Ben: It's simulations all the way up.

Stephen, thanks for your thoughts on Eli's thoughts. I'm going to have to think on them further - after all these helpful posts I can pretend I understand quantum mechanics, but pretending to understand how conscious minds perceive a single point in configuration space instead of blobs of amplitude is going to take more work.

I will point out, though, that the question of how consciousness is bound to a particular branch (and thus why the Born rule works like it does) doesn't seem that much different from how consciousness is tied to a particular point in time or to a particular brain when the Spaghetti Monster can see all brains in all times and would have to be given extra information to know that my consciousness seems to be living in *this* particular brain at *this* particular time.

Finally: "it is a common misconception that should be addressed at some point anyway" - it appears to me that Robin's paper is based on this same misconception, or something like it: the Born rule (and experiment!) give one result while counting worlds gives another, therefore we have to add a new rule ("worlds that are too small get mangled") in order to make counting worlds match experiment. Whereas without the misconception we wouldn't be counting worlds in the first place. Do you think I'm understanding Robin's position and/or QM correctly?

Thanks to Eliezer's QM series, I'm starting to have enough background to understand Robin's paper (kind of, maybe). And now that I do (kind of, maybe), it seems to me that Robin's point is completely demolished by Wallace's points about decoherence being continuous rather than discrete and therefore there being no such thing as a number of discrete worlds to count.

There seems to be nothing to resolve between the probabilities given by measure and the probabilities implied by world count if you simply say that measure is probability.

Eliezer objects. We're interpreting. We're adding something outside the mathematics.

I fail to see the problem.

If we're to accept that particles moving like billiard balls are an illusion, and configuration space is real, and blobs of amplitude are real, and time evolution of amplitude within configuration space according to the wave equations is real, and that configurations and amplitude and wave equations are fundamental parts of reality, because that's the best model we've come up with that agrees with experimental observation... why not accept that the modulus-squared law is real and fundamental, too?

It certainly agrees with experimental observations, and doesn't seem any less desirable a part of our model of reality than configurations, amplitude blobs, and wave equations.

I wish someone would explain the problem more clearly, although if Eliezer's explanations so far haven't cleared it up for me yet, perhaps nothing will.

Eliezer: So when I say that two punches to two faces are twice as bad as one punch, I mean that if I would be willing to trade off the distance from the status quo to one punch in the face against a billionth (probability) of the distance between the status quo and one person being tortured for one week, then I would be willing to trade off the distance from the status quo to two people being punched in the face against a two-billionths probability of one person being tortured for one week.

So alternatives that have twice the probability of some good thing X happening have twice the utility? A sure gain of a dollar has twice the utility of a gaining a dollar on a coin flip? Insurance companies and casinos certainly think so, but their customers certainly don't.

I think you are conflating utility and expected utility. I'm not convinced they are the same thing, although I think you believe they are.

There are no natural utility differences that large. (Eliezer, re 3^^^3)

You've measured this with your utility meter, yes?

If you mean that it's not possible for there to be a utility difference that large, because the smallest possible utility shift is the size of a single particle moving a planck distance, and the largest possible utility difference is the creation or destruction of the universe, and the scale between those two is smaller than 3^^^3 ... then you'll have to remind me again where all these 3^^^3 people that are getting dust specks in their eyes live.

If 3^^^3 makes the math unnecessary because utility differences can't be that large, then your example fails to prove anything because it can't take place. For your example to be meaningful, it is necessary to postulate a universe in which 3^^^3 people can suffer a very small harm, which necessarily implies that yes, in fact, it is possible in this hypothetical universe for one thing to have 3^^^3 times the utility of something else. At which point, in order to prove that the dust specks outweigh the torture, you will now have to shut up and multiply. And be sure to show your work.

Your first task in performing this multiplication will be to measure the harm from torture and dust specks.

Good luck.