Equivocation. The algorithmic (Kolmogorov) complexity cost of the conjunction of “simulated X” and Y is finite, but the “real X” is infinite, therefore, the former must be preferred by Occam’s razor. “Simulated X” is a deception by aliens and is not a full halting oracle, but a finite approximation of one. It can’t do everything the “real X” could.
I do not believe that aliens are performing miracles, just that that explanation is infinitely more probable on priors than an omniscient God. The miracles you have pointed to so far are best explained as natural accidents or hoaxes, not nearly enough evidence to even suggest aliens.
Ok. Looks like we started to go on circle, sorry for not being clear enough. Let me try to explain once again.
You have a lot of observation data. You have significantly more potential observation data you can gather. I was considered before that all the potential observation data as finite—however, I understood that it is not so, for example, if scientific breakthrough, aliens or God will turn us into the immortal creatures with every year increasing ability to gather, remember, and process information.
So, you want to find a theory based on already observed data, that would predict the data that is not yet observed. I bet we both believe that it is possible to do, but with some limitations.
1. Does finite theory exactly predicting all data exists? (In a sense of the Turing machine). Since all the data is infinite, a prior probability for such theory would be zero—without any other assumptions. You can introduce strong assumption of predictivity, basically stating that such theory exists. However, I think that this assumption is too strong (based on a posteriori results of quantum mechanics where you can predict only the probability of the observation but not the definite outcome—so you can recover with your theory only part of the observed data). Instead I would suggest weak predictivity assumption:
2. The theory exactly predicting all the data is infinite (such infinite theories exist—for example “witch did it” where “it” is “all the data to be observed”); however, its finite approximations can predict some part of the data with some precision.
You can try to make it stricter, saying: “Among all the finite approximations there is one with maximal predictive power” but I do not see any arguments for it. The prior expectations tells that you can increase the precision by increasing the length of the theory.
Now, we would like to classify the finite approximations based on their precision and length. First, is just the reference to existence of exact infinite theory makes the theory under consideration infinite too? No—otherwise we need to acknowledge that Tegmark theory of mathematical multiverse (all the mathematically consistent worlds) is infinite. It refers to the existence of all the possible worlds, not describing each of them. The same, theory stating that the God knows everything does not state what exactly He knows. Thus, our approximation of infinite theory of omniscient God is just “God exists with such and such attributes” and it is finite. The approximation “aliens fake God with such and such attributes” is also finite but longer. It may seems better because “aliens faking God” can potentially be an approximation of the finite exact theory, predicting everything—however, as we discussed before, there is no reason to assume that such finite theory exists, and think that “aliens fake God” dominates “God exists” because the first is approximation of finite theory, and the second of the infinite. We compare the lengths of the approximations, not of the full theories, and the approximation “God exists” is shorter and thus should be preferred.
″ I do not believe that aliens are performing miracles, just that that explanation is infinitely more probable on priors than an omniscient God. The miracles you have pointed to so far are best explained as natural accidents or hoaxes, not nearly enough evidence to even suggest aliens. ”
Let us first fix the priors and then move to discussing miracles, ok?
Yes, I just started to notice that after re-reading this thread. It seems like we’re talking past each other without understanding. For Double Crux to work, we’re not supposed to aim for direct persuasion until after we’ve identified the double crux, or we’ll get “lost in the weeds” discussing the parts that aren’t important to us. Have we found it yet? I think we have not, and that’s what went wrong here.
I have yet to identify a single crux, but part of that might be because I don’t understand your concept of God. I don’t know what crux could possibly convince me your God exists, because I still don’t know what “God” means (to you).
I’m honestly not that familiar with the Eastern Orthodox tradition. Protestant sects are more common in my country. The God concept worshiped by the average churchgoer here seems laughably naiive, and logically incoherent, but it does have some differences with what you’ve described so far. And the apologists, even in my country, seem to have a different definition that the average churchgoer (in my country), probably because the naiive definition is so indefensible. It’s motte-and-bailey rhetoric—a combination of bait-and-switch with equivocation.
So I’ll ask again: Is omniscience a crux for you? That is, if a source you would consider authoritative (the bishops, the Patriarch, archeology, visions from God, whatever it takes) explained to you that omniscience was not an attribute of God as He revealed Himself, but a later misrepresentation made by sinful philosophers, would you then say your God does not exist?
If you answer, “Then my God still exists and is not quite omniscient as I had once believed,” then omniscience is not a necessary attribute for your God definition, and there is no need to discuss it further, because it is not a crux.
But, if you answer, “A ‘God’ that is not omniscient is no God of mine,” then omniscience is a crux for you and we need to nail down what that means, because it might be closely related to a crux of mine.
For Double Crux to work, we’re not supposed to aim for direct persuasion until after we’ve identified the double crux, or we’ll get “lost in the weeds” discussing the parts that aren’t important to us.
I’m not sure this is part of the authoritative definition of doublecrux, but FYI the way I personally think of it is “Debate is when you try to persuade the other person [or third parties] that you’re right and they’re wrong. Doublecrux is when you try to persuade _yourself_ that they’re right and you’re wrong, and your collective role as a team is to help each other with that.” (I don’t think this is quite right, obviously the goal is for both of you to move towards the truth together, whatever that may be, but I think the distinction I just made can sometimes be helpful for shaking yourself out of debate mode)
I’m not sure this is part of the authoritative definition of doublecrux,
I’m not sure if anyone has an authoritative definition of doublecrux yet. But as this is my first real attempt at it, I appreciate guidance. We did open with the Litany of Tarski, but I might have lost sight of that for a moment. I maintain that I at least need to understand what my interlocutor is saying before I can conclude that he is right.
you try to persuade yourself that they’re right and you’re wrong … (I don’t think this is quite right, obviously the goal is for both of you to move towards the truth together …
Again, the Litany of Tarski: If a God exists, I desire to believe that is the case. An update for either side is a victory. But the goal is not to fool myself or give up, or give in to confusion. The update must be an honest one, or the whole exercise is empty.
Wouldn’t the prior probability of God to exist be a crux for you? I.e., if you change your prior probability from infinitesimal to somewhat not negligibly small, would it change your position? At least the infinitesimal probability is a crux for me.
Let me also notice that our positions do not completely cover all the spectrum of possible answers (it not exactly “A” or “not A” ). I.e., as far as I get you think the world is completely controlled by laws of nature, I think there is a God as Eastern Orthodoxy describe it. In between there are many other options:
-simulation
-aliens
-Higher Power (includes my believe as particular case)
-the world that is not describable by math fully but only approximately
-and whatever else that just does not come to my mind
Wouldn’t the prior probability of God to exist be a crux for you? I.e., if you change your prior probability from infinitesimal to somewhat not negligibly small, would it change your position? At least the infinitesimal probability is a crux for me.
Getting past an infinitesimal prior to a tiny finite one is a long way from “more likely than not”.
But more simply, my prior is my position. If you get my prior belief for the proposition “God exists” over 50%, then you’ve won: at that point I’ve become a theist by definition (though maybe not a very confident one). This isn’t a crux—It’s the original proposition!
Errr not completely—you have prior and you have experience. For example, suppose you agree after long discussion that probability of God to exist is not infinitesimal but 0.01% . Ok, you are still more atheist than a theist. Then if you observe miracles you update it to much higher probability—but you can’t do it if your prior is infinitesimal as now.
What would you put your priors now for the following:
-the Universe is completely describable by a finite set of laws, no other reality behind
-the Universe is approximately describable by the finite set of laws, approximation improves with the length of the theory (need infinite theory to full description)
the Universe is completely describable by a finite set of laws, no other reality behind
I don’t consider this question well-posed. Physics seems to be working pretty well. But what do you mean by “Universe”? The part we can observe? Surely there’s more to it than that. And “laws” can be dependent on context. The law that objects accelerate downward at 9.8m/s/s doesn’t apply on Mars, but there’s a similar law with a lower number and an underlying law of gravity connecting both cases. Laws that seem to be “fundamental” now are probably dependent on local conditions. The “symmetry breaking” observed in particle physics indicates this. And very simple rules like Conway’s Life can produce very complex behavior, with emergent “laws”, like “gliders travel diagonally”. Is this law from a reality behind or in front of Life?
Ok, let us put it more strict. What are your priors that there exist a finite theory that can predict all our potential future observations exactly? And what are your priors that such theory does not exist and we can only use approximations?
N.B. By all observations I mean ALL observations, including the results of measurements in QM (not just their probabilities, we observe results too, right?)
I still don’t understand. Are you asking if the universe is deterministic?
Which sense of “exist” do you mean? Mathematically, where we can “have” imaginary things like infinite uncomputable sets, or physically, where we obviously can’t construct an object corresponding to such a thing?
Solomonoff induction cannot be run on real physics. It’s an abstracted ideal that can only be approximated. Maybe quantum field theory predicts the motion of particles to an accuracy of eleven digits, but that doesn’t mean you can use it to predict the weather. You don’t have enough computing power, and you don’t know the initial conditions to that precision anyway.
Even AIXI, an ideal agent using Solomonoff induction (which can’t be physically built), can only make probabilistic predictions based on observations made so far. There’s always an infinite class of universes (hypotheses) that have produced the observations thus far, and they always disagree on the next bit.
There’s no need to invoke quantum physics here. Given what we already know of relativistic physics, it’s always possible that a particle could approach at the speed of light and mess up your plans. Because it’s moving at light speed, there’s no way in principle you could have observed it to take it into account in advance. Even AIXI can be “surprised” by low-probability events like this, even in a deterministic universe (because it has only observed a small part of the universe so far), and it has infinite computing power!
Well, of course I do not suggest to predict the weather from the laws of QFT, I mean mathematically. Let us consider all possible future observations as a data. Do you think that it can be exactly generated by the theory of the finite length (as an output of the universal Turing machine with the theory as an input), or you would require an infinite length of the theory for the exact reproducing?
The observable universe probably has a finite number of possible states.
The laws of physics appear to be deterministic and Turing computable.
Therefore, an infinite theory would never be required. (And this makes me sympathetic to the ultrafinitists.) The laws of physics can be mapped to a Turing machine, and the initial conditions to a (large, but) finite integer. There is nothing else.
But I’m not sure that “all possible future observations” means what you think it means.
In the MWI, any observer is going to have multiple future Everett branches. That’s the indexical uncertainty. Before the timeline splits, there is simply no fact of the matter as to which “one” future you are going to experience: all of them will happen, but the branches won’t be aware of each other afterwards.
And MWI isn’t even required for indexical uncertainty to apply. A Tegmark level I multiverse is sufficient: if the universe is sufficiently large, whatever pattern in matter constitutes “you” will have multiple identical instances. There is no fact of the matter as to which “one” you are. The patterns are identical, so you are all of them. When you make a choice, you choose for all of them, because they are identical, they have no ability to be different. Atoms are waves in quantum fields and don’t have any kind of individual identity. You are your pattern, not your atoms. But, when they encounter external environmental differences, their timelines will diverge.
if the universe is sufficiently large, whatever pattern in matter constitutes “you” will have multiple identical instances. There is no fact of the matter as to which “one” you are. The patterns are identical, so you are all of them. When you make a choice, you choose for all of them, because they are identical, they have no ability to be different.
Copies of you that arise purely from the size of the universe will have the same counterfacutal or funcitonal behaviour, that is they will do the same thing under the same circumstances...but they will not, in general, do the same thing because they are not in the same circumstances. (There is also the issue that being in different circumstances and making different decisions will feed back into your personality and alter it).
The observable universe probably has a finite number of possible states.”
Not so sure about that. For this you need at least
1. The Universe to be finite (i.e. you can not have open Universe, only the surface of 4d sphere). It is possible, the measured curvature of the Universe is approximately on the boundary, but the open is also possible.
2. The Universe to be discrete on microscale. Again, according to some theories it is the case, according to the others, it is not.
So, I would say: “maybe yes, it is finite, but the prior probability is far from being 1 ”.
Side note: the Universe with finite number of states is quite depressive picture since it means that inevitably everything will just end up in the highest entropy state, so, the inevitable end of humanity. Of course, it contradicts nothing, but in this model any discussion of existential threats for the humanity (like superintelligence quite popular here) makes no sense since the end is unavoidable.
″ And MWI isn’t even required for indexical uncertainty to apply. A Tegmark level I multiverse is sufficient: if the universe is sufficiently large, whatever pattern in matter constitutes “you” will have multiple identical instances. There is no fact of the matter as to which “one” you are. The patterns are identical, so you are all of them. When you make a choice, you choose for all of them, because they are identical, they have no ability to be different. Atoms are waves in quantum fields and don’t have any kind of individual identity. You are your pattern, not your atoms. But, when they encounter external environmental differences, their timelines will diverge. ”
Could you please explain it in more details? I am confused. If I measure the spin of the electron that is in the superposition of spin up and spin down, I obtain with probability p spin up and with probability 1-p spin down. How to exactly predict using Tegmark multiverse when I see spin up and when I see spin down?
Could you please explain it in more details? I am confused. If I measure the spin of the electron that is in the superposition of spin up and spin down, I obtain with probability p spin up and with probability 1-p spin down. How to exactly predict using Tegmark multiverse when I see spin up and when I see spin down?
I’m not saying that a Tegmark I multiverse is equivalent to MWI, that’s actually Tegmark III. I’m saying that Tegmark I is sufficient to have indexical uncertainty, which looks like branching timelines, even if MWI is not true. See Nick Bostrom’s Anthropic Bias for more on this topic.
Only if you’re interested. I haven’t actually read the whole book myself, but I have read LessWrong discussions based on it. I think the Sleeping Beauty problem illustrates the important parts we were talking about.
Ah, I think I got the point, thank you. However, it does not resolve all questions.
1. You can’t deduce Born’s rule—only postulate it.
2. Most important, it does not give you a prediction what YOU will observe (unlike hidden parameters—they at least could do it). Yes, you know that some copies will see X, and some will see Y, but it is not an ideal predictor, because you can’t say beforehand what you will see, in which copy you will end up. So all your future observed data can not be predicted, only the probability distribution can be.
Can’t you? Carroll calls it “self-locating uncertainty”, which is a synonym for the “indexical uncertainty” we’ve been talking about. I’ll admit I don’t know enough quantum physics to follow all the math in that paper.
Most important, it does not give you a prediction what YOU will observe (unlike hidden parameters—they at least could do it). Yes, you know that some copies will see X, and some will see Y, but it is not an ideal predictor, because you can’t say beforehand what you will see, in which copy you will end up.
Yeah, in this scenario, the “YOU” doesn’t exist. Before the split, there’s one “you”, after, two. But even after the split happens, you don’t know which branch you’re in until after you see the measurement. Even an ideal reasoner that has computed the whole wavefunction can’t know which branch he’s on without some information indicating which.
So all your future observed data can not be predicted, only the probability distribution can be.
More or less. You can compute all the branches in advance, but don’t necessarily know where you are after you get there. The past timeline is linear, and the future one branches.
″ Can’t you? Carroll calls it “self-locating uncertainty”, which is a synonym for the “indexical uncertainty” we’ve been talking about. I’ll admit I don’t know enough quantum physics to follow all the math in that paper. ”
That was super cool, thank you a lot for this link!
Side note: the Universe with finite number of states is quite depressive picture since it means that inevitably everything will just end up in the highest entropy state, so, the inevitable end of humanity.
Yes, according to our best current understanding of cosmology, the universe itself will eventually die (i.e. become unable to sustain life).
Of course, it contradicts nothing, but in this model any discussion of existential threats for the humanity (like superintelligence quite popular here) makes no sense since the end is unavoidable.
Again the laws of physics are what they are and don’t care what I want.
But in the most likely scenarios, this will take a very long time. The Stelliferous Era (when the stars shine) is predicted to last 100 trillion years, and we’re not even 14 billion years into it. Civilization may continue to extract energy from black holes for a time many orders of magnitude longer than that.
It’s not completely hopeless. Maybe in that time we’ll figure out how to make basement universes and transfer civilization into a new one, as Nick Bostrom et al have argued may be possible.
But even if we ultimately can’t, shouldn’t we try? Shouldn’t we do the best we can? Wouldn’t you rather live for over 100 trillion years than die at 120 at best?
″ It’s not completely hopeless. Maybe in that time we’ll figure out how to make basement universes and transfer civilization into a new one, as Nick Bostrom et al have argued may be possible. ”
Yeah, you see then all the future possible observations data becomes infinite.
″ But even if we ultimately can’t, shouldn’t we try? Shouldn’t we do the best we can? Wouldn’t you rather live for over 100 trillion years than die at 120 at best? ”
Of course, we should try—because there is a chance that we can. Not because we would live 10^14 years and all die. We will count that we survive forever, or it will be pretty miserable 10^14 years without any hope.
The observable universe probably has a finite number of possible states.”
Not so sure about that.
Not sure either, which is why I said “probably”.
For this you need at least
The Universe to be finite (i.e. you can not have open Universe, only the surface of 4d sphere). It is possible, the measured curvature of the Universe is approximately on the boundary, but the open is also possible.
Note that I said “observable universe”, not “multiverse” or “cosmos”. There are regions of the universe that are not accessible because they are too far away, the universe is expanding, and the speed of light is finite. This limit is called the Cosmic event horizon
The Universe to be discrete on microscale. Again, according to some theories it is the case, according to the others, it is not.
I think it is sufficient to say that the information content of the observable universe is finitely bounded. Space doesn’t necessarily have to be made of pixels like some cellular automaton for this to hold. The Bekenstein bound is proven from Quantum Field Theory. How true QFT is, is another question, but experimental evidence proves that it is very true.
″ Note that I said “observable universe”, not “multiverse” or “cosmos”. There are regions of the universe that are not accessible because they are too far away, the universe is expanding, and the speed of light is finite. This limit is called the Cosmic event horizon ”
On the one hand side, you are totally correct about it—assuming cosmological constant (lambda-term ) stays what it is. There are nuances however:
-if we are forever in the de Sitter space (lambda dominated, as now) the universe is explicitly not time-invariant (simply because it extending). There is non-zero particle production rate, for example (analog of Hawking radiation). It means that we potentially can construct a “first kind perpetuum mobile” which means that we can get to any energy—infinite space for the observations. Unless this will start to have a screening effect on lambda-term.
-If lambda desreases (or screened) the expansion may go back from lambda-dominated to matter-dominated, leading to its slowing down. In this case we can start observing areas of the universe that used to be beyond the horizon.
Anyway, there are a lot of speculations what can be and what can not. Can we maybe agree that both prior probabilities: that all our possible future observations are finite and that they are infinite are not negligible? What about 1⁄2 for each, to start with?
Anyway, there are a lot of speculations what can be and what can not.
I worry we may be getting lost in the weeds again. We need to try and find cruxes. Is this related to a crux of yours? What exactly are you getting at?
prior probabilities: that all our possible future observations are finite and that they are infinite are not negligible?
Even if time could be extended infinitely without the universe dying, there is no time at which the infinity has been completed. It’s always finite so far.
An “immortal” being with finite memory in infinite time will eventually forget enough things to repeat itself in a loop, living the same life over and over again.
Can this be avoided? There are limits to any physical realization of memory. If you try to pack too many bits in a given volume of space, it will collapse into a black hole. And then adding anything more will make the event horizon bigger. Infinite memory requires infinite space and energy. Maybe with basement universes it could be done. They might have to communicate through wormholes or something. This is all very speculative, so I don’t know.
Well we can also make infinite memory (as you suggested). But, ok, what would you put as prior probability that the theoretically possible observation data is infinite? Looks like you are not strongly against it, so what about something between 0.5 and 0.1? (Of course we can’t strictly prove it right now). If you say “yes, this works” we can move on. If you would claim that this probability is also supertiny, like 10^(-1000) , I will continue to argue (well, yes, if we can not at all observe in all the infinite future infinite data, it does not make sense to talk about omniscient God).
To show you what I am leading to:
-if the total possible observation data is infinite, what is prior probability that it is exactly reproduced by finite hypothesis? I argue that it is infinitesimal
-what is the probability that there exist such infinite hypothesis? I argue that 1, for example, “witch did (copypaste all the data)”. Predictive force of this hypothesis is zero
-we need predictivity so we assume that there are finite approximations that can partially reproduce the data. Such assumption is less strong than assumption of the finite exact hypothesis so it should be preferred.
-therefore, we should use Solomonoff’s lightsaber not on full theories, but on approximmations
-consider two classes of approximations. The first gives exact predictions where it can and predicts nothing whee it can not. The second is weaker, it sometimes gives wrong predictions. Since the second is weaker, the priors for this are significantly higher. So, I would say, if observable data is infinite, most of our approximate theory have from time to time give wrong predictions
-this does not say, of course, how often are these wrong predictions. If they are too often, such approximation is useless.
-Basically, since predictions are laws of nature, wrong predictions are miracles. We should expect to them to exist but to be rare.
-Talking about aliens. Infinite hypothesis “God with such attributes exists” can be used only as approximation (that is, basically, our understanding of it). The finite hypothesis “aliens fake us to believe that God with such attributes exists” also can be used only as approximation, (that is our understanding of God + assumption that it is faked by aliens). Thus such approximation is longer and should be given smaller probability.
well, yes, if we can not at all observe in all the infinite future infinite data, it does not make sense to talk about omniscient God
You are not a future hyper-mind made of basement universes and wormholes. You’re a mortal human like me, with a lifespan measured in mere decades so far. Yet you claim to have knowledge of an infinite God. How did you come to this conclusion? By what method can you make such an assertion? Is this special pleading for a special case or do you use this method for anything else? Why should I consider that method sound and reliable?
My best guess: you were indoctrinated in childhood by your parents and community, long before you were old enough to develop critical thinking skills of your own. For obvious survival reasons, children are very inclined to learn from their parents and elders. The memeplex of any of the old religions must be self-sustaining, or they wouldn’t still be here. They include psychological tricks to produce fake evidence, to stop questions, to make empty threats. They include answers to your questions or at least pretend to. It became part of your identity. You later learned of the methods of science, but they didn’t become a part of you the same way. You compartmentalized the lessons and didn’t use them to update your old thinking. You sought out evidence to support your belief instead of trying to disprove it to see if it would hold up, like a scientist.
Most people seem to use this method. You are not alone. And that’s exactly the problem with it. People are using the same methods to believe in other religions that you already know to be false. How can that method be reliable if it so reliably produces the wrong answers? What makes you any different from them? Accident of birth. That’s it. Your methods are the same.
Maybe that’s a crux for me. If it could be shown that a God belief was founded on a sound epistemology that reliably produced good results, instead of these obvious fallacies, I would have a much harder time dismissing the proposition as a fraud.
” You sought out evidence to support your belief instead of trying to disprove it to see if it would hold up, like a scientist. ”
1. If I would do this I would never go to this website discussing this with you. Assume good intentions.
2. As you said, for infinitesimal prior probability no evidence is enough. That is what I am arguing here. If I get persuaded that probability is indeed infinitesimal, all my evidence are nothing. I can see resurrection of the deads and still it won’t be enough then.
3. I can blame the same thing on you. I am not going to guess but there are so many stories of atheists who became atheists just because God didn’t do what they asked. “I do not want to deal with such God that does not do what I want, therefore there is no God.”
Ok, let us go back to our business if you don’t mind.
″ If it could be shown that a God belief was founded on a sound epistemology that reliably produced good results, instead of these obvious fallacies, I would have a much harder time dismissing the proposition as a fraud. ”
First, could you review the previous comment to see if you agree with the logic, and if not, what do you disagree in particular.
Second, if you agree with this logic, you should acknowledge that there is not negligible prior probability that miracles exist in principle. You can claim that they are rare, and each time you do not observe the miracle you can say it is even more rare.
Third, if you acknowledge that the miracles can happen, it is worth looking at the cases when someone claim them to happen in particular. If you have large organised religion (like Catholic, Anglican, Russian churches for example) you very often have special commitee (usually with scientists inside) that check if the miracle that people claim to be miracle, is indeed miracle. Very often they found it to be hoax or natural effect, but sometimes they acknowledge that this is indeed miracle. Other religions may also have miracles, as well as just something outside religion, but there may be no developed institution of miracle verification.
If I would do this I would never go to this website discussing this with you.
A fair point. But I still think you are compartmentalizing.
for infinitesimal prior probability no evidence is enough.
It’s never enough for induction, performed correctly. But an a priori deductive argument maybe could work. I’ve heard theists attempt these arguments, but have not found them convincing.
I can blame the same thing on you.
I am trying to find cruxes, not blame. I would rather leave our identities out of it and examine the question as objectively and impartially as possible. But your epistemology is extremely relevant in this case. It’s the rights of Mortimer Q. Snodgrass again. I don’t think the God hypothesis has enough going for it to even justify raising it to our attention. If we had started with a good scientific epistemology, this would not even be a question. Instead we started with a biased indoctrination, and have to dig ourselves out of it.
I am not going to guess but there are so many stories of atheists who became atheists just because God didn’t do what they asked. “I do not want to deal with such God that does not do what I want, therefore there is no God.”
It’s the availability heuristic again. Who have you heard these stories from? It’s probably not the atheists themselves! You can’t trust the clergy to be honest about this topic. They believe atheism is damnation, and so must present it as a sin. But for those raised atheist with a scientific worldview, believing in God seems as silly as believing in Santa Claus or the Tooth Fairy.
In my case, I was raised as a believer. My perspective changed due to an accumulation of a number of factors. The Problem of Evil was apparent to me in childhood. It introduced a doubt that I could not resolve. The biblical creation story also didn’t align with what I read of science as a child.
When I expressed my misgivings, my church told me that God was a God of Truth, and the teachings of the Church could not possibly contradict the Truth, once it was properly understood. So I withheld judgement until I could learn more. I held both the religious and the scientific worldview in my mind at once, in the hope that they could eventually be unified. I was compartmentalizing, but I was conscious that I was doing so. I could speculate and philosophize in either religious or scientific modes, and I knew which was which. I saw the fruits of science. Computers and rocket ships and vaccines. I had church-related experiences I could only describe as spiritual. Surely they both had to be true?
I studied my faith in depth. I was warned of the sin of pride. I was uncertain how to interpret that, but after study, concluded that the problem with pride was an unwillingness to learn from error. I resolved to always be honest with myself. God was a God of Truth, after all, so honesty could not be wrong. I learned to think more critically. I found many satisfying answers, but my doubts on these points, and more, only deepened. There was evidence against the faith, that was for certain. Doubts remained, but abandoning my faith would mean damnation and I could never convince myself it was false beyond a reasonable doubt.
Then I learned that civil cases were judged according to the preponderance of the evidence, rather than beyond a reasonable doubt. In my commitment to honesty, I judged my faith again by this standard. Suddenly, many of the faith-promoting stories I had considered “evidence” no longer appeared that way. They were indistinguishable from no God at all. Once seen, I could not unsee it. Why was God pretending so hard not to exist? So we are less culpable for sins? Then why have a church at all? My faith was shaken (and not for the first time), but still I believed. I resolved to study more, to try and rebuild what I had lost.
In my church, we brethren sometimes minister to the other members, usually in pairs. I was usually too shy to participate, but I had studied enough to know answers from the scriptures. When ministering to one poor sister who was struggling, I went into religious mode and spouted off the relevant doctrine. This happened to be a point I had doubts about. And then the realization struck me: I didn’t believe a word of it. I sounded that confident, and I didn’t believe a word. I had lied to her. And worse I had lied to myself, the exact thing I had resolved not to do. I had so easily broken my commitment to honesty, just by studying doctrine. And if I could do it, so could any of the other members! They could sound so convicted, and yet not know! The testimony of the others I had been relying on may have been founded on nothing but air.
I still had my spiritual experiences, but they had always resisted critical examination. I finally understood that what I thought was the witness of the Holy Spirit, was only those around me interpreting my emotions for me in a certain way. They were spouting off doctrine memorized by repetition, the same as I had done to that poor sister. In another context, the same emotions could have been a witness for a completely different god. My faith was shattered to its very core.
My church regards all others as apostates. I had rejected them long ago. There was nowhere to turn. For a time, I considered myself agnostic. I told my story to a confidante, and she replied with something like, “so you’re an atheist then”. And in that moment, I realized it was true. I’m an atheist. I can’t believe in God anymore, even if I try.
And after reading the Sequences, and understanding Bayes, I realized that the faith-promoting stories I had thought were evidence, and then eventually no evidence at all, were actually evidence against the church. The church had actually been preemptively preaching some of its worst stories, so we would learn to think of them in the best possible light, before we had a chance to hear a more critical presentation from anyone else.
-Basically, since predictions are laws of nature, wrong predictions are miracles. We should expect to them to exist but to be rare.
Due to indexical uncertainty, we can always be surprised by low probability events. I don’t see these as evidence of God though.
-Talking about aliens. Infinite hypothesis “God with such attributes exists” can be used only as approximation (that is, basically, our understanding of it). The finite hypothesis “aliens fake us to believe that God with such attributes exists” also can be used only as approximation, (that is our understanding of God + assumption that it is faked by aliens). Thus such approximation is longer and should be given smaller probability.
Around in circles again, but is there a difference this time? Do we agree “fake alien God hypothesis” dominates “infinite God hypothesis”? When using induction? You don’t seem to be disputing it. But is “approximate God” simpler than “fake alien God”? That depends! How good is your approximation of “infinite”? How complex are your aliens?
But if you want to argue for a non-infinite God, that’s OK with me, but even if you convince me, it won’t be the infinite God you have convinced me of, but the finite approximation: Something more powerful than mankind, but not infinitely powerful. Something more knowledgeable than mankind, but not infinitely knowing… this sounds like you’re describing advanced aliens. They’re the same thing. I would then argue that the aliens are the reality and the “infinite God” is the approximation of them made by ignorant humans.
Even I would be willing to call such aliens “gods” given certain conditions, but we’re using your definition of “God”.
Can you convince me of approximately-God aliens? Maybe. My prior is not zero, but like the pet purple dragon from Mars, it would take a lot of evidence to convince me.
First, could you review the previous comment to see if you agree with the logic, and if not, what do you disagree in particular.
It feels like we are going around in circles at this point. I’m not sure where the disconnect is.
-if the total possible observation data is infinite, what is prior probability that it is exactly reproduced by finite hypothesis? I argue that it is infinitesimal
The set of all natural numbers is infinite, yet can be enumerated by a finite computer program (when run on an infinite computer, AKA, a Turing machine). There are many many other examples of infinite patterns enumerable by finite programs. And some of them, like “compute the digits of pi” seem pretty chaotic, yet their Kolmogorov complexity is small.
One wrinkle, which you might be alluding to, is that no program with infinite output ever halts. This is true, but there are halting programs that can compute any finite prefix of pi. And like I said before, at no point is your observation infinite. It’s always finite so far. The infinity is never completed.
So the hypothesis “these are the digits of pi” is considered by Solomonoff induction, but maybe it looks like a weighted sum of a class of programs that say “compute pi up to the nth digit” for some n. These still compress quite well, (especially for compressible n’s) so their Kolmogorov complexity is small. I don’t think this is an obstacle for Solomonoff induction.
Has Solomonoff induction got it wrong? Close but not quite? I would argue no. I don’t believe uncomputable sets can physically exist. There are no perfect circles. The abstraction called pi is the approximation, for whatever algorithm physics is actually running, which Solomonoff induction would eventually find.
Errr not completely—you have prior and you have experience.
The posterior becomes the next prior when updating again, so we still call it a “prior” even though this is not the same prior as before. Sorry for the confusion. My current prior is my current level of belief/confidence.
Then if you observe miracles you update it to much higher probability
Higher, yes, but (say) ten times almost nothing is still almost nothing. And that’s only if the likelihood ratio for the evidence favors the hypothesis by that much, which it doesn’t.
but you can’t do it if your prior is infinitesimal as now.
That’s right. No finite amount of evidence can overcome an infinitesimal prior.
Your example “miracles” are evidence in favor of miracles existing (because we can hardly expect reports of miracles to be less common if miracles exist) but the likelihood ratio is very close to 1 because false positives (accidents, hallucinations, and hoaxes) are so common. On priors, these explanations are far more likely. That means your “miracle” reports are extremely weak evidence.
I cannot lower my epistemic standards on this, or I would invite in flat-Earthers, UFO-ologists and various other conspiracy theorists, not to mention all the other religions who have similarly dubious paranormal claims. Why should I favor your paranormal claims over theirs? It’s special pleading.
Strong enough evidence can overcome a very low prior, yes. And this doesn’t have to take very many observations.
But more instances do not necessarily stack like that. That can only happen to the degree they are independent sources. For example, suppose you write a dubious claim in a book, then you make nine more copies of the book. Does that make the claim ten times more likely to be true? What if it’s a hundred thousand copies? Did that help?
Of course it doesn’t! You’re re-counting the same evidence. The contribution of the nine books is completely screened off by the first; the new books have no new information.
I think the cases of miracle reports like weeping icons are similarly not independent enough. A thousand weeping icons is barely more evidence than one. It just means that the hoaxers copied each other’s scam.
Furthermore, we already know that some similar instances of miracles were hoaxes. Shouldn’t every new hoax report lower my prior that miracles are real?
OK. What does “omniscience” mean? The root words translate to something like “all knowing”. But what is “all”, and what is “knowing”? What’s the minimum qualification? Each successive option seems harder to prove:
Option A: (sufficiently advanced aliens) God’s knowledge isn’t infinite or anything, just far beyond our current level. “Omniscience” is more metaphorical than literal.
Option B: (semi-omniscient simulator) God can look up any past event in the world simulation, but isn’t simultaneously conscious of all of them and cannot predict the future short of actually simulating it. He does not know all the logical implications of His knowledge and can be surprised by events. (Janet from The Good Place might be at this level.) Although perhaps he can rewind the simulation and try a different timeline, if He makes any changes, He can’t always predict what would happen without actually trying it. He may also be ignorant of events in His native plane, outside of the world simulation.
Option C: (halting oracle of the first degree) God is a halting oracle machine able to solve the halting problem for any Turing machine, but is unable to solve the halting problem for halting oracle machines like Himself.
Option D: (higher-order halting oracle) God is a halting oracle machine able to solve the halting problem for any Turing machine, and halting oracle machines of some finite degree less than His own, but is unable to solve the halting problem for higher-order halting oracle machines like Himself, or those of any higher degree. There may possibly be beings of greater degree that know things God doesn’t.
Options A, and maybe B seem at least possible, but very very far from proven. Option C seems unprovable using any finite amount of evidence, but probably has a logically coherent definition. Option D seems unprovable even with infinite evidence, but again seems coherent.
Or did you have some other option in mind? I don’t know how to get past Option D without self-referential paradoxes invalidating the whole definition, but perhaps you have some new math for me?
Yes, I have option E: Everything. God just know everything, all the possible universes, - not calculating, just having them in His memory that is infinite.
As I stated in the previous comment , there is no reason for the exact theory to be finite, while approximations can be finite (would you like me to copy it or you can find it?).
That’s your crux? Lesser interpretations than E won’t do?
I am not convinced that E is logically coherent. It’s as meaningless as “married bachelor”.
Suppose that God’s memory is the set of “all facts” O.
The set of all subsets (or powerset) of O, we’ll call p(O).
Then, for any given fact f, there is a further fact f ′ stating that it’s either in or not in each subset of O in p(O).
Thus, there must be at least as many facts as there are elements of p(O), which, being the powerset of O, by Cantor’s Theorem must have a strictly greater cardinality than O.
But we assumed that O contains all facts. Contradiction!
And Cantor’s Theorem holds even for infinite sets! Q.E.D.
Well, your argument should be able to kill the concept of Tegmark mathematical multiverse then, so you can guess it is not a “silver bullet” :) Two possible answers:
1. You can not just change the word “mathematical universe” to the word “fact” in my definition E. “Mathematical universe stating that...” makes no sense for me.
However, there are different set theory axiomatics. Some of them allow universal sets
OK, that’s a good point. I had not heard of the universal sets that contain themselves, which I thought would lead to contradictions.
should be able to kill the concept of Tegmark mathematical multiverse
I’m really not persuaded by the MUH, but at least it’s based on reasoned a priori arguments. Do you have similar a priori arguments for God? There’s no way for evidence to ever be enough establish omniscience by itself.
Yeah, given New Foundations, I’m no longer confident that “omniscience” is a logical contradiction, but neither am I confident that it isn’t. And I still think it would take an infinite amount of evidence to prove inductively, so you would need some kind of a priori argument for it instead (or why believe it at all?). That’s one obstacle down, but still a long way to go.
Equivocation. The algorithmic (Kolmogorov) complexity cost of the conjunction of “simulated X” and Y is finite, but the “real X” is infinite, therefore, the former must be preferred by Occam’s razor. “Simulated X” is a deception by aliens and is not a full halting oracle, but a finite approximation of one. It can’t do everything the “real X” could.
I do not believe that aliens are performing miracles, just that that explanation is infinitely more probable on priors than an omniscient God. The miracles you have pointed to so far are best explained as natural accidents or hoaxes, not nearly enough evidence to even suggest aliens.
Ok. Looks like we started to go on circle, sorry for not being clear enough. Let me try to explain once again.
You have a lot of observation data. You have significantly more potential observation data you can gather. I was considered before that all the potential observation data as finite—however, I understood that it is not so, for example, if scientific breakthrough, aliens or God will turn us into the immortal creatures with every year increasing ability to gather, remember, and process information.
So, you want to find a theory based on already observed data, that would predict the data that is not yet observed. I bet we both believe that it is possible to do, but with some limitations.
1. Does finite theory exactly predicting all data exists? (In a sense of the Turing machine). Since all the data is infinite, a prior probability for such theory would be zero—without any other assumptions. You can introduce strong assumption of predictivity, basically stating that such theory exists. However, I think that this assumption is too strong (based on a posteriori results of quantum mechanics where you can predict only the probability of the observation but not the definite outcome—so you can recover with your theory only part of the observed data). Instead I would suggest weak predictivity assumption:
2. The theory exactly predicting all the data is infinite (such infinite theories exist—for example “witch did it” where “it” is “all the data to be observed”); however, its finite approximations can predict some part of the data with some precision.
You can try to make it stricter, saying: “Among all the finite approximations there is one with maximal predictive power” but I do not see any arguments for it. The prior expectations tells that you can increase the precision by increasing the length of the theory.
Now, we would like to classify the finite approximations based on their precision and length. First, is just the reference to existence of exact infinite theory makes the theory under consideration infinite too? No—otherwise we need to acknowledge that Tegmark theory of mathematical multiverse (all the mathematically consistent worlds) is infinite. It refers to the existence of all the possible worlds, not describing each of them. The same, theory stating that the God knows everything does not state what exactly He knows. Thus, our approximation of infinite theory of omniscient God is just “God exists with such and such attributes” and it is finite. The approximation “aliens fake God with such and such attributes” is also finite but longer. It may seems better because “aliens faking God” can potentially be an approximation of the finite exact theory, predicting everything—however, as we discussed before, there is no reason to assume that such finite theory exists, and think that “aliens fake God” dominates “God exists” because the first is approximation of finite theory, and the second of the infinite. We compare the lengths of the approximations, not of the full theories, and the approximation “God exists” is shorter and thus should be preferred.
″ I do not believe that aliens are performing miracles, just that that explanation is infinitely more probable on priors than an omniscient God. The miracles you have pointed to so far are best explained as natural accidents or hoaxes, not nearly enough evidence to even suggest aliens. ”
Let us first fix the priors and then move to discussing miracles, ok?
Yes, I just started to notice that after re-reading this thread. It seems like we’re talking past each other without understanding. For Double Crux to work, we’re not supposed to aim for direct persuasion until after we’ve identified the double crux, or we’ll get “lost in the weeds” discussing the parts that aren’t important to us. Have we found it yet? I think we have not, and that’s what went wrong here.
I have yet to identify a single crux, but part of that might be because I don’t understand your concept of God. I don’t know what crux could possibly convince me your God exists, because I still don’t know what “God” means (to you).
I’m honestly not that familiar with the Eastern Orthodox tradition. Protestant sects are more common in my country. The God concept worshiped by the average churchgoer here seems laughably naiive, and logically incoherent, but it does have some differences with what you’ve described so far. And the apologists, even in my country, seem to have a different definition that the average churchgoer (in my country), probably because the naiive definition is so indefensible. It’s motte-and-bailey rhetoric—a combination of bait-and-switch with equivocation.
So I’ll ask again: Is omniscience a crux for you? That is, if a source you would consider authoritative (the bishops, the Patriarch, archeology, visions from God, whatever it takes) explained to you that omniscience was not an attribute of God as He revealed Himself, but a later misrepresentation made by sinful philosophers, would you then say your God does not exist?
If you answer, “Then my God still exists and is not quite omniscient as I had once believed,” then omniscience is not a necessary attribute for your God definition, and there is no need to discuss it further, because it is not a crux.
But, if you answer, “A ‘God’ that is not omniscient is no God of mine,” then omniscience is a crux for you and we need to nail down what that means, because it might be closely related to a crux of mine.
I’m not sure this is part of the authoritative definition of doublecrux, but FYI the way I personally think of it is “Debate is when you try to persuade the other person [or third parties] that you’re right and they’re wrong. Doublecrux is when you try to persuade _yourself_ that they’re right and you’re wrong, and your collective role as a team is to help each other with that.” (I don’t think this is quite right, obviously the goal is for both of you to move towards the truth together, whatever that may be, but I think the distinction I just made can sometimes be helpful for shaking yourself out of debate mode)
I’m not sure if anyone has an authoritative definition of doublecrux yet. But as this is my first real attempt at it, I appreciate guidance. We did open with the Litany of Tarski, but I might have lost sight of that for a moment. I maintain that I at least need to understand what my interlocutor is saying before I can conclude that he is right.
Again, the Litany of Tarski: If a God exists, I desire to believe that is the case. An update for either side is a victory. But the goal is not to fool myself or give up, or give in to confusion. The update must be an honest one, or the whole exercise is empty.
Yes. Omniscience is a crux for me.
Wouldn’t the prior probability of God to exist be a crux for you? I.e., if you change your prior probability from infinitesimal to somewhat not negligibly small, would it change your position? At least the infinitesimal probability is a crux for me.
Let me also notice that our positions do not completely cover all the spectrum of possible answers (it not exactly “A” or “not A” ). I.e., as far as I get you think the world is completely controlled by laws of nature, I think there is a God as Eastern Orthodoxy describe it. In between there are many other options:
-simulation
-aliens
-Higher Power (includes my believe as particular case)
-the world that is not describable by math fully but only approximately
-and whatever else that just does not come to my mind
It means that we can be wrong simultaneously.
Getting past an infinitesimal prior to a tiny finite one is a long way from “more likely than not”.
But more simply, my prior is my position. If you get my prior belief for the proposition “God exists” over 50%, then you’ve won: at that point I’ve become a theist by definition (though maybe not a very confident one). This isn’t a crux—It’s the original proposition!
Errr not completely—you have prior and you have experience. For example, suppose you agree after long discussion that probability of God to exist is not infinitesimal but 0.01% . Ok, you are still more atheist than a theist. Then if you observe miracles you update it to much higher probability—but you can’t do it if your prior is infinitesimal as now.
What would you put your priors now for the following:
-the Universe is completely describable by a finite set of laws, no other reality behind
-the Universe is approximately describable by the finite set of laws, approximation improves with the length of the theory (need infinite theory to full description)
-Universe is simulation
-aliens
-something else
I don’t consider this question well-posed. Physics seems to be working pretty well. But what do you mean by “Universe”? The part we can observe? Surely there’s more to it than that. And “laws” can be dependent on context. The law that objects accelerate downward at 9.8m/s/s doesn’t apply on Mars, but there’s a similar law with a lower number and an underlying law of gravity connecting both cases. Laws that seem to be “fundamental” now are probably dependent on local conditions. The “symmetry breaking” observed in particle physics indicates this. And very simple rules like Conway’s Life can produce very complex behavior, with emergent “laws”, like “gliders travel diagonally”. Is this law from a reality behind or in front of Life?
Ok, let us put it more strict. What are your priors that there exist a finite theory that can predict all our potential future observations exactly? And what are your priors that such theory does not exist and we can only use approximations?
N.B. By all observations I mean ALL observations, including the results of measurements in QM (not just their probabilities, we observe results too, right?)
I still don’t understand. Are you asking if the universe is deterministic?
Which sense of “exist” do you mean? Mathematically, where we can “have” imaginary things like infinite uncomputable sets, or physically, where we obviously can’t construct an object corresponding to such a thing?
Solomonoff induction cannot be run on real physics. It’s an abstracted ideal that can only be approximated. Maybe quantum field theory predicts the motion of particles to an accuracy of eleven digits, but that doesn’t mean you can use it to predict the weather. You don’t have enough computing power, and you don’t know the initial conditions to that precision anyway.
Even AIXI, an ideal agent using Solomonoff induction (which can’t be physically built), can only make probabilistic predictions based on observations made so far. There’s always an infinite class of universes (hypotheses) that have produced the observations thus far, and they always disagree on the next bit.
There’s no need to invoke quantum physics here. Given what we already know of relativistic physics, it’s always possible that a particle could approach at the speed of light and mess up your plans. Because it’s moving at light speed, there’s no way in principle you could have observed it to take it into account in advance. Even AIXI can be “surprised” by low-probability events like this, even in a deterministic universe (because it has only observed a small part of the universe so far), and it has infinite computing power!
Well, of course I do not suggest to predict the weather from the laws of QFT, I mean mathematically. Let us consider all possible future observations as a data. Do you think that it can be exactly generated by the theory of the finite length (as an output of the universal Turing machine with the theory as an input), or you would require an infinite length of the theory for the exact reproducing?
The observable universe probably has a finite number of possible states.
The laws of physics appear to be deterministic and Turing computable.
Therefore, an infinite theory would never be required. (And this makes me sympathetic to the ultrafinitists.) The laws of physics can be mapped to a Turing machine, and the initial conditions to a (large, but) finite integer. There is nothing else.
But I’m not sure that “all possible future observations” means what you think it means.
In the MWI, any observer is going to have multiple future Everett branches. That’s the indexical uncertainty. Before the timeline splits, there is simply no fact of the matter as to which “one” future you are going to experience: all of them will happen, but the branches won’t be aware of each other afterwards.
And MWI isn’t even required for indexical uncertainty to apply. A Tegmark level I multiverse is sufficient: if the universe is sufficiently large, whatever pattern in matter constitutes “you” will have multiple identical instances. There is no fact of the matter as to which “one” you are. The patterns are identical, so you are all of them. When you make a choice, you choose for all of them, because they are identical, they have no ability to be different. Atoms are waves in quantum fields and don’t have any kind of individual identity. You are your pattern, not your atoms. But, when they encounter external environmental differences, their timelines will diverge.
Copies of you that arise purely from the size of the universe will have the same counterfacutal or funcitonal behaviour, that is they will do the same thing under the same circumstances...but they will not, in general, do the same thing because they are not in the same circumstances. (There is also the issue that being in different circumstances and making different decisions will feed back into your personality and alter it).
I’m pretty sure I said that:
I don’t understand your point.
”
The observable universe probably has a finite number of possible states.”
Not so sure about that. For this you need at least
1. The Universe to be finite (i.e. you can not have open Universe, only the surface of 4d sphere). It is possible, the measured curvature of the Universe is approximately on the boundary, but the open is also possible.
2. The Universe to be discrete on microscale. Again, according to some theories it is the case, according to the others, it is not.
So, I would say: “maybe yes, it is finite, but the prior probability is far from being 1 ”.
Side note: the Universe with finite number of states is quite depressive picture since it means that inevitably everything will just end up in the highest entropy state, so, the inevitable end of humanity. Of course, it contradicts nothing, but in this model any discussion of existential threats for the humanity (like superintelligence quite popular here) makes no sense since the end is unavoidable.
″ And MWI isn’t even required for indexical uncertainty to apply. A Tegmark level I multiverse is sufficient: if the universe is sufficiently large, whatever pattern in matter constitutes “you” will have multiple identical instances. There is no fact of the matter as to which “one” you are. The patterns are identical, so you are all of them. When you make a choice, you choose for all of them, because they are identical, they have no ability to be different. Atoms are waves in quantum fields and don’t have any kind of individual identity. You are your pattern, not your atoms. But, when they encounter external environmental differences, their timelines will diverge. ”
Could you please explain it in more details? I am confused. If I measure the spin of the electron that is in the superposition of spin up and spin down, I obtain with probability p spin up and with probability 1-p spin down. How to exactly predict using Tegmark multiverse when I see spin up and when I see spin down?
I’m not saying that a Tegmark I multiverse is equivalent to MWI, that’s actually Tegmark III. I’m saying that Tegmark I is sufficient to have indexical uncertainty, which looks like branching timelines, even if MWI is not true. See Nick Bostrom’s Anthropic Bias for more on this topic.
Mmmm is explanation really that long that I need to read a whole book? Can you maybe summarize it somehow?
Only if you’re interested. I haven’t actually read the whole book myself, but I have read LessWrong discussions based on it. I think the Sleeping Beauty problem illustrates the important parts we were talking about.
Ah, I think I got the point, thank you. However, it does not resolve all questions.
1. You can’t deduce Born’s rule—only postulate it.
2. Most important, it does not give you a prediction what YOU will observe (unlike hidden parameters—they at least could do it). Yes, you know that some copies will see X, and some will see Y, but it is not an ideal predictor, because you can’t say beforehand what you will see, in which copy you will end up. So all your future observed data can not be predicted, only the probability distribution can be.
Can’t you? Carroll calls it “self-locating uncertainty”, which is a synonym for the “indexical uncertainty” we’ve been talking about. I’ll admit I don’t know enough quantum physics to follow all the math in that paper.
Yeah, in this scenario, the “YOU” doesn’t exist. Before the split, there’s one “you”, after, two. But even after the split happens, you don’t know which branch you’re in until after you see the measurement. Even an ideal reasoner that has computed the whole wavefunction can’t know which branch he’s on without some information indicating which.
More or less. You can compute all the branches in advance, but don’t necessarily know where you are after you get there. The past timeline is linear, and the future one branches.
″ Can’t you? Carroll calls it “self-locating uncertainty”, which is a synonym for the “indexical uncertainty” we’ve been talking about. I’ll admit I don’t know enough quantum physics to follow all the math in that paper. ”
That was super cool, thank you a lot for this link!
Yes, according to our best current understanding of cosmology, the universe itself will eventually die (i.e. become unable to sustain life).
Again the laws of physics are what they are and don’t care what I want.
But in the most likely scenarios, this will take a very long time. The Stelliferous Era (when the stars shine) is predicted to last 100 trillion years, and we’re not even 14 billion years into it. Civilization may continue to extract energy from black holes for a time many orders of magnitude longer than that.
It’s not completely hopeless. Maybe in that time we’ll figure out how to make basement universes and transfer civilization into a new one, as Nick Bostrom et al have argued may be possible.
But even if we ultimately can’t, shouldn’t we try? Shouldn’t we do the best we can? Wouldn’t you rather live for over 100 trillion years than die at 120 at best?
″ It’s not completely hopeless. Maybe in that time we’ll figure out how to make basement universes and transfer civilization into a new one, as Nick Bostrom et al have argued may be possible. ”
Yeah, you see then all the future possible observations data becomes infinite.
″ But even if we ultimately can’t, shouldn’t we try? Shouldn’t we do the best we can? Wouldn’t you rather live for over 100 trillion years than die at 120 at best? ”
Of course, we should try—because there is a chance that we can. Not because we would live 10^14 years and all die. We will count that we survive forever, or it will be pretty miserable 10^14 years without any hope.
Not sure either, which is why I said “probably”.
Note that I said “observable universe”, not “multiverse” or “cosmos”. There are regions of the universe that are not accessible because they are too far away, the universe is expanding, and the speed of light is finite. This limit is called the Cosmic event horizon
I think it is sufficient to say that the information content of the observable universe is finitely bounded. Space doesn’t necessarily have to be made of pixels like some cellular automaton for this to hold. The Bekenstein bound is proven from Quantum Field Theory. How true QFT is, is another question, but experimental evidence proves that it is very true.
″ Note that I said “observable universe”, not “multiverse” or “cosmos”. There are regions of the universe that are not accessible because they are too far away, the universe is expanding, and the speed of light is finite. This limit is called the Cosmic event horizon ”
On the one hand side, you are totally correct about it—assuming cosmological constant (lambda-term ) stays what it is. There are nuances however:
-if we are forever in the de Sitter space (lambda dominated, as now) the universe is explicitly not time-invariant (simply because it extending). There is non-zero particle production rate, for example (analog of Hawking radiation). It means that we potentially can construct a “first kind perpetuum mobile” which means that we can get to any energy—infinite space for the observations. Unless this will start to have a screening effect on lambda-term.
-If lambda desreases (or screened) the expansion may go back from lambda-dominated to matter-dominated, leading to its slowing down. In this case we can start observing areas of the universe that used to be beyond the horizon.
Anyway, there are a lot of speculations what can be and what can not. Can we maybe agree that both prior probabilities: that all our possible future observations are finite and that they are infinite are not negligible? What about 1⁄2 for each, to start with?
I worry we may be getting lost in the weeds again. We need to try and find cruxes. Is this related to a crux of yours? What exactly are you getting at?
Even if time could be extended infinitely without the universe dying, there is no time at which the infinity has been completed. It’s always finite so far.
An “immortal” being with finite memory in infinite time will eventually forget enough things to repeat itself in a loop, living the same life over and over again.
Can this be avoided? There are limits to any physical realization of memory. If you try to pack too many bits in a given volume of space, it will collapse into a black hole. And then adding anything more will make the event horizon bigger. Infinite memory requires infinite space and energy. Maybe with basement universes it could be done. They might have to communicate through wormholes or something. This is all very speculative, so I don’t know.
Well we can also make infinite memory (as you suggested). But, ok, what would you put as prior probability that the theoretically possible observation data is infinite? Looks like you are not strongly against it, so what about something between 0.5 and 0.1? (Of course we can’t strictly prove it right now). If you say “yes, this works” we can move on. If you would claim that this probability is also supertiny, like 10^(-1000) , I will continue to argue (well, yes, if we can not at all observe in all the infinite future infinite data, it does not make sense to talk about omniscient God).
To show you what I am leading to:
-if the total possible observation data is infinite, what is prior probability that it is exactly reproduced by finite hypothesis? I argue that it is infinitesimal
-what is the probability that there exist such infinite hypothesis? I argue that 1, for example, “witch did (copypaste all the data)”. Predictive force of this hypothesis is zero
-we need predictivity so we assume that there are finite approximations that can partially reproduce the data. Such assumption is less strong than assumption of the finite exact hypothesis so it should be preferred.
-therefore, we should use Solomonoff’s lightsaber not on full theories, but on approximmations
-consider two classes of approximations. The first gives exact predictions where it can and predicts nothing whee it can not. The second is weaker, it sometimes gives wrong predictions. Since the second is weaker, the priors for this are significantly higher. So, I would say, if observable data is infinite, most of our approximate theory have from time to time give wrong predictions
-this does not say, of course, how often are these wrong predictions. If they are too often, such approximation is useless.
-Basically, since predictions are laws of nature, wrong predictions are miracles. We should expect to them to exist but to be rare.
-Talking about aliens. Infinite hypothesis “God with such attributes exists” can be used only as approximation (that is, basically, our understanding of it). The finite hypothesis “aliens fake us to believe that God with such attributes exists” also can be used only as approximation, (that is our understanding of God + assumption that it is faked by aliens). Thus such approximation is longer and should be given smaller probability.
You are not a future hyper-mind made of basement universes and wormholes. You’re a mortal human like me, with a lifespan measured in mere decades so far. Yet you claim to have knowledge of an infinite God. How did you come to this conclusion? By what method can you make such an assertion? Is this special pleading for a special case or do you use this method for anything else? Why should I consider that method sound and reliable?
My best guess: you were indoctrinated in childhood by your parents and community, long before you were old enough to develop critical thinking skills of your own. For obvious survival reasons, children are very inclined to learn from their parents and elders. The memeplex of any of the old religions must be self-sustaining, or they wouldn’t still be here. They include psychological tricks to produce fake evidence, to stop questions, to make empty threats. They include answers to your questions or at least pretend to. It became part of your identity. You later learned of the methods of science, but they didn’t become a part of you the same way. You compartmentalized the lessons and didn’t use them to update your old thinking. You sought out evidence to support your belief instead of trying to disprove it to see if it would hold up, like a scientist.
Most people seem to use this method. You are not alone. And that’s exactly the problem with it. People are using the same methods to believe in other religions that you already know to be false. How can that method be reliable if it so reliably produces the wrong answers? What makes you any different from them? Accident of birth. That’s it. Your methods are the same.
Maybe that’s a crux for me. If it could be shown that a God belief was founded on a sound epistemology that reliably produced good results, instead of these obvious fallacies, I would have a much harder time dismissing the proposition as a fraud.
” You sought out evidence to support your belief instead of trying to disprove it to see if it would hold up, like a scientist. ”
1. If I would do this I would never go to this website discussing this with you. Assume good intentions.
2. As you said, for infinitesimal prior probability no evidence is enough. That is what I am arguing here. If I get persuaded that probability is indeed infinitesimal, all my evidence are nothing. I can see resurrection of the deads and still it won’t be enough then.
3. I can blame the same thing on you. I am not going to guess but there are so many stories of atheists who became atheists just because God didn’t do what they asked. “I do not want to deal with such God that does not do what I want, therefore there is no God.”
Ok, let us go back to our business if you don’t mind.
″ If it could be shown that a God belief was founded on a sound epistemology that reliably produced good results, instead of these obvious fallacies, I would have a much harder time dismissing the proposition as a fraud. ”
First, could you review the previous comment to see if you agree with the logic, and if not, what do you disagree in particular.
Second, if you agree with this logic, you should acknowledge that there is not negligible prior probability that miracles exist in principle. You can claim that they are rare, and each time you do not observe the miracle you can say it is even more rare.
Third, if you acknowledge that the miracles can happen, it is worth looking at the cases when someone claim them to happen in particular. If you have large organised religion (like Catholic, Anglican, Russian churches for example) you very often have special commitee (usually with scientists inside) that check if the miracle that people claim to be miracle, is indeed miracle. Very often they found it to be hoax or natural effect, but sometimes they acknowledge that this is indeed miracle. Other religions may also have miracles, as well as just something outside religion, but there may be no developed institution of miracle verification.
A fair point. But I still think you are compartmentalizing.
It’s never enough for induction, performed correctly. But an a priori deductive argument maybe could work. I’ve heard theists attempt these arguments, but have not found them convincing.
I am trying to find cruxes, not blame. I would rather leave our identities out of it and examine the question as objectively and impartially as possible. But your epistemology is extremely relevant in this case. It’s the rights of Mortimer Q. Snodgrass again. I don’t think the God hypothesis has enough going for it to even justify raising it to our attention. If we had started with a good scientific epistemology, this would not even be a question. Instead we started with a biased indoctrination, and have to dig ourselves out of it.
It’s the availability heuristic again. Who have you heard these stories from? It’s probably not the atheists themselves! You can’t trust the clergy to be honest about this topic. They believe atheism is damnation, and so must present it as a sin. But for those raised atheist with a scientific worldview, believing in God seems as silly as believing in Santa Claus or the Tooth Fairy.
In my case, I was raised as a believer. My perspective changed due to an accumulation of a number of factors. The Problem of Evil was apparent to me in childhood. It introduced a doubt that I could not resolve. The biblical creation story also didn’t align with what I read of science as a child.
When I expressed my misgivings, my church told me that God was a God of Truth, and the teachings of the Church could not possibly contradict the Truth, once it was properly understood. So I withheld judgement until I could learn more. I held both the religious and the scientific worldview in my mind at once, in the hope that they could eventually be unified. I was compartmentalizing, but I was conscious that I was doing so. I could speculate and philosophize in either religious or scientific modes, and I knew which was which. I saw the fruits of science. Computers and rocket ships and vaccines. I had church-related experiences I could only describe as spiritual. Surely they both had to be true?
I studied my faith in depth. I was warned of the sin of pride. I was uncertain how to interpret that, but after study, concluded that the problem with pride was an unwillingness to learn from error. I resolved to always be honest with myself. God was a God of Truth, after all, so honesty could not be wrong. I learned to think more critically. I found many satisfying answers, but my doubts on these points, and more, only deepened. There was evidence against the faith, that was for certain. Doubts remained, but abandoning my faith would mean damnation and I could never convince myself it was false beyond a reasonable doubt.
Then I learned that civil cases were judged according to the preponderance of the evidence, rather than beyond a reasonable doubt. In my commitment to honesty, I judged my faith again by this standard. Suddenly, many of the faith-promoting stories I had considered “evidence” no longer appeared that way. They were indistinguishable from no God at all. Once seen, I could not unsee it. Why was God pretending so hard not to exist? So we are less culpable for sins? Then why have a church at all? My faith was shaken (and not for the first time), but still I believed. I resolved to study more, to try and rebuild what I had lost.
In my church, we brethren sometimes minister to the other members, usually in pairs. I was usually too shy to participate, but I had studied enough to know answers from the scriptures. When ministering to one poor sister who was struggling, I went into religious mode and spouted off the relevant doctrine. This happened to be a point I had doubts about. And then the realization struck me: I didn’t believe a word of it. I sounded that confident, and I didn’t believe a word. I had lied to her. And worse I had lied to myself, the exact thing I had resolved not to do. I had so easily broken my commitment to honesty, just by studying doctrine. And if I could do it, so could any of the other members! They could sound so convicted, and yet not know! The testimony of the others I had been relying on may have been founded on nothing but air.
I still had my spiritual experiences, but they had always resisted critical examination. I finally understood that what I thought was the witness of the Holy Spirit, was only those around me interpreting my emotions for me in a certain way. They were spouting off doctrine memorized by repetition, the same as I had done to that poor sister. In another context, the same emotions could have been a witness for a completely different god. My faith was shattered to its very core.
My church regards all others as apostates. I had rejected them long ago. There was nowhere to turn. For a time, I considered myself agnostic. I told my story to a confidante, and she replied with something like, “so you’re an atheist then”. And in that moment, I realized it was true. I’m an atheist. I can’t believe in God anymore, even if I try.
And after reading the Sequences, and understanding Bayes, I realized that the faith-promoting stories I had thought were evidence, and then eventually no evidence at all, were actually evidence against the church. The church had actually been preemptively preaching some of its worst stories, so we would learn to think of them in the best possible light, before we had a chance to hear a more critical presentation from anyone else.
Due to indexical uncertainty, we can always be surprised by low probability events. I don’t see these as evidence of God though.
Around in circles again, but is there a difference this time? Do we agree “fake alien God hypothesis” dominates “infinite God hypothesis”? When using induction? You don’t seem to be disputing it. But is “approximate God” simpler than “fake alien God”? That depends! How good is your approximation of “infinite”? How complex are your aliens?
But if you want to argue for a non-infinite God, that’s OK with me, but even if you convince me, it won’t be the infinite God you have convinced me of, but the finite approximation: Something more powerful than mankind, but not infinitely powerful. Something more knowledgeable than mankind, but not infinitely knowing… this sounds like you’re describing advanced aliens. They’re the same thing. I would then argue that the aliens are the reality and the “infinite God” is the approximation of them made by ignorant humans.
Even I would be willing to call such aliens “gods” given certain conditions, but we’re using your definition of “God”.
Can you convince me of approximately-God aliens? Maybe. My prior is not zero, but like the pet purple dragon from Mars, it would take a lot of evidence to convince me.
It feels like we are going around in circles at this point. I’m not sure where the disconnect is.
The set of all natural numbers is infinite, yet can be enumerated by a finite computer program (when run on an infinite computer, AKA, a Turing machine). There are many many other examples of infinite patterns enumerable by finite programs. And some of them, like “compute the digits of pi” seem pretty chaotic, yet their Kolmogorov complexity is small.
One wrinkle, which you might be alluding to, is that no program with infinite output ever halts. This is true, but there are halting programs that can compute any finite prefix of pi. And like I said before, at no point is your observation infinite. It’s always finite so far. The infinity is never completed.
So the hypothesis “these are the digits of pi” is considered by Solomonoff induction, but maybe it looks like a weighted sum of a class of programs that say “compute pi up to the nth digit” for some n. These still compress quite well, (especially for compressible n’s) so their Kolmogorov complexity is small. I don’t think this is an obstacle for Solomonoff induction.
Has Solomonoff induction got it wrong? Close but not quite? I would argue no. I don’t believe uncomputable sets can physically exist. There are no perfect circles. The abstraction called pi is the approximation, for whatever algorithm physics is actually running, which Solomonoff induction would eventually find.
The posterior becomes the next prior when updating again, so we still call it a “prior” even though this is not the same prior as before. Sorry for the confusion. My current prior is my current level of belief/confidence.
Higher, yes, but (say) ten times almost nothing is still almost nothing. And that’s only if the likelihood ratio for the evidence favors the hypothesis by that much, which it doesn’t.
That’s right. No finite amount of evidence can overcome an infinitesimal prior.
Your example “miracles” are evidence in favor of miracles existing (because we can hardly expect reports of miracles to be less common if miracles exist) but the likelihood ratio is very close to 1 because false positives (accidents, hallucinations, and hoaxes) are so common. On priors, these explanations are far more likely. That means your “miracle” reports are extremely weak evidence.
I cannot lower my epistemic standards on this, or I would invite in flat-Earthers, UFO-ologists and various other conspiracy theorists, not to mention all the other religions who have similarly dubious paranormal claims. Why should I favor your paranormal claims over theirs? It’s special pleading.
″ but (say) ten times almost nothing is still almost nothing”
Ok, cool. So if your prior will be one millionnth I will need just six miracles :)
Strong enough evidence can overcome a very low prior, yes. And this doesn’t have to take very many observations.
But more instances do not necessarily stack like that. That can only happen to the degree they are independent sources. For example, suppose you write a dubious claim in a book, then you make nine more copies of the book. Does that make the claim ten times more likely to be true? What if it’s a hundred thousand copies? Did that help?
Of course it doesn’t! You’re re-counting the same evidence. The contribution of the nine books is completely screened off by the first; the new books have no new information.
I think the cases of miracle reports like weeping icons are similarly not independent enough. A thousand weeping icons is barely more evidence than one. It just means that the hoaxers copied each other’s scam.
Furthermore, we already know that some similar instances of miracles were hoaxes. Shouldn’t every new hoax report lower my prior that miracles are real?
OK. What does “omniscience” mean? The root words translate to something like “all knowing”. But what is “all”, and what is “knowing”? What’s the minimum qualification? Each successive option seems harder to prove:
Option A: (sufficiently advanced aliens) God’s knowledge isn’t infinite or anything, just far beyond our current level. “Omniscience” is more metaphorical than literal.
Option B: (semi-omniscient simulator) God can look up any past event in the world simulation, but isn’t simultaneously conscious of all of them and cannot predict the future short of actually simulating it. He does not know all the logical implications of His knowledge and can be surprised by events. (Janet from The Good Place might be at this level.) Although perhaps he can rewind the simulation and try a different timeline, if He makes any changes, He can’t always predict what would happen without actually trying it. He may also be ignorant of events in His native plane, outside of the world simulation.
Option C: (halting oracle of the first degree) God is a halting oracle machine able to solve the halting problem for any Turing machine, but is unable to solve the halting problem for halting oracle machines like Himself.
Option D: (higher-order halting oracle) God is a halting oracle machine able to solve the halting problem for any Turing machine, and halting oracle machines of some finite degree less than His own, but is unable to solve the halting problem for higher-order halting oracle machines like Himself, or those of any higher degree. There may possibly be beings of greater degree that know things God doesn’t.
Options A, and maybe B seem at least possible, but very very far from proven. Option C seems unprovable using any finite amount of evidence, but probably has a logically coherent definition. Option D seems unprovable even with infinite evidence, but again seems coherent.
Or did you have some other option in mind? I don’t know how to get past Option D without self-referential paradoxes invalidating the whole definition, but perhaps you have some new math for me?
Yes, I have option E: Everything. God just know everything, all the possible universes, - not calculating, just having them in His memory that is infinite.
As I stated in the previous comment , there is no reason for the exact theory to be finite, while approximations can be finite (would you like me to copy it or you can find it?).
That’s your crux? Lesser interpretations than E won’t do?
I am not convinced that E is logically coherent. It’s as meaningless as “married bachelor”.
Suppose that God’s memory is the set of “all facts” O.
The set of all subsets (or powerset) of O, we’ll call p(O).
Then, for any given fact f, there is a further fact f ′ stating that it’s either in or not in each subset of O in p(O).
Thus, there must be at least as many facts as there are elements of p(O), which, being the powerset of O, by Cantor’s Theorem must have a strictly greater cardinality than O.
But we assumed that O contains all facts. Contradiction!
And Cantor’s Theorem holds even for infinite sets! Q.E.D.
Did I just disprove God?
Well, your argument should be able to kill the concept of Tegmark mathematical multiverse then, so you can guess it is not a “silver bullet” :) Two possible answers:
1. You can not just change the word “mathematical universe” to the word “fact” in my definition E. “Mathematical universe stating that...” makes no sense for me.
2. Cantor’s theorem is based on particular set axiomatic. However, there are different set theory axiomatics. Some of them allow universal sets https://en.wikipedia.org/wiki/Universal_set
OK, that’s a good point. I had not heard of the universal sets that contain themselves, which I thought would lead to contradictions.
I’m really not persuaded by the MUH, but at least it’s based on reasoned a priori arguments. Do you have similar a priori arguments for God? There’s no way for evidence to ever be enough establish omniscience by itself.
″ OK, that’s a good point. I had not heard of the universal sets than contain themselves, which I thought would lead to contradictions. ”
Great, the update of belief :)
Yeah, given New Foundations, I’m no longer confident that “omniscience” is a logical contradiction, but neither am I confident that it isn’t. And I still think it would take an infinite amount of evidence to prove inductively, so you would need some kind of a priori argument for it instead (or why believe it at all?). That’s one obstacle down, but still a long way to go.