As an aside; the use of "Org" (i.e. Rationality Org) seems really unusual and immediately makes me think of Scientology (Sea Org); am I unusual in having this reaction?

I posted this originally in the discussion section but deleted it since JGWeissman suggested that the meetup post be in the front page. Sark reposted this since I haven't been posting almost anything on LW, I didn't have enough karma to put the post on the front page.

To reiterate, I will be there and sark will almost certainly be there.

I've noticed lately a lot of websites seem to use some bizarre font that looks awful. But since they keep doing it, I'm beginning to wonder if it's just me that sees it looking awful. Does it look like this for anyone else?

http://img268.imageshack.us/img268/7224/fontyo.png

Either the answer is even in every possible world, or it is odd in every possible world.

Which is the case? What do you do if you're uncertain about which is the case?

Imagine this scenario happens 10000 times, with different formulae.

Given our prior, 5000 of the times the actual answer is even, and 5000 times the answer is odd.

In 4950 of the 5000 Q-is-even cases, the calculator says <correct answer>. And in the other 50 cases of Q-is-even, the calculator says <incorrect answer>. Then, in 4950 of the Q-is-odd cases, the calculator says <correct answer> and in 50 cases it says <incorrect answer>. Note that we still have 9900 cases of <correct answer> and 100 cases of <incorrect answer>.

Omega presents you with a counterfactual world that might be one of the 50 cases of Q-is-even, <incorrect-answer> or one of the 4950 cases of Q-is-odd, <correct answer>. So you're equally likely (5000:5000) to be in either scenario (Q-is-odd, Q-is-even) for actually writing down the right answer (as opposed to writing down the answer the calculator gave you).

We are in the world where the calculator displays even, and we are 99% sure it is the world where the calculator has not made an error. This is Even World, Right Calculator. Counterfactual worlds:

• Even World, Wrong Calculator (1% of Even Worlds)
• Odd World, Right Calculator (99% of Odd Worlds)
• Odd World, Wrong Calculator (1% of Odd Worlds)

All Omega told us was that the counterfactual world we are deciding for, the calculator shows Odd. We can therefore eliminate Odd World, Wrong Calculator. Answering the question is, in essence, deciding which world we think we're looking at.

So, in the counterfactual world, we're either looking at Even World, Wrong Calculator or Odd World, Right Calculator. We have an equal prior for the world being Odd or Even - or, we think the number of Odd Worlds is equal to the number of Even Worlds. We know the ratio of Wrong Calculator worlds to Right Calculator worlds (1:99). This is, therefore, 99% evidence for Odd World. The correct decision for the counterfactual you in that world is to decide Odd World. The correct decision for you?

Ignoring Bostrom's book on how to deal with observer selection effects (did Omega go looking for a Wrong Calculator world and report it? Did Omega go looking for an Odd World to report to you? Did Omega pick at random from all possible worlds? Did Omega roll a three-sided die to determine which counterfactual world to report?), I believe the correct decision is to answer Odd World for the counterfactual world, with 99% certainty if you are allowed to specify as such.

I reason that by virtue of it being a counterfactual world, it is contingent on my not having the observation of my factual world; factual world observations are screened off by the word "counterfactual".

The other possibility (which I tentatively think is wrong) is that our 99% confidence of Even World (from our factual world) comes up against our 99% confidence of Odd World (from our counterfactual) and they cancel out, bringing you back to your prior. So you should flip a coin to decide even or odd. I think this is wrong because 1) I think you could reason from 50% in the countefactual world to 50% in the factual world, which is wrong, and 2) this setup is identical to punching in the formula, pressing the button and observing "even", then pressing the button again and observing "odd". I don't think you can treat counterfactual worlds as additional observations in this manner.

edit: It occurs to me that with Omega telling you about the counterfactual world, you are receiving a second observation. For this understanding, you would specify Even World with 99% confidence in the factual world and either Even or Odd World depending on how the coin landed for the counterfactual world.

Nah. See, given that the real calculator says "even", there's a 0.99% chance that it's correct and that, in a repetition of the experiment, it would say incorrectly say "odd". There's also a 0.99% chance that the real calculator is incorrect and that, in a repetition of the experiment, it would correctly say "odd". The counterfactual case is just as likely to be the calculator being correct as the calculator being incorrect.

ETA: The above is wrong. I was confused about the problem because I wasn't thinking updatelessly. It's like Newcomb's problem.

Q is most likely even,

Derived from the likelihood of the calculator being in error

so in the counterfactual the calculator is most likely in error,

You can't conclude this - think about what evidence you have that the calculator is in error!

I'm not sure what to make of the fact that "lake" was the answer that jumped out at me.

My goodness, that bias is quite overcoming, wouldn't you say?