results as a function of prior conditions, x is one of the prior conditions, and σx is the spread of variable x. This quantity is no longer affected by the units of x.
In Responsibility and causality, I talk about how causality relates to ethics. The relationship is often mediated by game theory, which is... math! Well, okay, maybe ethics doesn't completely reduce to mathematics, but the math is important.
In Physics and causality, I talk about causality on a more fundamental level. Fundamentally, the state of the universe obeys some differential equations. By specifying the differential equations and the state of the universe at any given time, we end up specifying the entire history of the universe! Fun.
Now I am going to go through this post and delete most of the exclamation marks so I don't sound so excited.
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
I am not a serious philosopher. My discussions on causality are in the category of "personal musings", a tool for me to talk about other things that interest me. They aren't really informed by a dialogue with previous philosophical writings or anything. However, what they are informed by is a mathematical method of thinking. I may not have explained it in mathematical terms, but I was certainly thinking in them.
It's just part of my education, as a physicist. I see everything in mathematical terms, because that's the best way to understand physics. When I've explained physics in the past, I generally avoid math because it scares people. But when I'm talking to math people, physics is just so much easier to explain. It goes something like this:
"Could you explain String Theory? What's this about 11 dimensions?"
"Well, you're familiar with N-dimensional differential manifolds, right?"
"Yeah"
"It's like that, with N=11"
"Oooooh"
"And you can decompose it into a Cartesian product of space-time and a 7-dimensional compact manifold."
etc.
Math people: soooo cool.
Causation is easy to think of in mathematical terms. Causation is a derivative of results with respect to prior conditions. If the prior conditions are changed, then how much do the results change?
As I pointed out in Colds and causality, experimentally, we can't really measure derivatives. So instead we take multiple data points and infer the derivative. Usually there are a lot of random factors, so instead of looking at the results of individual data points, we look at the expected results.
In Women and causality I pointed out other complications with the definition as derivative. The derivative of a function varies from point to point. So causal relations may depend on current conditions.
Furthermore, results are not just a function of one variable. They are functions of many variables. I identify causation with the partial derivative with respect to one of the variables. But this definition is ambiguous unless we specify what the other variables are. For example, if I transform (u,v) to (u,w), this may change the partial derivative with respect to u, even though the value of u was unchanged.
In Nature/nurture and causality, I talked about another limitation of the derivative concept of causality. If we want to compare the relative effect of two causes (for example, the effect of nature and nurture on human behavior), it seems easy enough to just take the derivative with respect to each of those variables. However, the two variables have different units, and thus cannot be compared! The typical solution is to consider the quantity
∂f/∂x * σx
where f is the results as a function of prior conditions, x is one of the prior conditions, and σx is the spread of variable x. This quantity is no longer affected by the units of x.
In Responsibility and causality, I talk about how causality relates to ethics. The relationship is often mediated by game theory, which is... math! Well, okay, maybe ethics doesn't completely reduce to mathematics, but the math is important.
In Physics and causality, I talk about causality on a more fundamental level. Fundamentally, the state of the universe obeys some differential equations. By specifying the differential equations and the state of the universe at any given time, we end up specifying the entire history of the universe! Fun.
Now I am going to go through this post and delete most of the exclamation marks so I don't sound so excited.
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
Monday, April 22, 2013
The next series?
Now that I've finally finished my excessively long series on the cosmological argument, and I'm also writing a cap to my mini-series on causality, I was thinking of whether I should start any new series. Here are a few possibilities:
1. The ontological argument: This would be along the same lines of the cosmological argument, in that I'd meander through a bunch of pointless quibbles. I've already written a lot about the ontological argument, which shows that I have stuff to say about it. But I'll probably just end up saying a lot of stuff I've already said.
2. Some other apologetics argument? Fine-tuning? Pascale's Wager? I'm not sure I would have enough to say about these to fill a series.
3. I could read Mere Christianity (which I've never read) and talk about how terrible it is. Or maybe some other book!
4. I could reboot one of my really old series about basic physics. I wrote about quantum mechanics and special relativity, and most of it wasn't very good. My main goal back then was to explain stuff I had learned in courses, because that's fun. If I were to reboot these, I'm not sure what my new goal would be.
5. I had a fantasy about what would happen if I suddenly gained a large atheist audience, and had to explain asexuality to them, or if I suddenly gained a large asexual audience and had to explain atheism to them. What would I write?
Would any of these series sound interesting to you? Is there anything else you'd like me to write about?
1. The ontological argument: This would be along the same lines of the cosmological argument, in that I'd meander through a bunch of pointless quibbles. I've already written a lot about the ontological argument, which shows that I have stuff to say about it. But I'll probably just end up saying a lot of stuff I've already said.
2. Some other apologetics argument? Fine-tuning? Pascale's Wager? I'm not sure I would have enough to say about these to fill a series.
3. I could read Mere Christianity (which I've never read) and talk about how terrible it is. Or maybe some other book!
4. I could reboot one of my really old series about basic physics. I wrote about quantum mechanics and special relativity, and most of it wasn't very good. My main goal back then was to explain stuff I had learned in courses, because that's fun. If I were to reboot these, I'm not sure what my new goal would be.
5. I had a fantasy about what would happen if I suddenly gained a large atheist audience, and had to explain asexuality to them, or if I suddenly gained a large asexual audience and had to explain atheism to them. What would I write?
Would any of these series sound interesting to you? Is there anything else you'd like me to write about?
Friday, April 19, 2013
Getting from First Cause to God
I have this series, "A few things wrong with the cosmological argument", but have ignored it for over six months. I think that means this should be the last post, even if I didn't have the opportunity to point out every last problem in the cosmological argument.
In previous posts, I discussed lots of little problems in the cosmological argument as presented by William Lane Craig (henceforth WLC). It's mostly lots of nitpicking of little problems that maybe could have killed the cosmological argument if it weren't already killed by much bigger problems. But here I will discuss what many people consider to be the biggest problem of all: How do you connect the "First Cause" to God?
This is a major problem with most philosophical arguments for God. They argue for some ultimate entity, and then just take it for granted that it's God. And since this argument is typically made by Christian apologists, it's not just any god, it's the Christian God.* The argument feels like it's relying on the cultural dominance of Christianity. As soon as someone talks about a powerful entity, God seems like an obvious possibility, only because everyone talks about it so much. My boyfriend says that because he's played too many fantasy games, his gut feeling is that an epic-level wizard is more likely.
*To be fair, apologists usually supplement their philosophical arguments with historical arguments.
Chris Hallquist made the interesting claim that it wasn't always this way. Classical theologians used to have arguments for specific traits of God. Nowadays, people like WLC will only devote a minimal amount of space to the subject, and what's there doesn't make much sense.
I will only briefly address WLC's argument, as presented in his Kalam article:
The whole Kalam cosmological argument rests on an analogy between objects within the universe, which all require causes, and the universe itself. If the cause of the universe is so dissimilar to the causes of objects within the universe, one wonders why we accepted the whole analogy in the first place! Therefore, we should ask what causes look like normally.
Causality is a many-faced concept which I've mused about in another blog series. For example, there's the clinical concept of causation--if you tell a bunch of people to start smoking, they will be more likely to get cancer than a similar group that you told not to smoke, thus smoking causes cancer. But if we're making philosophical arguments about causation, we might need a more general notion of causation, like from physics. Here are the key points:
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
In previous posts, I discussed lots of little problems in the cosmological argument as presented by William Lane Craig (henceforth WLC). It's mostly lots of nitpicking of little problems that maybe could have killed the cosmological argument if it weren't already killed by much bigger problems. But here I will discuss what many people consider to be the biggest problem of all: How do you connect the "First Cause" to God?
This is a major problem with most philosophical arguments for God. They argue for some ultimate entity, and then just take it for granted that it's God. And since this argument is typically made by Christian apologists, it's not just any god, it's the Christian God.* The argument feels like it's relying on the cultural dominance of Christianity. As soon as someone talks about a powerful entity, God seems like an obvious possibility, only because everyone talks about it so much. My boyfriend says that because he's played too many fantasy games, his gut feeling is that an epic-level wizard is more likely.
*To be fair, apologists usually supplement their philosophical arguments with historical arguments.
Chris Hallquist made the interesting claim that it wasn't always this way. Classical theologians used to have arguments for specific traits of God. Nowadays, people like WLC will only devote a minimal amount of space to the subject, and what's there doesn't make much sense.
I will only briefly address WLC's argument, as presented in his Kalam article:
I think that it can be plausibly argued that the cause of the universe must be a personal Creator. For how else could a temporal effect arise from an eternal cause? If the cause were simply a mechanically operating set of necessary and sufficient conditions existing from eternity, then why would not the effect also exist from eternity? For example, if the cause of water's being frozen is the temperature's being below zero degrees, then if the temperature were below zero degrees from eternity, then any water present would be frozen from eternity. The only way to have an eternal cause but a temporal effect would seem to be if the cause is a personal agent who freely chooses to create an effect in time. For example, a man sitting from eternity may will to stand up; hence, a temporal effect may arise from an eternally existing agent.I basically disagree with everything:
- I don't think it's strange for a temporal event to arise from some entity that does not have a beginning. For instance, if that entity consists of two non-interacting particles moving past one another, then this is an eternal entity that has a special point in time (ie the moment of closest approach). It's also completely mechanistic.
- Perhaps the problem with the two-particle example is that WLC thinks the first cause must be timeless. I don't think this follows from the Kalam Cosmological argument, which only shows that there is an entity that did not begin. "Eternal" is not the same as "timeless".
- WLC seems to be imagining "personal agents" as agents with libertarian free will. (This is odd because in other contexts, Christians appear to believe in compatibilist free will.) I don't agree that libertarian free will is even a sensible concept. All personal agents we know of are mechanistic.
- A timeless libertarian agent is even less sensible. Usually, a libertarian agent is one who may make decisions independent of prior circumstance. When there is no time, there is no prior circumstance.
The whole Kalam cosmological argument rests on an analogy between objects within the universe, which all require causes, and the universe itself. If the cause of the universe is so dissimilar to the causes of objects within the universe, one wonders why we accepted the whole analogy in the first place! Therefore, we should ask what causes look like normally.
Causality is a many-faced concept which I've mused about in another blog series. For example, there's the clinical concept of causation--if you tell a bunch of people to start smoking, they will be more likely to get cancer than a similar group that you told not to smoke, thus smoking causes cancer. But if we're making philosophical arguments about causation, we might need a more general notion of causation, like from physics. Here are the key points:
- Every event is caused by all events in its past light-cone. Without the universe, there will be no light-cones, but it still makes sense that everything is caused by a multiplicity of previous things.
- In another sense, events are "caused" by general physical laws which connect past to future. Therefore, we might expect that among the universe's causes are abstract principles, or other things that aren't really "things".
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
Tuesday, April 16, 2013
Christian compatibilist free will?
Something interesting came up in the comments on my post about the free will defense against the problem of evil, and I wish to recap it.
First, commenter James brought up the argument that God's omniscience contradicts free will. Commenter Slightlymetaphysical brushed off the argument. I would brush it off too. Pshhh, why should omniscience contradict free will? Just because you know what someone chose doesn't mean that they didn't choose it.
Of course, the reason I would brush it off is because I'm very used to compatibilist free will. That is, I believe free will is compatible with determinism. An act of free will is just something that is arises directly from a set of conscious cognitive processes. Even if those cognitive processes are deterministic, that doesn't mean our decisions weren't caused by them.
But there are also incompatibilist conceptions of free will. For example, commenter Larry offered the following definition (without necessarily endorsing it):
As a result of the comment discussion, I realized that Christians are implicitly taking a compatibilist view of free will. As long as they accept the following premises, they must accept the conclusion:
The Christian* view on free will is that it is the ability to turn against God. Eve had the ability to eat that apple (or pomegranate or what have you), and the ability to choose not to. For reasons infathomable, this kind of free will is so desirable to God that it is worth the evil that proceeds from it. On the other hand, if we believe in compatibilist free will, then God can have his cake and eat it too. That is, people can have the ability to choose evil, even when it is predetermined that they will not exercise this ability.
*More accurately, a Christian view, which is not necessarily universal among Christians.
The problem of evil is the question, "Why does God allow evil?" The free will defense is, "Evil is a necessary consequence of free will." My proposed counter is, "But free will is compatible with a world where no one chooses evil."
Of course, this is one of those purely philosophical arguments, and we all know how unpersuasive those are. Here are a couple responses:
First, commenter James brought up the argument that God's omniscience contradicts free will. Commenter Slightlymetaphysical brushed off the argument. I would brush it off too. Pshhh, why should omniscience contradict free will? Just because you know what someone chose doesn't mean that they didn't choose it.
Of course, the reason I would brush it off is because I'm very used to compatibilist free will. That is, I believe free will is compatible with determinism. An act of free will is just something that is arises directly from a set of conscious cognitive processes. Even if those cognitive processes are deterministic, that doesn't mean our decisions weren't caused by them.
But there are also incompatibilist conceptions of free will. For example, commenter Larry offered the following definition (without necessarily endorsing it):
1. Assume there is some state of the world at time t.Clearly, this kind of "free will" is incompatible with determinism, because in a deterministic world, there is only one possible outcome, given initial conditions.
2. Agent A makes decision D at time t+1.
3. We "roll back" the world precisely to its state at time t
4. Agent A has "free will" if and only if she could make a different decision, D', at time t+1.
As a result of the comment discussion, I realized that Christians are implicitly taking a compatibilist view of free will. As long as they accept the following premises, they must accept the conclusion:
Premise 1: Free will exists.This is very interesting, because it is not in accordance with other Christian views on free will. And in particular, it's not in accordance with the free will defense against the problem of evil.
Premise 2: An omniscient being exists.
Premise 3: The existence of omniscience implies determinism.
Conclusion: Free will is compatible with determinism.
The Christian* view on free will is that it is the ability to turn against God. Eve had the ability to eat that apple (or pomegranate or what have you), and the ability to choose not to. For reasons infathomable, this kind of free will is so desirable to God that it is worth the evil that proceeds from it. On the other hand, if we believe in compatibilist free will, then God can have his cake and eat it too. That is, people can have the ability to choose evil, even when it is predetermined that they will not exercise this ability.
*More accurately, a Christian view, which is not necessarily universal among Christians.
The problem of evil is the question, "Why does God allow evil?" The free will defense is, "Evil is a necessary consequence of free will." My proposed counter is, "But free will is compatible with a world where no one chooses evil."
Of course, this is one of those purely philosophical arguments, and we all know how unpersuasive those are. Here are a couple responses:
- Omniscience does not imply determinism. An omniscient being could simply be aware of all possibilities and their outcomes, without knowing which possibilities will come to pass. One could counter that this kind of omniscience is hardly a proper omniscience at all. But I for one would still be very impressed by such a being, whether it's proper omniscience or not.
- It is not free will itself that God finds so desirable. Rather, God desires that people have the ability to go against him, and that they actually exercise this ability. God's desire does apply to heaven, where he is basically okay with the fact that everyone is choosing good. God sure has some strange desires, but the truth can be strange.
Wednesday, April 10, 2013
Bayesian reasoning and asexuality
This post will discuss why it is difficult to demonstrate that a person is asexual, and why this is unique to asexuals. I assure readers upfront that it is not my purpose to deny people's asexual identities, or to tell people that they must be above a certain age to identify as asexual. Rather, my purpose is to discuss a particular kind of analysis, and then discuss some problems with the analysis.
Introducing the problem
Asexuality is defined as the lack of sexual attraction. From a bayesian perspective, this makes it harder for a person to conclude that they are asexual. To demonstrate that you are a person who has a stable pattern of attraction towards one or more genders, all you have to do is experience attraction. To be really sure that it's "stable", you could experience it two or three times. But to demonstrate that you do not stably experience attraction, the best you can do is sit around and wait.
Asexuals are not the only people with this problem. Straight people have the same problem demonstrating to themselves that they are not bisexual. Gay and lesbian people do too. This can be illustrated in the Storms' Model diagram (published in 1979).
In this diagram, the purple arrows illustrate "hard" Bayesian problems. That is, if you're in the group at the base of an arrow, it may be "difficult" to demonstrate that you are not actually part of the group where the arrow is pointing, because you'd have to sit around and wait a while.
The orange percentages show, roughly, the number of people in each group. I know the estimates of homo- and bisexual people are pessimistic, but the estimate of asexuals is in accordance with the literature. What puts asexuals in a unique situation compared to the other three orientations, is that there are just so few asexuals as compared to heterosexuals. That means that any Bayesian estimate of probabilities will initially favor heterosexuality.
So what does the Bayesian calculation look like? (If you aren't familiar with Bayes' theorem, you should look it up. Alternatively, skip to "Result".)
Technical Section on Bayes' Theorem
Applying Literature on Sexual Attraction
We can estimate when heterosexual people experience attraction with research! Sciatrix recommended a 1996 review by McClintock & Herdt, which says that the average age of first sexual attraction is age 10. According to one of the references, the standard deviation is 3.6 years for gay and lesbian people. I glanced at another reference, and it reported a standard deviation of 4.7 years for lesbian women and 3 years for heterosexual women. Since heterosexuals are the relevant group, I will go with the 3-year estimate.
Let's start by assuming that the ages are normally distributed. There's a simple expression for the probability that a heterosexual at age y will not have experienced sexual attraction yet:
Erfc is the complementary error function. That's something you can easily put into Excel. The probability reaches 1% at about age 17. That means 99% of heterosexuals at age 17 have already experienced sexual attraction.
The tricky thing is that it is not safe to assume a normal distribution! A normal distribution is the result when there are lots of random factors, each of which contributes a small delay or a small advancement. But lots of real phenomena do not occur in normal distributions. And the differences in the distributions are very important here, because we're interested in the tails of the distributions. It's important to know, what is the skew of the distribution? What is the kurtosis? We may never know.
If I were to build a toy model (as I've been trained to do as a physicist), I'd say that at some age, sexual attraction "turns on" for a person (though this age may be different for different people). After this point, they have a certain probability per unit time of experiencing sexual attraction. This model predicts an "exponentially modified Gaussian distribution", and it would only increase the age necessary for a person to conclude they are asexual. But perhaps I'm getting too much into sketchy territory. Let's take a step back.
Problems with this analysis
You may be saying "Wait, 17? But aren't there lots of people who know they're asexual before that? How can that be right?" Indeed, based on a community survey, about 10% of the online community is under 17.
Those 10% aren't wrong. Actually, it's my analysis which is wrong. In so many ways.
The first problem is that people could have poor recollections of when they experienced sexual attraction. They're being asked many years after the fact. Poor recollection would probably inflate the variation between individuals.
The second problem is that I believe that there are gradations of sexual attraction. It's likely that it ramps up over a long period of time. People just recall the one event that felt most like a breakthrough, but this could occur at different times during the ramp-up for different people. This would also inflate the variation between individuals.
The third problem is that "so far no sexual attraction" is not the only possible evidence that a person can be asexual. If, as I believe, there is a ramp-up of sexual-attraction-like experience, then asexuals might be hyperaware of this ramp (since asexuals notice they're different from other people). If a person isn't even experiencing the beginning of that ramp, that's additional evidence for being asexual.
Oh, and don't forget that we don't really know the distribution of first sexual attraction experiences.
Feel free to point out further problems in the comments.
Conclusions
I think the Bayesian analysis I presented above is what a lot of questioning people want to exist. They'd like an objective tool, something to tell them what they really are. Preferably something involving MATH and SCIENCE. But this is the best you can get, and it still won't tell you much. There's a broader lesson in here about relying on math and science to describe one's experience. It's really hard!
But I'll at least say this: asexuals really are in a unique epistemic position compared to other orientations. It is harder to demonstrate asexuality than any of the others. It is unclear just how hard that is. For some people it may be harder than for others. Some people might know fairly early on, while others may be unable to know until they're older.
I am of the mind that we should accept that asexuality involves enhanced uncertainty. It is okay for people to be uncertain. It is okay for people to identify as one thing, and later change their mind. In fact, we should advocate a better etiquette of uncertainty. Don't assume that an identity is a commitment. Don't treat identity shifts as betrayals or marks of shame. Don't condescend to people as if you know better than them who they are. (Pretty much this is all stuff asexuals already do.)
Introducing the problem
Asexuality is defined as the lack of sexual attraction. From a bayesian perspective, this makes it harder for a person to conclude that they are asexual. To demonstrate that you are a person who has a stable pattern of attraction towards one or more genders, all you have to do is experience attraction. To be really sure that it's "stable", you could experience it two or three times. But to demonstrate that you do not stably experience attraction, the best you can do is sit around and wait.
Asexuals are not the only people with this problem. Straight people have the same problem demonstrating to themselves that they are not bisexual. Gay and lesbian people do too. This can be illustrated in the Storms' Model diagram (published in 1979).
In this diagram, the purple arrows illustrate "hard" Bayesian problems. That is, if you're in the group at the base of an arrow, it may be "difficult" to demonstrate that you are not actually part of the group where the arrow is pointing, because you'd have to sit around and wait a while.
The orange percentages show, roughly, the number of people in each group. I know the estimates of homo- and bisexual people are pessimistic, but the estimate of asexuals is in accordance with the literature. What puts asexuals in a unique situation compared to the other three orientations, is that there are just so few asexuals as compared to heterosexuals. That means that any Bayesian estimate of probabilities will initially favor heterosexuality.
So what does the Bayesian calculation look like? (If you aren't familiar with Bayes' theorem, you should look it up. Alternatively, skip to "Result".)
Technical Section on Bayes' Theorem
Let A be the proposition that a person is asexual, while H is the proposition that they are heterosexual. E is the proposition that so far they haven't experienced sexual attraction.Result: One may conclude that they are more likely to be asexual than heterosexual if they are such an age that more than 99% of heterosexuals would have experienced sexual attraction.
P(A|E)/P(H|E) = P(A)/P(H) * P(E|H)/P(E|A)
P(A)/P(H) is the prior odds ratio between being asexual and heterosexual. It's about 1/97, because there are about 97 times as many heterosexuals as asexuals. P(A|E)/P(H|E) is the new odds ratio, in light of the fact that a person has not yet experienced sexual attraction.
P(E|A) is the probability that an asexual would not have experienced sexual attraction yet. I think it is possible for asexuals to experience sexual attraction without having a stable pattern of sexual attraction, so I think P(E|A) is less than one. But let's approximate it as one.
P(E|H) is the probability that a heterosexual person would not have experienced any sexual attraction yet. When P(E|H) is less than 1/97, one may conclude that they are more likely to be asexual than heterosexual.
Applying Literature on Sexual Attraction
We can estimate when heterosexual people experience attraction with research! Sciatrix recommended a 1996 review by McClintock & Herdt, which says that the average age of first sexual attraction is age 10. According to one of the references, the standard deviation is 3.6 years for gay and lesbian people. I glanced at another reference, and it reported a standard deviation of 4.7 years for lesbian women and 3 years for heterosexual women. Since heterosexuals are the relevant group, I will go with the 3-year estimate.
Let's start by assuming that the ages are normally distributed. There's a simple expression for the probability that a heterosexual at age y will not have experienced sexual attraction yet:
0.5 * erfc( (y-10) * 0.2357 )
The tricky thing is that it is not safe to assume a normal distribution! A normal distribution is the result when there are lots of random factors, each of which contributes a small delay or a small advancement. But lots of real phenomena do not occur in normal distributions. And the differences in the distributions are very important here, because we're interested in the tails of the distributions. It's important to know, what is the skew of the distribution? What is the kurtosis? We may never know.
If I were to build a toy model (as I've been trained to do as a physicist), I'd say that at some age, sexual attraction "turns on" for a person (though this age may be different for different people). After this point, they have a certain probability per unit time of experiencing sexual attraction. This model predicts an "exponentially modified Gaussian distribution", and it would only increase the age necessary for a person to conclude they are asexual. But perhaps I'm getting too much into sketchy territory. Let's take a step back.
Problems with this analysis
You may be saying "Wait, 17? But aren't there lots of people who know they're asexual before that? How can that be right?" Indeed, based on a community survey, about 10% of the online community is under 17.
Those 10% aren't wrong. Actually, it's my analysis which is wrong. In so many ways.
The first problem is that people could have poor recollections of when they experienced sexual attraction. They're being asked many years after the fact. Poor recollection would probably inflate the variation between individuals.
The second problem is that I believe that there are gradations of sexual attraction. It's likely that it ramps up over a long period of time. People just recall the one event that felt most like a breakthrough, but this could occur at different times during the ramp-up for different people. This would also inflate the variation between individuals.
The third problem is that "so far no sexual attraction" is not the only possible evidence that a person can be asexual. If, as I believe, there is a ramp-up of sexual-attraction-like experience, then asexuals might be hyperaware of this ramp (since asexuals notice they're different from other people). If a person isn't even experiencing the beginning of that ramp, that's additional evidence for being asexual.
Oh, and don't forget that we don't really know the distribution of first sexual attraction experiences.
Feel free to point out further problems in the comments.
Conclusions
I think the Bayesian analysis I presented above is what a lot of questioning people want to exist. They'd like an objective tool, something to tell them what they really are. Preferably something involving MATH and SCIENCE. But this is the best you can get, and it still won't tell you much. There's a broader lesson in here about relying on math and science to describe one's experience. It's really hard!
But I'll at least say this: asexuals really are in a unique epistemic position compared to other orientations. It is harder to demonstrate asexuality than any of the others. It is unclear just how hard that is. For some people it may be harder than for others. Some people might know fairly early on, while others may be unable to know until they're older.
I am of the mind that we should accept that asexuality involves enhanced uncertainty. It is okay for people to be uncertain. It is okay for people to identify as one thing, and later change their mind. In fact, we should advocate a better etiquette of uncertainty. Don't assume that an identity is a commitment. Don't treat identity shifts as betrayals or marks of shame. Don't condescend to people as if you know better than them who they are. (Pretty much this is all stuff asexuals already do.)
Monday, April 8, 2013
If everything looks one-sided...
Earlier in the comments of The Uncredible Hallq, the topic was same-sex marriage, and someone was saying, "Policy Debates Should Not Appear One-Sided." The point being that if same-sex marriage looked like such a one-sided issue, then we're obviously biased.
My reaction was, "Possibly true, definitely unhelpful."
I put "Policy Debates Should Not Appear One-Sided" in quotes, because this is the title of a well-known piece on Less Wrong. In brief, you might expect issues of fact to be one-sided, because most of the strongest evidence will converge (though by chance there may be some weak contrary evidence). But issues of policy generally should not be one-sided.* Any proposed policy has costs and benefits. The good policies are the ones where the benefits outweigh the costs. But it would be very strange if it appeared that a policy literally had no costs whatsoever. If policy issues look one-sided, then we must be biased.
*I recall one time Leah Libresco said "Arguments shouldn't look one-sided" in the context of atheism vs Catholicism. This was an incorrect application of the idea, since atheism vs Catholicism is analogous to an issue of fact rather than an issue of policy.
I agree with the general point, but is this really something that can used in any specific argument? As I've said before, accusing your opponent of cognitive bias is a pretty shitty argument, even if it's true. I mean, we all know that we have our own cognitive biases. But that doesn't mean that any particular belief is wrong.
The argument is made worse by the fact that "Policy Debates Should Not Appear One-Sided" is not a universal rule. You'd expect that most policies would have costs and benefits, but who is to say that this is true of any particular policy? One could imagine, for instance, an issue of policy that reduces to a single issue of fact. Or you could imagine an issue of policy that only has a few distinct effects, so it's not so outlandish that the effects could all happen to be positive. Or you could imagine an issue of policy which has one effect which is so big and important, that it's not really necessary to consider the other smaller effects.
Even when you're just trying to evaluate a policy for yourself, rather than trying to argue with someone else, "Policy Debates Should Not Appear One-Sided" still seems unhelpful. If a policy debate looks one-sided, what are you supposed to do about it? You can search for new evidence and arguments that oppose you. But if you've already seen the opposing arguments and found them wanting, that's that. There's no point in trying to fill a quota of disadvantages to your own side, just because you have the prior expectation that your side should have disadvantages. You might as well just believe your prior expectations and ignore evidence.
My reaction was, "Possibly true, definitely unhelpful."
I put "Policy Debates Should Not Appear One-Sided" in quotes, because this is the title of a well-known piece on Less Wrong. In brief, you might expect issues of fact to be one-sided, because most of the strongest evidence will converge (though by chance there may be some weak contrary evidence). But issues of policy generally should not be one-sided.* Any proposed policy has costs and benefits. The good policies are the ones where the benefits outweigh the costs. But it would be very strange if it appeared that a policy literally had no costs whatsoever. If policy issues look one-sided, then we must be biased.
*I recall one time Leah Libresco said "Arguments shouldn't look one-sided" in the context of atheism vs Catholicism. This was an incorrect application of the idea, since atheism vs Catholicism is analogous to an issue of fact rather than an issue of policy.
I agree with the general point, but is this really something that can used in any specific argument? As I've said before, accusing your opponent of cognitive bias is a pretty shitty argument, even if it's true. I mean, we all know that we have our own cognitive biases. But that doesn't mean that any particular belief is wrong.
The argument is made worse by the fact that "Policy Debates Should Not Appear One-Sided" is not a universal rule. You'd expect that most policies would have costs and benefits, but who is to say that this is true of any particular policy? One could imagine, for instance, an issue of policy that reduces to a single issue of fact. Or you could imagine an issue of policy that only has a few distinct effects, so it's not so outlandish that the effects could all happen to be positive. Or you could imagine an issue of policy which has one effect which is so big and important, that it's not really necessary to consider the other smaller effects.
Even when you're just trying to evaluate a policy for yourself, rather than trying to argue with someone else, "Policy Debates Should Not Appear One-Sided" still seems unhelpful. If a policy debate looks one-sided, what are you supposed to do about it? You can search for new evidence and arguments that oppose you. But if you've already seen the opposing arguments and found them wanting, that's that. There's no point in trying to fill a quota of disadvantages to your own side, just because you have the prior expectation that your side should have disadvantages. You might as well just believe your prior expectations and ignore evidence.
Friday, April 5, 2013
Further issues with the free will defense
The "free will defense" is a response to the problem of evil. Namely, a benevolent omnipotent god allows evil to exist in the world because it is necessary in a world with free will. God apparently believes free will is worth the evil. The corollary is that we live in the best of all possible worlds that God can create without defying human free will.
Another corollary is that evil should be roughly constant in time. People had just as much free will several centuries ago as we do now. We live in the best of all possible worlds with free will, and so did they. Therefore, we'd expect that our world is about as good as the world several centuries ago. I don't think that's what the actual world looks like.
In the context of Christian beliefs, I'm also confused how it's supposed to fit in with heaven. Ideas about heaven are quite diverse, but I gather that it's supposed to be a world that is better than our world.
One possibility is that heaven has free will. But that implies that our world is not the best of all possible worlds with free will. The alternative is that heaven does not have free will. But if free will is so important on Earth, why isn't it important in heaven?
(These are intended to be a "light" or "fun" arguments against the free will defense, not an especially serious ones. For reference, I've previously discussed the problem of evil.)
Another corollary is that evil should be roughly constant in time. People had just as much free will several centuries ago as we do now. We live in the best of all possible worlds with free will, and so did they. Therefore, we'd expect that our world is about as good as the world several centuries ago. I don't think that's what the actual world looks like.
In the context of Christian beliefs, I'm also confused how it's supposed to fit in with heaven. Ideas about heaven are quite diverse, but I gather that it's supposed to be a world that is better than our world.
One possibility is that heaven has free will. But that implies that our world is not the best of all possible worlds with free will. The alternative is that heaven does not have free will. But if free will is so important on Earth, why isn't it important in heaven?
(These are intended to be a "light" or "fun" arguments against the free will defense, not an especially serious ones. For reference, I've previously discussed the problem of evil.)
Tuesday, April 2, 2013
A portrait of an "unsolved problem"
I study high-temperature superconductivity (henceforth HTSC). It's one of the largest fields of condensed matter physics, which itself is the largest field of physics. HTSC is one of the outstanding unsolved problems in physics, and unsolved problems attract research. The two big questions are:
So my perspective is very limited. Superconductivity is a vast field, and I occupy one tiny little corner. I don't have a great idea of the big picture, because I'm too busy trying to understand the details of the stuff near my own corner. And I don't even fully understand that. Consider this a distorted portrait.
What "unsolved" means
In fact, superconductivity is already understood. It was solved in 1957, when BCS theory was proposed. BCS theory is named for its creators: Bardeen, Schrieffer, and Cooper. The solution is that electrons pair up. In order to pair up, there needs to be an attractive force between electrons. There is an interaction between electrons and the ionic lattice that creates an effective attractive interaction between electron pairs.
But superconductivity reasserted itself as a mystery with the discovery of HTSC in 1986. BCS theory does not work for HTSC materials. It does not predict that superconductors could exist at such high temperatures (ie minus 140 degrees celsius). We need a new theory of superconductivity for the newly discovered materials. But it's not completely up for grabs. We're still fairly sure that electrons must be pairing up due to some effective attractive interaction. We're just unsure where the effective attractive interaction comes from.
Mind you, when I say low-temperature superconductivity is "understood" and high-temperature superconductivity is not understood, I'm not referring to my personal level of understanding. I don't really understand BCS theory. That is to say, I don't know how to calculate the electron-phonon interaction, and I don't know how to get from the microscopic theory to the Ginzberg-Landau theory. But that previous sentence might have been gibberish to most of you. Perhaps what I call "not understanding" is a much deeper understanding than the most educated lay person.
Surely when HTSC is solved, the solution will involve all these little technicalities. I will not be able to understand the solution. I will understand the cartoon picture that accompanies the solution, but I will not understand the calculations.
An excess, not a scarcity, of theories
People generally don't talk about mechanisms for HTSC. The expression "elephant in the room" comes to mind. My impression is that lots of mechanisms were proposed around 1986-1990, and then it became unfashionable. The problem isn't that we don't have a theory, it's that we have too many theories. We need evidence to knock down some of those theories.
New mechanisms for HTSC are occasionally proposed on ArXiV (which is where most physicists share their upcoming publications). I often wonder if these are cranks. There's nothing really to stop cranks from putting things up on ArXiV, since it's not peer-reviewed. I'm told there's even an unwritten special section for cranks (the "general physics" section). But perhaps many of these papers are completely legitimate and respectable. The point is I wouldn't be able to the difference. I've never gotten the impression that they have high impact anyway.
At March Meeting (a huge condensed matter physics conference with over 8000 talks) a few weeks ago, I saw a couple proposals for HTSC mechanisms. One proposal was made during a 12 minute talk trying to explain the observations of some recent experiment. The talk sounded exciting, but I didn't understand it at all. That's not unusual; I don't understand most of the talks.
The other proposal occurred in a poster presentation. The guy had a theory that did not involve electron pairing. That makes it "wacky". I had the impression that he was sort of a crank, since he said he was unable to get published or get funding. But I respected him anyway. I don't understand BCS theory, and I didn't understand his theory. If I'm honest, I can't argue with him. Let the knowledgeable theorists do the arguing.
I mentioned my impression that people don't really talk about mechanisms for superconductivity. He said that's because everyone thinks superconductivity is already solved, and that the solution happens to be the idea they themselves proposed. He alluded to (Nobel Laureate) Phil Anderson's theory. I'm told that Anderson's mechanism involves electron pairing, but a repulsive force is sufficient to allow the pairing. That sounds "wacky" too, but what do I know?
Approaching the problem indirectly
Earlier I said that as an experimentalist, I just test ideas proposed by theorists. But we don't really talk about mechanisms for HTSC. Instead, we test smaller ideas.
For example, one of the big debates is about a "kink" in the electronic structure. Is it caused by an interaction between electrons and phonons, or an interaction between electrons and magnons? And is it related to superconductivity or not? I suppose there must be a class of theories involving phonons, and a class of theories involving magnons, but we don't talk about the theories directly. We're just trying to establish the basic facts.
Another big debate is about the so-called "pseudogap" state, which is a strange state that has been observed above the superconducting temperature. What is the nature of this state of matter? Is it competing with superconductivity, or is it perhaps an incipient form of superconductivity? Perhaps it has something to do with CDWs or stripes? Not that any of this makes sense to you unless you're in the same field as me. But once we figure out the answer, I'm sure I'll be able to draw a cartoon of it that you'll understand.
I think when we think of historical physics discoveries, we often think of the Eureka! moment. Someone writes a great paper, and all the problems are solved as it clicks into place. I'm suspicious of this narrative, because that's not how the field of HTSC looks. It will be a slow and incremental progression. Slowly working out incomprehensible technicalities. But afterwards it will have looked simple. We'll have a nice cartoon, and we'll tell stories about the scientists who, in a flash of brilliance, dreamed up those cartoons.
- What is the mechanism for HTSC? That is, how does it work?
- Can we find a superconductor that works at even higher temperatures, like room temperature?
So my perspective is very limited. Superconductivity is a vast field, and I occupy one tiny little corner. I don't have a great idea of the big picture, because I'm too busy trying to understand the details of the stuff near my own corner. And I don't even fully understand that. Consider this a distorted portrait.
What "unsolved" means
In fact, superconductivity is already understood. It was solved in 1957, when BCS theory was proposed. BCS theory is named for its creators: Bardeen, Schrieffer, and Cooper. The solution is that electrons pair up. In order to pair up, there needs to be an attractive force between electrons. There is an interaction between electrons and the ionic lattice that creates an effective attractive interaction between electron pairs.
But superconductivity reasserted itself as a mystery with the discovery of HTSC in 1986. BCS theory does not work for HTSC materials. It does not predict that superconductors could exist at such high temperatures (ie minus 140 degrees celsius). We need a new theory of superconductivity for the newly discovered materials. But it's not completely up for grabs. We're still fairly sure that electrons must be pairing up due to some effective attractive interaction. We're just unsure where the effective attractive interaction comes from.
Mind you, when I say low-temperature superconductivity is "understood" and high-temperature superconductivity is not understood, I'm not referring to my personal level of understanding. I don't really understand BCS theory. That is to say, I don't know how to calculate the electron-phonon interaction, and I don't know how to get from the microscopic theory to the Ginzberg-Landau theory. But that previous sentence might have been gibberish to most of you. Perhaps what I call "not understanding" is a much deeper understanding than the most educated lay person.
Surely when HTSC is solved, the solution will involve all these little technicalities. I will not be able to understand the solution. I will understand the cartoon picture that accompanies the solution, but I will not understand the calculations.
An excess, not a scarcity, of theories
People generally don't talk about mechanisms for HTSC. The expression "elephant in the room" comes to mind. My impression is that lots of mechanisms were proposed around 1986-1990, and then it became unfashionable. The problem isn't that we don't have a theory, it's that we have too many theories. We need evidence to knock down some of those theories.
New mechanisms for HTSC are occasionally proposed on ArXiV (which is where most physicists share their upcoming publications). I often wonder if these are cranks. There's nothing really to stop cranks from putting things up on ArXiV, since it's not peer-reviewed. I'm told there's even an unwritten special section for cranks (the "general physics" section). But perhaps many of these papers are completely legitimate and respectable. The point is I wouldn't be able to the difference. I've never gotten the impression that they have high impact anyway.
At March Meeting (a huge condensed matter physics conference with over 8000 talks) a few weeks ago, I saw a couple proposals for HTSC mechanisms. One proposal was made during a 12 minute talk trying to explain the observations of some recent experiment. The talk sounded exciting, but I didn't understand it at all. That's not unusual; I don't understand most of the talks.
The other proposal occurred in a poster presentation. The guy had a theory that did not involve electron pairing. That makes it "wacky". I had the impression that he was sort of a crank, since he said he was unable to get published or get funding. But I respected him anyway. I don't understand BCS theory, and I didn't understand his theory. If I'm honest, I can't argue with him. Let the knowledgeable theorists do the arguing.
I mentioned my impression that people don't really talk about mechanisms for superconductivity. He said that's because everyone thinks superconductivity is already solved, and that the solution happens to be the idea they themselves proposed. He alluded to (Nobel Laureate) Phil Anderson's theory. I'm told that Anderson's mechanism involves electron pairing, but a repulsive force is sufficient to allow the pairing. That sounds "wacky" too, but what do I know?
Approaching the problem indirectly
Earlier I said that as an experimentalist, I just test ideas proposed by theorists. But we don't really talk about mechanisms for HTSC. Instead, we test smaller ideas.
For example, one of the big debates is about a "kink" in the electronic structure. Is it caused by an interaction between electrons and phonons, or an interaction between electrons and magnons? And is it related to superconductivity or not? I suppose there must be a class of theories involving phonons, and a class of theories involving magnons, but we don't talk about the theories directly. We're just trying to establish the basic facts.
Another big debate is about the so-called "pseudogap" state, which is a strange state that has been observed above the superconducting temperature. What is the nature of this state of matter? Is it competing with superconductivity, or is it perhaps an incipient form of superconductivity? Perhaps it has something to do with CDWs or stripes? Not that any of this makes sense to you unless you're in the same field as me. But once we figure out the answer, I'm sure I'll be able to draw a cartoon of it that you'll understand.
I think when we think of historical physics discoveries, we often think of the Eureka! moment. Someone writes a great paper, and all the problems are solved as it clicks into place. I'm suspicious of this narrative, because that's not how the field of HTSC looks. It will be a slow and incremental progression. Slowly working out incomprehensible technicalities. But afterwards it will have looked simple. We'll have a nice cartoon, and we'll tell stories about the scientists who, in a flash of brilliance, dreamed up those cartoons.
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