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Notes -
So imagine we have two hypotheses, to simplify.
Hypothesis 1 is that there's a 95% chance of a rational being coming into existence.
Hypothesis 2 is that there's a 0.001% chance of a rational being coming into existence.
You, the observer, notice, hey, I'm a rational being who came into existence!
I'm saying that it's rational to think that this should update your priors towards hypothesis 1 over hypothesis 2. But only if there's a one-shot or few-shot universe.
It's 95000 times more likely for a rational being to come into existence under hypothesis 1 than under hypothesis 2. So this piece of evidence should update our beliefs by 95000 times using the odds form of Bayes' theorem, I believe.
For a comparison (and I'm not certain that this is a perfect analogy, but I think it works), let's say you are told that there's a 50/50 chance a surgery succeeds. Under the 50% chance you survive, you always wake up. Under the 50% where it fails, they freeze your body, and you estimate that there's a 1/50 chance that they manage to revive you in the distant future.
You wake up. Assuming there's not going to be any distinguishing sensation between the two ways you could wake up, which should you think is more likely? I would think you should think that there's a 50:1 chance that it worked.
No, it shouldn't change your priors, irrespective of whether there's a one-shot or multi-shot universe.
Given that you are a rational being, the odds that you will observe a universe where a rational being came into existence are exactly 100%. This is true regardless of whether hypothesis 1 or hypothesis 2 is true, and therefore it tells you no additional information about which hypothesis is correct.
That's true, because this situation is materially different from the one we are talking about above. Here, we know two sets of probabilities ex ante (both of which can occur), and are now trying to decide, ex post, which is more likely to have occurred. Given two different possibilites, the one with the higher probability is, by definition, the one that was more likely to occur (this is true whether the surgery is one-shot or many-shot, by the way).
In the situation we are discussing, we don't know anything about the probabilities ex ante, and we are trying to derive those probabilities based on our ex post observations.
A better analogy would be: you go into a surgery and nobody knows your odds of survival. You wake up after the surgery. What, if anything, does this tell you about your ex ante odds of surviving the surgery? The answer is, it tells you nothing about those odds. It just tells you that you survived. Your odds of survival could have been 0.001% or 99.9%, but since you can only observe outcomes in which you survive, that fact that you observe your own survival gives you no additional information about the ex ante likelihood of that outcome.
Another example to illustrate the point. Suppose an alien hands you a black box with a screen and a button on it. You push the button, and the number "21" appears on the screen. Pushing the button again does nothing and you cannot disassemble the box to learn how it works. What are the odds that the box was going to display the number "21" when you pushed the button? The answer is, you have no idea (except you know the odds are not 0%). It might have been a 100% chance, it might have been a 0.000000001% chance. You have no way of knowing based on your single ex ante observation.
By starting with "given that you exist," you're assuming away the part you can learn from. Starting from an objective not-taking-into-account-yet-that-you-exist estimate of likelihood that a random universe would be able to contain life, you should have some estimate of a likelihood that a universe could contain life.
But now that there's some agent, that's data! That's information! You can use that to shift your beliefs. Now you're about to respond that there will always be an agent whenever you have the opportunity to think about these things. Maybe so. But there won't always be an agent in the universes in the world-model we were just talking about. And those worlds where there is one look different from the worlds where there isn't one. They were created by mechanisms that result in a higher probability that such agents come to exist. And so you should assume that you, in actuality, are more likely to be in the higher-probability portions, than you'd think on a basis that ignores your coming to exist.
Per your surgery case, I don't think your conclusion is true? Most people who survive a surgery do it in cases where survival is likely, so I would think that you should think that you're among that pool. That seems like another case where the bare fact of your existence provides evidence about the world.
Well, that's not quite just your existence, since what I just said requires knowing how often other people survive surgery, but it would still seem in the general case that you should update to some extent (it may be a small one, depending on your prior knowledge) towards your surgery having odds of survival by waking up.
See Joe Carlsmith's account of SIA here for one analysis that would incline one towards being in universes where more people exist. It's fairly rigorous, but not without difficulties. I don't remember it addressing the question exactly as we've posed it, but it's definitely very relevant.
I'm not convinced that it's quite the same framing as I had used above for the first two paragraphs, so maybe I'll have to think about whether any of that needs revising. But I'm still pretty confident that you coming to exist provides you information that you can use to shift your beliefs.
If we could start there then we would gain some information from the later observation that the universe contains life. But we cannot start there. We start in a universe where the existence of life is a given, with 100% probability.
It's not. You can only observe a universe with agents because you are an agent. That statement is always true, no matter the prior probabilities, so you cannot draw any conclusion about prior probabilities from the fact that it happened.
Right, if we could bring in outside information about how likely a universe is to contain life and what factors influence that, then we might be able to draw some conclusions from the fact of our existence, but we have no such outside information, so we cannot draw such conclusions.
Why can't we start there? Isn't that equivalent to stating that you can't think about universes where life doesn't exist? That's transparently false. Working out what our beliefs should be if we ignore a piece of information is something we're allowed to do.
No, that statement isn't always true. It's only always true for observers. That means that you should shift your probability mass from what they would be if you ignored which worlds you're more likely to exist in as an observer, to what they should be after taking that into account.
Assuming our thinking is at all Bayesian, shouldn't we have some sort of probability distribution? Not sure exactly what one should look like, but that should exist. In any case, did you miss what I said about how it should always be the case, whatever that probability distribution is, that you should update (ignoring other post-waking-up information, on your existence alone) towards the chance of your survival having been higher than you thought it was before your surgery?
I'm saying we literally can't start there. We can't go back and observe before the beginning of the universe. We don't have any information about what was happening then, or what the dynamics of the situation looked like. We only have information about the universe we currently inhabit.
We can certainly think about it, but we don't know anything about it, so it doesn't do us much good.
You are an observer, so it's always subjectively true for you 100% of the time.
Yes, so start with whatever your Bayesian priors are. You think there's an x% chance that the universe would contain observers. For every possible value of x other than x=0, the odds that you will observe a universe with observers is equal to 100%. So there is no basis to either raise or lower your prior based on this observation, because the odds of it being true are exactly the same in every possible scenario other than x=0.
Assuming you have no outside information about the surgery, there is no basis to update your priors. This is true for the same reason I explained above. For any prior other than x=0, the chance that you will observe you survived the surgery is exactly equal to 100%. If you did not survive, you would not make any observation, so the only possible observation you can make is "I survived."
But you've acknowledged that we should have some sort of prior probability distribution (it may be pretty uncertain), so we can use that.
If you're saying that we always have to take into account that we exist, we can't think about cases where that's not true, how does it not follow that you can't imagine worlds where you don't exist?
I understand that. What I'm trying to make clear is (something similar to that) that the space of all worlds and the space of all worlds with observers don't look the same. And so observers will have things that look more like the latter. And worlds with observers will look more like multiverses, there is some reason why the universe's fine-tuning is necessary, or theism, because in our ideas of the possibilities, observers are relatively more likely to occur in worlds of those varieties, as compared to one-shot worlds that require high degrees of fine-tuning.
No, it isn't 100%. You're ignoring all the scenarios where you don't exist. Yes, you won't be around in those worlds to decrease your estimate of the probability of life existing, but that doesn't mean you shouldn't take them into account.
And we've estalished that we're talking about a one-shot universe, so there's definitely a good chance that there is no observer, in which case the odds taht you will observe a universe is less than 100%, because in some of those worlds you don't observe anything at all. That you exist is information that every observer should take into account, but that doesn't mean that it isn't information.
You definitely can make observations.
Let's say you have two hypotheses (in actuality, it should be distributions, but I haven't looked into the math for how to handle those). You think there's a 67% chance the surgery works, and a 33% chance it fails. It doesn't matter whether this is based on data, we're assuming you have priors. Next, you think there's an 80% chance you wake up again if the surgery works, and a 20% chance that you wake up if it fails. The doctors have told you that it should feel the same upon your waking up, if you survive, regardless of whether it worked or not.
You wake up. How likely should you think it is that the surgery worked?
Well, there's a 4:1 ratio of survival, so I'm pretty sure under Bayes' theorem, we'd multiply that by the 2:1 and get a 89% chance that the surgery worked, instead of the 67% chance that the surgery would work originally.
To check that that makes sense, we indeed find that 89% of rational agents who thought this way and woke up had surgery that worked.
You don't need more formal knowledge, subjective probabilities are good enough. If you don't try to update, your agents will be wrong more frequently than mine.
For a comparison, you clearly think the anthropic principle means that most planets with observers will along certain axes, look like Earth—that is, unusually good for a planet at sustaining life. But under the reasoning that you have, shouldn't that not be the case? That is, given that you exist, it's a 100% chance that you exist. Therefore, you can't distinguish between the "looks like Earth, well suited for life" hypothesis and the "chance quantum fluctuations brought me and an oxygen mask into being on an inhospitable planet" hypothesis—on both of these, if there's any observer, the observer has a 100% subjective chance of existing, so you can't adjust your priors from how likely you think each sort of planet is to form. And since inhospitable planets are so much more common overall, I would think, shouldn't you be shocked that we're on a hospitable one? You clearly don't actually think that, but I don't see how that's different from the case that we're arguing over. You think that we should expect to find ourselves on a hospitable planet, but have no problems with asserting that we should not expect to find ourselves in an hospitable world (where world is meant to extend beyond just the universe).
You're probably about to respond to the last paragraph by saying that "inhospitable planets are much less common in worlds with observers, so it makes sense to look at those." This is undoubtedly correct. But why should we not similarly expect that inhospitable worlds are much less common for observers, and prefer the hospitable ones: the ones where the fine-tuning is actually only apparent, and the physical constants are either necessary or much more likely to be hospitable to life, the ones where there's a multiverse, and so it's practically guaranteed that some of the universes are favorable to life, the ones where it was intentionally made to be hospitable to life, whether by a God or runners of a simulation, or whatever. All these are to the one-shot, heavy-fine-tuning-required-that-we'll-just-have-to-luck-into world what Earth is to Pluto.
I probably shouldn't waste too much more time on this, so I'll be willing to respond once more, and then will (probably) stop.
You can imagine worlds where you don't exist, but imagining such worlds doesn't tell you anything about how likely they are.
This is the claim I am pushing back against. We have, broadly, three categories of possibilities:
God created universe(s)
Natural processes created multiverses
Natural processes created a one-shot universe
We have no information about which of these scenarios are even possible to begin with. Even if each is possible, we don't know which one is more likely to create observers. So let's naively assign a 33% probability to each. Now we are going to make empirical observations and see if that moves our priors.
Given that you (an observer) exist, what is the chance that you will empirically observe a universe with observers in scenario 1? Answer: 100%.
Given that you (an observer) exist, what is the chance that you will empirically observe a universe with observers in scenario 2? Answer: 100%.
Given that you (an observer) exist, what is the chance that you will empirically observe a universe with observers in scenario 3? Answer: 100%.
So after making the observation, our priors should remain the same, 33% for each scenario, because our observation is equally likely to occur in each scenario.
You're ignoring what I said: "the odds that you will observe a universe with observers is equal to 100%." There may be some probability of a universe without observers existing, but you can never actually observe this, and you therefore have no information about how likely it is to occur. You have no way to "take this into account" because you don't know if this scenario can even exist, or how likely it is.
First of all, it's not a given that the odds of observers are less than 100%. They are less than or equal to 100%. It's possible that a one-shot universe must necessarily create observers. We have no clue about the underlying physical process that would create such a universe and therefore we have no clue about the likelihoods. There may be no randomness involved.
Second, the odds that you will observe a universe with observers is 100% because the word "you" in that sentence necessarily implies the existence of at least one observer. The statement "in some of those worlds you don't observe anything at all" is incoherent, because there is no "you" in such worlds. The statement "you will always observe observers" is a tautology, it is necessarily true based on the definition of the word "you."
My point is that here, in the universe scenario, we have no way of testing whether the agents are correct or wrong. In the surgery scenario we can look back and ask the doctor "did the surgery work" and find out whether the agents' guesses were right or wrong. Here, there is no way to check the truth value of the agents' guesses, and therefore no way to find out if their priors are correct or way off.
A better analogy would be: suppose you go in for surgery, and no one has any clue about the likelihood of success or the likelihood you will wake up. So let's say the odds of success are x%, the odds of failure are (100-x)%, the odds you will wake up if the surgery's successful are y%, and the odds you will wake up if the surgery's a failure are z%. You're a Bayesian so you assign arbitrary probabilities to x, y, and z, say 50% for each. You go in for the surgery and you wake up after. You are provided no additional information. How, if at all, should you adjust your priors?
The difference is, we know that hospitable planets are relatively rare. We have external knowledge about how planets form and can observe both planets with and without life. We didn't come to this conclusion based on the fact of our existence. We came to this conclusion by observing the external universe.
Imagine we had zero information about the universe beyond planet earth. Should we assume that planets with life are rare based on the fact that humans exist? Should we assume that earth is especially hospitable for life? Should we assume other planets even exist at all? In the absence of any external information, it's totally possible that planets with life are common and that earth is uniquely hostile to life compared with those other planets. Or it's possible that earth is the only planet. We would have no way of knowing, based merely on the observation that we exist.
No, because we have no idea how "unlikely" the fine-tuning of our universe is. We have no reason to think that dice were rolled. It's possible that what seems to us like fine-tuning is actually just some necessary constraint of an underlying physical system that created the universe, such that the odds of fine-tuning were 100%. Or its possible that a fine-tuned universe was super unlikely and we just got lucky. We have no way of knowing.
Likewise, there's no reason to assume that God likes creating fine-tuned universes. He might love rolling dice and creating trillions and trillions of dead universes for every living one. After all, he seems to love creating uninhabited planets, so why not uninhabited universes?
Should we be able to come up with some prior probabilities?
You seem to think that it's necessary to price into all predictions that you exist. I don't see why. Ignoring information while calculating probabilities is something you're allowed to do. The surprise only happens when you ask questions like "if, for now, we don't take that I exist into consideration, what would be the likelihood that there'd be any observation going on for a world in scenario 1? What about 2? Or 3?"
I hadn't ignored it, it just seems that we'd parsed the sentence differently, once again disagreeing on whether we're a priori assuming you exist. I'd taken "no one exists" to be among the pool we're drawing from, while you didn't. In those cases, no one observes. Of course, if we're only taking into account the ones you observe, you are correct. I've just been trying to argue that we shouldn't do that.
Yes, that's one of the three possibilities that I'd mentioned (second quote in your last comment) that we should be updating towards.
I don't think it's incoherent, it's just evidently not the way you specifically use sentences, and you're probably right that your use in this case is more normal.
That's largely irrelevant. Yes, we should adjust our beliefs if we can get any evidence on that, but we should go with this in the mean time.
Alright. We have x:1-x (I'll go with this since going up to 1 is nicer than up to 100. No real difference, though.). We multiply by y:z. We get xy:z-xz. (This gives a 100xy/(xy+z-xz) chance it worked). We know that this is higher than before, since xy/(xy+z-xz)+(z-xz)/(xy+z-xz) still equals 1 and the ratio's been shifted towards the first, since y>z.
So you update from x to xy/(xy+z-xz), which is an increase in probability.
Do note that this analysis was holding y and z constant and only updating x, I assume you'd in actuality be having to update several things at once. I don't know the math to know how to do that. I'll note that this general case was explicitly what I was trying to do—I said that a few times. The numbers before were just examples.
I think you might have been misunderstanding the argument I was trying to make right there. I was not making an argument about how common hospitable planets should be. I was making an argument about how commonly observers should find themselves on hospitable planets, interplanetary travel excepted.
It was my point that hospitable planets are relatively rare, and yet somehow we find ourselves on one. Why could that be? Did we just luck out? It's not like there couldn't be observers on inhospitable planets (I gave the example of chance quantum fluctuations, also providing a space suit or whatever is needed). And so, by your reasoning, you should pick priors on how likely any given planet is to be hospitable in this universe. Let's say 1/100000. I don't know the actual figure, but let's go with it. Okay, how should we decide which is more likely for you, an observer to exist on? Well, since both can happen, and, considering any given planet, given that you exist, the probability that you exist is 100%, we can't update our beliefs (per your reasoning), so we should still have a 1/100000 chance that we're on a hospitable planet, and we should be rather surprised to find ourselves on one.
See the equivalence:
You say:
We pick priors for the relative likelihood of any random world being habitable.
We draw no inferences the fact that we exist, since that happens in every world where we exist to observe it.
We keep those probabilities for the chance we're in a habitable world.
Now, swap "world" for "planet".
We pick priors for the relative likelihood of any random planet being habitable.
We draw no inferences the fact that we exist, since that happens on every planet where we exist to observe it.
We keep those probabilities for the chance we're on a habitable planet.
But in the planet case, those priors are clearly very different from what we see, due to the anthropic principle, which I think your arguments disallow.
Now let's look at how it appears under what I say.
We pick priors for the relative likelihood of a random planet being habitable.
We do draw inferences from the fact that we exist, shifting our probabilities very strongly towards planets that give us decent chances to exist.
We use those adjusted probabilities to give us the chance we're on a habitable planet.
And for worlds:
We pick priors for the relative likelihood of a random world being habitable.
We draw inferences from the fact that we exist, shifting our probabilities very strongly towards worlds that give us decent chances to exist.
We use those adjusted probabilities to give us the chance we're in a habitable world.
I'm not seeing how this touches the arguments that I was making before. I wasn't arguing for the frequency of habitability among other planets, I was arguing for the likelihood that the particular one we're on is habitable. Am I seeing here that your argument is that we can have no priors? But I was kind of assuming that we were taking into account scientific knowledge of most planets being inhospitable. (I'm also confused since your arguments are all backwards—I don't see why humans existing should shift our beliefs towards life being rare, and so on.)
But we should, I suppose, think that many planets is more likely than in worlds where we don't exist, for anthropic principle reasons. (which, again, is exactly what I've been doing, but with worlds). And we should expect ourselves to be in one of the planets where life is common, I think, because more life exists on those, I'd think, so the "earth is uniquely hostile" seems less likely?
See once again that it being necessary, or at least, fairly likely, even if it's one-shot was one of the possibilities I said we should update towards.
We don't have to assume he does to shift in that direction, we just need to think a God is more likely to create life than the one-shot real-and-not-just-apparent-fine-tuned case to shift probability from the latter toward the former. This doesn't seem like a crazy possibility to me, unlike the we-just-got-stupidly-lucky option, so the relative probability of theism to super-lucky should be raised.
If your response is much the same, I'll stop, since
you won't listen(sorry, that's not true, that's just what it feels like) this is going nowhere, so feel free to have the last word. Thanks for the conversation.More options
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