« This seems like a bad idea when the laws of physics as far as we can tell don't seem to allow you to simulate n particles interacting with fewer than n particles. »
Hum, it does allow it, if you are allowed to take some precision loss/uncertainity. You can't simulate exactly n particles with fewer than n particles, but if you're allowed to make some mistakes, to lose some information you can gain a lot in term of "simulated particles"/"real particles" ratio. And somehow, quantum mechanics does look like it loses precision, throw dices, do "lossy compression" and then estimate probabilities to get us back a result. (That's if you forget about Many Worlds, but I don't think a simulation would run Many Worlds). When see the laws of QM, it somehow feels like the kind of quirks I could make in implementing a simulator (and relativity, by limiting the interactions to near objects, would allow to split the computing over a cluster efficiently). But that's just a wild thought, I didn't take the time (yet) to really ponder it much.
When see the laws of QM, it somehow feels like the kind of quirks I could make in implementing a simulator
It feels like it, but if anything it's the opposite. It's my experience that many people on the border between CS and physics have this thought. However, it's actually much harder to simulate quantum systems than classical systems, and in fact quantum simulation is one of the reasons physicists are interested in quantum computers. (Other people are interested in other problems that quantum computers can do better than classically.)
Let P(chr) = the probability that the statements attributed to Jesus of Nazareth and Paul of Tarsus regarding salvation and the afterlife are factually mostly correct; and let U(C) be the utility of action C, where C is in {Christianity, Islam, Judaism, atheism}.
Two of the key criticisms of Pascal's wager are that
If, however, P(chr) is not infinitessimal, and U(Christianity) is merely very large, these counter-arguments fail.
Many poor arguments have been made that P(chr) > .1. But as far as I know, no one has ever made the best argument in favor of Christianity:
If you accept the simulation argument, then P(sim) > .99.
If you look at the fraction of computing power used for entertainment, I don't know what it is, but the top 100 supercomputer list for June 2011 lists a total of 4,531,940 cores in the top 100 supercomputers in the world; versus (rough guess) a billion personal computers and video game consoles, and a similar number of ordinary computers used at work. It would be reasonable to set p(ent|sim) = .5.
If you set P(ego|ent, sim) according to the fraction of entertainment simulations in which the person playing the game has an avatar in the game, then P(ego|ent, sim) is large. I originally set this at p > .99, but am now setting it to p = .5 in response to Jack's comment below.
We notice there are no obviously immortal world leaders on Earth (but see vi21maobk9vp's comment below). If we therefore limit the possible avatars that our simulator God is using on Earth to the major monotheistic religions of Christianity, Islam, and Judaism, and consider them all equiprobable; plus a 25% chance that this God is jumping from one avatar to another, or chose to reveal Himself via Jesus but then Paul screwed everything up, or some other minority position; then p(chr0|ego, ent, sim, Earth) = .25.
P(follow-thru) is difficult to estimate; I will set it somewhat arbitrarily as .1. Given our observations of game-players here on Earth, it is not independent of p(ego), as players of self-glorifying games are likely to be young adolescent males, and so are people who enjoy burning insects with magnifying glasses.
We now have p(chr) > .99 x .5 x .5 x .25 x .1 = .0061875. As stipulated, your afterlife accounts for at least 99% of your utility if follow-thru (and hence chr) is true. If we suppose that the length of time for which God rewards us in Heaven or torments us in Hell has an exponential distribution, and we are considering only the part of that distribution where >= 99% of your utility is in the afterlife, then almost certainly p(chr) * U(Christianity | chr) > (1-p(chr)) * U(atheism | not(chr)). It now appears we should accept Pascal's wager.
(The expected utilities for Christianity and Islam are similar, and this argument gives no reason for favoring one over the other. That is of only minor interest to me unless I accept the wager. The important point is that they both will have expected utilities similar to, and possibly exceeding, that of atheism.)
You can argue with any of the individual numbers above. But you would have to make pretty big changes to make p(chr)(U(Christianity|chr)) negligible in your utility calculation.
(IMHO, voting this article up should indicate it passed the threshold, "That's an interesting observation that contributes to the discussion", not, "Omigod you're right, I am going out to get baptized RIGHT NOW!".)