I think it's reasonable not to count any religions that don't have a single head God.
That adds a lot more religions. And then one has to treat the different forms of the major religions separately. The extremist Catholic and Jack Chick fanatic both think the other is going to hell. As to being restricted to religions where there is a single head God, have you heard of MMPORGs?
And it's reasonable not to count religions that have lost - if God really was the god of the Aboriginal dream-time, It would have quit or restarted by now.
Or it is really annoyed at how it lost against the computer played religions and is running the simulation for a few more seconds from its perspective seeing if on an off chance its religion becomes more popular again.
(There's a fundamental problem with any sort of Pascal's Wager situation like this. One can keep constructing narratives like the above. And it isn't at all clear how likely they are.)
But BQP lies in PP and therefore lies in fact in PSPACE.
You totally lost me.
BQP is the set of problems that can be in some sense quickly solved on a quantum computer. BQP lies in the class PP) and therefore lies in the class of PSPACE which is the set of problems which on a classical (deterministic) computer can be solved with memory bounded by a polynomial on the size of the input. Now, if there were some m such that is possible to simulate m+1 particles with m particles (possibly with some slowing things down), then one can by iterating this simulate n particles for any n. So the only restriction of what you can simulate with your m particles is time-based, not space based. In particular, you can use the particles to simulate things that require more space than PSPACE allows.
But I can simulate m particles with an appropriate number of qbits. So, putting it all together, I'd have to conclude that BQP doesn't lie in PSPACE. That's a contradiction.
Quantum mechanics can be construed as a way to limit computation and avoid arithmetic overflows.
This seems strange to me. Quantum computational issues are if anything much tougher than standard, deterministic computations. It is very difficult to simulate using normal computers the behavior of even a handful of particles in a quantum mechanical setting. We also know that there are things that a quantum computer can do that an equivalent classical machine simply cannot do in reasonable time. The most prominent example is Grover's algorithm. I don't see how quantum mechanics limits computation or avoids arithmetic overflows. If anything, it strongly suggests that we're not in a classical simulation.
No one plays computer games in which their avatar claims to be the God running the simulation. That wouldn't be fun - it would break God's suspension of disbelief.
This assumes an extremely narrow cognitive attitude. Note how many people when playing games like WoW are more than willing to give their characters names which strongly don't support suspension of disbelief. (Tangent: I sort of see where you are going here. When my brother and I were much younger we played some games like Phantasie and I'd actually go and try to give the characters fanstasy sounding names while he'd name them things like wiz1, wiz2, fig1, fig2, etc.)
You'll forgive me if these numbers look just slightly too convenient.
I find them highly inconvenient.
What I mean is that you had as one of your inputs a number that by your own description was nearly completely arbitrary and then ended up with a result that was a tiny bit over 1%, which was just the value you needed given your earlier assumptions. This looks a lot like there was an attempt, either conscious or unconscious to pick values that made your argument go through.
We also know that there are things that a quantum computer can do that an equivalent classical machine simply cannot do in reasonable time.
I thought it was still an open question whether there are computations that a classical computer is necessarily slower at than a quantum computer. From Aaronson's Philosophy/Comp-Complexity paper, p.35 :
...More generally, that quantum computers can solve certain problems superpolynomially faster than classical computers is not a theorem, but a (profound, plausible) conjecture. [49] [50]
Footnote 49: A formal version
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!".)