Though, formalizing this intuition is murder. Literally.

No, murder requires that you kill someone (there are extra moral judgements necessary but the killing is rather unambiguous.)

In that case, Archimedes and his successors spend a few hundred years working on the problem, and then recalibrate the chronophone to communicate over a correspondingly shorter interval, just so they can seem smarter by giving the answer immediately.

Of course this is true, as far as it goes.

But I'm inferring something from it in context that you perhaps don't mean, and I'd like to clarify. (Assuming you even read comments from this far back.)

Specific example: a couple of months after you posted this, I suffered a brain aneurysm that significantly impaired my working memory, to the point where even elementary logic problems -- the sort that currently would barely register as problems that needed solving in the first place - required me to laboriously work them out with paper and pen. (Well, marker... my fine motor control was shot, also.)

The question arises: could I have passed this initiation ceremony?

I certainly could not have given the right answer. It would have been a challenge to repeat the problem, let alone solve it, in a verbal examination. My reply would in fact have been "I'm not sure. May I have a pen and paper?"

If the guide replies more or less as you do here, then I fail.

I draw attention to two possibilities in that scenario:

(A) This is a legitimate test of rationality, and I failed it. I simply was less rational while brain-damaged, even though it didn't seem that way to me. That sort of thing does happen, after all.

(B) This test is confounding rationality with the ability to do mental arithmetic reliably. I was no less rational then than I am now.

If A is true, then you and the guide would be correct to exclude me from the club, and all is as it should be.

But if B is true, doing so would be an error. Not because it wasn't fair, or wasn't my fault, or anything like that, but because you'd be trying to build a group of rationalists while in fact excluding rationalists based on an irrelevant criterion.

Now, perhaps the error is negligible. Maybe the Bayesian Conspiracy will collect enough of the most rational minds of each generation that it's not worth giving up the benefits of in-group formation to attract the remainder.

OTOH, maybe not... in which case the Bayesian Conspiracy is on the wrong track.

I'd lay a high likelihood that you have quite a few more advantages than the kind of person I'm thinking of. You probably have your fair number of disadvantages too, but you've (through being lucky enough to have good health, intelligence, time and/or money for education and maybe good friends/family for support) been able to overcome those "on your own" (except for the aforementioned support)... which means you are categorically not the kind of person I'm thinking of when I am talking about people that need more support than others.

Some people need extra, and those people do try to pay for their extra.. but even so... some of them will still not be able to, due to circumstances that isn't their fault.

Do you condemn to death?

No one has complicated thoughts about several dreams from totally different genres while experiencing that one is unable to move a muscle without being awake.

...I've had some pretty complicated dreams, where I've woken up from a dream(!), gone to work, made coffee, had discussions about the previous dream, had thoughts about the morality or immorality of the dream, then sometime later come to a conclusion that something was out of place(I'm not wearing pants?!) then woken up to realize that I was dreaming. I've had nested dreams a good couple of layers deep with this sort of thing going on.

That said I think you have something there, though. Sometimes I wake up (Dream or otherwise) and I remember my dream really vividly, especially when I awake suddenly, due to an alarm clock or something

But I've never had a dream that I struggled to remember what was in my dream inside of my dream. At the least, such an activity should really raise my priors that I'm toplevel.

I think it's more complex than that.

Zaire's argument is that some people actually need more of "the pie" than others. Equal portions aren't necessarily fair, in that situation.

For example: would it be fair if every person on the globe got an equal portion of diabetic insulin? No, obviously not. We disproportionately give insulin to diabetics. Because that is more fair than to distribute it equally amongst all people (regardless of their health situation).

The disagreement here is between two perfectly understandable concepts of fairness. Both of them make sense in different ways. I see no easy solution to this myself.

There's also a linguistic issue here. The English "and" doesn't simply mean mathematical set theoretical conjunction in everyday speech. Indeed, without using words like "given" or "suppose" or a long phrase such as "if we already know that", we can't easily linguistically differentiate between P(Y | X) and P(Y, X).

"How likely is it that X happens and then Y happens?", "How likely is it that Y happens after X happened?", "How likely is it that event Y would follow event X?". All these are ambiguous in everyday speech. We aren't sure whether X has hypothetically already been observed or it's a free variable, too.