Ph.D. student at UCLA, theoretical biophysics
" 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.
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 :)