Ph.D. student at UCLA, theoretical biophysics
valentinslepukhin(Valentin Slepukhin)
Thank you!
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.
Maybe you are right. For everyone who thinks it is better—my cruxes are in the bottom of my comment.
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).
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.
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.
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?
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
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.
Here I need more time.
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.
Thank you! I will read and try to understand it
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? :)
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.
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.
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).
I will leave for a few days—need to do my job and to learn everything you recommended. Thanks to everyone, see you soon!
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.
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.
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?