Intelligence itself is highly non-arbitrary and rule-governed
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.
So, yes; I think that intelligence can arise from arbitrary randomness. I’d go further, and claim that if it can’t arise from arbitrary randomness then it can’t exist at all; either intelligence arose in the form of God who then created an orderly universe (the theist hypothesis), or an arbitrary universe came into existence with random (and suspiciously orderly) laws that then led to intelligence in the form of humanity (the atheist hypothesis).
So in this particular case, no, I don’t think you can assume that if God exists, then He is sufficiently intelligent, just like I can’t respond to your original point by assuming that if the universe exists, then it is orderly.
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.
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 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.
It’s not arbitrary in the sense of random. It’s arbitrary in the sense of not following obvious apriori principles. It may impose its own higher-order rules, but that is something that happens in a system that already combines order and chaos in a very subtle and hard to duplicate way. Simple, comprehensible order of the kind you detect and admire in the physical unverse at large is easier to do than designing a brain. No one can build an AGI, but physicists build models of physical systems all the time.
It’s not arbitrary in the sense of random. It’s arbitrary in the sense of not following obvious apriori principles.
Agreed. The human brain is the output of a long, optimising process known as evolution.
Simple, comprehensible order of the kind you detect and admire in the physical unverse at large is easier to do than designing a brain. No one can build an AGI, but physicists build models of physical systems all the time.
Yes. Simple, comprehensible order is one of the easiest things to design; as you say, physicists do it all the time. But a lot of systems that are explicitly not designed (for example, the stock market) are very chaotic and extremely hard to model accurately.
Why is positing unobserved Matrix Lords better than positing unobserved randomness or unobserved failed universes?
Those options would also explain the observations that I am basing my argument on. I don’t have any argument for why any one of those options is at all better than any other one.
I’m not sure I understand your argument, then. If intelligence can arise from “arbitrary randomness”, then a universe that contains intelligence is evidence neither for nor against a creator deity, once you take the anthropic principle into account.
Yes, intelligence can arise from arbitrary randomness; I’m not using intelligence as evidence of an intelligent Creator. Using intelligence as an indicator of anything falls foul of anthropic principles.
My argument is that a universe that’s as straightforward, as comprehensible in its natural laws, as our universe seems about as unlikely as tossing a coin ten thousand times and getting an exact alternating pattern of heads and tails (HTHTHTHTHTHT...), or a lottery draw that consists of the numbers 1, 2, 3, 4, 5, 6 in that order.
Isn’t this just the anthropic principle in action ? Mathematically speaking, the probability of “123456” is exactly the same as that of “632415″ or any other sequence. We humans only think that “123456” is special because we especially enjoy monotonically increasing numbers.
Isn’t this just the anthropic principle in action ?
I’m not sure. The anthropic principle is arguing from the existence of an intelligent observer; I’m arguing from the existence of an orderly universe. I don’t think that the existence of an orderly universe is necessarily highly correlated with the existence of an intelligent observer. Unfortunately, lacking a large number of universes to compare with each other, I have no proof of that.
Mathematically speaking, the probability of “123456” is exactly the same as that of “632415″ or any other sequence. We humans only think that “123456” is special because we especially enjoy monotonically increasing numbers.
Yes. I do not claim that the existence of an orderly universe is undeniable proof of the existence of God; I simply claim that it is evidence which suggests that the universe is planned, and therefore that there is (or was) a Planner.
Consider the lottery example; there are a vast number of sequences that could be generated. Such as (35, 3, 19, 45, 15, 8). All are equally probable, in a fair lottery. However, in a biased, unfair lottery, in which the result is predetermined by an intelligent agent, the sort of patterns that might appeal to an intelligent agent (e.g. 1, 2, 3, 4, 5, 6) are more likely to turn up. So P(bias|(1, 2, 3, 4, 5, 6)) > P(bias|(35, 3, 19, 45, 15, 8)).
anthropic principle is arguing from the existence of an intelligent observer; I’m arguing from the existence of an orderly universe. I don’t think that the existence of an orderly universe is necessarily highly correlated with the existence of an intelligent observer.
This depends on the direction of correlation doesn’t it? It could well be that P[Observer|Orderly universe] is low (plenty of types of order are uninhabitable) but that P[Orderly universe|Observer] is high since P[Observer|Disorderly universe] is very much lower than P[Observer|Orderly universe]. So, for example, if reality consists of a mixture of orderly and disorderly universes, then we (as observers) would expect to find ourselves in one of the “orderly” ones, and the fact that we do isn’t much evidence for anything.
Another thought is whether there are any universes with no order at all? You are likely imagining a “random” universe with all sorts of unpredictable events, but then are the parts of the universe dependent or independent random variables? If they are dependent, then those dependencies are a form of order. If they are independent, then the universe will satisfy statistical laws (large number laws for instance), so this is also a form of order. Very difficult to imagine a universe with no order.
It could well be that P[Observer|Orderly universe] is low (plenty of types of order are uninhabitable) but that P[Orderly universe|Observer] is high since P[Observer|Disorderly universe] is very much lower than P[Observer|Orderly universe].
Yes, it could be. And if this is true, then my line of argument here falls apart entirely.
Another thought is whether there are any universes with no order at all? You are likely imagining a “random” universe with all sorts of unpredictable events, but then are the parts of the universe dependent or independent random variables? If they are dependent, then those dependencies are a form of order. If they are independent, then the universe will satisfy statistical laws (large number laws for instance), so this is also a form of order. Very difficult to imagine a universe with no order.
Huh. A very good point. I was thinking in terms of randomised natural laws—natural laws, in short, that appear to make very little sense—but you raise a good point.
Hmmm… one example of a randomised universe might be one wherein any matter can accelerate in any direction at any time for absolutely no reason, and most matter does so on a fairly regular basis (mean, once a day, standard deviation six months). If the force of the acceleration is low enough (say, one metre per second squared on average, expended for an average of ten seconds), and all the other laws of nature are similar to our universe (so still a mostly orderly universe) then I can easily imagine intelligence arising in such a universe as well.
Hmmm… one example of a randomised universe might be one wherein any matter can accelerate in any direction at any time for absolutely no reason, and most matter does so on a fairly regular basis
Well let’s take that example, since the amount of “random acceleration” can be parameterised. If the parameter is very low, then we’re never going to observe it (so perhaps our universe actually is like this, but we haven’t detected it yet!) If the parameter is very large, then planets (or even stars and galaxies) will get ripped apart long before observers can evolve.
So it seems such a parameter needs to be “tuned” into a relatively narrow range (looking at orders of magnitude here) to get a universe which is still habitable but interestingly-different from the one we see. But then if there were such an interesting parameter, presumably the careful “tuning” would be noticed, and used by theists as the basis of a design argument! But it can’t be the case that both the presence of this random-acceleration phenomenon and its absence are evidence of design, so something has gone wrong here.
If you want a real-word example, think about radioactivity: atoms randomly falling apart for no apparent reason looks awfully like objects suddenly accelerating in random directions for no reason: it’s just the scale that’s very different. Further, if you imagine increasing the strength of the weak nuclear force, you’ll discover that life as we know it becomes impossible… whereas, as far as I know, if there were no weak force at all, life would still be perfectly possible (stars would still shine, because that ’s the strong force, chemical reactions would still work, gravity would still exist and so on). Maybe the Earth would cool down faster, or something along those lines, but it doesn’t seem a major barrier to life. However, the fact that the weak force is “just in the right range” has indeed been used as a “fine-tuning” argument!
Dark energy (or a “cosmological constant”) is another great example, perhaps even closer to what you describe. There is this mysterious unknown force making all galaxies accelerate away from each other, when gravity should be slowing them down. If the dark energy were many orders of magnitude bigger, then stars and galaxies couldn’t form in the first place (no life), but if it were orders of magnitude smaller (or zero), life and observers would get along fine. By plotting on the right scale (e.g. compared to a Planck scale), the dark energy can be made to look suspiciously small and “fine-tuned”, and this is the basis of a design argument.
You raise a good point, and I do indeed see the pattern that you are claiming. I personally suspect that radioactivity, and dark energy, will both turn out to be inextricably linked to the other rules of the universe; I understand that that is already the case for the weak force, apparently a different aspect of electromagnetism (which is exceedingly important for our universe).
Yes. I do not claim that the existence of an orderly universe is undeniable proof of the existence of God; I simply claim that it is evidence which suggests that the universe is planned, and therefore that there is (or was) a Planner.
Wait, isn’t the Planner basically God, or at least some kind of a god ?
However, in a biased, unfair lottery, in which the result is predetermined by an intelligent agent, the sort of patterns that might appeal to an intelligent agent (e.g. 1, 2, 3, 4, 5, 6) are more likely to turn up.
That would be an interesting test to run, actually, regardless of theism or lack thereof: are sequential numbers more likely (or perhaps less likely) than chance in our current American lottery ? If so, it would be pretty decent evidence that the lottery is rigged (not surprising, since it was in fact designed by intelligent agents, namely us humans).
That depends on the value of P(Agent prefers sequential numbers|Agent is intelligent).
In any case, are sequential numbers more likely to turn up in sequences that are not directly controlled by humans, f.ex. rolls of reasonably fair dice ?
Wait, isn’t the Planner basically God, or at least some kind of a god ?
Yes. That was my point.
That would be an interesting test to run, actually, regardless of theism or lack thereof: are sequential numbers more likely (or perhaps less likely) than chance in our current American lottery ? If so, it would be pretty decent evidence that the lottery is rigged (not surprising, since it was in fact designed by intelligent agents, namely us humans).
Hmmm. I’m not sure about the American lottery, but the South African one has 49 numbers, from which 6 are chosen (for the moment, I shall ignore the bonus ball). There are 44 sets of sequential numbers; a set of sequential numbers should be drawn, in sequential order, an average of once in 228 826 080 draws; or drawn in any order (e.g. 6, 3, 4, 2, 5, 1) once every 317814 draws.
There have been, to date, 1239 draws. These results are available. There is just under a 0.4% chance that at least one of these sets of results would consist of six sequential numbers, in any order. There is a 99.6109% chance that none of the draws consist of six sequential numbers, drawn in any order.
I imported the data above into a spreadsheet, looked at the difference between the highest and the lowest numbers in each draw, and then found the minimum of those differences; it is 10. Therefore, the South African lottery has never had six sequential numbers drawn, in any order. This is the result that I would expect from an unrigged draw.
That depends on the value of P(Agent prefers sequential numbers|Agent is intelligent).
Surely it depends more directly on the value of P(Agent is intelligent|Agent prefers sequential numbers)? To convert between those requires Bayes’ Theorem, which depends on finding a good approximation for P(Agent is intelligent), which is going to be a whole debate on its own.
I think I may have misread your previous statement then:
I do not claim that the existence of an orderly universe is undeniable proof of the existence of God; I simply claim that it is evidence which suggests that the universe is planned, and therefore that there is (or was) a Planner.
But since you agreed that the Planner is basically God, I read that sentence as saying,
I do not claim that the existence of an orderly universe is undeniable proof of the existence of God; … it is evidence which suggests that the was planned by a God.
Is the only difference between the two statements the “undeniable” part ? If so, then I get it.
Surely it depends more directly on the value of P(Agent is intelligent|Agent prefers sequential numbers)?
My point was that it’s possible that any intelligent agent who developed via some form of evolution would be more likely to prefer sequential numbers, merely as an artifact of its development. I’m not sure how likely this is, however.
Is the only difference between the two statements the “undeniable” part ? If so, then I get it.
Yes. That is correct. I see the orderly universe as evidence of God, but not as undeniable proof thereof.
My point was that it’s possible that any intelligent agent who developed via some form of evolution would be more likely to prefer sequential numbers, merely as an artifact of its development. I’m not sure how likely this is, however.
...hmmm. It is possible. I’m not sure how that can be measured, or what difference to my point it would make if true, though.
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.
So, yes; I think that intelligence can arise from arbitrary randomness. I’d go further, and claim that if it can’t arise from arbitrary randomness then it can’t exist at all; either intelligence arose in the form of God who then created an orderly universe (the theist hypothesis), or an arbitrary universe came into existence with random (and suspiciously orderly) laws that then led to intelligence in the form of humanity (the atheist hypothesis).
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.
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.
It’s not arbitrary in the sense of random. It’s arbitrary in the sense of not following obvious apriori principles. It may impose its own higher-order rules, but that is something that happens in a system that already combines order and chaos in a very subtle and hard to duplicate way. Simple, comprehensible order of the kind you detect and admire in the physical unverse at large is easier to do than designing a brain. No one can build an AGI, but physicists build models of physical systems all the time.
Agreed. The human brain is the output of a long, optimising process known as evolution.
Yes. Simple, comprehensible order is one of the easiest things to design; as you say, physicists do it all the time. But a lot of systems that are explicitly not designed (for example, the stock market) are very chaotic and extremely hard to model accurately.
I still don’t see why you would think order of a kind comprehensible to humans in the universe is evidence it was designed by a much smarter entity.
I’m trying to use it as evidence that it was designed at all.
Would it’s being designed by a Matrix Lord of non-superhuman intelligence help your case?
It would certainly explain the observations that I am using as evidence.
Why is positing unobserved Matrix Lords better than positing unobserved randomness or unobserved failed universes?
Those options would also explain the observations that I am basing my argument on. I don’t have any argument for why any one of those options is at all better than any other one.
The zero-one-infinity rule might help you out.
So, you’re suggesting there should be either zero, one, or a potentially infinite number of Matrix Lords, and never (say) exactly three?
Did you mean to say “can not” in that sentence ?
No, I did not.
I’m not sure I understand your argument, then. If intelligence can arise from “arbitrary randomness”, then a universe that contains intelligence is evidence neither for nor against a creator deity, once you take the anthropic principle into account.
Yes, intelligence can arise from arbitrary randomness; I’m not using intelligence as evidence of an intelligent Creator. Using intelligence as an indicator of anything falls foul of anthropic principles.
My argument is that a universe that’s as straightforward, as comprehensible in its natural laws, as our universe seems about as unlikely as tossing a coin ten thousand times and getting an exact alternating pattern of heads and tails (HTHTHTHTHTHT...), or a lottery draw that consists of the numbers 1, 2, 3, 4, 5, 6 in that order.
Isn’t this just the anthropic principle in action ? Mathematically speaking, the probability of “123456” is exactly the same as that of “632415″ or any other sequence. We humans only think that “123456” is special because we especially enjoy monotonically increasing numbers.
I’m not sure. The anthropic principle is arguing from the existence of an intelligent observer; I’m arguing from the existence of an orderly universe. I don’t think that the existence of an orderly universe is necessarily highly correlated with the existence of an intelligent observer. Unfortunately, lacking a large number of universes to compare with each other, I have no proof of that.
Yes. I do not claim that the existence of an orderly universe is undeniable proof of the existence of God; I simply claim that it is evidence which suggests that the universe is planned, and therefore that there is (or was) a Planner.
Consider the lottery example; there are a vast number of sequences that could be generated. Such as (35, 3, 19, 45, 15, 8). All are equally probable, in a fair lottery. However, in a biased, unfair lottery, in which the result is predetermined by an intelligent agent, the sort of patterns that might appeal to an intelligent agent (e.g. 1, 2, 3, 4, 5, 6) are more likely to turn up. So P(bias|(1, 2, 3, 4, 5, 6)) > P(bias|(35, 3, 19, 45, 15, 8)).
This depends on the direction of correlation doesn’t it? It could well be that P[Observer|Orderly universe] is low (plenty of types of order are uninhabitable) but that P[Orderly universe|Observer] is high since P[Observer|Disorderly universe] is very much lower than P[Observer|Orderly universe]. So, for example, if reality consists of a mixture of orderly and disorderly universes, then we (as observers) would expect to find ourselves in one of the “orderly” ones, and the fact that we do isn’t much evidence for anything.
Another thought is whether there are any universes with no order at all? You are likely imagining a “random” universe with all sorts of unpredictable events, but then are the parts of the universe dependent or independent random variables? If they are dependent, then those dependencies are a form of order. If they are independent, then the universe will satisfy statistical laws (large number laws for instance), so this is also a form of order. Very difficult to imagine a universe with no order.
Yes, it could be. And if this is true, then my line of argument here falls apart entirely.
Huh. A very good point. I was thinking in terms of randomised natural laws—natural laws, in short, that appear to make very little sense—but you raise a good point.
Hmmm… one example of a randomised universe might be one wherein any matter can accelerate in any direction at any time for absolutely no reason, and most matter does so on a fairly regular basis (mean, once a day, standard deviation six months). If the force of the acceleration is low enough (say, one metre per second squared on average, expended for an average of ten seconds), and all the other laws of nature are similar to our universe (so still a mostly orderly universe) then I can easily imagine intelligence arising in such a universe as well.
Well let’s take that example, since the amount of “random acceleration” can be parameterised. If the parameter is very low, then we’re never going to observe it (so perhaps our universe actually is like this, but we haven’t detected it yet!) If the parameter is very large, then planets (or even stars and galaxies) will get ripped apart long before observers can evolve.
So it seems such a parameter needs to be “tuned” into a relatively narrow range (looking at orders of magnitude here) to get a universe which is still habitable but interestingly-different from the one we see. But then if there were such an interesting parameter, presumably the careful “tuning” would be noticed, and used by theists as the basis of a design argument! But it can’t be the case that both the presence of this random-acceleration phenomenon and its absence are evidence of design, so something has gone wrong here.
If you want a real-word example, think about radioactivity: atoms randomly falling apart for no apparent reason looks awfully like objects suddenly accelerating in random directions for no reason: it’s just the scale that’s very different. Further, if you imagine increasing the strength of the weak nuclear force, you’ll discover that life as we know it becomes impossible… whereas, as far as I know, if there were no weak force at all, life would still be perfectly possible (stars would still shine, because that ’s the strong force, chemical reactions would still work, gravity would still exist and so on). Maybe the Earth would cool down faster, or something along those lines, but it doesn’t seem a major barrier to life. However, the fact that the weak force is “just in the right range” has indeed been used as a “fine-tuning” argument!
Dark energy (or a “cosmological constant”) is another great example, perhaps even closer to what you describe. There is this mysterious unknown force making all galaxies accelerate away from each other, when gravity should be slowing them down. If the dark energy were many orders of magnitude bigger, then stars and galaxies couldn’t form in the first place (no life), but if it were orders of magnitude smaller (or zero), life and observers would get along fine. By plotting on the right scale (e.g. compared to a Planck scale), the dark energy can be made to look suspiciously small and “fine-tuned”, and this is the basis of a design argument.
Do you see the pattern here?
You raise a good point, and I do indeed see the pattern that you are claiming. I personally suspect that radioactivity, and dark energy, will both turn out to be inextricably linked to the other rules of the universe; I understand that that is already the case for the weak force, apparently a different aspect of electromagnetism (which is exceedingly important for our universe).
Wait, isn’t the Planner basically God, or at least some kind of a god ?
That would be an interesting test to run, actually, regardless of theism or lack thereof: are sequential numbers more likely (or perhaps less likely) than chance in our current American lottery ? If so, it would be pretty decent evidence that the lottery is rigged (not surprising, since it was in fact designed by intelligent agents, namely us humans).
That depends on the value of P(Agent prefers sequential numbers|Agent is intelligent).
In any case, are sequential numbers more likely to turn up in sequences that are not directly controlled by humans, f.ex. rolls of reasonably fair dice ?
Yes. That was my point.
Hmmm. I’m not sure about the American lottery, but the South African one has 49 numbers, from which 6 are chosen (for the moment, I shall ignore the bonus ball). There are 44 sets of sequential numbers; a set of sequential numbers should be drawn, in sequential order, an average of once in 228 826 080 draws; or drawn in any order (e.g. 6, 3, 4, 2, 5, 1) once every 317814 draws.
There have been, to date, 1239 draws. These results are available. There is just under a 0.4% chance that at least one of these sets of results would consist of six sequential numbers, in any order. There is a 99.6109% chance that none of the draws consist of six sequential numbers, drawn in any order.
I imported the data above into a spreadsheet, looked at the difference between the highest and the lowest numbers in each draw, and then found the minimum of those differences; it is 10. Therefore, the South African lottery has never had six sequential numbers drawn, in any order. This is the result that I would expect from an unrigged draw.
Surely it depends more directly on the value of P(Agent is intelligent|Agent prefers sequential numbers)? To convert between those requires Bayes’ Theorem, which depends on finding a good approximation for P(Agent is intelligent), which is going to be a whole debate on its own.
I think I may have misread your previous statement then:
But since you agreed that the Planner is basically God, I read that sentence as saying,
Is the only difference between the two statements the “undeniable” part ? If so, then I get it.
My point was that it’s possible that any intelligent agent who developed via some form of evolution would be more likely to prefer sequential numbers, merely as an artifact of its development. I’m not sure how likely this is, however.
Yes. That is correct. I see the orderly universe as evidence of God, but not as undeniable proof thereof.
...hmmm. It is possible. I’m not sure how that can be measured, or what difference to my point it would make if true, though.