I agree that more information would help the beauty, but I'm more interested in the issue of whether or not the question, as stated, is ill-posed.

One of the Bayesian vs. frequentist examples that I found most interesting was the case of the coin with unknown bias -- a Bayesian would say it has 50% chance of coming up heads, but a frequentist would refuse to assign a probability. I was wondering if perhaps this is an analogous case for Bayesians.

That wouldn't necessarily mean anything is wrong with Bayesianism. Everyone has to draw the line somewhere, and it's good to know where.

That's fine. I guess I'm just not a Bayesian epistemologist.

If Sleeping Beauty is a Bayesian epistemologist, does that mean she refuses to answer the question as asked?

It illustrates fairly clearly how probabilities are defined in terms of the payoff structure (which things will have payoffs assigned to them and which things are considered "the same" for the purposes of assigning payoffs).

I've felt for a while that probabilities are more tied to the payoff structure than beliefs, and this discussion underlined that for me. I guess you could say that using beliefs (instead of probabilities) to make decisions is a heuristic that ignores, or at least downplays, the payoff structure.

We know she will have the same credence on monday as she does on tuesday (if awakened), because of the amnesia. There is no reason to double count those.

Well, she does say it twice. That seems like at least a potential reason to count it as two answers.

You could say that 1/3 of the times the question is asked, the coin came up heads. You could also say that 1/2 of the beauties are asked about a coin that came up heads.

To me, this reinforces my doubt that probabilities and beliefs are the same thing.

EDIT: reworded for clarity

I agree, but I upvoted it anyway because I thought it was interesting and funny.

I read it as a commentary on how, when we daydream about "breaking the rules" (or discovering a fundamental rule that changes the way we live) all the myths have trained us to think selfishly. She wants to use her three wishes to end disease for everyone, and it's like she asked to accept an Academy Award in a clown suit.

EDIT: grammar

A theologian, a lawyer, and a rationalist meet at a cocktail party.

"Theology is the most intellectually demanding field," says the theologian. "The concepts are so abstract, and many key texts are obscurely written."

"Oh please," says the lawyer. "I once knew a bright fellow who became a theologian because he couldn't make it as a lawyer. He read and studied and tore his hair out, but he just couldn't get how the law works."

"I've got you both beat," says the rationalist. "Rationalism is so hard, no one's figured it out!"

EDIT: Too bad there's no prize for the lowest rated joke. Sorry if this joke offended people. It wasn't meant to reflect badly on any of the characters or anyone in real life.

And it certainly doesn't help that most peoples' knowledge of non-Earth gravity comes entirely from television, where, since zero-gravity filming is impractical, the writers invariably come up with some sort of confusing phlebotinum (most commonly magnetic boots) to make them behave more like regular-gravity environments.

I think you're on to something. I was wondering why the "heavy boots" people singled out the boots. Why not say "heavy suits" or that the astronauts themselves were heavier than pens. Didn't 2001: A Space Odyssey start the first zero-gravity scene with a floating pen and a flight attendant walking up the wall?

You should offer a reward for the best top-level anti-cryonics post. Something to entice quiet dissenters to stick their necks out.

You can post it together with a pro-cryonics reading list, so people know what they're up against and only post arguments that haven't already been refuted.

EDIT: reworded for clarity, punctuation

I'm telling it to give the reader the feeling of what it's like to see a smart person fail at something basic because they fail to cross domains, but when writing I couldn't actually come up with a real example that was simple enough to fit in one paragraph.

I would suggest the example of someone not getting the evil bit joke.

It's good because it works both ways. You only need common sense to understand it, but lay people can be intimidated by the context into not applying common sense, and you'll sometimes see domain experts try to implement essentially the same thing because they turn off common sense while in their domain.

I think that, in this case, the underlying problem was not caused by the way frequentist statistics are commonly taught and practiced by working scientists:

In the present case, the null hypothesis is that the old method and the new method produce data from the same distribution; the authors would like to see data that do not lead to rejection of the null hypothesis.

I'm no statistician, but I'm pretty sure you're not supposed to make your favored hypothesis the null hypothesis. That's a pretty simple rule and I think it's drilled into students and enforced in peer review.

I see that as the underlying problem because it reverses the burden of proof. If they had done it the right way around, six data points would have been not enough to support their method instead of being not enough to reject it. Making your favored hypothesis the null hypothesis can allow you, in the extreme, to rely on a single data point.