but an infinity of metagods and metametagods and so on is clearly an absurd result.
That’s not clear.. There is presumably something like that in Tegmark’s level IV.
The chain has to stop somewhere, and that ‘somewhere’ has to be with an intelligent being.
You haven’t established the ‘has to’ (p==1.0). You can always explain Order coming from Randomness by assuming enough randomness. Any finite string can be found with p>0.5 in a sufficiently long infinite string. Assuming huge amounts of unobserved randomness is not elegant, but neither is assuming stacks of metagods. Your prreferred option is to reject god-needs-a-metagod without giving a reason, but just because the alternatives seem worse. But that is very much a subjective judgement.
That’s not clear.. There is presumably something like that in Tegmark’s level IV.
Assume that P(
%5E{x+1})god |
^{x})god) = Q, where Q < 1.0 for all x. Consider an infinite chain; what is P(
^{\infty})god|god)?
This would be lim{xtoinfty} P(
^{x})god|god) = Q∞. Since Q<1.0, this limit is equal to zero.
...hmmm. Now that I think about it, that applies for any constant Q. It may be possible to craft a function Q(x) such that the limit as x approaches infinity is non-zero; for example, if I set Q(1)=0.75 and then Q(x) for x>1 such that, when multiplied by the product of all the Q(x)s so far, the distance between the previous product and 0.5 is halved (thus Q(2)=5/6, Q(3)=9/10, Q(4)=17/18, and so on); then Q(x) asymptotically approaches 1, while P(
^{\infty})god|god) = 0.5.
You haven’t established the ‘has to’ (p==1.0)
You’re right, and thank you for pointing that out. I’ve now shown that p<1.0 (it’s still pretty high, I’d think, but it’s not quite 1).
You seem to be neglecting the possibility of a cyclical god structure. Something which might very well be possible in Tegmark level IV if all the gods are computable.
Not strictly speaking. Warning, what follows is pure speculation about possibilities which may have little to no relation to how a computational multiverse would actually work. It could be possible that there are three computable universes A, B & C, such that the beings in A run a simulation of B appearing as gods to the intelligences therein, the beings in B do the same with C, and finally the beings in C do the same with A. It would probably be very hard to recognize such a structure if you were in it because of the enormous slowdowns in the simulation inside your simulation. Though it might have a comparatively short description as the solution to a an equation relating a number of universes cyclically.
In case that wasn’t clear I imagine these universes to have a common quite high-level specification, with minds being primitive objects and so on. I don’t think this would work at all if the universes had physics similar to our own; needing planets to form from elementary particles and evolution to run on these planets to get any minds at all, not speaking of computational capabilities of simulating similar universes.
I don’t really follow this. Things in Platonia or Tegmark level IV don’t have separate probabilities Any coherent mathematical structure is guaranteed to exist. (And infinite ones are no problem). So the probabilty of a infinite stack of metagods depends on the coherence of a stack of metagods being considered a coherent mathematical structure, and the likelihood of our living in a Tegmark IV.
I don’t see why the probability would decompose into the probability of its parts—a T-IV is all or nothing, as far as I can see. It actually contains very little information .. it isn’t a very fine-grained region in UniverseSpace.
My intuition is that universes with more metagods will be less common in the space of all that can possibly be. We exist in a given universe, which is perforce a universe that can possibly be; I’m trying to guess which one.
T-IV is already a large chunk of UniverSpace—it is everything that is mathematically possible. The T-IV question is more about how large a region of UnverseSpace the universe is, than about pinpointing a small region.
That’s not clear.. There is presumably something like that in Tegmark’s level IV.
You haven’t established the ‘has to’ (p==1.0). You can always explain Order coming from Randomness by assuming enough randomness. Any finite string can be found with p>0.5 in a sufficiently long infinite string. Assuming huge amounts of unobserved randomness is not elegant, but neither is assuming stacks of metagods. Your prreferred option is to reject god-needs-a-metagod without giving a reason, but just because the alternatives seem worse. But that is very much a subjective judgement.
Assume that P(
This would be lim{xtoinfty} P(
...hmmm. Now that I think about it, that applies for any constant Q. It may be possible to craft a function Q(x) such that the limit as x approaches infinity is non-zero; for example, if I set Q(1)=0.75 and then Q(x) for x>1 such that, when multiplied by the product of all the Q(x)s so far, the distance between the previous product and 0.5 is halved (thus Q(2)=5/6, Q(3)=9/10, Q(4)=17/18, and so on); then Q(x) asymptotically approaches 1, while P(
You’re right, and thank you for pointing that out. I’ve now shown that p<1.0 (it’s still pretty high, I’d think, but it’s not quite 1).
You seem to be neglecting the possibility of a cyclical god structure. Something which might very well be possible in Tegmark level IV if all the gods are computable.
Huh. You are right; I had neglected such a cyclical god structure. That would appear to require time travel, at least once, to get the cycle started.
Not strictly speaking. Warning, what follows is pure speculation about possibilities which may have little to no relation to how a computational multiverse would actually work. It could be possible that there are three computable universes A, B & C, such that the beings in A run a simulation of B appearing as gods to the intelligences therein, the beings in B do the same with C, and finally the beings in C do the same with A. It would probably be very hard to recognize such a structure if you were in it because of the enormous slowdowns in the simulation inside your simulation. Though it might have a comparatively short description as the solution to a an equation relating a number of universes cyclically.
In case that wasn’t clear I imagine these universes to have a common quite high-level specification, with minds being primitive objects and so on. I don’t think this would work at all if the universes had physics similar to our own; needing planets to form from elementary particles and evolution to run on these planets to get any minds at all, not speaking of computational capabilities of simulating similar universes.
...congratulations. I thought time travel would be a neccesity, I certainly didn’t expect that intuition to be disproved so quickly.
It may be speculative, but I don’t see any glaring reason to disprove your hypothesised structure.
I don’t really follow this. Things in Platonia or Tegmark level IV don’t have separate probabilities Any coherent mathematical structure is guaranteed to exist. (And infinite ones are no problem). So the probabilty of a infinite stack of metagods depends on the coherence of a stack of metagods being considered a coherent mathematical structure, and the likelihood of our living in a Tegmark IV.
Ah. I was trying to—very vaguely—estimate the probability that we live in such a universe.
I hope that closes the inferential gap.
I don’t see why the probability would decompose into the probability of its parts—a T-IV is all or nothing, as far as I can see. It actually contains very little information .. it isn’t a very fine-grained region in UniverseSpace.
My intuition is that universes with more metagods will be less common in the space of all that can possibly be. We exist in a given universe, which is perforce a universe that can possibly be; I’m trying to guess which one.
T-IV is already a large chunk of UniverSpace—it is everything that is mathematically possible. The T-IV question is more about how large a region of UnverseSpace the universe is, than about pinpointing a small region.
Ah. Then I think we’ve been talking past each other for some time now.