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" 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!
" 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.
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.
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.
Mmmm is explanation really that long that I need to read a whole book? Can you maybe summarize it somehow?
" 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?
" 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. 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?
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?
" 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 :)
" 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 :)
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?)
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
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
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?).
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.
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?
"that dominates "there is an omniscient being" (which must have an infinitesimal prior)"
It must not, because the theory does not completely describe omniscient being, but states its existence. If your theory claim that the Universe is infinite (which can be true, we might live in the open Universe) it does not mean that your theory is infinite.
Once again, how did you distribute priors? By how easy you can use the theory to make predictions. In both cases, hidden parameters or hidden aliens, you say: ok, let us keep our old assumptions, but introduce hidden thing Y that works such that our observations can be explained by X. X alone is not good - it requires to go from deterministic to random Turing machine (QM) or acknowledge that the theory exactly describing our observations can be infinitely large, while we can only approximate it. Y gives some hope to resolve it - to stay within deterministic Turing machine, or within finite though large theory of everything. However, in both cases using of Y is just "Y simulates X". Well, in my opinion you even do not need a Solomonoff's lightsaber here - simple Occam razor is enough to see that Y is redundant.
Of course, the Universe as a whole is deterministic since it obeys Schreodinger equation. However, the only thing we have access to is observation, and the observation is probabilistic. You can not predict with the deterministic Turing machine, what is the outcome of the observation, only the probabilities for this outcome.
Well, the laws of nature of course what they are. However, you can interpret it in different ways. You can say that there is fundamental probability, wavefunction, and all this stuff, as the most scientist do when they perform calculations. Or you can start introducing hidden non-local variables, that does not improve your predictions but just make theory more complicated. There was an April, 1st paper introducing particles as sentient beings communicating with each other superluminously to deceive experimentalists. It is your choice which representation you prefer, but I thought you wanted the simplest one.
Oh yeah I heard about this stuff too. No I do not consider pareidolia as miracle. Basically, I listed above (replying to what would disprove me) what I assume to be miracles. In short - stuff that not only one old lady claim to be miracle, not only few local priests and bishop, but special committee from the Church (after a certain investigation), and, a result, whole Church.
"You seem to be arguing that we can bias our prior to accept an approximate God at the very edge of the "width". I say the rights of Mortimer Q. Snodgrass are being violated."
No. If you read the comment about the width of the function you can see that my argument is not about God at all, but about what we need from the hypothesis (predictivity).
" The alien hypothesis dominates the God hypothesis, because God is infinitely improbable, but aliens are only finitely improbable. "
No. We use the approximation, and approximation has the same size for both of them (we consider the case of comparing hypothesis "There is a God with such and such attributes" and " There are aliens forge us to believe that there is a God with such and such attributes"). The algorithm of construction of this approximation, though, is simpler for pure God's hypothesis (using the mere fact of its existence, not formulating the hypothesis itself, like we establish dualities between different types of string theories using that M-theory exists but without formulating it) since it does not require transitional link of "hidden aliens".
"Why your God,
Rather than Allah, the Flying Spaghetti Monster, or a trillion other gods no less complicated—never mind the space of naturalistic explanations![?]
"
Suppose I tell you soon after the discovery of muon that there is another particle, like the electron, but with the mass 105.6583745 (24) MeV and lifetime 2.19698119(22) microseconds. You would tell me: "Ok I can assume that there is a particle like the electron, although I would put quite low probability to it. But to believe, that its mass is 105.6583745(24) MeV !? No, it is absurd - there is a trillion of other possibilities!"
Of course. A priori possibility for all different gods is approximately the same. In total, they add to the prior probability that there is some God - and I was arguing that this prior probability is finite. Then, after you make an observation, you can discover more attributes of God and come to Allah, Christ, Flying Spaghetti Monster, Aliens or nothing beyond Laws of Nature.
Yes it is for the observer. You can not deduce Born's rule from the . No interpretation of quantum mechanics can help you with it.
" Bell's Theorem only rules out local hidden variables. " - ok. Do you prefer non-local theory then?
Well, violation of Laws of Nature is violation of Laws of Nature, whether they applied to the remote drawing without any interactions or to star moving. If Steve can draw pictures on toast remotely he violates the Laws of Nature and the hypothesis that the Universe is completely controlled by the Laws of Nature, without any Higher Power, aliens, the guy who runs a simulation etc - is falsified.
Now, going back to aliens vs God hypothesis.
" The dragon is at least compatible with what we know of science. Magical powers, not so much. "
The problem that compatibility of the hypothesis with what we know before is not an argument at all when we are talking about fundamental hypothesis (i.e., not "who stole my car" but the hypothesis explaining the Universe). Indeed, look at the history of Quantum Mechanics. Initially, a lot of scientists hated the idea that the probabilistic description of the Universe is fundamental, so they come up with hidden parameters idea. All they now before was deterministic. If you knew all the velocities and positions of all the molecules, you could predict everything exactly - but you did not, and here the classical probability was coming. So they just suggested the same idea for Quantum Mechanics. That actually everything is still deterministic, we just don't know hidden variables, and then the observation appears to be probabilistic. You do not need to invent modified Turing machine that would produce different input with different probability, you still good to have good old deterministic Turing machine. Looks much better, right?
Then it appears that actually you can distinguish between these hidden parameters hypothesis and fundamentally probabilistic hypothesis - see Bell's inequalities. And the experimental test demonstrated, that there are no hidden parameters. QM is fundamentally probabilistic.
Thus, the fact that we need to throw to the trash can all our current assumptions and build the theory based on new assumptions does not mean that we should put small probability to this new theory and need hidden parameters or hidden aliens given the same observations. It just means we maybe were wrong.
Well, my expectations would decrease if some of the miracles I believe would be proven to be fakes or natural events. The miracles that I believe are not those that people believe locally, but those that the Church recognizes globally - usually they send a special commission to check if it is indeed miracle or just natural event (or fake). I would say, I put high probability that the miracles that was approved by this commission are indeed miracles, and if you demonstrate me that they are not it would decrease my probability. The miracles I can name:
-different myrrh-streaming icons, as long as it passed the check by church officials not only on the local level
-witnesses that are collecting for the canonization of saints. Each time when new person is canonized one of the main criteria is whether there are miracles by prayers to him. So it is quite large data of different witnesses. Most of them can be explained by coincidence or natural effects, however, there are more difficult witnesses such as very fast curing from disease that by doctor prognosis should have taken few orders of magnitude longer time (or should not have happen at all).
-relics of saints. In some cases (quite often actually) when after long time the body of the dead person who is considered to be saint is taken back from the ground, it discovered to be not decomposed. It is not necessary condition - there are many saints who does not have it. However, it is interesting question, whether this effect is more often among saints that among usual people (taking into account only the cases when relics were taken from the ground after canonization, to exclude the bias). If it is indeed significantly more often, what can be the reason? Why would the situation be opposite on mount Athos, where non-decomposition of the body is considered to be a bad thing?
I am feeling that our crux is prior probability for God that we are discussing in the other thread. I think that it is a little bit smaller than no God hypothesis, and gilch thinks that it is infinitesimal.
" God, who can likewise be credited for anything (even what looks like evil--"all part of God's plan", or "God works in mysterious ways", right?) is the same as the witch: no predictive power over "it" whatsoever."
Not exactly. First, I can predict that if I throw the stone it will fall down and stuff like that. A miracle may happen, but the probability for it to happen from nowhere is very small (also not zero). Second, I give higher probabilities to what is common place for miracles to happen (like myrrh-streaming icon mentioned above, or healing, or answer to the prayers). With no God hypothesis I must put to zero such probabilities, and if there is a God I keep them finite. So, first, such theory can predict something (whether predictions correct or not, it is separate thread discussion, I will go back to it when I have time from this thread). Second, the predictions do not always coincide with no God theory predictions (like deist theory, that there is a God that does not interact with the Universe) - so it is different theory.
" And worse, God's complexity cost is not just relatively big like any intelligent mind (such as the witch) would be, but literally infinite if we say that God is omniscient: If God is a "halting oracle", then God is not even contained in the set of all computer programs, because He is not computable: He can't even be a hypothesis, only approximated. And to get a better approximation, you must use a longer computer program that encodes more of Chaitin's constant, which is provably not compressible by any halting program. Better approximations of God get bigger without limit. The approximate God hypothesis has literally infinitesimal probability--you can't escape it: The better the approximation gets, the less likely it is. "
Hmmm. Indeed, you are totally right here. I actually never thought that incomprehensibility is directly connected with the omniscience. Thank you very much for this, it make me to reconsider a lot of things.
We indeed can have only approximate knowledge of God. However, this approximate version of the whole hypothesis can be short enough to compete with no God hypothesis (remember, I was talking about the width of the function? ).
So, for example, the zero approximation of the God hypothesis is that God does not interact with the Universe. It basically leads to the same predictions, as no God hypothesis, so it should be eliminated (actually not that simple, I will talk more about it closer to the end of this comment). The first order approximation will be the God very rarely interacting with the Universe, so there are miracles with very low probability. Next orders will be clearer classification of these miracles. You see that these approximations have predictive power, not significantly longer than no God hypothesis, and the set of predictions is not identical - so they are decent competitors.
What is the difference between such approximation and the same approximation for alien teens etc? Why would we prefer the God hypothesis to the alien teens? Well, because to say: "there is a God with such and such attributes" is simpler than to say "there are alien teens who form around us a reality such that it looks like that there is a God with such and such attributes".
But why do we need to say that there is the omniscient God at all if all we are going to do is to use approximations? Well, let me give you an analogy from mathematical physics. There is such thing as M-theory. Well, to be honest, M-theory is not formulated. However, only the assumption that such theory exists (even though not formulated) leads to some interesting dualities between other theories. The same is here. Assumption of the omniscient God gives fruitful approximations. Whether they are correct or not - it is the discussion on miracles in the different thread. But we can not simply say that they have very low prior probabilities, since they are not significantly longer than no God hypothesis and are within the width of the maximum of the probability function distribution.
We are still discussing :)
Ok, let me repeat more precisely so you would see if I understand all things correctly, and if not you would correct me.
1. We have the Universe, that is like a black box: we can make some experiment (collide the particles, look at the particular region of the sky) and get some data. The Universe can be described as a mapping from the space of all possible inputs (experiments) to all possible outputs (observations). To be very precise, let us discuss not observations of humanity as a whole (since you do not observe them directly), but only your own observations in a particular moment of time (your past experiments and observations are now coming from your memory, so they are outputs from your memory).
2. If there are 2^K possible inputs and 2^M possible outputs, there are totally 2^N = (2^M)^(2^K) possible mappings.
3. We can represent this mapping as an output for the universal Turing machine (UTM), which input will be our hypothesis. There are different realizations of the UTM, so let us pick one of the minimal ones(see Wikipedia).
4. There will be more than one hypothesis giving correct mapping. "Witch did it", "Dumbledore did it" etc. Let us study the probability that the given hypothesis is the shortest that reproduces correct mapping. (If we have more than one shortest, let's pick the one that is assigned to a smaller binary number, or just pick randomly). For such a rule, there is only one shortest hypothesis. It exists because there is a correct hypothesis "Witch did it" , that might be not the shortest, so we will just look for those that are shorter.
5. The probability for a hypothesis with length n be the shortest hypothesis for n < N is a priori not larger than 2^(n - N) since there are 2^N possible mappings and only 2^n possible hypothesis.
6. The antropic principle does not help here. You know that you perceive input and produce output, but you can't assume anything about future input and output - a priori.
7. Now you want to introduce the new principle - predictivity, that you actually can predict stuff. I agree with introducing it. This leads to the strong assumption that actually our mapping is one of such that can be produced by a short hypothesis. So, you redefine the probabilities such that you would have a pick for short hypothesis, and integral still be 1.
8. Let us look closer at ou options. Funny that the Solomonoff's lightsaber actually does not converge fast enough. Indeed, you have 2^(-n) probability for a particular hypothesis of length n, but there are in total 2^n hypothesis of length n, that give you 1 for all the hypothesis of length n. Thus you integrate 1 from 0 to infinity obtaining divergence. To fix it you can simply say that the probability 2^(- a n) with a > 1.
9. However, is convergence the only a prior thing that we require? I would say no. Indeed, can the input of length 1 to one of the minimal UTMs make it produce an output of the length N>>1 and halt? My probability for this is incredibly low. (Of course, you can construct UTM so that it will make it - but it will not be minimal). Notice that I do not say "complex input" or something like that, I am concerning only about the size. The same I would say for all very small numbers. If you have some free time and good at coding, you can play with the minimal known UTMs to see which smallest input produces large but finite output - this would give an estimation of how small n can be. Let us call it n_0
10. Now we would like to have a function such that it is almost zero at n significantly smaller than n_0, growth fast around n_0 and then decays (fast enough to keep the integral convergent). So it will have a maximum, and this maximum will have some width. What is its width? Is it just a matter of taste? To understand it let us return to the reason why we started the search of this function - the need for predictivity.
11. So, since we basically need to be able to predict future observations, the width of the function is limited by us. If it is too wide and we need to include a highly complicated hypothesis, we fail - simply because it is too hard for us to calculate based on such complicated hypothesis. Thus, we just limit ourselves by hypothesis simple enough to use, and this gives the width of the function.
12. To sum up, if hypothesis B is more complicated than A, but still can be used to give predictions, it should not be discarded by adding very low prior probability to it in comparison with hypothesis A.
Ok, so I have studied the Solomonoff's lightsaber. I used this blog https://www.lesswrong.com/posts/Kyc5dFDzBg4WccrbK/an-intuitive-explanation-of-solomonoff-induction
Please correct me if I am wrong, but I feel that there is a ... well, not mistake... assumption that is not necessarily true. What I mean is the following. Let us consider the space of all possible inputs and the space of all possible outputs for the Turing machine (yeah, both are infinitely dimensional, who cares). The data (our Universe) is in the space of outputs, theory to test in the space of inputs. Now, before any assumptions about data and theory, what is the probability for the arbitrarily chosen input of length n lead to output with length N (since the output is all the observed data from our Universe, N is pretty large) - this is what is prior probability, correct?
Now we remember the simple fact about data compression: the universal algorithm of compression does not exist, otherwise you would have a bijection between the space of all possible sequences with length N and length N1 < N, which is impossible. Therefore, the majority of the outputs with length N can not be produced by the input with length n (basically, only 2^n out of 2^N has any chance to be produced in such way). For the vast majority of these outputs the shortest input producing them will be just the algorithm that copies large part of itself to output - i.e., a priory hypothesis is incredibly long.
The fact that we are looking always for something simpler is an assumption of simplicity. Our Universe apparently happened to be governed by the set of simple laws so it works. However, this is the assumption, or axiom. It is not corollary from some math - from math prior should be awfully complex hypothesis.
If you put this assumption as initial axiom, it is quite logical to set incredibly low priors for God. However, starting from the pure math, the prior for this axiom itself is infinitesimal. The prior for God's hypothesis is also infinitesimal, no doubts. Well, for my God's hypothesis, since it is then lead to your axiom (limited by the Universe) as a consequence. For "witch from neighborhood did it" and then copy paste all the Universe data to "it" priors actually should be higher for reason discussed above.
Why don't we then keep the "witch" hypothesis? Well, because its predictivity strength is zero. So basically we keep simplicity hypothesis in spite of its incredibly low priors because of its predictivity strength. And if we want to compare it with different supernatural hypothesis we should compare the predictivity strength. You can not cast them out just because of priors. They are not lower.
I will leave for a few days - need to do my job and to learn everything you recommended. Thanks to everyone, see you soon!
I thought about it immediately after reading HPMOR :) . It is just seems to me still quite unlikely (if I would one time out of hundred correctly guess the natural number from the interval from 1 to 100 it would be absolutely a bias; but I feel that for me frequency is significantly higher than the probability).
Well, ok we discuss priors later, I need some time to learn it.
- why I don't think it is natural effect - well, simply because of the amount and the longitude. Everything that could been inside should have gone away.
- why I don't think it is hoax. Well, it is more complicated. I would say the probability of it to be hoax is very low, and since my priors are not that low as yours, it works for me. Now why I estimate the probability of the hoax to be low:
- 1. If you read the story attentively, you see that there was an icon like that before (pretty recently actually, last quarter of XXth century), there also was a person who discovered it and was traveling with this icon everywhere (the same as current person travels now). The previous person was killed and tortured, the icon disappeared. The murderers were not found. It would be quite crazy idea, knowing this story, to make this mystification. To put your life under risk for what? For stupid hoax? You must be crazy to do it. And this person (current keeper) serves in police, so he must have some regular checks of his phychological state. Finally, simply anecdotical evidence - I saw him once, he seems to be normal guy (of course, I am not a specialist, it is just slight decreasing of probability him being a psycho)
- 2. If I would need to do such a hoax, I would put some source of myrrh inside, and refill it periodically. It can be done of course. I could even believe that it can be done such that observer, taking the icon, would not notice any difference from the usual icon. But is it possible to avoid X-rays somehow? They travel by plane, I bet they do not put icon into luggage (it is too precious). So they must go with it as hand luggage. There the custom, using X-rays, observe small vessels inside the icons and asks what is it. And it is done, the hoax is over.
I will disappear from here for few days - need to do my job, and also learn everything you send to me.
So, regarding the omnibenevolence - again, we first need to clarify what means "good" and "evil". So, first we need to get, if we have the same understanding of this, otherwise it is the argument about definitions. I am not sure if it is possible to give a precise definition, but let me ask few question to see if we have the same answer to them or we understand it differently.
1) Is "good" only utilitarian (i.e. for some higher purpose - then which one?) or deontological (i.e., there are some good things that are good by default. It is good to bring some joy to the life of the old person even if he is totally useless and senile - like that).
2) Is good only result or there can be some goodness in the process? Is there any goodness in striving and gaining, playing hard game and winning - or only final result is important?
Regarding no need of this hypothesis - somewhere below there is a thread where we argue about miracles.
1) No, it is logically impossible (I think so).
2) 3) I don't know. I would say "can but will not because of omnibenevolence".
4) The thing in the Old Testament I understand as sarcasm from God. I would say we can become "lower gods".
This problem requires the definition "what is good" first basically. For example, is it better to give the gift immediately, or to give the person a difficult task first, knowing that he is capable to do it, and then to give this gift as an award? When the person would feel better?
Also, when you are saying it is your crux, do you mean the statement "omnipotent omnibenevolent God is incompatible with observed Universe" is crux for "There is no omnipotent omnibenevolent God" ? So if this statement is false you would believe that there is a God? :)
Thank you! I will read and try to understand it
I would say that God do not have a God, otherwise we would consider the second one as the true God.
Regarding halting oracle, let me first read it and understand what is it.
Here I need more time.
Well ok I do not mean some kind of visions, voice etc. (I mean it can happen but I did not experience it). For me it is rather answers to my questions in form of quite unlikely coincidence. But this is for me, I would expect that it is individual.
I am not familiar with the miracles of other religions. I would even say I do not have a solid opinion about them. My idea of God does not forbid miracles outside Christianity. (It is not syncretism - it is just that the same God for some reason may do miracles for people outside Christianity too).
I would even agree that really a lot of things that are considered to be miracles are not such. However, I can name a couple things I believe to be actually miracles. This, for example https://www.orthodoxhawaii.org/icons
It would we helpful if there was some algorithm or formula that connects complexity with prior probability. Otherwise, I can say that probability decays logarithmically with complexity, and you will say that it decays exponentially, and we will get totally different prior probabilities and totally different results. Do you know if such thing exists?
Ok. Maybe you could think why is your prior for the Christian God is extremely low to find at least one crux? I mean there should be a reason for such low prior, and if you find it, it can be a crux.
I can try to add more co-cruxes
- I believe that there are not just random miracles but such that directly connected with Christian practice (like associated with objects of veneration or worship).
- I believe that many of the New Testament books are reliable historical documents, written when they are said to be written, telling the true story with possible mistakes in minor details. I would prefer not to work with this co-crux because I am not a professor of Ancient Rome history, but if it is your choice that is ok.
- Regarding my crux 3: I personally believe in the fact that perception of the human is not equivalent to the perception of the simulation. I can expand more on it.
- I believe that if you will try hard you can have a contact with God. If you try and not succeed though I might always say though that you did not try hard enough or did not follow the instructions properly, and since I can't read your mind, it will be hard to persuade me.
Omnipotence is necessary but only in a sense of programmer analogy.
Personality is totally one of these attributes, otherwise it is just Laws of Nature
Omnibenevolence - yes, but then we will need to define properly "what is love", "what is good" etc. We can do it if it is necessary.
First of all, let me apologize for two things.
A) I am not a native speaker so I will have mistakes in my English, especially articles. So why "There is God", not "There is a God" - because of my English.
B) I am pretty new here, so I simply don't know what is "rot13" and how can I do it.
Second, about my statement A.
The very specific statement that I actually believe is "The Eastern Orthodox Christianity has a correct description of God". But to discuss it here would be too complicated, since it has a lot of details. I don't think it makes a lot of sense to discuss Trinity before we agree on the question whether there is a God. So, let me be slightly more general than this very specific statement, but more specific that I initially was.
There is the God. God is individual being (i.e., has personality). God is omnipotent in the naive meaning of this word (i.e., you do not simply generate the random statement X and add "God can do X" assuming it to be true; I would rather say He is omnipotent like programmer who can do whatever he wants within the simulation he runs - it would be not exactle what I mean but a good approximation).
Maybe you are right. For everyone who thinks it is better - my cruxes are in the bottom of my comment.
Great! Ok, I am honestly reciting:
If there is God.
I desire to believe that there is God;
If there is not God,
I desire to believe that there is no God;
Let me not become attached to beliefs I may not want.
I say it, I mean it. Stop me if I appear to be attracted to the good effects of placebo more than to the truth.
I am ok with many interlocutors, but you will need to explain how to use double crux in this case. And yes, let us do it here in comments. Do you have your cruxes already? If no, please do not read further. If yes, here are mine (go to the very bottom):
1. I believe that there are miracles. By the miracle I understand event or series of events that have either extremely low probability, seems to break the laws of Nature or have significantly higher probability to occur in the world with God rather than without.
2. I believe that the person can have contact with God through prayer. I would say - every person, but I am not that confident.
3. If the perception of the human mind is equivalent to the perception of the full-brain simulation, I believe that we live in the simulation (what is basically means that there is a Programmer who is like God). If the perception is not equivalent, I believe that it means indeducibility of the perception from the laws of Nature, what significantly increases my expectation that there is a God.
Thank you!
Thank you for your reply. I agree with it. However, how would one estimate these prior probabilities at all and decide whether it is rational or not to try X? It should depend on its cost (basically the time spent since you have all the equipment according to the set up of the problem) and on the gain (for example, if X in (1) is just one more asteroid, gain is not large, if it is asteroid that might collide with Earth gain is larger). Most difficult, how to do it in the third case? How much time X would require to be rational to try? 5 seconds? 5 years? Where this estimate can come from?