I disagree. Intelligence makes its own rules once it is there; but the human brain is one of the most arbitrary and hard-to-understand pieces of equipment that we know about. There have been a lot of very smart people trying to build AI for a very long time; if the creation of intelligence were highly non-arbitrary and followed well-known rules, we would have working AI by now.
I agree that intelligence itself is an optimizing process (which I presume is what you mean by “making its own rules”), but it is also the product of an optimizing process, natural selection. Your claim that it is arbitrary confuses the map and the territory. Just because we don’t fully understand the rules governing the functioning of the brain does not mean it is arbitrary. Maybe it is weak evidence for this claim, but I think that is swamped by the considerable evidence that intelligence is exquisitely optimized for various quite complex purposes (and also that it operates in accord with the orderly laws of nature).
Also, smart people have been able to build AIs (albeit not AGIs), and the procedure for building machines that can perform intelligently at various tasks involves quite a bit of design. We may not know what rules govern our brain, but when we build systems that mimic (and often outperform) aspects of our mental function, we do it by programming rules.
I suspect, though, that we are talking past each other a bit here. I think you’re using the words “random” and “arbitrary” in ways with which I am unfamiliar, and, I must confess, seem confused. In what sense is the second horn of your dilemma an “arbitrary universe [coming] into existence with random (and suspiciously orderly) laws”? What does it mean to describe the universe as arbitrary and random while simultaneously acknowledging its orderliness? Do you simply mean “uncaused”, because (a) that is not the only alternative to theism, and (b) I don’t see why one would expect an uncaused universe (as opposed to a universe picked using a random selection process) not to have orderly laws.
Fair enough. Then let me put it this way; if God is not sufficiently intelligent, then God would be unable to create the ordered universe that we see; in this case, an ordered universe would be no more likely than it would be without God. An ordered universe is therefore evidence in favour of the claim that if God exists, then He is sufficiently intelligent to create an ordered universe.
OK, but this doesn’t respond to Eliezer’s point. If you conditionalize on the existence of (a Christianish) God, then plausibly an intelligent God is more likely than an unintelligent one, given the orderliness of the universe. But Eliezer was contesting your claim that the orderliness of the universe is evidence for the existence of God, while also not being evidence for the existence of a Metagod.
So Eliezer’s question is, if P(orderliness | God) > P(orderliness | ~God), then why not also P(intelligent God | Metagod) > P(intelligent God | ~Metagod)? Your response is basically that P(intelligent God | God & orderliness) > P(~intelligent God | God & orderliness). How does this help?
I don’t really follow this. Things in Platonia or Tegmark level IV don’t have separate probabilities Any coherent mathematical stucture is guranteed 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.
In what sense is the second horn of your dilemma an “arbitrary universe [coming] into existence with random (and suspiciously orderly) laws”? What does it mean to describe the universe as arbitrary and random while simultaneously acknowledging its orderliness? Do you simply mean “uncaused”, because (a) that is not the only alternative to theism, and (b) I don’t see why one would expect an uncaused universe (as opposed to a universe picked using a random selection process) not to have orderly laws.
What I mean is, not planned. If I toss a fair coin ten thousand times, I have an outcome (a string of heads and tails) that would be arbitrary and random. It is possible that this sequence will be an exactly alternating sequence of heads and tails (HTHTHTHTHTHT...) extending for all ten thousand tosses (a very orderly result); but if I were to actually observe such an orderly result, I would suspect that there is an intelligent agent controlling that result in some manner. (That is what I mean by ‘suspiciously orderly’ - it’s orderly enough to suggest planning).
So Eliezer’s question is, if P(orderliness | God) > P(orderliness | ~God), then why not also P(intelligent God | Metagod) > P(intelligent God | ~Metagod)? Your response is basically that P(intelligent God | God & orderliness) > P(~intelligent God | God & orderliness). How does this help?
Well, it makes sense that P(intelligent God | Metagod) > P(intelligent God | ~Metagod). And therefore P(Metagod | Metametagod) > P(Metagod | ~Metametagod), and so on to infinity; but an infinity of metagods and metametagods and so on is clearly an absurd result. The chain has to stop somewhere, and that ‘somewhere’ has to be with an intelligent being. Therefore, there has to be an intelligent being that can either exist without being created by an intelligent creator, or that can create itself in some sort of temporal loop. (As I understand it, the atheist viewpoint is that a human is an intelligent being that can exist without requiring an intelligent creator).
And my point was that P(intelligent God | ~Metagod) is non-zero. The chain can stop. P(Metagod | intelligent God) may be fairly high; but P(Metametagod | intelligent God) must be lower (since P(Metametagod | Metagod) < 1). If I go far enough along the chain, I expect to find that P(Metametametametametametametagod | intelligent God) is fairly low.
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.
I agree that intelligence itself is an optimizing process (which I presume is what you mean by “making its own rules”), but it is also the product of an optimizing process, natural selection. Your claim that it is arbitrary confuses the map and the territory. Just because we don’t fully understand the rules governing the functioning of the brain does not mean it is arbitrary. Maybe it is weak evidence for this claim, but I think that is swamped by the considerable evidence that intelligence is exquisitely optimized for various quite complex purposes (and also that it operates in accord with the orderly laws of nature).
Also, smart people have been able to build AIs (albeit not AGIs), and the procedure for building machines that can perform intelligently at various tasks involves quite a bit of design. We may not know what rules govern our brain, but when we build systems that mimic (and often outperform) aspects of our mental function, we do it by programming rules.
I suspect, though, that we are talking past each other a bit here. I think you’re using the words “random” and “arbitrary” in ways with which I am unfamiliar, and, I must confess, seem confused. In what sense is the second horn of your dilemma an “arbitrary universe [coming] into existence with random (and suspiciously orderly) laws”? What does it mean to describe the universe as arbitrary and random while simultaneously acknowledging its orderliness? Do you simply mean “uncaused”, because (a) that is not the only alternative to theism, and (b) I don’t see why one would expect an uncaused universe (as opposed to a universe picked using a random selection process) not to have orderly laws.
OK, but this doesn’t respond to Eliezer’s point. If you conditionalize on the existence of (a Christianish) God, then plausibly an intelligent God is more likely than an unintelligent one, given the orderliness of the universe. But Eliezer was contesting your claim that the orderliness of the universe is evidence for the existence of God, while also not being evidence for the existence of a Metagod.
So Eliezer’s question is, if P(orderliness | God) > P(orderliness | ~God), then why not also P(intelligent God | Metagod) > P(intelligent God | ~Metagod)? Your response is basically that P(intelligent God | God & orderliness) > P(~intelligent God | God & orderliness). How does this help?
I don’t really follow this. Things in Platonia or Tegmark level IV don’t have separate probabilities Any coherent mathematical stucture is guranteed 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.
What I mean is, not planned. If I toss a fair coin ten thousand times, I have an outcome (a string of heads and tails) that would be arbitrary and random. It is possible that this sequence will be an exactly alternating sequence of heads and tails (HTHTHTHTHTHT...) extending for all ten thousand tosses (a very orderly result); but if I were to actually observe such an orderly result, I would suspect that there is an intelligent agent controlling that result in some manner. (That is what I mean by ‘suspiciously orderly’ - it’s orderly enough to suggest planning).
Well, it makes sense that P(intelligent God | Metagod) > P(intelligent God | ~Metagod). And therefore P(Metagod | Metametagod) > P(Metagod | ~Metametagod), and so on to infinity; but an infinity of metagods and metametagods and so on is clearly an absurd result. The chain has to stop somewhere, and that ‘somewhere’ has to be with an intelligent being. Therefore, there has to be an intelligent being that can either exist without being created by an intelligent creator, or that can create itself in some sort of temporal loop. (As I understand it, the atheist viewpoint is that a human is an intelligent being that can exist without requiring an intelligent creator).
And my point was that P(intelligent God | ~Metagod) is non-zero. The chain can stop. P(Metagod | intelligent God) may be fairly high; but P(Metametagod | intelligent God) must be lower (since P(Metametagod | Metagod) < 1). If I go far enough along the chain, I expect to find that P(Metametametametametametametagod | intelligent God) is fairly low.
Does that help?
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.