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Note: the hypothesis submitted by the people who proposed the experiment was correct:

(Written before watching)

Skill #1. I would have failed this if I had not had the opportunity explicitly pointed out to me.

Skill #2.

a. Water forms a cylindrical shell around the towel.

b. Water is pushed into the parts of the towel which are least compressed, but does not exit from the towel.

c. Water flies off from towel equally in all directions perpendicular to the towel axis.

d. Water adheres to towel, in a spiral pattern following the way the towel is wrung out.

e. (Something else I haven't thought of.)

Skill #3. I'm not really sure what you mean by "incorporate prior information", and how it differs from skill #2/4. To generate the possibilities in number 2, I used my model of how wrung towels behave on earth, and my knowledge of how things behave in space, mostly from Don Pettit videos (which I assume is also the source of the linked video). But I don't really have clear physical intuitions about the situation, nor do I have enough knowledge of physics to be able to work it out.

Skill #4. Of my options in number 2, I'd go for c. 20% d. 10% a. 10% b. 5%. ( therefore e. 100-45=55%) Note: I was loath to put down numbers, because I have basically no way to calibrate those guesses, but in the spirit of the exercise, those are as close to my true expectations as I can manage. On reflecting, I do actually expect greater than even odds that none of my answers are right, so even though it feels like cheating to say " 55% something I haven't thought of", I'm sticking with it.

(Video watching time) Skill #5. I can see in a very superficial way why it works the way it does. I don't think this equates to real understanding though.

Skill #6. So first of all, it wasn't Don Pettit. So I lose points there. :p Secondly, the answer is somewhere between my prediction a. and my non-prediction e. I don't think I can chalk that down as a win. Partial success: something I hadn't thought of happened (water moving onto the hands), which I had predicted at 55%. Partial failure: something I had thought of happened (water forming a cylindrical shell around the towel), but I had only predicted it was 10% likely. Neither of these are clear cut, you could swap the labels of "success" and "failure" and not be inaccurate…

Thanks for the puzzle!

ETA: line breaks, formatting

To be fair, we do also owe it to those who are effected by our actions (e.g. our children).

As a non-American, the way I listen to American public radio is via podcasts. And the programmes that I listen to are, in general, about topics I find interesting.

What about the aliens who landed on earth, murdered Fred and then went away again? Or the infinite number of other possibilities, each of which has a very small probability?

What confuses me about this is that, if we do accept that there are an infinite number of possibilities, most of the possibilities must have an infinitesimal probability in order for everything to sum to 1. And I don't really understand the concept of an infinitesimal probability -- after all, even my example above must have some finite probability attached?

This! I had already emailed Eliezer about this, so I was delighted when he mentioned it in the preamble for the current chapter (71).

An advantage that hasn't been mentioned thus far: audiobooks are very useful for people who are visually impaired.

Woah, I think that's a little overconfident...

You're saying that in the mid nineteenth century (half a century before relativity), the anomalous precession of Mercury made it seem 99.999999% likely that Newtonian mechanics was wrong?

After all, there are other possibilities.

cf. "When it was noticed in the 1800's that the perihelion of Neptune did not match what Newton's inverse-square law of gravity predicted, did we change the way math works? Or did we change our understanding of gravity?" In this case we actually postulated the existence of Pluto.

Similar solutions were suggested for the Mercury case, e.g. an extremely dense, small object orbiting close to Mercury.

And that's leaving aside the fact that 99.999999% is an absurdly high level of confidence for pretty much any statement at all (see ).

If I were a nineteenth century physicist faced with the deviations in the perihelion of Mercury, I'd give maybe a 0.1% probability to Newton being incorrect, a 0.001% probability to maths being incorrect, and the remaining ~99.9% would be shared between incorrect data /incomplete data/ other things I haven't thought of.

However, I agree that we can probably be more confident of results in maths than results in experimental science. (I was going to distinguish between mathematical/empirical results, but given that the OP was to do with the empirical confirmation of maths, I thought "mathematical/experimental" would be a safer distinction)

The vim movement keys actually work surprisingly well in Dvorak. Up/Down are next to each other on your left hand, right/left are on the appropriate sides of your right hand.