Is fine-tuning evidence of the multiverse? I argue that no, but paradoxically the inference to the multiverse may still be valid. All of the background is in my main multiverse article, but this one is still pretty self-contained. You actually don't even need to know what fine-tuning is, because all we'll be using is a very useful analogy from Steven Novella's article on the matter:
Here is another, hopefully helpful, analogy. Let’s say that we encounter a super-advanced alien race. They claim they created the Earth (and for the sake of argument, let’s say their claim scientifically checks out). The features they decided to give the Earth were determined at random. They reveal the process they used to determine these factors, and by their own calculation there was only a one in 1 quadrillion chance that the Earth would be compatible with life. Now – is it more likely that Earth is the one and only planet they created, or that they go around the universe creating lots of planets? Do we need to explain why Earth specifically is compatible with life?
The bottom line is that, given these premises, we can infer that it is more likely (not a certainty) that the aliens have been creating lots of planets, so that there is a good chance that at least one is compatible with life.
I encourage you to read the background, to understand why we are interested in this science fiction story. But even if you don't, you can make sense of the two questions we'll be concerned with:
- Is Steven right about his inference to MP (multiple planets)?
- Is fine-tuning, i.e. the chance of life only one in a quadrillion, a crucial component of this inference?
1. What is Steven right about?
That inference is correct. But it has an unstated assumption, that it's not too unlikely that the aliens would choose to create many planets rather than just one. I.e. that the prior for MP (multiple planets) isn't too low. Goff seems to disagree with this inference, he is wrong.
2. What is Steven missing?
It's this: FT (fine-tuning, i.e. the chance of life being 1 in a quadrillion) plays no part in the above inference:
Here Goff is right, FT is not evidence for MP. I know this seems counterintuitive. I work this out in detail in the other, longer, fine-tuning article, but let me give a very condensed, but hopefully still understandable, proof. The next section provides this quick proof, and the section after that clarifies the logic, in case some of the steps seem puzzling or unmotivated.
3. Quick proof.
First fix some prior, for example assume the aliens had no preference between SP (single planet) and MP42 (42 planets; of course you can use any huge number instead), so they flipped a coin. Then imagine, as we often do when analyzing probabilities, that this whole experiment was performed a gazillion times. Let's say there are a gazillion galaxies, and each one has such aliens, so that half the galaxies have SP-choosing aliens, and half have MP42-aliens.
And now it's super simple to find how many life-permitting planets were made by MP42-aliens vs SP-aliens. The table below shows that the proportion is always 42:1 regardless of whether FT is true or not. Which means the odds of being made by MP- vs SP-aliens a random civilization should assign itself are always 42:1. Here it is, with p = chance of life (one-quadrillionth for FT, 1 for no FT):
MP | SP | |
---|---|---|
Galaxies | 0.5 gazillion | 0.5 gazillion |
Planets | 42*0.5 gazillion | 0.5 gazillion |
Planets w/life | p*42*0.5 gazillion | p*0.5 gazillion |
Odds | 42 | 1 |
We can clearly see that p, the degree of fine-tuning, has no bearing on the final result.
4. Clarifying the logic.
The discussion in the comments has helped me to better understand my own argument and what parts of the logic might seem unclear or objectionable to some people. This is, as I mentioned, a condensed, bare-bones version of the main multiverse article, in which the logic is spelled out in more detail, but I would like to make it as self-contained as possible by clarifying the key points underpinning the argument, while still keeping the overall length to a minimum.
P1. Simple prior. Without loss of generality, we can assume equal likelihood for the aliens to choose MP42 vs SP. Why? It's easy to redo the math for a more general prior {p_1, p_2, p_3,...}, where p_n is the probability for the aliens to decide on n planets. All the steps and the results will be the same.
P2. The ensemble premise. We can assume, without loss of generality, that this experiment with the aliens making planets has been done gazillions of times in parts of reality causally disconnected from ours (I called those other parts galaxies for simplicity). Why? The main reason is that stipulations about what's going on in parts of reality that are so distant from us that they have no causal physical influence on us should not matter. So all that should matter are the exact parameters of the experiment here in our galaxy, not any stipulations about whether this is the only place in the cosmos with such an experiment or there are other places like that far far away.
P3. Self-locating uncertainty. If there are gazillions of civilizations scattered throughout the cosmos, and we are one of them with no way of knowing which one, then we should just treat ourselves as "selected at random". In our case, if for every 43 civilizations in all the galaxies 1 is made by SP-aliens, then we should assign ourselves a 1 in 43 chance of being such a civilization, and similarly for MP42.
The calculation in this article follows mathematically from these considerations. The calculation then shows that the chances we should assign ourselves of living in an SP vs MP galaxy do not depend on the parameter p, the degree of fine-tuning. This, by definition, would mean that fine-tuning is not evidence of MP.
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I find it to be unreasonably interesting the assumption you've made here (of which I'm sure you're aware).
ReplyDeleteThe assumption that the aliens are just as likely to create one world over creating 42 worlds - or in your extension N worlds. Let's call this Tn/T1
I think your analysis remains reasonably valid given Tn/T1 << N (please let me know if you would like an explanation). I think in Steve's IVF scenario it is reasonably valid that this holds and possibly the alien scenario.
I think to steel man Goff isn't what he's saying that we can't know Tn/T1 in the multiverse scenario at all? Maybe each universe spawned creates a chain reaction which spawns other universes or maybe each universe spawned decreases the chance of other universes from being created? So in that sense we really can't draw any conclusions.
Hey platypus,
DeleteGood question about the assumption that the aliens are equally likely to with 1 or N. This is of course just a simplification, but which doesn't actually affect the conclusion. There is another simplification here too - that the aliens were only choosing between two options.
So in a more general case we would start with a prior distribution {p1, p2, p3,...} encoding our best estimates of the probabilities that the aliens would decide to make 1, 2, 3,... planets. We would then calculate the posterior distribution, which incorporates the evidence of our existence, by constructing the ensemble, just like we do in the article, and then calculating the number of civilizations made by 1,2,3... planet choosing aliens.
The bottom line will be exactly the same though: the ratios among those numbers will be independent of the degree of fine-tuning p (Goff is right), but scenarios with higher numbers of planets will receive a boost (inference to more planets a la Steven).
And yes, I would need an explanation you offered because I don't quite follow you in that part.
Finally, I don't think Goff is saying what you are suggesting.
Hi thanks for your response.
ReplyDelete(Please note these are just my thoughts as I'm working through this problem - I think my answer requires considering all values of n - I wouldn't consider I've thought it all the way through yet so it's very possible I'm wrong! Really appreciate your responses.)
Yes I see that it is independent of fine tuning which kind of blows my mind!
The reason I am questioning is more of a steel man for the "we can't say" case (which I previously disagreed with).
Consider your alien scenario but instead of assigning a 50% to 50% for both let's parameterise it.
Let T1 be the tendency (or probability) that a given alien will create one planet.
Let Tn be the tendency that a given alien will create n (or 42 in your case) planets.
In your calculation the probability of being on a planet which was made by these N aliens is:
P(N|L) = N * Tn / (T1 + N* Tn)
(Apologies I made a mistake before in my calculation!)
I think that P(N|L) is pretty close to one given N*Tn >> T1 or T1 is either about Tn or not far more likely than Tn.
I think this is quite reasonable for the alien case (why not make more if they can?) and the IVF (if the doctors done it once he's probably a bit "weird" and he'd do it again).
With the universe I think it's very unreasonable to suggest any estimate on Tn or Tn in relation to T1. I understand we'd say they're about the same because we have no other option but in some sense are we not just trading one unknown for another?
Though if I still had to guess I'd go with N.
A minor correction first :"I think that P(N|L) is pretty close to one given N*Tn >> T1 or T1 is either about Tn or not far more likely than Tn." Only the part before the "or" is correct.
DeleteA far more important correction. "I think this is quite reasonable for the alien case (why not make more if they can?) and the IVF (if the doctors done it once he's probably a bit "weird" and he'd do it again)."
This confuses the prior with the posterior. What you are talking about in your quote are considerations about your best guesses at the aliens ' or the doctor's psychology that you would use to form an educated guess about how likely the doctor would be to choose N vs 1. That's your prior, that's what we took to be 50-50 in our example in the article.
The posterior, on the other hand, is the credences you should assign after you account for all the information, that's what turned out to be 42:1. So your quote doesn't actually provide an explanation for why we shift our credences towards the N scenario.
One explanation I would give would be: If the doctor used 42 embryos there was a 42 times higher chance that one of them was mine than if he only used 1.
Finally in the multiverse case, we assign the prior based on our opinion of the plausibility of the physical mechanisms for the multiverse vs single universe cosmology based on our current understanding of theory and empirical data. If this sounds vague, it should - that's the nature of priors. But we still always have to start with some prior, and we always do, though often not explicitly.
We do it every time we say we now have evidence for a new particle, or gravitational waves, etc based on statistical evidence. More generally, what happens when you take the fact that your results are say different by 3 standard deviations from the mean predicted by the null hypothesis? If you then conclude that the null hypothesis must be rejected (unlikely to be true) that means you implicitly presuppose that the alternative hypothesis is not wildly implausible. Which is the same thing as saying that for whatever reason you assigned a not too low prior credence in the alternative hypothesis.
Hi Dmitriy,
ReplyDeleteAs discussed elsewhere, I think the ensemble analysis here is deeply flawed, because it doesn't deal with our credences of M vs S, and I think fine tuning has more to do with these credences than the relative ratios you're analysing.
Please see here for an interactive illustration of my thinking:
https://run.plnkr.co/preview/ckme55ked0006306i23zu3qjq/
You can edit and view source code here:
https://plnkr.co/edit/93TzXHlxZRSP8gww?preview
Please fork it if you want to make your own version, although I do have my own copy elsewhere too.
Hi DM,
DeleteThe simulation is pretty cool, and make it clearer how you understand the problem. As I am sure you expected I disagree that they produce the right results though. I can explain why here, or, if you prefer, we can publish your simulation,with the great explanation you wrote accompanying it, here as a guest post from you, and discuss it in the comments there. Let me know what works best for you.
As a quick first point, I disagree that my analysis doesn't deal with credences in M and S, that's all it does! If one accepts EP, the ensemble premise, which says that the credences you assign to M and S are unaffected by how many other similar experiments are performed, then the credences fall out immediately from the ratios of civilizations:
Step 1. By EP we can assume that we are living in a galaxy among G total galaxies where such an experiment was performed, with the ratio of S and M galaxies corresponding to our priors.
Step 2. We note, from the calculation in the article, that 1 out of every 43 civilizations have property S (living in an S galaxy).
Step 3. Since we have no other information that gives us a clew about which type galaxy ours is, we have to assign ourselves a 1 in 43 credence of having property S. This last step is easy to understand I hope: if all you knew was that you are among 43 people, one of whom had the letter S drawn on his or her forehead in their sleep, and you didn't have other clews, you would assign yourself a 1 in 43 chance of being the S person.
Hi Dmitriy,
ReplyDeleteThanks for the offer. I have my own (mostly dormant) blog too where I could publish a writeup. The problem in either case is time. It may be a while before I can get around to preparing an article, as I think an article may need a bit more background than is currently there. Also if it were to be integrated into a blog, it would be nice to embed the simulation more directly, as you did with your lovely chaos example. I'm not sure how to do that but you obviously do.
> then the credences fall out immediately from the ratios of civilizations:
What I mean is that I think you need to have credences embedded in the model explicitly, and that the ratios are not enough. That's what the simulation is trying to show.
Your ensemble model may fit the aliens who are seeding various different galaxies, but I see this as a poor analogy to single universe/multiverse, as M galaxies can coexist with S galaxies but M universes cannot coexist with S universes. Your model is analogous instead to China/Chile.
"What I mean is that I think you need to have credences embedded in the model explicitly, and that the ratios are not enough. That's what the simulation is trying to show."
ReplyDeleteI am not sure I understand, do you mean prior credences or posterior ones? The priors are set in my model at 50-50, but everything works the same for more general ones, p-q.
And embedding JS more directly in my case involves manipulating the canvas tag, in your case you could either do that too or manipulate some div tag with text.
> I am not sure I understand, do you mean prior credences or posterior ones? The priors are set in my model at 50-50, but everything works the same for more general ones, p-q.
DeleteYou set the credences in the model by having as many multiverse instances as single universe instances. So you're basically treating it as another level of population ratios, nesting populations within populations, or effectively weighting the populations in S versus M universes. That's essentially what the "naive prediction" does in the simulation. But I think that's insufficient, I think you need to model them as credences more explicitly as I do in the "sophisticated prediction" simulation, where you consider separately the possibilities that M or S is true according to those credences.
Anyway, that's what I was originally trying to get at when I said you didn't deal with credences.
But if EP is true, which I know you probably disagree with, then the steps 1,2,3 above explain how the correct credences are calculated. We start with the prior credences, which I took to be 50-50 (but could take them to be anything), construct the ensemble according to EP, and the correct posterior credences emerge as explained in those three steps.
ReplyDeleteSo besides the ensemble principle, is there any separate objection to those three steps having to do with credences?
Hi Dmitriy,
DeleteI don't think I understand EP, at least as it applies to the multiverse.
If EP is "the credences you assign to M and S are unaffected by how many other similar experiments are performed", I'm not sure what experiments are being performed in the multiverse, unless you mean the setup of all of reality itself is an experiment. By definition, that can only occur once, because by "reality" I mean all that exists.
I can see what it might mean for your alien analogy, where each galaxy seeded according to M or S could be seen as an experiment, but I don't see this as analogous to our situation when trying to predict M vs S for our universe. Even if we interpret "similar experiments" to mean the creation of other universes or multiverses, if there are any other "similar experiments" at all, then M is true by definition (at least according to my definition). S is just the case when no other "similar experiments" are performed.
So I probably do reject EP, at least for cases like this. Accepting EP may be modelling the situation as China/Chile according to the naive prediction. While this may be a good model for credences in situations of self-locating uncertainty among populations we know to exist, I don't think is the correct model for credences about whether certain populations exist in the first place. You only get the right answer in special cases such as where P(A) = 1 and P(B) = 1 or maybe some other special cases too, I don't know.
So, I think I should clarify my claim. Rather than claiming that the ensemble model "doesn't deal with our credences of M vs S", which could be construed as claiming that there is no attempt to model credences about whether we will find ourselves in population M or population S, I should say instead that it "doesn't deal with our credences of whether M is the case vs S is the case", because I think of the question as trying to predict which mutually exclusive global situation is the case and not which of two co-existing populations we will be born into. To the extent that the ensemble models credences at all, it does so incorrectly.
I feel like there is a contradiction between you saying
ReplyDelete"I can see what it might mean for your alien analogy, where each galaxy seeded according to M or S could be seen as an experiment... So I probably do reject EP, at least for cases like [the multiverse, not aliens or presumably the IVF case etc].", and, on the other hand,
saying you disagree with the analysis in this article (which deals with the aliens scenario) and also saying " While this may be a good model for credences in situations of self-locating uncertainty among populations we know to exist, I don't think is the correct model for credences about whether certain populations exist in the first place"
Obviously in the aliens analogy there is *either* a galaxy with a population spread over 42 planets our aliens created, *or* a population on only one created planet - our aliens didn't create both. So I am unclear then if you do or don't accept EP for the aliens.
"
Hi Dmitriy,
DeleteYou imagine the experiment was carried out a gazillion times, so we are to imagine that there are aliens seeding gazillions of planets. So it can be the case both that there is a galaxy with a population spread over 42 planets as well as another galaxy with a population on only one created planet. Maybe *our* aliens didn't create both, but you are helping yourself to the assumption that we can imagine the same sort of experiment being carried out many times.
I don't think that this kind of assumption is tenable for the universe when assessing S vs M.
I realise we've been over this before, but I don't think even treating them as separate possible worlds will work as long as you're analysing the ratio of observers across all populations. I've tried to argue before that such combined populations are incoherent, but I failed to communicate the idea successfully.
This is why I turned to the simulation, which is by its nature more precise and less prone to misunderstanding. I think the simulation demonstrates the kind of mistake I think you are making. By treating the separate populations of M and S as different possible worlds which all coexist as possibilities and then doing an ensemble analysis across the combiend population, as happens in the "naive prediction", you ignore the fact that M and S are mutually exclusive and you get the wrong answer.
Hi DM,
ReplyDelete" Maybe *our* aliens didn't create both, but you are helping yourself to the assumption that we can imagine the same sort of experiment being carried out many times.
I don't think that this kind of assumption is tenable for the universe when assessing S vs M."
If I understand correctly, you are saying for the aliens the ensemble technique based on EP is fine but for the multiverse it's not. So does that mean you accept the results of the calculation in this article, that the final credences are 42/43 and 1/43, assuming the priors are 50-50?
If the aliens seeded a gazillion galaxies, and randomly decided for S vs M each time then the ensemble argument is fine.
DeleteIf either the aliens seeded only one galaxy or had some unknown reason for consistently preferring S vs M, and our credence of 50%/50% merely represents our ignorance as to this preference, then I don't think it is.
DM,
ReplyDelete"You imagine the experiment was carried out a gazillion times, so we are to imagine that there are aliens seeding gazillions of planets. So it can be the case both that there is a galaxy with a population spread over 42 planets as well as another galaxy with a population on only one created planet. Maybe *our* aliens didn't create both, but you are helping yourself to the assumption that we can imagine the same sort of experiment being carried out many times.
I don't think that this kind of assumption is tenable for the universe when assessing S vs M."
I'm surprised you're still repeating the same points, given that we can clearly set up the analysis so that either we are running it as a combined population, or as two separate populations (I showed this). You haven't given any reason to prefer the former, which you yourself admitted.
But let met quickly dispel this point (once again) that it is "incoherent to reason on a combined population". Because this is confused talk, and runs counter to all counterfactual reasoning. Firstly, as Dmitry pointed out, we are doing a combined population analysis in the alien experiment case. The analysis supposes that *either we have a galaxy that implements one or the other scenario.
You seem to agree that the actual reality is irrelevant to the soundness of the probabilistic calculations (there don't actually have to be aliens for us to make the above conclusions). So, your claim ultimately just boils down to this: Because it is possible that the aliens scenario could have been drawn from two actual separate populations it is a legitimate analysis, whereas the multiverse analysis is not. No justification is given for this assumption, but it is easily refuted anyway.
Because:
a) It is definitely logically possibly that the multiverse and single universe could have been drawn from two separate *actual populations.
b) If you subscribe to modal realism, or Tegmark's mathematical universe, then not only is it physically possible, but physically necessary! Under modal realism, there would exist sub-groups of multiverse observers and single universe observers. That's because 'universe' just means a physical space-time region. As long as our universe wasn't physically/causally connected to other space, then it could exist 'side by side' with a multiverse of physicals space, in the set of all logical space. In fact, you are guaranteed to find such things in the set of all logical space. So your claim would have to fail under modal realism, which it seems you subscribe to anyway.
c) We don't need modal realism. There are all kinds of ways we can use physical possibility in our universe to say that it might be possible for a single universe and multiverse to be drawn from two separate *actual populations. Suppose that pre-inflation, our universe did not begin with a singularity but entered into a new phase transition where lifeforms of some kind existed. In this pre-inflationary state, we have no multiverse, but after inflation we do have a multiverse. That's a real possibility in our own physical universe we could imagine, wherein it is possible for two separate populations to exist in either a single universe or a multiverse, even though we have just one universe/multiverse.
d) Your reasoning if true invalidates all counterfactual, mutually contradictory scenarios. It is possible for there to be two separate galaxies that instantiate both scenarios in the alien case. But it's not possible for me to be in two separate prisons at once. Yet, it is surely legitimate for me to construct an ensemble and ask whether I am more likely to end up in Prison A or Prison B upon being sentenced. But we can't do that if your objections go through. That's because there's not even the possibility of such two scenarios existing side by side; a result of the fact that we're doing a mutually exclusive scenario analysis on a combined population of one observer (myself).
Hey Alex, for a and b: DM defines the multiverse to be all universes anywhere. I of course think that is a very non-standard definition, the standard one used in physics, especially in the context of fine-tuning, is basically the contiguous physical entity that we inhabit, likely produced by inflation and/or the many worlds of quantum mechanics.
DeleteBut under DM's definition a and b don't apply. c is a really good point which I have not considered before, that means that DM would need to define the multiverse to be all universes, past and future, to maintain that on his definition a and b don't apply.
Hey Dmitriy,
DeleteI agree that is his preferred definition. But arguing from that basis only tells us that if we accept his stipulation that the multiverse analysis can't be run with two separate populations, and if we accept the consequences of D (an ensemble analysis with one combined population in such cases is invalid), and that c isn't a possible case, then it follows that one can show that an ensemble argument based on such a multiverse doesn't work.
Naturally, I don't accept any of the above, but even our doing so doesn't in any way invalidate your ensemble analysis. That's precisely because we are using a different definition of the multiverse; so this would just mean that we're talking past each other at best. If DM wants to prove the analysis is wrong, he must go further and demonstrate that we must adopt his definition for the multiverse. He must show that our talking about 'merely' a physical universe, or multiple physical universes (our definition for a multiverse) somehow entails that we are talking about all actual reality.
I should also point out that DM’s definition of a multiverse is fully compatible with a as well. To refute a, we would also need DM’s additional postulate that: ensemble reasoning is illegitimate if the two scenarios are mutually exclusive (so that we can’t host them “side by side”). But of course there’s no justification for such a principle.
DeleteEven if there were, the objections in my lists above (we would have to accept the implications of D above, and that c isn’t possible) apply. Finally, even after all that, this would only work under DM’s definition of the multiverse. So, ultimately we would just be talking past each other, unless he can show that we need to adopt his definition.
I meant to say “ensemble reasoning is illegitimate if the two scenarios are necessarily mutually exclusive”.
DeleteThat’s important because the aliens scenario is just about one galaxy and therefore entails mutual exclusivity, but the possibility of our reconstructing the scenario to be about two different universes nevertheless entails (according to DM) legitimacy. Whereas, we can’t possibly construct such a non-exclusive scenario under DM’s definition of a multiverse.
Hi Alex,
Delete> You haven't given any reason to prefer the former, which you yourself admitted.
Perhaps I am misremembering, but I think what I admitted was that I wasn't making any progress with how I was trying to explain my problem with the ensemble argument, and took another tack. I thought that what I was trying to get at should be clear from the simulation so I'm trying to explain it again.
> It is definitely logically possibly that the multiverse and single universe could have been drawn from two separate *actual populations.
I think it's very important that we define "single-universe" and "multiverse" as mutually exclusive states for all of reality. Because I claim that the question for people who are skeptical of the multiverse or who say that fine-tuning is evidence for a multiverse is whether this universe is all there is. If we allow multiple single universes to exist even without the multiverse of inflation, then that could also account for fine tuning (because if there are lots and lots of single universes, it's not so surprising if some of them support life). Hence, if modal realism or the mathematical universe hypothesis are true, then M is true and S is not true. It's not as clear whether we should treat the Everettian quantum multiverse as M or S -- it depends on whether the constants vary across it, as they might if they are determined by quantum fluctuations. But if we allow that there are multiple regions with varying laws of nature and/or constants, then M is true.
> Yet, it is surely legitimate for me to construct an ensemble and ask whether I am more likely to end up in Prison A or Prison B upon being sentenced.
The idea of "mutually exclusive populations" is not that you can't be in both at the same time.If you're doing it with an ensemble, whereby the only relevant factor is the relative populations of the two prisons, then those populations are not mutually exclusive. You are assuming that both populations can exist at the same time.
As to the temporal point, I would count a single universe that goes through a succession of different epochs, each with different laws and/or constants, as a case of M. M as it pertains to fine-tuning should just be the hypothesis that there is a great deal of variation of constants and/or laws across reality. If there are lots of different configurations of laws or constants anywhere or anywhen in reality, then M is true.
ReplyDeleteHey DM,
DeleteI see you’ve given an argument for why we should adopt your definition for M. But notice that your definition of M isn’t sufficient; that’s because we need your additional postulate that ensemble reasoning is illegitimate if the two scenarios are mutually exclusive (so that we can’t host them “side by side”). But you haven’t tried to give justification for this principle of yours.
As for its problems:
“The idea of "mutually exclusive populations" is not that you can't be in both at the same time.If you're doing it with an ensemble, whereby the only relevant factor is the relative populations of the two prisons, then those populations are not mutually exclusive. You are assuming that both populations can exist at the same time.”
I’m not sure I understand; the point is precisely that both populations can’t exist at the same time. Remember that both populations are supposed to include me!
To see this with a hopefully clearer example of a plural case; imagine instead that some evil demon decides to transport small groups of humans at a time to other planets, until finally it is our turn (the last group). He will use the same selection methodology that he has always been using that resulted in the asymmetric populations of the two planets (x and y) to which we are being sent.
He will either transport our group population to Planet X and destroy all the other matter/space in the multiverse (your definition of M), or he will transport us to planet Y and do the same for the other matter/space. Planet X’s population is 1 million and planet Y’s is 7 billion.
This scenario is mutually exclusive in the sense that these scenarios cannot both be implemented within your multiverse, but I can rightfully conclude that I ended up in Y by doing an ensemble analysis (surely?).
Finally, on your attempt to justify your definition:
“If we allow multiple single universes to exist even without the multiverse of inflation, then that could also account for fine tuning (because if there are lots and lots of single universes, it's not so surprising if some of them support life). Hence, if modal realism or the mathematical universe hypothesis are true, then M is true and S is not true”
But that’s the whole point of specifying that S is physically causally closed from other physical regions of logical space. So that an observer in S couldn’t possibly have been born in other S’s in remote ‘parts’ of logical space. Depending on how we think about consciousness, one may indeed hold to weird identity conditions. But whatever that identity condition is; it is surely logically possible that there exist single universes like ours that lack that condition.
In fact, it would lead to incoherence to attempt to quantify over the infinite logical space of infinite observers; to see which category of observer you are most likely to be in. Physicists deal with similar problems as well when encountering infinities.
The point is that just as the set of all even numbers is equal to the set of all natural numbers; one will find that multiple types of conscious observers are paradoxically equal in magnitude to each other (One is just as likely to have been born a pink elephant as all other possible conscious observers).
This tells us that we need some local criteria for sorting out our likelihood of observing fine tuning. Which of course means that we are forced to reason as if causally disconnected single universes elsewhere in logical space have no bearing on our potentially observing fine tuning.
Additionally, you haven’t given us any reason as to why reasoning from a combined population is bad.
Or rather, we are forced to reason as if the infinite number of single universes casualty disconnected from us have no bearing on our local situation, but we are still free to say that we could have been born in a finite subset of causally closed single universes.
DeleteTo see why that is irrelevant, we need to appreciate that we should still conclude that P doesn’t modify the credences for M, regardless of the ratio of single universes to multiverse within our local section of logical space. That’s because as Dmitriy and I have repeatedly pointed out, the actual M:S ratios are irrelevant.
Even if we are way more likely to have been born in a S universe; our fine tuning results still hold. So it’s important to mention that your objections are just semantically oriented; they have no real bearing on our analysis. We are still right at the end of the day that we are not more likely to have been born in a landscape multiverse (which to us means a physical region of space that shares a common causal origin point) on account of observations of fine tuning.
The reply in my post above was just focused on pointing out that under your definition of the multiverse, it still doesn’t follow that we can’t talk of multiple S and M physical regions (in the way Dmitriy and I define them).
More importantly however, you still haven’t given us good reason for why we are obligated to adopt your definition.
I wrote:
Delete“ The reply in my post above was just focused on pointing out that under your definition of the multiverse, it still doesn’t follow that we can’t talk of multiple S and M physical regions (in the way Dmitriy and I define them).”
I meant:
“the above reply was focused on saying that you still must show that we could have been born in all other casually disconnected universes”
Hi Alex,
ReplyDelete> But you haven’t tried to give justification for this principle of yours.
The simulation I did is the best evidence -- a naive ensemble argument gets the wrong results when trying to predict the outcome when sampling from mutually exclusive populations. I'm not sure if you've looked at it. I realise now that the main link I gave for it does not persist, but you should be able to access it from the edit link here: https://plnkr.co/edit/93TzXHlxZRSP8gww?preview
I've tried to explain that the reason we get the wrong results is because you're calculating probability across an incoherent population, but it seems that this explanation is not communicating the idea successfully.
Another way to put it is that if we have mutually exclusive populations, we need to think of the problem in two stages. (1) What populations might exist and (2) given what populations exist, what are the relative chances that I will find myself in each population? The ensemble argument collapses the two stages by implicitly assuming that both populations exist and then treating the relative chances as a proxy for the question of which population exists.
> Remember that both populations are supposed to include me!
No they're not. If you're reasoning from the sizes of the two populations only, you're not assuming that you are in one or the other or both. One of the populations is supposed to include you, and you don't know which. You assume that the probability that you are in a population is proportional to the size of the population. I do not agree that this is the same as assuming that you are in both populations at the same time. In any case, even if there is some aspect of mutual exclusivity to prison A vs prison B or China vs Chile, there's a whole level of additional mutual exclusivity to M vs S and that's what I'm concerned about.
More later...
Hey DM,
Delete“I do not agree that this is the same as assuming that you are in both populations at the same time.”
Let me repeat my argument again because I feel you may have forgotten the beginning (buried as it was in the wall of text).
1) Neither the M vs S case, or the IVF or alien cases are supposed to be actually instantiated. We agree that the reasoning in the IVF/ alien cases work even if there aren’t multiple galaxies or multiple IVF trials.
2) Therefore, your objection boils down to this: it is illegitimate to engage in ensemble reasoning if it is impossible for the multiple scenarios of the ensemble to be mutually instantiated.
3) Because it is at least possible that there could be multiple such galaxies (42 and single) side by side, such reasoning is legitimate, whereas the M vs S analysis is not.
4) But it isn’t possible for either prison scenario to exist ‘side by side’.
5) And it isn’t possible for either evil demon scenario to exist side by side.
6) Hence, we would have to come to the absurd conclusion that I can’t reason in either 5 or 6, if 2 is correct.
I will check out your simulation (sorry I didn’t see it yet), to see your justification for 2. In the meantime, do keep in mind that we still need a good reason for why we are obligated to accept your definition of the multiverse.
Remember that in the prison case there isn’t any selection effect. The specific details of my existence are relevant; whereas this is not so for the multiverse, IVF, and aliens case. Hence why the prison scenarios can’t be mutually instantiated.
DeleteHi Alex and DM,
ReplyDeleteI am not sure I agree (or understand) with Alex's points 3 and 4. I don't see any difference between:
- not knowing if I am in a 42 planet or a 1 planet galaxy, AND
- not knowing if I am in a large prison or a small prison
Alex, can you explain?
This relates to my question about DM's ensemble simulation. I don't understand the justification for the underlying assumptions behind it, or even what those assumptions even are. In comparison, the underlying assumption behind my ensemble analysis (and pretty much all other ensemble analyses in thermodynamics and everywhere else as far as I can see) is EP.
In particular, since DM accepts EP for the aliens, and realizes that we are not saying that an S and an M galaxy exist simultaneously, it is unclear to me how his ensemble methodology handles this case. It is not a China/Chile situation, in which both exist at the same time, so then it must fall under the S vs M type situation. But then his simulation produces an answer contradicting EP. So it's inconsistent, it seems, to simultaneously believe:
- EP is valid for the aliens
- the two populations in the aliens case don't exist simultaneously, unlike Chile and China
- DM's ensemble simulation produces correct results for the aliens
Hey Dmitriy,
DeleteI don’t think it’s inconsistent to believe these three things:
“ - EP is valid for the aliens
- the two populations in the aliens case don't exist simultaneously, unlike Chile and China
- DM's ensemble simulation produces correct results for the aliens”
Provided that we believe my premise 2:
“it is illegitimate to engage in ensemble reasoning if it is impossible for the multiple scenarios of the ensemble to be mutually instantiated“
Such a principle would allow DM to say that the alien galaxies case can be legitimate whereas the multiverse cannot. EP is preserved because the actual fact of multiple experiments happening still has no bearing on the legitimacy of the analysis; what would have bearing (if 2 is sound) is whether such an outcome can be possibly realized. And under DM’s definition of a multiverse, M and S can’t both be realized.
Obviously, I don’t believe in 2 (and I think that DM has also failed to justify it), but DM must believe it to avoid contradicting EP. So I give him a “way out” by coming up with 2. As for the prison case, that’s just a side tangent (it’s better to use my evil demon case I think) where I’m trying to demonstrate that 2 is not in actual fact a good principle. Of course this is an extra step on my part that has no bearing on the general argument. It is up to DM to justify step 2; my potential failure to invalidate it in no way supports his claim.
The point about my prison case is that while one can construct a generic ensemble of random prisoners, and then use the likelihood of a generic prisoner ending up in A or B to represent my case. I had in mind a more specific ensemble involving my being in A or B; so that we could construct two counterfactual scenarios in prison A and prison B (both which incorporate me).
For instance where the first scenario is my being in prison A, and then seeing how likely that would be to instantiate my holding a particular prison tag in the population of all prison tags. And the same for scenario B.
That being said, I think mine is a bad example because the mutual exclusiveness is forced by the type of ensemble one runs, and not by the particulars of the situation. My evil demon hypothetical is better I believe, because there the particulars of the situation force a mutually exclusive scenario.
I meant to say: I don’t think it’s inconsistent to believe those three things AND that the M vs S ensemble reasoning is invalid; provided we adopt my premise 2.
DeleteBut those 3 things are all about the aliens, so premise 2 doesn't apply. So I don't see how it could be consistent for DM to believe them, since EP gives one answer but his ensemble simulation gives another.
ReplyDeleteSorry, there's too much here for me to keep up on right now.
DeleteBut there's one point I want to make quickly. I'm not sure that I do accept EP for the aliens. Part of that is not entirely following what accepting the EP is supposed to entail. I only know whether I would accept a form of your ensemble argument or not, and this depends on clarifying a few points. I said:
"If the aliens seeded a gazillion galaxies, and randomly decided for S vs M each time then the ensemble argument is fine.
If either the aliens seeded only one galaxy or had some unknown reason for consistently preferring S vs M, and our credence of 50%/50% merely represents our ignorance as to this preference, then I don't think it is."
So you can make alien scenarios analogous to China/Chile or you can make them analogous to M/S.
To make them analogous to China/Chile, you say there are more than one galaxy seeded by aliens and you assume a certain proportion of S vs M cases. All you need is two galaxies, really, and say one is S and one is M.
To make them analogous to M/S, you stipulate that only one galaxy anywhere is so seeded and you don't know whether it's S or M. You have a credence of 50% for each case.
When analogous to China/Chile, the ensemble argument works. When analogous to M/S, it doesn't.
Also, when I'm saying it is illegitimate to engage in ensemble reasoning, I mean only that the ensemble argument presented here is too simple. You could potentially fix it to capture the possibilities about which populations exist, and then still have something you could call an ensemble argument at the end.
I think DM goes too far in his latest replies (implying that we need the ensemble to be actual to draw conclusions). Although in any case, everything is potentially salvageable under his interpretation of modal realism.
DeletePremise 2 is just a general statement, the point is that it is definitely not logically impossible to believe those three things and that your ensemble is invalid.
Specifically, it doesn’t have to follow that if you think DM’s ensemble about aliens is not like China/Chile “then it must fall under the S vs M type situation”
With premise 2 we would introduce a third category of not-actual and not-possible which only M and S would fall under. The aliens case would be not actual but possible. Whereas China Chile is both actual and possible. If only our third category is bad, then we don’t run into any tensions I think.
I guess what I would hope for at this point is an acknowledgement that I have simulated some process that the ensemble argument does not accurately model, and proposed an alternative that does accurately model it.
ReplyDeleteThe only way you can defend the ensemble argument, as far as I can see, is to point out how the process I have modelled is not analogous to M vs S. And if ensemble arguments are so all-powerful and universally applicable, how would you model the process I have simulated with an ensemble argument?
Sorry, was thinking this over while brushing my teeth, and I think I get where you're coming from with EP, for the first time.
ReplyDelete> If one accepts EP, the ensemble premise, which says that the credences you assign to M and S are unaffected by how many other similar experiments are performed, then the credences fall out immediately from the ratios of civilizations:
So what you're getting at here is that it shouldn't matter whether there's one galaxy or gazillions of galaxies for whether you think we're in M or S. While the starting credences are unaffected, I agree, that doesn't mean that the ensemble argument is valid in each case.
The two scenarios are quite different. If there are gazillions of galaxies, then there are a lot of M populations and a lot of S populations, and you should use the ensemble to decide your self-location as you did in this article. You're more likely to be the more common of the two kinds of observers. But if there is just one galaxy, then there is only one kind of observer, and all that matters is whether the coin was heads or tails, and the relative populations have nothing to do with your final credence for what kind of observer you are.
Hi DM, I think things are becoming clearer, I understand now that you actually do not accept EP for the aliens. Just to make sure we're completely on the same page about what EP says, it's talking about the final, posterior credences you assign, not the prior. The priors are not in dispute, we are assuming the aliens flipped a coin (or we have a more general prior p:q). So then:
DeleteEP. The posterior credences for M and S are unaffected by how many other similar experiments are performed.
If you don't accept EP for the aliens, then you presumably also don't accept it for the IVF case and other cases. But then your non-acceptance has nothing to do with the multiverse defined to include ALL observers in existence. It also has nothing to do with the impossibility to have the M and S scenarios coexisting within one possible world. Both of these are inapplicable to the aliens (there could be lots of such aliens, or those exact aliens could have performed the experiment many times), or to the IVF case (similarly, in some possible world there are lots of such doctors).
So is that true, you do not accept EP even in cases where your previous objections are inapplicable, i.e. objections about the definition of M including all observers, and the impossibility of fitting M ans S scenarios into one possible world?
Hi Dmitriy,
DeleteWhether I accept EP or not depends on how the experiment is set up.
I think my thinking is becoming a little clearer as this discussion continues. What matters is not so much mutual exclusivity except the possible actual ratios, and mutual exclusivity matters insofar as it affects this.
The way I would state EP is that what matters is the ratio between the different populations that are actual. The absolute numbers do not matter. So having a gazillion galaxies divided between M and S in the ratio p:q is the same as having p M galaxies and q S galaxies.
As such, it matters which populations are actual. If there's only one population, then all that matters is which population it is (i.e. the flip of the coin). The ratio is either going to be 1:0 or 0:1, it can never be p:q, so it's wrong to analyze it as if it is p:q. Instead, you need to consider each case separately, weighted by the probability of each case. For two experiments, the possibilities are 2:0, 1:1, 1:1 and 0:2. Again, each case should be considered separately, but 1:1 is weighted more strongly as there are two ways of getting this ratio. As the number of populations tend to infinity, and M vs S is decided randomly for each, the safer is the assumption that the populations exist in exactly the ratio 50:50 (or more generally p:q) and the more accurate will be a naive analysis considering only the p:q case and not each possible actual ratio.
> If you don't accept EP for the aliens, then you presumably also don't accept it for the IVF case and other cases.
They're probably all the same. We'd need to clarify the relevant points. One complication is that as a modal realist, I find it hard to accept that there could only be one population. I think all possible populations are actual. Even if I try to set that aside, I'm inclined to think that any very unlikely event under observer selection might be evidence for a multiverse (as opposed to evidence that there were lots of embryos in the IVF scenario, i.e. there could have been lots of parallel Everettian worlds with small IVF trials). So the multiverse case is a bit special because it cannot appeal to any broader scale of multiplicity.
> But then your non-acceptance has nothing to do with the multiverse defined to include ALL observers in existence. It also has nothing to do with the impossibility to have the M and S scenarios coexisting within one possible world.
It has to do with both, because this is what makes M and S mutually exclusive, and the mutual exclusivity is what means that there can only be one experiment, and so we are stuck with the ratios 1:0 or 0:1. If you can have lots of S universes co-existing, then presumably S can also coexist with M, and ratios other than 1:0 and 0:1 are possible. Your ensemble analysis might make sense in such circumstances.
But apart from this, I think this is the only sensible definition of M and S in the context of the fine-tuning debate, as already explained.
If we stipulate that the aliens are confined to one galaxy, and we rule out the idea of lots of aliens seeding lots of galaxies, then we have the same setup for the aliens. Similarly for ObserverCoin, I tried to make this point clear by saying each ObserverCoin was trying to predict how many ObserverCoins had been created by me here today. Under these conditions, M is incompatible with S and there is only one experiment.
> So is that true, you do not accept EP even in cases where your previous objections are inapplicable, i.e. objections about the definition of M including all observers, and the impossibility of fitting M ans S scenarios into one possible world?
I don't know how to answer this with a simple yes/no. I hope the above covers it.
Hi Dmitriy & Alex,
ReplyDeleteI feel like I'm close to 100% sure that I see a problem with the ensemble argument, but I'm not at all sure how to explain the problem. My uncertainty is all on this latter point, which explains my trying different tacks with regard to incoherent populations, mutual exclusivity and actual ratios, etc. This is why I resorted to a simulation. Code removes all ambiguities. You can see what I'm doing in the code, and the simulation is pretty self-documenting anyway. You can see that naive predictions akin to the ensemble argument get the wrong result.
My point is that you ought to be in as good a position as I to explain why (e.g. whether the problem is mutual exclusivity, incoherent populations, actual ratios or something else). I have no idea what explanation is most clear. But what is clear is that there is a problem.
So rather than picking holes in my explanations, I would invite you to explain why the ensemble argument as represented by the naive prediction does not predict the result my simulation gives. Either it's because the simulation of M vs S is not analogous to the original problem (if not, why not?), or the naive prediction does not correctly capture the ensemble argument (if not, then how should we use the ensemble argument to predict the result of the simulation?)
DM,
Delete“You can see that naive predictions akin to the ensemble argument get the wrong result”
I am not sure how you came to this conclusion. If you mean that the posteriors in the naive prediction are different from the priors; that is a feature not a big. That is supposed to reflect the impact of N (the number of observers).
The obvious reason why your simulation results differ from the ‘naive’ simulation results is that the naive simulation takes into account N, whereas yours does not.
Whether we should take into account N in anthropic reasoning is hotly contested. But our not doing so will definitely have consequences.
In any case, I am certainly sympathetic to the argument that N shouldn’t matter in all cases, but I don’t see how this has anything to do with our previous discussion on fine tuning. I thought that you were trying to specifically show that the ensemble is faulty to infer that fine tuning doesn’t affect credences in M.
But arguing about the role of N in no way jeopardizes this inference, or the Bayesian analysis which comes to the same conclusion. Note that your two tier simulation process is fully compatible with the inference we are discussing.
Hi DM,
Delete1. EP for the aliens.
Let's make sure we are on the same page about the definition of EP I gave, so we know where we agree it applies and where you believe it doesn't. This will be also very important in explaining why your simulation gives different results than my ensemble, and which result is correct.
Definition. EP = The posterior credences for competing hypotheses are unaffected by how many other similar independent experiments are performed.
Example. If I roll a die, my credence that I will get a six should be unaffected by whether I am the only person in existence doing this experiment, or there are many people doing this experiment.
Important note. Those other people might include people in your reference class, meaning people who are not relevantly different from you. In particular, they can include people so much like you that you can't tell which of them you are (self-locating uncertainty). Of course those copies of you don't live on Earth, but if the cosmos is sufficiently big there will be such copies of you (and even of the whole galaxy). EP says that your credence of being one of those people that will get a six is unaffected by how many copies exist.
Does that clear up exactly what EP is asserting? It looks like you don't agree with EP for the aliens IF it's stipulated that there are no similar aliens in other galaxies (and therefore no relevant copies of you). But do you agree or disagree with EP if we don't have such a stipulation? In other words, what if we don't know how big the cosmos is to know whether there are or aren't relevant copies?
2. Explanation for discrepancy between my ensemble and your simulation.
I am assuming that if you were actually part of an IVF experiment, or part of an alien scenario and you wanted to use your simulation to help you assign posterior credences to being a multi-embryo case IVF baby, or living in a 42 planet galaxy, you would use the settings in your simulation corresponding to there not being multiple copies of the whole experiment. As a result your simulation will give the final credences as 1:1, not 42:1.
Is that correct? And if it is, then your trust in the result of your simulation over my ensemble relies on two suppositions:
- EP is incorrect
- The actual cosmos is not big enough to have multiple relevant copies of you+rest of experiment
So one natural objection against your simulation results is that there are no good reasons to make the second assumption.
Hi Alex,
DeleteI'm afraid I don't follow your argument. I don't see how it relates to the point I'm making or the simulation I made.
> If you mean that the posteriors in the naive prediction are different from the priors; that is a feature not a big.
No, that's not what I mean at all.
In the simulation, we get
1) A naive prediction, that I think works similarly to the ensemble argument and predicts what results we should expect to see in 100 trials
2) A sophisticated prediction, that shows how I think we should do the mathematics instead and predicts what results we should expect to see in 100 trials
3) A simulation which runs the scenario 100 times and reports the results we saw in 100 trials.
I think the ensemble argument is wrong because its proxy, the naive prediction, only works in China/Chile and gets completely the wrong result for M/S, whereas the sophisticated prediction is always pretty close.
I think we're talking at cross purposes because I can't follow the rest of your comment. For instance I don't know what you mean by "The obvious reason why your simulation results differ from the ‘naive’ simulation results is that the naive simulation takes into account N, whereas yours does not."
I understand that the simulations get different results. What I’m saying is that you never bothered to further justify your statement that “You can see that naive predictions akin to the ensemble argument get the wrong result”
DeleteInstead of continuing to argue for your previous justifications (e.g. the ensemble gets the wrong results because of mutual exclusiveness etc...) you instead put forth your simulation in the hopes that the purported problems with our ensemble would self evidently manifest.
But I don’t see anywhere a problem with the naive ensemble in your simulation. The only thing your simulation shows is that we get different results with both attempts; obviously you prefer the sophisticated results, but why?
In other word, your simulation is based on your sophisticated predictions anyway. So it’s not surprising that it shows that your predictions are correct. The simulation presupposes that the correct way to argue for M vs S is to adopt a two-tier approach; to predict first the likelihood of M being the case (independent of N), and only then to take into account N if M.
DeleteHowever, the naive ensemble uses N to predict the likelihood of M. Nowhere in your simulation do you actually justify your belief that this is the wrong approach.
I wrote:
Delete“I understand that the simulations get different results”
I meant that the predictions get different results.
Hi Dmitriy,
ReplyDeleteYou want me to accept both
"The posterior credences for competing hypotheses are unaffected by how many other similar independent experiments are performed."
As well as
"we don't have such a stipulation: [there are no similar aliens in other galaxies]", i.e. "there may be aliens in other galaxies".
There's a subtle tension there, as you're both saying that it doesn't matter whether there are aliens in other galaxies, but perhaps only if we insist that there may be aliens in other galaxies. I'm not sure this is coherent.
EP seems reasonable in lots of cases but since I think I can see cases where it doesn't work, I'm forced to reject it. I think I agree that the actual truth value of hidden variables such as how many other experiments there are shouldn't affect our subjective credences one way or another. But we can have credences about the value of those variables, and those credences can affect our overall posterior credences.
So, in particular, I would not agree with the following:
"The posterior credences for competing hypotheses are unaffected by our credences about how many other similar independent experiments are performed."
particularly in cases where our competing hypotheses are about how many other similar independent experiments are performed, and that's what we're dealing with in M vs S and the aliens and IVF.
I've attempted to explain why I have doubts about EP but I despair of convincing you of any of my ad hoc general explanations. But I think we can see it's wrong based on the simulation.
I think you're right to say that if I modelled IVF or aliens in my simulation on the understanding that there was to be one experiment only ever in the cosmos then I would get a ratio of 1:1.
> then your trust in the result of your simulation over my ensemble relies on two suppositions:
>- EP is incorrect
My simulation makes no suppositions about EP. I say nothing at all about EP in my simulation. My simulaiton just runs the scenario and spits out the results. If the results are incompatible with EP, then I think that this simply proves that EP is wrong without assuming that it is wrong.
> - The actual cosmos is not big enough to have multiple relevant copies of you+rest of experiment
For the question of M vs S, this is true by definition, because the experiment is supposed to encompass all of reality over all time. This marks out M vs S as a unique case, so all this analogising may be a waste of time.
Hi Alex,
ReplyDeleteI started reading your most recent comments under the impression that you were confusing simulations with predictions, because you were seemingly using the two interchangeably, but by your last comment you seemed to appreciate the difference.
For absolute clarity, there are three separate things going on.
1) A naive prediction, modelled on the ensemble argument
2) A sophisticated prediction, giving what I think is the correct approach to prediction
3) A simulation actually generating results according to how I think M vs S should be simulated.
The reason I prefer the sophisticated prediction is because it gets results that match the simulation.
Now, you say that this is to be expected as the simulation is based on the sophisticated prediction. I would instead say both are based on how I understand the problem. They are still two completely different ways of getting the answer. (2) is analytic. (3) is based on running a large number of probabilistic trials. So as I was saying, I think you need to show how my understanding of the problem is not correct.
My understanding of the problem is perhaps best explained via the aliens analogy. If we were to simulate one experiment of the aliens analogy on a computer, how would you do it? The way I would do it is:
(1) the aliens flip a coin and decide M vs S.
(2) We populate the galaxy according to the results of the coin flip.
(3) We sample from the resulting population to simulate being born.
What part of that is mistaken?
If this experiment protocol is correct, we can repeat it lots of times and see what the results are. That's what I've done.
I forget what N is exactly -- I think it's something to do with how much greater the population in M is vs the population in S. On that understanding, I agree that I think that N has nothing to do with the problem for M vs S. But this is because it plays no part in the most straightforward simulation of the scenario, just because M and S are mutually exclusive. If they weren't mutually exclusive, then N would play a role in step 3, because it would make one population more likely than another when sampling in cases where both populations happen to coexist.
DM,
DeleteYou still need to give justification for your first step. That is what I meant by saying that yours is a two-tier approach. Instead of plunging in straight away by modeling the different alien galaxies (and M vs S) side by side; you would have us introduce a first step which would determine the likelihood of M or S irrespective of the number of observers in M.
Some justification has to be given for that. Of course as I mentioned earlier, this is a contested topic (the relevancy of N in anthropic reasoning), but you would have to address Dmitriy’s counters (his evil doctor ensemble) that argue for N being relevant. And you must give clearer conditions for how the first step is to be modeled.
For notice that if your first step is absolutely applied, then we couldn’t appropriately reason in the aliens case (we would have to apply a 1:1 credence) as Dmitriy pointed out. So you would have to introduce an exceptions clause for your first step.
All that being said, this is ultimately irrelevant to your contention that fine tuning doesn’t impact our credence in the multiverse. Even if you are correct that your way of doing things is the better approach, that doesn’t undermine the above point.
So it’s not that this has to be mistaken:
Delete“(1) the aliens flip a coin and decide M vs S.
(2) We populate the galaxy according to the results of the coin flip.
(3) We sample from the resulting population to simulate being born.“
But rather that you haven’t given any justification for what I term your ‘first step’, which is your notion that we should base our modeling in premise 2 on the outcomes of premise 1. Obviously, the ‘naive’ ensemble would be simulated differently.
“ultimately irrelevant to your contention that fine tuning doesn’t impact our credence in the multiverse“
DeleteI meant *our contention
:)
Hi Alex,
DeleteGiven the setup of the alien scenario "for example assume the aliens had no preference between SP (single planet) and MP42 ... so they flipped a coin" I don't see how you can object to step 1 and step 2.
I completely agree that my interpretation is incompatible with N mattering and that N is a contested topic. But steps 1 and 2 are so transparently there in the thought experiment for this article I don't see how you can object to them. I think the correct reaction should be to realise that N does not in fact matter and the topic should be contested no more! But that's just me.
At this point I'm just wondering how you would distinguish what I've done from the setup of the thought experiment as described. How would you simulate a single experiment of birth in a galaxy seeded by aliens?
> For notice that if your first step is absolutely applied, then we couldn’t appropriately reason in the aliens case (we would have to apply a 1:1 credence)
Yes, for the one galaxy scenario at least. QED!?!
> All that being said, this is ultimately irrelevant to your contention that fine tuning doesn’t impact our credence in the multiverse.
The main point I'm trying to establish here is whether the ensemble argument in this article has anything to do with the fine tuning debate. I maintain it doesn't, because it rests on a disanalogy (treating China/Chile as M/S).
Whether fine tuning gives reason to believe in the multiverse is another issue, and perhaps largely rests on TER. That seems to me to be a genuinely hard problem. What seems clearer to me is that the ensemble argument is being misapplied here.
Hey DM,
ReplyDeleteIt seems like your main argument is that running one experiment is different from running multiple ones. The notion that running the aliens experiment just once yields a different posterior of 1:1 contradicts EP. Needless to say, it’s definitely not ‘obvious’ that EP is faulty!
However, I’m not here to defend EP, one day I’ll tackle that subject because I think it very interesting (I may write an article about it). I would just like to again ask this, given our state of epistemic ignorance (we don’t know how many M or S’s there could be), why should we assume that only one M or S case has happened? In fact, if we adopt your preferred version of modal realism; you need to give us a justification for why our definition for M is invalid, because in that case there would definitely be multiple M’s and S’s.
Finally, I would also like to reiterate yet again that this discussion has no bearing on the ultimate argument that fine tuning doesn’t affect our credences in M. Even if we accept that EP is faulty, and that there is only one M or S scenario; it doesn’t follow that fine tuning changes the probability of M being true.
Best,
Alex
Arguments against the fact that running the experiment just once should change things (i.e. EP is faulty) are that a single coin still has a probability of 1/2 of landing tails. So, probability should be thought of as an intrinsic property of a single event, and not an emergent property of multiple events.
DeleteHi Alex,
Delete> It seems like your main argument is that running one experiment is different from running multiple ones.
My main point is that the ensemble argument cannot be right because when we simulate according to the rules outlined in the article we don't get the predicted results
Secondary to this are proposed explanations for what's gone wrong. I know how to calculate the right result but I don't know how best to describe what exactly is going wrong with the ensemble argument. Running an experiment once may indeed be the same as running it many times in the right circumstances. For China/Chile, it doesn't seem to matter how many times the experiment is run.
You raise two questions:
1. why should we assume that only one M or S case has happened?
2. you need to give us a justification for why our definition for M is invalid
I feel like I've answered both already. The second question needs to be answered first.
Any definition of S that allows multiple universes to co-exist (by which I mean multiple universes are actual, though perhaps in different multiverses or at different times) cannot be the right definition in the context of a debate about fine-tuning, because if we allow there to be many universes then we can account for fine tuning. Those who think fine-tuning is reason to believe in a multiverse ought to be satisfied with any explanation that allows lots of universes with a variety of laws and constants to be actual. There is no reason to suppose that those universes are all in the same multiverse or exist at the same time. Even Roger Penrose's idea of Conformal Cyclic Cosmology would do, where there may be only one universe at a time but where each universe has a successor and an ancestor going in either direction eternally -- as long as each universe in sequence can have different laws and/or constants.
If fine tuning is supposed to raise our credence in the existence of other universes, then the alternative hypothesis S has to mean that there is only one universe anywhere or anywhen.
Given these definitions, the first question answers itself.
> if we adopt your preferred version of modal realism ... there would definitely be multiple M’s and S’s.
If modal realism is true, then M is true and S is false.
> Finally, I would also like to reiterate ...
And then I would like to reiterate that this point is not the one I am most interested in. Particularly on this thread, and really since the very beginning, the thing I am exercised about is the claim that the ensemble argument simply settles this question. It doesn't. Whether fine tuning should affect our credences in M remains a difficult question and it cannot be answered with the approach in this article.
So I agree that the inapplicability of the ensemble argument certainly doesn't automatically mean that fine tuning should change our credence in M. That's not in dispute. If I were arguing for fine tuning changing our credence in M, I'd be focusing instead on TER right now. I'm not because that problem is well rehearsed in the literature and there is no consensus. The ensemble argument is an original contribution, but I think a very flawed one. If you're willing to concede that the ensemble argument doesn't work (not that I think you are), then that's all I really wanted to show. Personally, I'm happy to agree to disagree on TER.
> Arguments against the fact that running the experiment just once should change things (i.e. EP is faulty) are that a single coin still has a probability of 1/2 of landing tails.
DeleteI'm happy to accept that before the fect, we can say that a single coin has a property of 1/2 of landing tails.
But from my perspective, what you are doing with the ensemble argument is a bit like flipping a single coin and expecting the result to be half heads and half tails. This is a possible result when you flip it many times, not a possible result when you flip it once. The reason I think what you are doing is like this is because you are quantifying over a mixed population of S and M worlds, but such a mixed population is not a possible result from a single trial.
Again, the simulation shows empirically (as far as I can see) that the ensemble argument doesn't work. If we can agree on that (not that I think we can, necessarily), then I'm happy to leave it to you to work out why, as I've tried plenty of ideas that haven't rung true to you and Dmitriy.
> So, probability should be thought of as an intrinsic property of a single event, and not an emergent property of multiple events.
I have no strong views on whether probability should be thought of as an intrinsic property of a single event or an emergent property of multiple events. I think both ideas might work, especially in the appropriate context.
Hi guys, a few points:
ReplyDelete1. Relevance to the question about fine tuning.
Alex, the discussion about whether the number of observers matters seems highly relevant to whether fine tuning is evidence for the multiverse. That's because my ensemble argument says that it does matter, therefore if it turns out that it actually does not matter that would mean my ensemble argument is wrong. And if it's wrong then of course we cannot use it to justify our view on fine tuning. We would still have the other argument of course, based on TER, but it would still be a significant blow.
2. About the underlying assumptions of the simulation.
Yes, the simulation does not assume directly that EP is false. Instead, it directly relies on some sort of underlying assumption X, which is logically incompatible with EP.
The problem is we haven't yet been told what that underlying assumption is. So pretty much the only thing we know about it is that it logically entails that EP is false.
Until we know what it is and what the justification for it is we have no idea whether the credences produced by the simulation have anything to do with the actual correct credences we should assign.
So the crucial question is: my ensemble argument is built upon the underlying assumption EP, for which there are several arguments, the main one being of course that it seems bizarre that the credences we should assign should somehow depend on what's going on in completely disconnected parts of the cosmos. What is the equivalent of that for the simulation? What is X and why X?
3. About the idea that the hypotheses in question concern how many such experiments have been performed.
This is an unfortunate confusion. An experiment is not one planet, in the alien case. An experiment is a whole galaxy, which has either 42 planets or one planet, depending on the flip of the coin. So the hypotheses in question, namely whether the number is 42 or one, do not ask how many experiments, meaning galaxies, there are. Apart from other possible objections to the ensemble premise, this one completely misses the mark I think.
4. Results of the simulation for the aliens.
I, and I think Alex as well, am still confused about what the simulation says about the aliens case. Can we clear that up? If the actual alien case presented itself, or the IVF case for that matter, how would you apply your simulation to solve it? That obviously relates to Alex’s question, would you assume that there’s only one such experiment in the whole cosmos, instead of gazillions? If so, why? And if instead you would assume gazillions, then your stimulation which produce the same result as my ensemble argument, correct? Or would you simply not be able to get any answer, because you would not know how many such experiments exist in the whole cosmos?
(Of course these complications arise because the simulation‘s underlying assumption X contradicts EP. For my argument, based on EP, it of course makes no difference how many such experiments exist in the whole cosmos.)
Hi Dmitriy,
DeletePoint 1: Thanks, I agree entirely (as you might expect).
Point 2: I don't think that way, in terms of simple foundational principles. There is no X. I didn't start from some a priori metaphysical world view and work backwards to design a simulation to give me the results I want. I'm a programmer, so I simply took your description of the alien setup as a requirements document and I wrote a program that does what the aliens are doing and simulates being born somewhere random in the resulting galaxy. As far as I can see, the only way this approach will go wrong is if I've misunderstood the setup, something you can tell by looking at either my source code or my description of what the simulation is doing. I only worked out how to get the right predictions after the simulation was complete. There was even a point while dog-tired and confused where I thought the results were actually going to prove you right rather than me.
Point 3: > Apart from other possible objections to the ensemble premise, this one completely misses the mark I think.
Fair enough, point taken. I did make this mistake. But as I'll explain in my answer to Point 4, I think the question about the number of planets in this galaxy is the wrong question to ask. We should be asking about the number of similar opportunities anywhere and anywhen.
Point 4: > That obviously relates to Alex’s question, would you assume that there’s only one such experiment in the whole cosmos, instead of gazillions?
It depends on what question we're trying to answer, and why.
As I explained in my justification for my definitions of M and S, when we're explaining fine tuning we're really trying to see if the improbability of our universe being just right for life gives us reason to believe that there were many opportunities for universes to have such conditions, anywhere or anywhen. In general, if you're trying to figure out whether the improbability of some event should give you reason to believe in a multiplicity of opportunities for such an event to occur, then I would assume neither one experiment or gazillions. Instead, this is just the question we seek to answer. So here I personally would choose S to mean I was a freak single occurrence, and M would mean there were gazillions of opportunities, whether on this planet or in other galaxies or in other universes.
But my simulation would be of no use in answering the question because it would simply spit out results in accordance with the priors, as we see when we simulate M vs S. The point of my simulation is not to answer the fine tuning question but to illustrate how the ensemble argument misses the mark. The question itself would be answered with Bayesian reasoning, for which we would need to determine the correct interpretation of TER.
If we're trying to use IVF or aliens to be an analogy for M vs S, then I would stipulate that there was only one experiment, because this is the case for M vs S.
> And if instead you would assume gazillions, then your stimulation which produce the same result as my ensemble argument, correct?
Yes, which is hardly a surprise, because you're just getting out the assumption you put in. The way I think of it, if you assume gazillions of galaxies or IVF trials, then M is true by definition because you have gazillions of those opportunities I was talking about. I realise this again seems to clash with your "M42", where you want to predict a number of planets in the current galaxy, but I think that's the wrong question. When it comes to fine tuning and analogies to fine tuning, what we should be trying to answer really is whether there was one opportunity or many.
Hey Dmitriy,
Delete“Alex, the discussion about whether the number of observers matters seems highly relevant to whether fine tuning is evidence for the multiverse. That's because my ensemble argument says that it does matter, therefore if it turns out that it actually does not matter that would mean my ensemble argument is wrong”
I’ll have to write more on this topic later, because I think it an interesting one. I do think we can definitely use DM’s version of the ensemble (where we introduce a first step determining the probability of M or S irrespective of N, and everything afterwards really fails to matter) to show that fine tuning makes no difference. Provided however, we treat the single universe or single multiverse as holding inherent probabilistic states as properties.
So it wouldn’t make any difference that we’ve run the experiment just once, provided we calculate our chances by quantifying over all the possibilities; which is of course what we do in other such cases (a single coin flip).
That said, it would definitely be true that IF modal realism is true and IF M or S was run only once in all logical space then it would follow that we couldn’t use any ensemble to prove fine tuning doesn’t affect our credences in M.
But of course it’s up to DM to show that we must adopt his definition of M (in cases of modal realism). Because if not, the latter IF conjunct would definitely fail (there would be infinite M’s and S’s in logical space).
Hey DM,
ReplyDeleteYou did write about us being forced to adopt your definition, and you made the same exact point, but it’s an easily addressable one which I wrote about in a previous post (perhaps you missed it?). So let me quickly address this point yet again.
“ Any definition of S that allows multiple universes to co-exist (by which I mean multiple universes are actual, though perhaps in different multiverses or at different times) cannot be the right definition in the context of a debate about fine-tuning, because if we allow there to be many universes then we can account for fine tuning”
Firstly, as mentioned before this would only be a supposed problem under modal realism. If there’s no modal realism then we can get away with our definitions because there’s no reason to suppose that there’s more than one such physically connected space-time region. And of course we would just be quantifying over possible entities in our ensemble (as in any other such scenario). However, this supposed problem doesn’t follow after all. For,
There’s no good reason under modal realism to assume that there is only one S. We defined S to be any physically/causally disconnected space-time region. And a multiverse to be multiple such regions that are causally/physically connected. Therefore, under modal realism there must be infinite such regions.
Hence, your argument can only work if you treat the infinite S regions as just being one S, or the infinite M’s as just being one M.
But then you have self-invalidated your own points. Either we should use the term S to refer to just one such physical/causally disconnected region (against your argument) or we use the term to refer to all such regions; in which case fine tuning is accounted for under S because there are infinite S’s. Meaning that there will definitely be observers in S.
If your definitions of M and S don’t logically follow from our adoption of our definitions, then your entire argument fails to work. We would just be talking past each other; you wouldn’t have actually shown that the ensemble is invalid.
DeleteSo it seems like you want to say that actually S is just a single physical space time region, which of course is logically incompatible with modal realism. But why should we be forced to adopt such a definition (as opposed to a physically disconnected region of space-time)?
DeleteFurther, it’s not actually a bad thing that our being in S could potentially account for fine tuning; I have no idea why you think that. That just means that there are way more S’ than M’s, and so we should conclude that we ended up in S over M. Simply assuming that S better accounting for fine tuning is bad; is rather begging the question in favor of M.
That said, as an interesting side tangent: it doesn’t follow that our ending up in S can logically account for fine tuning; unless you quantify over all possible/actual observers. But we can’t actually do that because that would lead to logical absurdities (like the number of pink elephants equaling the number of all actual observers).
And so we are forced to quantify over local observers One possibility, if we think consciousness is physical, is that we couldn’t have been born outside our S region of space anyway. As all other space is physically disconnected. Therefore, we shouldn’t quantify over all S’s and S is not more preferable than M.
It’s important to point such a thing out, because the belief that we could have been any observer in logical space is potentially incompatible with certain theories of consciousness like the above.
In any case, we have to quantify over local regions of logical space. Once we do so we can see that it’s the ratios between M and S (our definitions) that matters to the likelihood of an observer being born in either. Hence, the concern about S better accounting for fine tuning compared to M evaporates unless the number of S universes vastly outstrips the number of M universes. But of course we have no reason to assume such a thing is the case.
I wrote:
Delete“ S is just a single physical space time region, which of course is logically incompatible with modal realism”
I meant:
“S is just a single physical space time region, and there is only one S in reality”
In case it wasn’t clear. So, this problem under modal realism is a non-problem; the only reason most people think that our being in S can’t account for fine tuning is precisely because they don’t subscribe to modal realism!
But in any case, as demonstrated above, we can definitely still maintain that M is better than S at accounting for fine tuning, even under modal realism.
I don’t see how you could believe that you invalidated our definitions of M and S; given that this is only a supposed problem under modal realism? If there’s no modal realism, then obviously in reality there is only one S or one M most likely.
So to sum up what I take the situation to be at the moment:
ReplyDeleteDM,
For both options A and B,
You must show that:
1) EP fails for solitary cases
2) Your definition of M vs S is the only valid option
A) No modal realism:
Meaning that we are quantifying over possible entities. The first premise is just that running the experiment once yields different probabilities. The second follows under our definition of M. Since (in option a) there could be multiple M’s in reality, we have no reason to assume a solitary case; hence the need to demonstrate 2.
B) Modal realism:
In this case however, premise 2 is much harder to prove. That’s because under modal realism there have to be infinite numbers of S and M’s as Dmitriy and I define them. Your argument about us quantifying over multiple such S’s being ‘bad’ because people want to believe that S cannot account for fine tuning, doesn’t work. Where ‘accounting for fine tuning’ means that our being born in one member of the set of all S’ can explain why we are in a fine tuned universe.
The reason most physicists don’t think that S accounts for fine tuning is because they don’t buy into modal realism in the first place! Hence, S possibly accounting for fine tuning follows from our stipulation of modal realism; it has nothing to do with the definition of S being improper.
So the common denominator here in addition to the critique of EP is your definition being the only legitimate one. That, I feel, is your weakest reasoning of all; because you haven’t really demonstrated any good reason for why we should adopt your definition. I went into what I thought were a lot of interesting tangents in my replies above, but the objection to your argument is easily summarized:
That our being in S could potentially account for fine tuning in no way invalidates our definitions. That would just be begging the question in favor of M.
Hi guys,
ReplyDelete1. Modal realism.
If modal realism is true and if we adopt DM's definition of M, then automatically M is true and S is false: all observers live in M, and none in S. But for the purposes of this discussion DM is willing to assume that at least one of the above two ifs is not fulfilled. It looks like he is suspending his belief in modal realism. If that's true we need not worry about it in this discussion, and perhaps leave it for another day.
2. I think it's also critically important that we separate the two questions:
Q1. What's the correct credence assignment specifically for the case of the multiverse vs single universe case, and - moreover - specifically for DM's definition of the multiverse?
Q2. What's the correct credence assignment for all other anthropic scenarios discussed by Steven, Philip, this blog post etc, meaning scenarios where an ensemble of experiments (reminder: galaxies, not planets) can fit into one possible world?
While I and Alex believe the answers to those questions are the same, I understand that DM doesn't. But I am far less fascinated by this question (are the answers the same or different?) than by Q2. And so, it seems, is Alex, Steven, Philip etc - they are all discussing Q2 (that's why all those analogies were proposed.
So I propose, so that we don't spread ourselves too thin, to concentrate on Q2, and not on Q1 or on whether the answers are the same. Then we can figure out whether the ensemble argument, DM's simulation, or neither constitute correct methodology for solving all questions that belong to the Q2 category.
Hey Dmitriy,
DeleteI think DM concedes that in Q2, the naive ensemble and his simulation give similar results. So by default, there’s no issue with Q2 as has been stated.
The real difference occurs in singular cases; because DM believes that singular cases violate EP. So that if there were multiple alien galaxies then we could correctly reason that our chances are proportional to N (1:42). But according to DM, we should reason that there is a 1:1 credence in a singular case (@DM let me know if I have misinterpreted anything).
This basically all boils down to quantification; when we deal with singular cases, are we quantifying over possible entities or just actual entities? I think I’ll write up my thoughts on this subject (EP) in terms of the way quantification in modal logic impacts things. There is a lot of philosophical talk relating to the proper interpretations of probability. I’ll send you my thoughts on the subject later.
In any case, DM needs both his definition to be correct and for EP to fail. I don’t wish to get into the EP discussion in this thread (until I have sorted out my thoughts concretely in my writings). I will say that his argument in favour of his definition is, in my opinion, his weakest link. Without which, the argument against your ensemble can’t work.
In other words, it seems to me that DM believes that the actual fact of the matter regarding whether A or B is a singular or plural case, determines the legitimacy of EP. By proposing that the possible world in Q2 consists of an ensemble of experiments; you equate DM’s simulation with the naive ensemble. The real question is what the possible world in Q2 is meant to represent. According to DM, we definitely shouldn’t use such a possible world to represent probabilities for singular experiments being done in reality.
DeleteThis seems to me to be advocating for quantification being restricted to actual events. So that we shouldn’t be dealing with possible worlds at all. When we ask what is the probability of a coin toss for instance, we just solve this by quantifying over all actual coin tosses. As you can imagine, these probabilities would be radically modified if the sample size (in actuality) was few or singular.
Naturally, this interpretation of probability comes with a whole host of side issues. If on the other hand, we allow quantification over possible events/entities then the most natural interpretation of such quantification would determine credences similar to the naive ensemble methodology (unless one has a very non-standard way of determining reference class).
That’s why modal realism would actually be really important here; it would allow DM to maintain that singular evens in our world can still have regular probabilities (because we quantify over all logical space), and it allow him to say, in combination with his definition for M and S, that the probabilities for M and S won’t conform to our naive ensemble predictions. That’s because M would basically be the only example of a thing/event in logical space which is singular.
I’m not saying that DM believes this of course, but that’s what his position logically entails.
Alex, I think you may have misinterpreted exactly what Q2 is because I don't think DM agrees at all that his simulation and my ensemble give the same results. So let's be more careful:
ReplyDeleteQ1. What's the correct credence assignment specifically for the case of the multiverse vs single universe case, and - moreover - specifically for DM's definition of the multiverse?
Q2. What's the correct credence assignment for all other anthropic scenarios discussed by Steven, Philip, this blog post etc, meaning scenarios where an ensemble of experiments (reminder: galaxies, not planets) can fit into one possible world?
Q2.1 it is additionally stipulated that there is only one such experiment in the actual world.
Q2.2 it is additionally stipulated that there are gazillions of such experiments in the actual world.
DM only agrees that Q2.2 has the same answer whether we use his simulation or my ensemble.
So what do you guys think about my suggestion to not spread ourselves too thin and concentrate on Q2?
There are several questions on the table, and I think we need to pick one. I am definitely more interested in Q2 now, especially in the context of the specific blog post (discussing the ensemble for the aliens), than any of the following:
Q1.
Q3. Are the answers to Q1 and Q2 the same?
Q4. What is the correct definition of the multiverse?
Q5. How do things change if modal realism is true?
I also think it's not just me who is specifically interested in Q2 over all the other questions, because that's the question that Steven and Philip are discussing, since they propose all these analogies where an ensemble fits into one possible world.
Hey Dmitriy,
DeleteWhen you write “ meaning scenarios where an ensemble of experiments (reminder: galaxies, not planets) can fit into one possible world”
Do you mean a scenario about a possible world with multiple ensemble experiments? If multiple ensembles can fit in that possible world, by definition that possible world has multiple such ensembles.
An anthropic scenario is a possible world by definition, since in actuality of course there aren’t any IVF or aliens cases. So we’re just discussing possible worlds right?
In that case, I think DM would say that in such a possible world, your naive ensemble and his simulation yield the same results. Hence, I don’t think he’s just limiting himself to the actual world (except when we adopt modal realism). Do you disagree?
Or do you mean to refer to a scenario about a possible world, which is not the same possible world that hosts multiple such scenarios? A possible world which may or may not carry multiple experiments (and then I assume you mean Q2.2 to refer to this possible world, not actuality?).
My apologies for any misunderstanding of Q2.
In any case, it seems like we agree that there is a difference in singular and plural cases. I do think it important for all of us to realize that the naive ensemble and DM’s simulation can yield different, as well as similar results, in both possible and actual worlds. The question is just about whether any such simulation about a possible world would accurately model the realty. To which I assume DM would say that we should rely on our knowledge of the number of experiments in actuality to choose the correct possible world to model.
Hi Alex,
ReplyDeleteDmitriy is right that I'm suspending my belief in modal realism, or trying to at any rate. It's a non-issue.
I honestly don't understand your problem with my definition though. You've spent a lot of words on trying to clarify but I'm not following.
To me it's very simple. Scientists such as Lenny Susskind react to fine-tuning by saying that since our universe is fine-tuned, we should suppose that there are many such universes. Here, a universe is clearly just any opportunity for a fine-tuned environment conducive to life, because that's all that would be needed to account for fine tuning. It gives no reason at all to favour an eternal-inflation string landscape multiverse to a conformal cyclic cosmology multiverse or a mathematical universe hypothesis/modal realist multiverse. Even an Everettian multiverse could do if constants are determined by quantum fluctuations. If there are reasons to prefer some kinds of multiverses to others, they have nothing to do with fine tuning as long as they all support varying the constants.
So for me, it is clear that S = there was one opportunity to get fine-tuning right, and M = there were many opportunities to get fine tuning right. We don't need to bring in additional assumptions about universes being part of the same contiguous spacetime or being causally connected. Such connections have nothing to do with the fine-tuning problem.
You do offer one argument in favour of the relevance of such connections:
> One possibility, if we think consciousness is physical, is that we couldn’t have been born outside our S region of space anyway.
I don't see what consciousness has to do with it. You might be talking about personal identity instead. I don't buy this kind of argument as it is bound up with the specialness of our identity and taking identity too seriously as a strong metaphysical reality rather than a pragmatic thinking tool. You might as well be saying that we couldn't have been born on any planet outside earth and so the existence of other planets can't account for earth's fine tuning.
So there's nothing special about modal realism here. It's just one kind of constants-varying multiverse that could exist. The existence of any kind of constants-varying multiverse means M is true.
> the only reason most people think that our being in S can’t account for fine tuning is precisely because they don’t subscribe to modal realism!
If your argument is really that fine-tuning gives us no reason to believe that we are in a multiverse just because there could be lots of single universes (and multiverses!) out there with varying constants, and of course we must find ourselves in a universe that supports life, then it seems to me that you haven't understood the problem, and in fact your argument is just the same as those who think that fine tuning gives us reason to believe in a multiverse. Your conclusion is the same even though you don't use the same terminology.
Hey DM,
Delete“S = there was one opportunity to get fine-tuning right, and M = there were many opportunities to get fine tuning right.”
None of this is an argument for why we should prefer your definition. Dmitriy and I, as well as most cosmologists, prefer to define S and M in terms of physical regions. You haven’t given any reason for why we should adopt your stipulation that (there was one opportunity to get fine tuning right) is a necessary condition for S.
Of course, cosmologists do believe that the opportunities for fine tuning are related in some way to the definitions for M and S. But that’s because most cosmologists would say that S entails that there was one opportunity to get fine tuning right in our physical space time region. It’s pretty obvious that when cosmologists talk about a single universe, they just mean that our physical universe is not causally/physically connected to anything else.
Whether there exists a god who created many heavens or hells outside our single universe, has no bearing on whether we live in a single universe; that’s the standard cosmological interpretation to which Dmitriy and I subscribe, it’s not just my opinion.
“If your argument is really that fine-tuning gives us no reason to believe that we are in a multiverse just because there could be lots of single universes (and multiverses!)”
I don’t think you understood my point, fine tuning has nothing to do with what you wrote. It may indeed be that there are a huge amount of S’ relative to M, and that therefore we were more likely to end up in S than M. But that has no bearing on the fact of the matter that we can’t choose M because of fine tuning. Even without fine tuning; if the above holds then we are still more likely to end up in S.
However nowhere did I make such a stipulation; that point of mine was just related to why (under modal realism) we encounter the non-intuitive result that being in S can possibly explain fine tuning. Which you were saying was some kind of demonstration that the ensemble was faulty, and for which I showed that actually that’s just a condition of modal realism being true in that scenario.
In the end, you just laid out your reasons for why you prefer to speak about M or S in the way you do. But you need to go further than to simply state that your semantic interpretation of M or S is preferable (which of course I don’t agree with; I think your use is very non-standard). Even if true, we can just substitute our definitions for M and S in our ensemble. So it would still be true that Dmitriy’s ensemble shows that fine tuning doesn’t modify our credence in (multiple regions of universes, where M is physically/causally disconnected from other such regions).
I have already clogged up this thread far too much; I think it’s best that I leave to give you and Dmitriy space to talk about EP and Q2. Since it seems that interests you both.
Best,
Alex
Hi Alex, yes, when I say the actual world in my definitions of the questions, I technically speaking mean a possible world, since we don't actually have those aliens bothering us in reality. But I think such terminology, even though technically more correct, would be more confusing. Because when I then say that in these scenarios an ensemble can fit into one possible world I mean that there exists ANOTHER possible world, in which there ARE gazillions of galaxies with aliens.
ReplyDeleteIn other words, for ease of discussion I'm just imagining that the aliens are in fact bothering us demanding an answer, here in the actual world.
ReplyDeleteAnd of course when I say that an ensemble can fit into one possible world, translated into human language that just means: there could be many such aliens. (it does not mean: there definitely are many such aliens, that case would be specifically Q2.2, on which there is no disagreement)
Hey Dmitriy,
DeleteI got it, and I agree with your convention. Sorry for my misinterpretation. I’m planning on leaving this thread to give you and DM space to focus on Q2 etc...
Have fun!
Hi Dmitriy,
ReplyDeleteI'm far more interested in Q1, because as far as I can see the only reason to be interested in any of the other situations is because they're supposed to be analogous to fine-tuning. Even though this blog post is mostly about aliens, the very first couple of sentences is "Is fine-tuning evidence of the multiverse? Surprisingly, no, but the inference to the multiverse may still be valid." and that's what I object to, and what ideally I'd like to see you either successfully defend or retract.
> Q2.1 it is additionally stipulated that there is only one such experiment in the actual world.
Then use my analysis.
> Q2.2 it is additionally stipulated that there are gazillions of such experiments in the actual world.
The use your analysis or my analysis as they give the same result.
> Q3. Are the answers to Q1 and Q2 the same?
They are, but the reasons depend on which version of Q2 you're asking.
On Q2.1, there are more opportunities if there are more planets, so we should conclude M42 because of fine tuning. Fine-tuning is relevant here because if each opportunity is likely to succeed, there is no strong reason to prefer M42, and if each opportunity is certain to succeed, there's no reason at all to prefer M42.
On Q2.2, we presuppose that there are lots of opportunities so fine-tuning is a non-issue. The analogy to multiverse vs single universe would be just to assume that M is true. But there are more opportunities in M42 galaxies than in S galaxies so we should conclude M42 for this reason (which has nothing to do with fine-tuning, as you argue in the article).
Q4. What is the correct definition of the multiverse?
That there have been many opportunities to get fine-tuning right.
Q5. How do things change if modal realism is true?
If modal realism is true then there have been many opportunities to get fine-tuning right, so fine-tuning is accounted for and there is nothing futher to explain. This counts as a kind of multiverse.
Hi Alex,
Delete> None of this is an argument for why we should prefer your definition.
I feel like I've explained this, but I'll try to be as clear as I can. Here follows the argument. It's not quite a syllogism (please don't ask me for a syllogism) but I think it's clear enough.
1. Many (most?) people are predisposed to think there was only one opportunity, i.e. that no other universes exist anywhere. I would characterise the reasons for this position as falling out of default common sense, but if pushed then some will appeal to parsimony on the (mistaken) view that one opportunity is simpler than many.
2. We are presented with evidence of fine tuning from cosmology.
3. One explanation of fine tuning is that there were a lot of opportunities (at least if we are allowed to deny TER).
4. The mainstream debate then (irrespective of what we're discussing here) is whether we should believe there are a lot of opportunities. We have common sense (one opportunity) versus Bayesian TER-denying arguments (many opportunities).
In the context of this debate then, the two sides are clearly S (one opportunity) and M (many opportunities). In other contexts you can use other definitions of multiverse. Different people in the debate may have preferred interpretations of M. Many cosmologists may for instance prefer an inflationary string landscape.
If you think that fine tuning gives us reason to believe there were many opportunities, as there would be in modal realism, then I think your position will be accepted more readily by those on the M-side of the debate than by those on the S-side. If you think that acceptance of modal realism is compatible with the S-side of the debate, then I think you are simply wrong. But that is an empirical question. You'd have to do a survey of multiverse-skeptics. I imagine that most if not all of them would reject modal realism and would regard modal realism as a kind of multiverse.
DM,
Delete“ Many (most?) people are predisposed to think there was only one opportunity, i.e. that no other universes exist anywhere. I would characterise the reasons for this position as falling out of default common sense, but if pushed then some will appeal to parsimony on the (mistaken) view that one opportunity is simpler than many”
I agree with this, but this is a result of the fact that most cosmologists/physicists don’t accept modal realism. Hence, why it is so natural to intuit that the existence of S entails the condition that no fine tuning opportunities presented themselves elsewhere.
My point is that this is an artefact of our rejecting modal realism, and not a consequence of some defect in the standard interpretation (our definition) of what a single universe is. These definitions are fully compatible with modal realism; it’s only our “intuitions” which are not.
Note that without modal realism, its natural to assume that there is only a single S or M. In which case the naive ensemble is used as a representation of possible reality (and not actual reality). The ensemble is still legitimate so long as we quantify over possible worlds (which is the standard way of quantifying when we deal with probabilities). But that’s a discussion over EP.
Put it this way Alex:
ReplyDeleteDo you or do you not think that fine-tuning gives us reason to increase our credence that there were lots of opportunitiies to get fine-tuning right?
If yes, then I agree with you and as far as I can tell the only difference between us is what we choose to call a multiverse.
If no, then we disagree and we can refer to the competing hypotheses with my definitions.
No, I definitely don’t think that fine tuning has any bearing on our credences for the physical multiverse (the way we define it) nor the existence of multiple causally disconnected single universes, nor modal realism.
DeleteUnder modal realism, it will be true that S can explain quite well why some observers in S perceive fine tuning. In other words, there will definitely be some observers in the set of all S that experience fine tuning. And the only reason this seems non-intuitive is because modal realism is non-intuitive, and not because our definition of S is erroneous.
DeleteHi Alex,
DeleteThe only thing that makes definitions erroneous is if usage of said definitions is an obstacle to effective communication. It's therefore something of an empirical matter what people mean when they say things like "fine tuning ought to increase our credence in the multiverse".
But since you disagree with me that fine tuning ought to increase our credence in the multiplicity of any kind of fine-tuning-opportunity, then why not define S vs M as I do? Because on my definition, I think fine tuning ought to increase our credence in M and you think it should not. Since that is exactly where the fault line lies, that is exactly how we ought to define our terms. Otherwise we're talking past each other.
Hey DM,
DeleteThere are two separate issues here:
1) Whether fine tuning increases our credence in your type of M. We should definitely adopt your definition to sort that out
2) Whether our ensemble for our type of M is invalidated. Because your arguments against our ensemble rest on your definition of M, you must show that we must adopt your definition.
Notice that your definition for M (all physical reality) is equivalent to our definition if we drop modal realism AND assume there is only one M or S. Doing so makes our ensemble stronger in that it can show that fine tuning doesn’t affect all versions of M.
The point is that we can’t show this using the ensemble if modal realism is true, so our claim becomes weaker in that sense, but it’s more than sufficiently strong for me because I just wanted to know where I was more likely to be born and whether fine tuning had any affect on this likelihood. Adopting our definition of M and S allows us to answer that.
Remember, it was you argued that we shouldn’t use our definition of S on the grounds that if there are multiple such S’s (i.e if there is modal realism or something like it) that would mean that S could potentially explain fine tuning.
Your definition is ‘bad’ only if we argue from modal realism, in that it would prevent us from answering the question the ensemble wishes to address. So, it’s not that adopting your definition (for modal realism) somehow entails that our claim is wrong; it’s just that it prevents us from proving our claim. But our claim is proved anyway under our definition.
That said, this isn’t an issue in the absence of modal realism. What’s at issue is whether EP is valid for single cases or not. Although of course we disagree about that.
I must point out that even in the absence of modal realism, and assuming EP is faulty, it still doesn’t follow that our ensemble is wrong (because there could be multiple M or S’). We have no reason to assume there is just one S or M (as we define it). But if you grant that there is just one M or S, then the argument boils down to the validity of EP.
DeleteMy point is that I feel that using our definition reveals that fine tuning definitely doesn’t impact our credences in our being born anywhere. That’s because our ensemble captures the ratios between different M’s and S’s. So this shouldn’t somehow be viewed as a competition between different definitions. Rather, it’s just that your definition blocks a correct inference, and not that using it somehow proves another thing.
But we can narrow this down to that specific case of only one physical M or physical S to make the definitions equivalent; so that we can just debate the merits of EP, if you wish.
Hi Alex,
ReplyDeleteGlad we're agreed on the first question -- that we should use my definitions to sort out our disagreement regarding my version of M.
On the second question, I'm not sure if we agree or disagree because I'm not clear on what you're claiming, and I'm not sure if Dmitriy is going along with you. I don't understand this sentence: "Doing so makes our ensemble stronger in that it can show that fine tuning doesn’t affect all versions of M."
> because I just wanted to know where I was more likely to be born and whether fine tuning had any affect on this likelihood. Adopting our definition of M and S allows us to answer that.
If you're claiming that fine-tuning gives you no reason to believe in a multiverse because you think modal realism is true regardless and there are lots of single universes, then my only quibble with you is that you are using confusing terminology in the context of this debate. If you said to Lenny Susskind "Have you considered that there is no multiverse but just lots of disconnected universes?" I think he would answer "How is that not a mulitverse?", although he might also say there's no physical basis to believe in such a scenario and so prefer a more physicsy multiverse like that of eternal inflation.
So I'm honestly not sure if I disagree with you. I mean, I would say that personally fine tuning doesn't increase my credence in a multiverse because I'm a modal realist for other reasons, and so my credence is already near 100% that there is a modal realist multiverse and my credence is already maxed out. If that's your position then we're pretty close.
But I can imagine that if I were not a modal realist then fine tuning would give me reason to increase my credence in some sort of multiverse (perhaps including modal realism). You seem to want to disagree with me on the latter point (your first question).
> My point is that I feel that using our definition reveals that fine tuning definitely doesn’t impact our credences in our being born anywhere.
And my point is that if you already suppose that there are lots of S and M worlds, then nobody is claiming that fine tuning should impact your credence of being born in S vs M. That misunderstands the debate, in my view. So you would be arguing against a straw man.
Hey DM,
DeleteI think you are operating under a serious misconception which is that our utilization of multiple S’s and M’s in an ensemble necessarily entails that there are multiple such entities in reality. But this doesn’t follow at all because we hold to EP.
So this:
“ If you're claiming that fine-tuning gives you no reason to believe in a multiverse because you think modal realism is true regardless and there are lots of single universes”
Doesn’t follow at all from the utilization of our ensemble with our definitions.
“And my point is that if you already suppose that there are lots of S and M world“
Again same problem, our use of the ensemble with the standard definitions for M and S in no way entails that we believe there must be multiple M’s or S’ in reality.
This confusion has permeated your entire response I feel. Because your reasoning as to why we should adopt your definitions basically presupposes that there is modal realism under our use of the standard definitions. But of course, the lack of modal realism is fully compatible with our/the standard definitions used in the ensemble.
Notice that Dmitriy’s ensemble takes into account the ratios for M and S. Such ratios can be merely epistemic, modeling our knowledge of M or S, or they can be actual (if modal realism were true).
These ratios in turn are supposed to represent our probability of having been born in M or S, therefore the ensemble by definition shows that fine tuning plays no role regarding our likelihood of being born in multiple interconnected space-time regions.
“Glad we're agreed on the first question -- that we should use my definitions to sort out our disagreement regarding my version of M.”
Yes, and provided we hold to EP, it’s still true that fine tuning doesn’t modify our credences for your type of M. This is easy to see in a case where we either have only one physical universe or only one physical multiverse (our/the standard definition). In that case (where modal realism is false) your definition of M is equivalent to ours.
Since that is exactly the kind of scenario of that Dmitriy’s ensemble is supposed to model (remember we are dealing with epistemic probabilities), it follows that his ensemble demonstrates that fine tuning plays no role regarding whether (your definition) M is more likely or not.
And this is going to be true no matter how many such M’s or S’s there are. Precisely because we are quantifying over possible worlds (meaning the M’s and S’s in the ensemble are not supposed to be actual). It’s only in that weird case of modal realism that we get an exception. But I already discussed above how, even in such a case (which I am definitely not a fan of), the conclusions of the ensemble still logically follow (albeit using your definition would block us from arriving at the correct conclusions).
Hi Alex,
Delete> This confusion has permeated your entire response I feel.
Yes, I'm still confused as to your position. If you're only talking about possible worlds, and not relying on the idea that more than one S may be actual, then I don't understand why you are resistant to my definition, where S is "there is one actual world" and M is "there is more than one actual world". Every time I try and grasp what you are trying to say, it slips away and you seem to be saying something else. I'd prefer just to talk about what the ensemble means for my definitions of M and S because at least then I can get a grip on what you're claiming.
> Because your reasoning as to why we should adopt your definitions basically presupposes that there is modal realism under our use of the standard definitions.
No, my reasoning is that your definitions allow the possibility of more than one actual S world to exist. My objection does not presuppose you've gone full modal realist. I may have talked about you as a modal realist because you seem to be and because this is an illustrative of a problem with your definitions, but I'd have the same problem if you proposed the existence of just two S-worlds.
> Such ratios can be merely epistemic, modeling our knowledge of M or S
And that would be a mistake. If it's merely epistemic and not actual, then I assume you're supposing that only one of these is actual. If there is a 50/50 chance that M exists or S exists (mutually exclusively), then using the ratios of the populations simply doesn't work, as shown in my simulation.
> In that case (where modal realism is false) your definition of M is equivalent to ours.
If my definition of M is equivalent to yours, then you must be talking about a mutually-exclusive scenario. If we model this with a simulation, then the ensemble argument gets the wrong result.
> it follows that his ensemble demonstrates that fine tuning plays no role
It doesn't follow because his ensemble gets the wrong result. It's the wrong model, so nothing can follow from it.
<“S is "there is one actual world" and M is "there is more than one actual world“>
DeleteLet’s not confuse definitions with conditions. We have to separate what M and S are, from what the necessary conditions for their being fulfilled are.
S and M refer to entities, which in our case are physically/causally closed space-time regions. The existence of S satisfies the condition that “there is one actual world"
And the existence of M satisfies the condition that “there is more than one actual world” where ‘world’ refers to a universe. Note that our definition for M and S satisfies both conditions.
In order to effectively argue that, even under modal realism, M and S are mutually exclusive, you would have to define M as being all physical reality (referring to multiple M’s that are physically/causally disconnected in logical space). I’m not sure if you consciously believe that M is “all physical reality”, but that is what is logically entailed by your position.
The rest of your objections about your simulation showing otherwise only follow if EP is wrong.
“If my definition of M is equivalent to yours, then you must be talking about a mutually-exclusive scenario.”
So this doesn’t follow unless EP is wrong and/or modal realism is true. I don’t believe EP is wrong, and I’ve already addressed the modal realism part by pointing out that:
A) Using our definition of the multiverse would still allow us to prove the ensemble’s results
B) We can’t actually coherently quantify over your version of M if modal realism is correct (we would be forced to adopt some probabilistic scheme which would have us ignore larger regions of logical space). So we should prefer our definition anyway.
Hi Alex,
ReplyDeleteI really think that all this modal realism talk is a red herring. It has very little to do with the problem. I only brought up modal realism in the first place to express by worries that my personal modal realism might have infected and confused my thinking even as I tried to set it aside.
> S and M refer to entities, which in our case are physically/causally closed space-time regions.
I can accept that. Am I to take it that on this definition there could be many S worlds and many M worlds? It seems so, and yet...
> The existence of S satisfies the condition that “there is one actual world"
On the above definition, I don't know what it means to say "the existence of S". Surely it should be "the existence of one S", because on the above definition it seems there can be many instances of S.
> you would have to define M as being all physical reality (referring to multiple M’s that are physically/causally disconnected in logical space).
On my definitions *both* S and M are conditions that pertain to all of physical reality. S means "there is only one actual universe in all of physical reality" and M is "there are many actual universes in all of physical reality".
Anyway, you say here that S and M refer to actual worlds. But other times you seem to talk about them only being possible worlds and that I'm confused if I take you to be talking about them as actual. Of course you can have different possible worlds containing different mixes of M and S entities, and that's fine as long as you're explicit about the boundaries of each possible world. The ensemble is not so explicit. It just postulates a lot of M and S entities and does not partition them into possible worlds. I'm not sure if each M and each S is a possible world in its own right or if we ought to pair M and S worlds into possible worlds each containing a single M and a single S or whether the power set of all M and S worlds describes the set of all possible worlds. Once you've set up your partitions corresponding to possible worlds, you should then proceed according to your credences for each possibility.
That the ensemble argument does not do this is a symptom of the issue I pointed out before where the ensemble argument is modelling a two-stage problem as a one-stage problem. Those two stages are (1) what worlds are actual? and (2) what is the ratio of the populations in the worlds that are actual? The ensemble argument just asks "what is the ratio of the populations in the worlds?".
My approach models these distinctions properly. My simulation supports only two populations (what you call entities), but up to 4 possible worlds, corresponding to (1) no populations exists, (2) A exists only, (3) B exists only and (4) both A and B exist.
I think I'm verging on insisting on debating question 1 only (that is: whether fine tuning gives us reason to increase our credence in M on my definition) just because the question you want to ask seems incoherent to me. That's not to say that it actually is incoherent, I just haven't managed to interpret it as a coherent question and I'm beginning to despair of ever doing so.
DeleteIf you can code, then I would suggest that you code up a simulation of the scenario you are trying to model with the ensemble. Like mine, you should be able to run it many times, and each time you should find that M is true or S is true. The number of times that M is true versus S is true should approach the correct posterior credence after many runs. The virtue of doing this would be that I could at least see what it is you are proposing, because the ambiguity of language is defeating me.
DM,
ReplyDelete<“The existence of S satisfies the condition that “there is one actual world">
“On the above definition, I don't know what it means to say "the existence of S". Surely it should be "the existence of one S", because on the above definition it seems there can be many instances of S.”
This seems to be confused. Multiple S’ (along with M) also satisfies the above condition. I think you meant to write “there is ONLY one actual world” in which case whether S satisfies such a condition will indeed relate to whether there is only one S in all physical reality.
And I understand what your simulation does. You still have to justify your arguments against EP (if you wish to demonstrate that our ensemble is wrong).
Note that even if there was one M or S in actuality, our ensemble (which expresses multiple M’s and S’s) just quantifies over possible worlds. Quantifying over possible worlds is the standard interpretation of how we should treat probabilities for singular events; though I agree that this is contentious.
But again, there is no reason to assume that there is only one S or M. If there are multiple such S’s or M’s (as we define them), then your objections against EP on the grounds that it does not account for singular cases can’t possibly follow.
I wrote:
Delete“ But again, there is no reason to assume that there is only one S or M”
Or rather I should say, there is no good reason to assume this. You haven’t given a cogent reason for why we must prefer your definition over ours; other than your point that our definition of S would violate some intuitions of ours (which only arise under modal realism). That is a very weak claim.
So it should be clear that I don’t think that there is any situation: modal realism vs. no modal realism, multiple S’s or M’s in actuality vs. just a singular case; wherein your argument works.
I don’t believe you’ve made a good case for why we should abandon the ensemble for any such situations, much less showed that it generally fails. Simply continuing to reiterate the conditions of your simulations does not make for a good argument; you must actually justify these conditions.
Best,
Alex
And it should be somewhat clear (I hope) by this stage that you need to demonstrate that EP fails for singular cases, in order to show that in such cases (singular M or S in reality) our ensemble fails. And you need to additionally demonstrate that we must adopt your definition for M to extrapolate that all cases of Dmitriy’s ensemble reasoning are bad (so that we can reduce multiple M’s to one M).
DeleteHi Alex,
ReplyDelete> You still have to justify your arguments against EP
I don't agree. For one thing, I don't necessarily reject EP. I'm not sure I understand it well enough. It may seem straightforward but I think it may be more subtle than you appreciate.
There seem to be cases where EP is false or ambiguous.
Quoting EP again: ""the [posterior] credences you assign to M and S are unaffected by how many other similar experiments are performed"
1. EP is perhaps false if M and S are connected to how many other similar experiments are performed, even indirectly. Whether this is case applies to our discussion is potentially a matter of interpretation.
2. EP is ambiguous between whether "the credences are unaffected by how many other similar experiments are actually performed" or "unaffected by our credences about how many other similar experiments are performed". It seems to me that our credences might well be affected by our credences about how many other similar experiments are performed. I see no reason to block that, at least.
So, in particular, if we're discussing our posterior credences about some hypothesis that has a connection however indirect with our credences about how many experiments were performed, then I see no reason why the latter credences should not influence the former.
But if EP is just that the actual number of experiments should not affect our credences, or if there is no connection between the two, then I'm inclined to agree with EP.
So I'm not rejecting EP, I'm rejecting the idea that the ensemble argument presented here establishes the promised conclusion "Is fine-tuning evidence of the multiverse? Surprisingly, no,"
> Simply continuing to reiterate the conditions of your simulations does not make for a good argument; you must actually justify these conditions.
The justification is that the simulation faithfully implements the conditions described in the article, while being general enough to model any problem of this kind with two kinds of population. We flip a coin or coins to determine which possible world we are in: whether population A or B exists or both, or neither, according to our credences, and then we generate the resulting population(s), then we select an observer from the resulting population(s). The results only match the ensemble argument where the existence of both populations is guaranteed, as in China/Chile. This means that the ensemble argument is only relevant to the question if you believe that in all possible worlds, there is both an M entity and an S entity (or many of each). Even on your definitions of M and S, this is simply not plausible, as there is a possible world where there are only S entities and there are possible worlds where there are only M entities. So the ensemble argument cannot be applied to the problem of fine tuning.
I realise I'm just reiterating the conditions of the simulation.
DeleteTo be clear, the justification is that these conditions *faithfully* reproduce the conditions of the article. This is a claim you can dispute if you like, but if so you have to do so by pointing out which step is incorrect. I don't think it will do just to say you don't like the conclusion because you think it is incompatible with EP.
> And it should be somewhat clear (I hope) by this stage that you need to demonstrate that EP fails for singular case
DeleteIt's worse than that. It fails for any cases which are not analogous to China/Chile, and in particular any cases where the existence of each population is less than 100% certain. It will also fail for Lichtenstein/Narnia, for instance.
Or suppose you will flip a coin and iff heads you throw 10 small fish in a lake, and then you'll flip again and if heads you'll throw 100 large fish in a lake, and then (assuming you threw any fish in a lake at all) you'll try to pull a random fish from the lake with your magic net. This isn't singular or mutually exclusive, but you can't use the ensemble argument in its present form for this scenario. If you tried, you'd predict 10:1 odds that you'd get a large fish, and you'd be wrong. The correct answer is 9:16 (according to my sophisticated prediction and borne out by a simulation I just ran).
Hi DM,
ReplyDeletein some sense yes, your simulation reproduces the conditions of the article, your steps 1,2,3 are fine (although step 3 is somewhat unclear). But your description of the process stops there, even though the most crucial step is yet to come:
4. Calculate credences.
That part is not faithful to the conditions. You need some theory how to go from facts (1,2,3) to credences (4). I called that theory assumption X. What is that theory?
By contrast my theory is EP.
I made up some calculation using some elementary probability theory based on what seemed correct to me. It's complicated and is not based on a simple soundbite principle such as EP. I don't think I need to justify it because it gets the right answer. This calculation is entirely independent of the simulation. The simulation itself makes no use of it and just calculates steps 1 to 3 and reports the results.
DeleteThe calculation for the big fish/small fish scenario I mentioned in my last comment follows:
SOPHISTICATED PREDICTION ROUGH WORK
The sophisticated prediction takes each of the following possibilities
into account and makes predictions what we expect to sample based on which
populations exist or not.
The possibilities are exhaustively described as (1) only one population exists,
(2) only the other population exists, (3) both populations exist and (4)
neither population exists.
For each trial, the probability that we will sample from a given population X
is the probability that only X exists plus the probability that both
populations exist and we sample from X.
Probability of sampling from small fish...
The probability of only small fish existing
= P(A) - P(A&B)
= 0.5 - 0.25
= 0.25
The probability of both populations existing and we sample from small fish
= P(A&B) * the proportion of the joint population in small fish = 0.25 * 10/(10 + 100)
= 0.022727272727272728
The probability of sampling from small fish
= the two probabilities above added
= 0.25 + 0.022727272727272728
= 0.2727272727272727
Probability of sampling from big fish...
The probability of only big fish existing
= P(B) - P(A&B)
= 0.5 - 0.25
= 0.25
The probability of both populations existing and we sample from big fish
= P(A&B) * the proportion of the joint population in big fish = 0.25 * 100/(10 + 100)
= 0.22727272727272727
The probability of sampling from big fish
= the two probabilities above added
= 0.25 + 0.22727272727272727 = 0.4772727272727273
Predictions...
We predict by multiplying the probabilities of sampling by the number of trials
Prediction for small fish
= 0.2727272727272727 * 100
= 27.27272727272727 results out of 100 trials where you are born in small fish
Prediction for big fish
= 0.4772727272727273 * 100
= 47.72727272727273 results out of 100 trials where you are born in big fish
The simulation itself just runs something like the following process 100 times and reports the results, without making use of a step 4:
DeleteRunning one experimental trial with blow-by-blow descriptions...
First, decide which populations exist for this trial...
We must select from alternatives with respective weights:
"Only small fish": 0.25,
"Only big fish": 0.25,
"Both small fish and big fish": 0.25,
"Neither population": 0.25
To do so, we will generate a random number from 0 to 1, and
if it is between 0 and 0.25, we will choose "Only small fish"
if it is between 0.25 and 0.5, we will choose "Only big fish"
if it is between 0.5 and 0.75, we will choose "Both small fish and big fish"
if it is between 0.75 and 1, we will choose "Neither population"
The random number is 0.33834955472966355
The chosen alternative is "Only big fish"
Now decide which population you are born in by sampling from the populations that exist...
We must select from alternatives with respective weights:
"big fish": 100
To do so, we will generate a random number from 0 to 100, and
if it is between 0 and 100, we will choose "big fish"
The random number is 19.748467754489486
The chosen alternative is "big fish"
The result is that you are born in big fish!
Hi DM,
ReplyDeleteAbout EP failing.
"""It's worse than that. It fails for any cases which are not analogous to China/Chile, and in particular any cases where the existence of each population is less than 100% certain. It will also fail for Lichtenstein/Narnia, for instance."""
It doesn't fail. Imagine there are a gazillion places where the fish experiment was done.
In 0.25G places, there are only small fish, your clone catches a small fish
in 0.25G places, there are only big fish, your clone catches a big fish
in 0.25G places, there are no fish
in 0.25G places, there are 100 big fish and 10 small fish. The fraction of those places where your clone catches a small fish is 10/110, so
- in 10/110 * 0.25G places your clone catches a small fish
- in 100/110 * 0.25G places your clone catches a big fish
----------------
In total,
Clones that catch a big fish: 0.25G + 100/110 * 0.25G = 0.25G * (1 + 10/11)
Clones that catch a small fish: 0.25G + 10/110 * 0.25G = 0.25G * ( 1 + 1/11)
Clones in total: G
Since you don't know which one you are, your self-locating uncertainty of being a person who will catch a big fish is given by the ratio of big fish catching clones to total clones:
P(Big) = 0.25G * 21/11 / G = 21/44
P(Small) = 0.25G * 12/11 / G = 12/44
Hi Dmitriy,
DeleteI feel like we're almost there.
The analysis you gave is 100% correct. It's the very same as the "sophisticated prediction" in the simulation, apart from having a pointless G factor which you could remove.
I just don't think it's how you're doing things in the ensemble argument. But rather than argue about that I would invite you now to do a similar analysis but for the case where you flip a single coin and decide to throw either 1 fish or 42 fish in the water.
1 small fish or 42 big fish, I should say.
DeleteHey DM,
ReplyDeleteAs Dmitriy showed, his ensemble achieves similar results to your simulation in large plural cases. That’s because Dmitriy’s ensemble is functionally equivalent to running multiple experiments in your simulation.
Therefore, we say that you violate EP in singular cases. That’s because, according to EP, a singular *actual case of M or S should result in the same probabilities of a person being born in either, when compared to a huge number of *actual M’s or S’s.
“The results only match the ensemble argument where the existence of both populations is guaranteed, as in China/Chile. This means that the ensemble argument is only relevant to the question if you believe that in all possible worlds, there is both an M entity and an S entity (or many of each). Even on your definitions of M and S, this is simply not plausible, as there is a possible world where there are only S entities and there are possible worlds where there are only M entities.”
I think you are confused about how possible worlds function. Firstly, there are possible worlds where Chile or China don’t exist (or where both don’t exist). Secondly, the reason for this:
“The results only match the ensemble argument where the existence of both populations is guaranteed, as in China/Chile”
is of course because you have introduced an additional step in your simulation (modeled on the sophisticated prediction) which first determines the likelihood of the entity in question (e.g. Narnia, M), irrespective of N (the number of observers in the entity). It is you who must give justification for such a step (and why N shouldn’t matter).
Therefore, the above reasoning completely fails to justify the addition of this first step. Many posts back I attempted to introduce such a potential justificatory component that would allow you to defeat M vs S cases, but still retain the reasoning for hypothetical cases like the aliens and IVF scenarios. Which was this:
“It is only legitimate to engage in ensemble reasoning if it were possible for both/all scenarios to be simultaneously instantiated.”
But there is no reason why we should accept such a statement, and I’ve provided plenty of defeaters (like the fact that this runs contrary to a great deal of counterfactual probabilistic reasoning).
Also this postulate would only refute singular cases (i.e. if we were stipulating that there is *only one M or *only one S).
As I said to Dmitriy, I think we're almost there.
DeleteI want to see how he responds to my invitation to analyse 1 small fish vs 42 big fish.
... before replying to any of your points, because it seems to me that everything is about to be cleared up.
DeleteHey Alex,
ReplyDeleteI think this might be a bit confusing:
“”” is of course because you have introduced an additional step in your simulation (modeled on the sophisticated prediction) which first determines the likelihood of the entity in question (e.g. Narnia, M), irrespective of N (the number of observers in the entity). It is you who must give justification for such a step (and why N shouldn’t matter). ”””
In some sense my ensemble does exactly the same. It starts with a population of S and M scenarios (galaxies for example) in the exact proportion of the prior (50-50 for example)
Yes, “introducing first step” means assigning a posterior credence to the entities in the first step of the analysis (irrespective of N). Whether you wish to view such a thing as just a modification of your first step, or a different step altogether seems to me subjective.
DeleteHey DM,
ReplyDeleteFirst, the G factor is very important. You have it too, except you set it to something like 100, but to have the frequencies match the probabilities the factor has to be basically infinite.
And second, about the fish question with 42 big fish and one small fish, obviously my ensemble will give you the result that half the clones pull out a big fish.
The G factor is only required when simulating, not when predicting. When predicting, it all factors out and plays no role. Having the G factor allows you to pretend you're talking about some fraction of an ensemble, but without it you're just doing elementary probability.
Delete> obviously my ensemble will give you the result that half the clones pull out a big fish.
Yes, obviously. And obviously, if we had a galaxy instead of a lake, and planets instead of fish, and you're expecting to be born in the galaxy, then N has nothing to do with it and you should have 50% posterior credence of being born in a galaxy with 1 planet and 50% with 42. So the ensemble argument is wrong.
The ensemble argument correctly models a situation where you have thrown 1 small fish and 42 big fish into the lake without flipping a coin first. It does not model a scenario involving a coin flip.
DM,
ReplyDeleteI feel you are failing to appreciate the significance of the selection effect. We aren’t going to get differing results for a singular experiment/case of one or 42 fish, because there is no selection effect in play, so N (the number of fish) can’t modify the likelihood of either scenario being actually realized.
Once we introduce a selection effect however, N (the number of observers) does affect the likelihood of being born in M or S. Your ensemble only accounts for this effect when undertaking multiple experiments, but fails to do so in singular cases (which are supposed to be represented by a single trial in your simulation).
There is no selection effect in the aliens scenario, just as there is no selection effect in 1 vs 42 fish.
DeleteThere is only a selection effect when both populations exist. We can see this when the coin flips for big fish and small fish are independent. The selection effect comes into play only when both populations exist (where Dmitriy uses 10/110 and 100/110).
To say there is always a selection effect in play for M vs S is to assert that both populations exist, which is unjustified.
I am telling you the reason why our ensemble models the single trial of the big fish scenario vs the singular case of M vs S differently.
DeleteSo this,
“ To say there is always a selection effect in play for M vs S is to assert that both populations exist, which is unjustified.”
Is exactly what I addressed in my previous posts. This only follows if we don’t accept EP; it’s on you to justify doing so. Further, attacking EP is not enough to prove the ensemble wrong in all cases (only for singular ones) because there could be multiple M’s or S’s in reality.
Or rather I should say,
DeleteAttacking EP in the manner that you have done would only make an exception for singular cases. There are definitely many ways to attempt to discredit EP.
There is also a hidden layer of complexity here that I have deliberately ignored thus far, so as to not excessively complicate things. The idea is that there are multiple variables the analysis. Just because one feels that the impact of N, for example, changes depending on the number of experiments that are conducted (violating EP), doesn’t imply that other variables must also be impacted.
That is why earlier in a side discussion with Dmitriy, I noted that even if we accepted the stipulations of your simulation (which violates EP for singular cases of M or S) we might still construct a scenario wherein it was demonstrated that fine tuning plays no role. We could still, for example, express the solitary S’ probability of being fine tuned by quantifying over possible worlds, and then using the ratios of the civilizations in the possible worlds to show that fine tuning doesn’t affect things.
But this is to excessively complicate the picture, and so I won’t get into that (I might write about it later though). That said, if one thought, for instance, that all quantification must be over actual entities, then that could refute the fine tuning analysis for singular/few cases of M or S. So this very much depends on the justification for violating EP.
Hi Alex,
Delete> This only follows if we don’t accept EP
EP is still too ambiguous for me to know if I accept or reject it. Any time you talk about EP you lose me and I fail to follow your argument.
I'd really rather forget about EP as an unhelpful idea (much like many of my unhelpful ideas such as "fungibility"). If you're going to insist on continuing to talk about EP, can you state it again as clearly as you can for me please? In particular, can you clarify if you're talking about whether other experiments actually exist or only your credences for whether they exist?
> Further, attacking EP is not enough
I'm not attacking EP. I don't understand EP. I'm attacking the argument in this article, which though it may be based on EP, does not mention EP. For all I know, EP is perfectly correct and the problem lies elsewhere. I have no idea. I only know that the conclusions reported by this article are unsupported by the argument.
> We could still, for example, express the solitary S’ probability of being fine tuned by quantifying over possible worlds, and then using the ratios of the civilizations in the possible worlds to show that fine tuning doesn’t affect things.
What's the difference between that and what's in this article? Is it that you would be treating M and S as per my definition? Sure, go ahead, let's see the analysis in detail. I expect that it will either get the result I predict or there will be some mistake. The mistake I anticipate is that you will try sampling from the observers across different possible worlds, which I flatly reject as incorrect. In this context, you can't include observers who don't exist in any population you're sampling from, and unless we're adopting modal realism, not all observers in all possible worlds exist.
I expect you to say that this flies in the face of established counterfactual reasoning, but I don't think so. I agree, we are indeed allowed to consider possible worlds which may not exist. We are not allowed to quantify over entities within possible worlds as if they are one population (at least unless we presuppose that both possible worlds exist as in modal realism).
A while back Dmitriy brought up the example of possible configurations of air particles in a room as a standard example of ensemble analysis done well. The air particles couldn't be in more than one configuration at a time, he said, but we can still put the possibilities in an ensemble and quantify over them despite this mutual exclusivity. This is all correct.
But we can't quantify over the entities in the possible worlds as if they are all one population. If we have 50% credence that there is one air particle in a box, and 50% credence that there is 1 trillion air particles in a box, then we don't answer the question of whether we should expect 1 trillion or 1 air particle to be in the room by quantifying over the combined population and determining that the odds are 1 trillion to 1 in favour of 1 trillion. And I say the same goes if you imagine being one of those air molecules yourself and doing a self-location calculation. When quantifying over populations, those populations have to stay within their own possible worlds. You can't quantify across possible worlds.
“In particular, can you clarify if you're talking about whether other experiments actually exist or only your credences for whether they exist?”
DeleteIt’s this:
Whether and how many other *actual experiments have been done, has no affect on the soundness of the ensemble predictions. Even if there were only one M or S in reality, the probability predictions should be unaffected.
“ What's the difference between that and what's in this article”
DeleteThe difference is that we would reach your conclusion that N doesn’t matter, and the likelihood M or S would be determined by the credence assigned to the coin toss. But we would also conclude that fine tuning does not impact our posterior credences for M.
Also,
“ We are not allowed to quantify over entities within possible worlds as if they are one population”
You are forgetting that we have been over this, and we definitely don’t have to quantify over a single population, unless we both
A) Adopt your definition for M
B) Modal realism is true
So that there really is only one population of M to quantify over. And it’s not so much that we are not “allowed”, but that we could no longer demonstrate the results of our ensemble (for either the impact of N or the non-impact of fine tuning) of this was true.
Hi DM,
ReplyDeleteAs Alex said, the selection effect is very important here. The selection in fact doesn't exist only when the two populations coexist. For example, it also exists in the Dr. K scenario.
Perhaps one clear way of explaining this is the following: you are right that there is a definite analogy between the 42/1 fish situation and the aliens situation. But you're not correctly identifying which entities are analogous.
Clone/fisherman = aliens
Each fish = a civilization
And we are of course not one of the aliens, but one of the civilizations. So basically we are one of the fish :)
DeleteHi Dmitriy,
Delete> And we are of course not one of the aliens, but one of the civilizations. So basically we are one of the fish :)
And yet, if we throw 1 small fish and 42 big fish into the lake at the same time, we reproduce exactly the circumstances and predictions of your ensemble argument. So why do we now get the same results, if the problem is that the analogy is misapplied?
I put it to you that the problem is that your ensemble argument has no analogue of dice flipping, or partitioning populations into distinct possible worlds. In your analysis of fish, you remembered to do this partitioning, and you ended up with four possible worlds each with 0.25 possibility. There is nothing like this in your ensemble argument, despite the fact that it is supposed to model a coin-flipping scenario where S or M (or both?) may exist without certainty.
But again, I need not prove this with argument. I can prove it with my simulation. I You've already agreed to steps 1-3, and yet steps 1-3 yield results that confirm my view and not yours. If you think the results of my simulation are also disanalogous in the same way as the fish, then you can retract your acceptance if you like and propose some alternative set of steps. As long as there's a step where a coin is flipped which meaningfully affects the results.
I said I don't need to prove it with argument, but to explain what I think is your mistake, the fisherman is not analogous to the aliens because the fisherman is sampling from the population and the aliens are not. A civilisation under self-location uncertainty is sampling from the population.
DeleteSome confusion might arise from the fact that I said the fisherman flips the coin, just like the aliens do. So we can separate the roles. A groundskeeper flips the coin and stocks the lake with fish. A fisherman samples the population and selects a fish. Groundskeeper = aliens. Fisherman = civilisation.
Hi DM,
ReplyDelete"I put it to you that the problem is that your ensemble argument has no analogue of dice flipping,"
It does, in the same way as in step 1 of your simulation. You generate G (100 or 10000, I forget) runs of the experiment, with half the runs corresponding to flipping heads. I generate G independent experiments (here, galaxies), with half of them with the coin landing heads (and hence 42 planets).
Now I see what you meant by warning me of the perils of my talking about DM introducing a “first step”!
Delete:)
If we interpret it so, then the problem is you lack the third step. Each run of the experiment, you should self-select. You only self-select when all runs are complete. Either way each run is missing a step.
Delete"""
ReplyDeleteA groundskeeper flips the coin and stocks the lake with fish. A fisherman samples the population and selects a fish. Groundskeeper = aliens. Fisherman = civilisation.
"""
In the aliens case and this story, we have an entity (groundskeeper, aliens) that flips the coin and populates the world with 42/1 other entities (fish, civilizations).
So I don't know what would be the analog of the fisherman in your new story, but it's not a civilization. The M scenario contains 42fish/civilizations.
Just thinking this through. I'm going on a bit of a journey with this one.
DeleteMy first reaction is to say that the fisherman is us (i.e. a particular civilisation), trying to figure out whether we are in an S galaxy or an M42 galaxy, or equivalently what kind of planet we're on.
To make the analogy closer, you could imagine having N fishermen, where N is the number of fish in the lake, as along as each fisherman is unaware of the others. In these circumstances we could imagine that the fish are seeded planets rather than civilisations.
This makes it more complicated as we have to suppose that in some sense the existence of the fishermen is also decided by a coin flip. I guess you could say that the number of fishermen invited to fish in the lake is determined by the coin flip, and that the fishermen are unaware of the lake if uninvited.
Under these amendments, I think the analogy is very tight. But now it's not so clear that you should have a 50% credence of selecting a small fish and a 50% credence of selecting a big fish.
By now I know you well enough to foresee your objection -- you're more likely to be invited if there are 42 fish and 42 invitations, so the fact that you are invited is evidence for more fish. This seems to bring us back to TER issues. Once we take our own existence as evidence, we get into debates about whether the appropriate evidence is "a fisherman was invited" or "I was invited".
But the ensemble argument only takes a 3rd person view dispassionately sampling from the population, without taking the evidence of our own existence into account. So I return to the original version, where there's just one fisherman. In this version, the fisherman is us, considering the ensemble from a 3rd person view and sampling from it at random, as you do in the ensemble argument. As with the ensemble argument, the evidence of the specific fisherman's invitation is excluded from the analysis.
So as I've said before, it's possible that the ensemble argument gets the right result for the wrong reasons. If we fully accept TER, then our specific existence might be evidence for M just because we would be more likely to exist on M. But the ensemble argument is still crap (sorry) because it doesn't use this evidence and instead reasons from a third person perspective with an inaccurate model of the problem. The problem I have with it then is that it purports to be a simple solution to a difficult problem, when the problem really is difficult and the simple solution doesn't resolve it.
But all these issues aside, how would you simulate the alien scenario if not the way I did? If you agree with how I simulated it, then you must explain why the results are not as the ensemble argument would predict.
If you want to go back to the original story, where an entity (fisherman, aliens) populates the world with 42 / 1 secondary entities (fish in lake, civilizations) then us being a civilization trying to decide if we live in a 42 or 1 planet galaxy means we are one of the secondary entities. So then in your fish story we are a secondary entity, a (intelligent) fish trying to decide if it's living in a 42 or 1 fish lake.
ReplyDeleteMy ensemble definitely does account for our (a fish's) perspective because it calculates the self-locating uncertainty. The "self" here is not some third person, it's your (a fish's) self.
Right, but then the fish does so by imagining sampling from the lake. Which is equivalent to the fish postulating a fisherman picking a random fish out of the lake.
DeleteThat's what they do in your simulation. In my ensemble they use the self-locating uncertainty. That's the difference between our approaches (since we do step 1, generating G experiments, the same way).
ReplyDeleteNo, that's not a difference. The fisherman is just a personification of self-locating uncertainty. The fisherman selects from the population randomly. Reasoning about credences under self-locating uncertainty is the same a reasoning about credences about selecting from the population randomly.
DeleteThe difference is you do self-locating uncertainty once, at the end of G experiments, and I say you should be simulating it by selecting randomly for each experiment and then your credences will be reflected in the results.
Hi Dmitriy,
ReplyDeleteShould credences about self-location be equivalent to credences about sampling from a population at random? I have been assuming so, and I think your ensemble argument does too.
If yes, then I don't see that the fisherman is disanalogous. Credences about which fish the fisherman will catch are credences about sampling from a population at random, just as are credences about self-location.
If no, then what's the alternative, and wouldn't you need to change the ensemble argument accordingly?
Hey DM,
ReplyDelete"No, that's not a difference. The fisherman is just a personification of self-locating uncertainty. "
That helps to understand the role of sampling in your simulation and its relationship to self-locating uncertainty. So the difference is:
“Right, but then the fish does so by imagining sampling from the lake. Which is equivalent to the fish postulating a fisherman picking a random fish out of the lake. "
They do that in your simulation, but not in my ensemble. If the fisherman personifies self-locating uncertainty, then we are both using it but we are using it differently:
Simulation. G fishermen, then average the results.
Ensemble. One “fisherman” for the whole ensemble.
Do you agree with this summary?
Hi Dmitriy,
DeleteYes, that's right I think. That's what I was getting at with
"If we interpret it so, then the problem is you lack the third step. Each run of the experiment, you should self-select. You only self-select when all runs are complete. Either way each run is missing a step."
And
"The difference is you do self-locating uncertainty once, at the end of G experiments..."
I don't know if it's important but I feel like we should acknowledge that there's more than one way to map your ensemble to the simulation. What you have here is a particular mapping that makes sense to you, and I'm happy to go along with it.
But we could also map it as a single trial containing a population of 0.5*G M worlds and 0.5*G S worlds and no coin flip (or a coin flip with 100% credence for each set of worlds), then having the "fisherman" at the end of each trial as I do (but again you only carry out one trial). On this mapping, it's China/Chile.
Either way, yours turns out to be a 2-step process per trial and mine turns out to be a 3-step process per trial.
But yes, let's go with:
> Simulation. G fishermen, then average the results.
> Ensemble. One “fisherman” for the whole ensemble.
Hi Alex,
ReplyDeleteThanks for clarifying EP.
> EP: Whether and how many other *actual experiments have been done, has no affect on the soundness of the ensemble predictions
"Actual experiments" is an important point which I'm glad you've clarified.
"Soundness of the ensemble predictions" still feels a bit vague to me. On this wording, we might still have different predictions for different numbers of experiments and all might still be OK as long as the predictions remain sound for each case.
"Ensemble predictions" is also vague, because an ensemble doesn't predict anything by itself. You have to analyse it somehow, and how you analyse it might depend on what kind of question you're trying to answer.
My best attempt to steel man the EP into something I could accept is:
> EP: Whether and how many other actual experiments have been done can have no effect on our credences regarding what we should expect from a single run of an experiment, provided we have no way of knowing how many actual experiments have been done.
I do not reject this form of EP, and I don't think anything I'm saying does reject this.
However, I would still think it reasonable to reach different conclusions for cases when when we believe or stipulate that there have been no other experiments than when we believe or stipulate that there have been many other experiments. This is because such beliefs and stipulations pertain to our credences and not to whether there actually are other experiments we don't know about.
> and the likelihood M or S would be determined by the credence assigned to the coin toss. But we would also conclude that fine tuning does not impact our posterior credences for M.
Agreed. But I would argue that it does impact our prior (relative to the ensemble argument) credences, at least if we're flexible on TER. On my view, neither the ensemble argument nor even my own simulation can help us answer how we should adjust our credences based on fine tuning. The entirety of the case for changing our credences based on fine tuning rests on Bayesian reasoning from the evidence that "some fine-tuned universe exists". But this is just to remind you of my position. Let's not get into it. I already know you don't buy this.
> You are forgetting that we have been over this, and we definitely don’t have to quantify over a single population, unless we both
You say I'm forgetting. I would say I haven't understood any of the points against this that I haven't answered. I'm having a harder time pinning down and grasping your position than Dmitriy's, for whatever reason. Maybe it's that Dmitriy tends to speak in terms of fairly precise short points and you, like me, have a tendency to wax poetic.
Hey DM,
Delete“ I do not reject this form of EP, and I don't think anything I'm saying does reject this”
Yes, that’s why I said that even if we did away with EP (our version) your critiques could only work provided we thought that there were few M’s or S’s in reality, but there is no need to assume this. In fact, under your preferred version of modal realism, our ensemble would work well in the absence of the soundness of EP.
But the actual point of EP is to emphasize that even (in the aliens case) if there were only one galaxy in reality, and the aliens had decided to populate this galaxy according to a coin flip, we should still reason as though we had a 42:1 chance of being born in the multi vs single planet galaxy.
Hence, if this is true, then we can correctly say that even if there were only one M or S in reality, our ensemble results still hold. This all goes back to what I was saying earlier about our quantifying over possible worlds being dependent on your interpretation of what probability is.
In the aliens case, if we’re just looking at the actual picture, then it seems like we had a 50/50 chance of being born in either galaxy. However, it’s also true that in all possible worlds where such an experiment was undertaken, the average possible observer has a 42:1 odds of ending up in a multi galaxy (note that each possible observer knows that there is only one galaxy in their world). If you assume that the question “in which galaxy could I have been possibly born, knowing that there is only one galaxy?” entails the assumption that we could have been any possible observer, then you must grant that the odds are 42:1. It is this assumption that forms the core of EP.
Hence, if we knew there was only one galaxy which the aliens populated, but didn’t know the number of planets, we should still reason (according to EP) that we are more likely to be in 42.
Hi Alex,
Delete> under your preferred version of modal realism, our ensemble would work well in the absence of the soundness of EP.
Under my preferred version of modal realism, which I deem to be a case of M, you mean?
I agree that under modal realism, fine tuning gives us no reason to believe our local universe is part of a bigger physical multiverse. Because we already live in a modal realist multiverse, which would mean there are many opportunities to get fine tuning right. My only claim here is that fine tuning gives us reason to increase our credence in many opportunities, as long as our credence is not already 100%. But our credence is already 100% if we assume modal realism.
> we should still reason as though we had a 42:1 chance of being born in the multi vs single planet galaxy.
I don't agree that the version of EP I agreed to entails this.
> However, it’s also true that in all possible worlds where such an experiment was undertaken, the average possible observer has a 42:1 odds of ending up in a multi galaxy
Only if you weight all possible observers equally. I maintain that this is a mistake. Some possible observers are more probable than others.
If you flip coins in a black box coin flipping machine 100 times that only reports the count of heads, then there will be a possible version of you for all possible counts from 0-100. Yet it would be wrong to assume that you should have equal credence for observing 0 as observing 50.
This kind of thinking should seem familiar if you understand Everettian quantum mechanics. All possibilities are real, but not all have the same measure. The probability (or weight, or measure) of each is given by the square of the amplitude of the wave function (the Born rule), so in the context of QM it is a mistake to weight each possibility equally.
I don't think you should weight all observers equally in S/M42 either. For simplicitly, let's assume that each civilisation has one observer.
The first decision is the coin flip, and this partitions our problem immediately into two possible worlds S and M42 with equal weighting. As long as we're saying only one of these is actual, then your probability of being an S observer is 0.5, and your probability of being any M42 observer is 0.5 and your probability of being any specific M42 observer is 0.5 * 1/42.
If you calculate a weighted average according to the probability of being each specific observer, you find that your credence is 0.5 for S and 0.5 for M42, because in the M42 case there are 42 observers each with 0.5 * 1/42 probability, which adds to 0.5.
When I've made points like this before, you argue that I'm begging the question by assuming that the higher population in M42 shouldn't change the credence, and presumably you think I'm working backward from there. But I think this is just standard probability with no ad hoc assumptions of the sort. For you to be any specific M42 observer, you need both a coin flip to go your way and to be a specific one out of a population of 42. To be any specific S observer, you just need the coin flip to go your way.
This is different from if it were like China/Chile, where both populations exist. Now there's no coin flip, and the population is 43. To be an S observer is 1/43. To be any specific M42 observer, your probability is also 1/43. But there are 42 of them, so overall your probability to be in M42 is 42/43.
“ My only claim here is that fine tuning gives us reason to increase our credence in many opportunities, ”
DeleteRight, but this must be justified through an independent argument.
“Only if you weight all possible observers equally”
Of course, but the default assumption is that all observers are weighed equally until we have reason to believe otherwise. In other words, until we have reason to think we belong in some special reference class, we should assume that we are in the generic reference class (of all possible observers).
Note that in the Everettian case we do have good reason to think that not all possible realities are equally probable (we have Schrodinger’s equation to govern the wave function).
But you need some similar sort of justification for why we should make an exception in the multiverse case; which you have not provided.
In any case, I don’t want to get into a drawn out discussion over EP. I am content with the point that we have no reason to assume that there are only few M’s or S’. And under your favored version of reality (modal realism) you must admit that your critiques (in this thread) against our ensemble, which are based on your simulation, have no merit. Meaning that we have to go back to some independent argument (your Bayesian analysis for instance) to argue against it.
“As long as we're saying only one of these is actual, then your probability of being an S observer is 0.5, and your probability of being any M42 observer is 0.5“
Again, only if we think that we shouldn’t reason as if we’re a generic possible observer; who knows that there is only one galaxy, but doesn’t know the number of alien picked planets within it. So, what’s so special about us?
Hi Dmitriy,
ReplyDeleteI thought you might come back once that point was clarified. Perhaps you're busy.
The question now is which approach is correct?
It seems obvious to me that mine is.
Previously, I used the simulation to back up my analytic approach. But since we agree on the analytic approach to the fish problem, I can use the analytic approach to back up my simulation. We know ahead of time that you should have a 50% credence of selecting a small fish and a 50% chance of selecting a big fish. Whichever approach gives that answer is the correct approach.
On my approach, we sample on each trial. On your approach, we sample at the end of all trials.
Thus, for a single trial, we would both get the same results. But G is critically important, so what happens as we increase G?
On my approach, we start with an empty lake on each trial and select a fish at the end of each trial. Half of the fish we select will be big and half will be small, so my approach gives the correct answer.
On your approach, where we sample at the end, this is to say that on each trial we add more fish to the same lake, and at the end choose a fish from the lake. After many trials, the ratio of the fish in the lake will obviously approach 42:1 in favour of big fish, so you you should expect to select a big fish with credence 42/43. Therefore your approach is incorrect.
Hi DM,
DeleteI had an idea of how to proceed, but your comment derailed my genius plan :-)
“ We know ahead of time that you should have a 50% credence of selecting a small fish and a 50% chance of selecting a big fish.”
“ so you you should expect to select a big fish with credence 42/43. Therefore your approach is incorrect.”
I thought we were on the same page on this: a few comments ago I did a detailed calculation demonstrating that my ensemble handles an even more complicated fish problem easily. Don't you remember all the clones?
Hi Dmitriy,
DeleteI do remember all the clones. The clones are all fishermen. But in the ensemble analysis on this article, we agreed there was only one fisherman.
> Ensemble. One “fisherman” for the whole ensemble.
G clones is correct. That's what you had in your analytic analysis of the fish case, and that's what I have in my simulation.
1 clone is what you have for the whole ensemble. This is what is incorrect.
Hi Alex,
ReplyDeleteWe often disagree about whether I've justified something or not. It's not simply that I'm refusing to provide justifications. From my perspective I'm offering justifications and you're refusing to accept them, for reasons which aren't always clear to me.
For instance:
> Right, but this must be justified through an independent argument.
Independent of what? I feel like I've been arguing for this, but I don't understand this independence requirement.
Or here:
> But you need some similar sort of justification for why we should make an exception in the multiverse case; which you have not provided.
I have, in the very comment you're answering. Here is the justification:
"For you to be any specific M42 observer, you need both a coin flip to go your way and to be a specific one out of a population of 42. To be any specific S observer, you just need the coin flip to go your way."
> Again, only if we think that we shouldn’t reason as if we’re a generic possible observer; who knows that there is only one galaxy, but doesn’t know the number of alien picked planets within it. So, what’s so special about us?
There is no assumption that there is anything special about us.
We only know that we are either an S observer with probability 0.5 or an M42 observer, with a probability of 0.5 (because there are 42 of them each with a probability of 0.5 * 1/42 of being us). I'm not assuming that *we* are not generic, I'm assuming that the population of 43 possible observers is not a generic population, because it is set up specifically so that the above probabilities are correct, as a result of the initial coin flip. Without the initial coin flip, where all of these observers exist in the same population then it would indeed be a generic population.
Hey DM,
DeleteI think there is confusion on your part over what the nature of justification is, as well as what your purported justification would be doing anyway.
There are two parts to this conversation; the first regards your justification for your critique of EP. The second has to do with what this critique of EP would entail if it were successful.
"> Right, but this must be justified through an independent argument.
Independent of what? I feel like I've been arguing for this, but I don't understand this independence requirement."
This relates to the second part of the conversation, wherein I pointed out that even under your preferred version of reality (modal realism), and even if EP is wrong as you claim, it still follows that our ensemble results are correct. Your argument about our needing to argue that a single S or M case should be treated as a coin flip (whatever the credences we assign to this coin flip) has to do with the first part of our conversation (whether EP is legitimate); it has no bearing on my point about your needing an independent argument.
By which I mean that you need some reason to suppose this: "My only claim here is that fine tuning gives us reason to increase our credence in many opportunities, as long as our credence is not already 100%"
You would require something like your original Bayesian reasoning, because the argument against EP in no way supports this above contention. Hence, my point that even if we accept that EP is wrong, it still follows that your critiques against the ensemble fail on your version of modal reality. We would just end up having to go back to the Bayesian argument, our ensemble is not defective independent of that, because you concede that "I agree that under modal realism, fine tuning gives us no reason to believe our local universe is part of a bigger physical multiverse."
Now onto your critique of EP:
"I have, in the very comment you're answering. Here is the justification:
For you to be any specific M42 observer, you need both a coin flip to go your way and to be a specific one out of a population of 42. To be any specific S observer, you just need the coin flip to go your way."
This is not a justification; this is just a repetition of your claim. My claim was that we should treat all possible observers equally, which in turn implies that we shouldn't assume we have a 50/50 probability of being born in either galaxy 1 or galaxy 42. Your claim is that we need to treat every possible observer unequally because we have an equal likelihood of being born in either galaxy. I asked you to provide justification for this, to which you responded by repeating the above claim.
In other words this:
Delete"For you to be any specific M42 observer, you need both a coin flip to go your way and to be a specific one out of a population of 42. To be any specific S observer, you just need the coin flip to go your way.""
Which amounts to the belief that an M42 observer needs two things to go his/her way, is just another way of putting your claim that an M observer is not treated equally to an S observer (because we should assume that we have a 50/50 likelihood of being born in either galaxy). I am asking you to justify this assertion.
My reason for why we should think that we are in the general reference class (i.e. treat every possible observer equally) is because this is the simplest approach. Notice that this is fully compatible with the proposition that there are an equal number of M or S galaxies in the possible worlds ensemble (in fact it assumes this). Preferring a different framing of our reference class requires us to believe that there is something more significant about an S observer than a M observer. There's nothing inherently bad to this, but it necessitates that we have some additional information at hand which goes beyond the premises of the thought experiment (like in the Everettian case).
Hi Alex,
DeleteFirst, again, I'm not critiquing EP. I have no problem with EP, or at least my interpretation of it which you seemed to accept. So I don't recognise what you call the first part of the conversation where I'm supposedly trying to justify my critique of EP.
> I pointed out that even under your preferred version of reality (modal realism), and even if EP is wrong as you claim, it still follows that our ensemble results are correct.
The claim you asked me to justify is "fine-tuning gives us reason to increase our credence in many opportunities".
So, my confusion is partly that I've already provided an independent justification with the Bayesian argument, as you acknowledge.
But even worse, I don't think I actually have to justify this to defeat your point about modal realism. The core claim we're debating is the claim you're asking me to justify. Your modal realism point appears to be part of an argument trying to refute the claim. But if the claim "fine tuning gives us reason to increase our credence in many opportunities" is true, then your modal realist point is irrelevant because your ensemble analysis is compatible with the claim, as there are many opportunities on modal realism. If the claim is false, then your modal realist point is irrelevant because the claim is false regardless. Your modal realist point is irrelevant either way and so is defeated without any need to justify the claim.
> because the argument against EP in no way supports this above contention.
I have no beef with EP. I'm not presenting an argument against EP. In this part of the conversation I'm just saying "modal realism would support our ensemble => so what?"
> you concede that "I agree that under modal realism, fine tuning gives us no reason to believe our local universe is part of a bigger physical multiverse."
This is a minor point, but if you think that this is a concession of some kind then I have evidently failed to communicate my point of view adequately. Again, my claim is only that fine tuning gives us reason to believe in more opportunities for fine tuning. It has nothing to say about the nature of those opportunies. Loosely speaking, "many opportunities" = "a multiverse", but if you want to be very precise about what counts as a multiverse then you should understand the claim to be talking generally only about "many opportunities".
> This is not a justification; this is just a repetition of your claim.
The claim you want me to justify is why I don't think it's right to treat all observers as equivalent. I justified it by showing how we would calculate the probability of selecting any particular observer from this scenario according to standard probability theory. I think that counts as a justification. The only reason I can ascertain for why you're rejecting it as a justification is because it proves the thing you demand that it prove, which you are interpreting as assuming the thing you demand that it prove.
In particular:
> My claim was that we should treat all possible observers equally
All being equal. But not all is equal. Some observers are in a possible world with 42 observers and some observers are in a possible world with 1 observer, with each world being equally possible given the conditions of the experiment, where we stipulate that each world has a 50% chance of being actual. Under these conditions, the chance of selecting one of any of these possible observers is an elementary question of probability and is not correctly answered by assuming that we should treat all possible observers equally.
“ First, again, I'm not critiquing EP. I have no problem with EP, or at least my interpretation of it which you seemed to accept. ”
DeleteObviously I’m taking about our version of EP, the one I’ve stated, and the one we’ve been using all along. Not your possible interpretation which was the statement we all found agreeable.
The point is that you claim that singular cases should be treated with different probabilistic results; that’s what I’m disputing. And that’s what your critique about the aliens galaxy case yielding different probabilities to what Dmitriy and I think it should, is about.
This is an entirely separate like of reasoning from the notion that fine tuning should give us some type of credence for your version of the multiverse. That’s why I pointed out that in the end your criticisms of the ensemble about EP can’t amount to much on your end (because you believe in modal realism) anyway. We are just in the end reduced to arguing about the Bayesian analysis, if your criticisms of EP have merit (again, the original one we’ve been using all along). Since you wanted to go over and above the Bayesian analysis, by demonstrating that there was some additional flaw in the ensemble; it can’t be said that you have accomplished this.
Finally about EP:
It’s definitely not true that yours is the *standard probabilistic interpretation. There are definitely criticisms of EP, but I wouldn’t say that’s the standard approach (in any case, all interpretations require justification).
“All being equal. But not all is equal. Some observers are in a possible world with 42 observers and some observers are in a possible world with 1 observer, with each world being equally possible given the conditions of the experiment, where we stipulate that each world has a 50% chance of being actual”
But we’re not stipulating that each world has a 50% of being actual; only you are, and that is what I am denying and asking you to justify. So again, you are merely repeating your claim.
Sorry for any grammatical errors in my post above (I was typing on my phone). In any case, I think you are still confused about what I am contesting. We are definitely not in agreement that there is a 50/50 chance of an M or S galaxy being actually realized for an observer (although of course I agree that there are an equal number of M and S galaxies in the possible worlds ensemble).
DeleteWhat you have shown, in fact, is that *if we concede that there is a 50/50 chance of M or S being actualized in our universe, then it follows that not all observers are equal.
Naturally I don’t dispute that, only the premise which such reasoning is based on. This premise still needs to be justified.
Or rather I should say that I’m talking about the original EP, and not your modification to it.
DeleteYours is a modification which adds the extra condition about our state of knowledge; it’s not an interpretation. This extra modification does away with the problem of singular/few cases (which we disagree about), and so of course we are both going to find such a modified statement agreeable. It’s in the case of the singular types of scenarios wherein we have a disagreement, and to which your critiques have been addressed.
Hi DM,
ReplyDeleteThere is a lot of confusion now, because in your original story the following two entities were the same:
1. The coin flipper, aka the person whose credences we are trying to determine. That was an actual entity in the story. The ensemble, yours and mine, has G clones of them.
2. The fisherman, who as you told me, was the personification of self locating uncertainty. Your simulation has G of these metaphorical entities, mine has only one.
Do you see how confusion arises because of these weird identifications in your story?
The bottom line, however, was that the detailed calculation I gave a few comments ago demonstrated that my ensemble works perfectly well with the fish story. To reiterate, my ensemble most definitely has G clones, but only one metaphorical personification of self locating uncertainty.
So the crucial question is: do you agree that the detailed calculation I provided of how the ensemble argument works for your fish story demonstrates that it handles it easily and gets the correct answer?
Hi Dmitriy,
DeleteOn the confusion, I think we clarified all these points to both our satisfaction as follows:
Groundskeeper: Alien: flips a coin and seeds Lake/Galaxy accordingly
Lake: Galaxy: Contains 1 or 42 Fish/Civilisations
Fish: Civilisation
Big Fish: Civilisation in a Galaxy with 42 Civilisations
Small Fish: Civilisation in a Galaxy with 1 Civilisation
Fisherman: Self-location uncertainty: Random (uniform) selection from some population
The weakest or weirdest part of the analogy is between Fisherman and self-location uncertainty. But we seem to agree that in both cases their credences are derived from looking at the problem as random uniform selection from some population, so unless you want to argue that point they seem to be analogous. In particular, if we want to simulate either scenario, I say we need to select randomly from a population on each trial and you think you need to do it only once. But this is not a problem of analogy, this is a problem of correct procedure.
With all this resolved, it ought to be clear that the coin flipper plays no role other than to flip coins and seed the population. It is not an agent for whom we are trying to establish credences. It's just the setup of the experiment. It could be a machine or some natural process. Whether we are trying to establish credences of the fisherman or of the fish does not seem to me to matter as the calculation is the same either way. I prefer to say we're calculating the credences of the fisherman only because the story makes more sense this way (fish don't ponder such questions, and if we're sticking with big fish/little fish a fish can just observe its own size).
> The bottom line, however, was that the detailed calculation I gave a few comments ago demonstrated that my ensemble works perfectly well with the fish story.
The detailed calculation you gave a few comments ago was perfectly correct, but I don't think it reflects the ensemble calculation in the article, or even that it's really an ensemble calculation at all. It's just the correct probabilistic calculation dressed up to look like an ensemble by including the factor G which has no effect on credences as it cancels out.
Apart from including G, your calculation is exactly the same as the "sophisticated prediction" I coded in Javascript. Though G plays a role in my simulation, it is not used at all in generating credences in the prediction. The only trivial role it plays in the prediction is to convert the credences into a prediction for a definite number of outcomes in G trials, but only so we can easily compare the prediction to the results of the simulation.
> do you agree that the detailed calculation I provided of how the ensemble argument works for your fish story demonstrates that it handles it easily and gets the correct answer?
I agree that it gets the right answer and in the right way, but I don't agree that it is representative of how the ensemble argument in the article works.
Again, you agreed with me about what the right answer for fish should be:
> about the fish question with 42 big fish and one small fish, obviously my ensemble will give you the result that half the clones pull out a big fish.
i.e. our credence should be 50% for big fish.
But under the above mappings, the case seems to be perfectly analogous to the alien scenario described in the article. And yet the article claims that the ensemble will give you credence 42/43 for the analogue of big fish (M42).
S,o either the ensemble argument in the article is incorrect or there is a disanalogy between lakes and galaxies I'm not seeing.
Hi DM,
ReplyDelete"""
Groundskeeper: Alien: flips a coin and seeds Lake/Galaxy accordingly
Lake: Galaxy: Contains 1 or 42 Fish/Civilisations
Fish: Civilisation
Big Fish: Civilisation in a Galaxy with 42 Civilisations
Small Fish: Civilisation in a Galaxy with 1 Civilisation
Fisherman: Self-location uncertainty: Random (uniform) selection from some population"""
Yes, perfect, I wasn't sure if we were in agreement there.
"""
With all this resolved, it ought to be clear that the coin flipper plays no role other than to flip coins and seed the population. It is not an agent for whom we are trying to establish credences. It's just the setup of the experiment. It could be a machine or some natural process."""
Also fine, assuming we are not trying to establish credences for the aliens. But now comes the absolutely critical part:
"""
Whether we are trying to establish credences of the fisherman or of the fish does not seem to me to matter as the calculation is the same either way.
"""
Only the coin flipper / aliens and the fish / civilizations have credences, the fisherman is nobody! This is not a minor nitpick, this is crucial. Previously, when you wanted me to show how my ensemble method handles your fish question and I provided the detailed calculation I calculated the credences for the coin flipper (who, by the confusing identification was the fisherman at the time, but now I'm glad we agree on a clear separation between the actual and the metaphorical entities), because that's how the question was posed. You didn't ask about what credences the fish should assign.
So, my ensemble handled the question about the coin flipper's credences according to the following general method, which is the ensemble method I use in the article and elsewhere:
1. Construct G copies of the whole situation, split between M and S based on the prior (step 1 in your simulation)
2. Out of all entities whose credences we are calculating (all the coin flippers if we want his credences, all the fish/civilizations if we wanted their credences!) find what fraction have the desired property (living in an M42 lake for example). By self-locating uncertainty (metaphorical "sampler" - maybe best not to call him fisherman anymore, but notice - only one of those in my method!) this fraction is the credence for the entities in question for having the property in question.
So do you see how this ensemble method is precisely what I did in my detailed calculation from a few posts ago, which got the correct answer for the coin flipper's credences you asked about? And the blog post follows the exact same methodology.
Now, you don't have to agree with the methodology, because in yours you have G samplers, not one. And we can discuss why I think my methodology is correct. But do you now understand how the methodology works and how it got the correct answer in my detailed calculation from a few posts ago?
Hi Dmitriy,
DeleteThanks for this clarification. I'll note a few disagreements by just stating them but I'm not asking you to respond if you're busy. I have noted your position and I just want to clarify mine. To avoid getting on tangents there's just one question I'll ask you to answer, at the end.
> Only the coin flipper / aliens and the fish / civilizations have credences, the fisherman is nobody!
Can accept for the sake of argument. Disagree that this is an important point. For me, the fisherman is not a metaphorical entity but a person in the fish analogy. Even so, the fact that he has no counterpart in the aliens analogy does not for me break the analogy because he has a metaphorical counterpart which I think serves the same purpose.
I don't see that there should be any difference in the calculation if we're calculating credence for the fish vs for the fisherman, assuming each fish doesn't know if it's small or big. Whether the perspective is that of the fisherman or the fish, the available evidence seens to be the same: there is at least one fish in the lake, and the nature of the problem seems to be the same: sampling from a population. Or at least I see no difference. I'm open to being persuaded on this but it's far from obvious to me.
I think I see but am not clear on how step 2 of your ensemble method was applied to calculated the fisherman's credences. What properties does he have? Standing outside a lake with one of your 4 possible setups, or catching a large fish/small fish?
OK, so my question to you is how would you do the calculation for the credence of the fish in the exact same scenario?
The scenario, for reference is:
Suppose a groundskeeper flips a coin and iff heads throws 10 blue fish in a lake, then flips again and iff heads throws 100 red fish in a lake. So there could be 0 fish in the lake, 10 blue fish in the lake, 100 red fish in the lake or 110 mixed fish in the lake. Assume each fish is only aware of itself and is colour blind. If there are fish in the lake, what credence should each fish have for B (I am blue) vs R (I am red)?
For me the calculation would be exactly the same as you gave above, substituting blue for small and red for big. What about for you?
Let me answer this first:
ReplyDelete"""
I think I see but am not clear on how step 2 of your ensemble method was applied to calculated the fisherman's credences. What properties does he have? Standing outside a lake with one of your 4 possible setups, or catching a large fish/small fish?
"""
We are assuming the coin flipper / fisherman wants to know: what's the chance of me catching a big fish? So in the ensemble, where we have G coin flippers, we, according to the two step method above, would want to calculate the fraction of all coin flippers who will have the desired property, namely that of catching a big fish.
And for your red and blue fish question, my methodology says consider all the entities in the ensemble whose credences we're calculating. Previously it was the coin flipper, now it's the fish. So we apply the self-locating uncertainty for the fish now and hence calculate the fraction of all the fish that are blue. Again, my methodology says we do this once for the whole ensemble, your simulation says we do this G times then average the results.
DeleteSo my method would say:
there are 0.25G * (110 + 100 + 10) total fish,
there are 0.25G * (10 + 0 + 10) blue fish
credence of B a fish should have = fraction = 20 / 220
This comment has been removed by the author.
DeleteThis comment has been removed by the author.
DeleteThanks Dmitriy, I see how it works. I think it's wrong, but I can at least see that your methodology is consistent with the ensemble argument.
DeleteMy next question would be how would you simulate a single such experiment on a computer? Would you follow my steps or do something different?
My 3 steps were:
(1) Decide which possibility is actualised
(2) Build a population based on the results of (1)
(3) Sample from the population built in (2), report the result.
Hey DM,
ReplyDeleteThere’s a lot going on in this comment thread and I don’t wish to further distract you. Nevertheless, I do want to elaborate on one final point; to hopefully tease away potential confusions.
It seems to me that there is a subtle, but important, piece of implicit reasoning to which you subscribe (but to which I do not). That is the belief that, given the fact that there is a 50/50 chance that any random possible galaxy will be actualized, it must follow that our galaxy also has a 50/50 chance of being M or S.
However this doesn’t logically follow. The former statement only entails the latter provided that we already believe that our likelihood of ending up in one galaxy is randomly determined. Yet the EP principle necessitates that our likelihood of being born (in a singular case) is not randomly determined, because what kind of galaxy we should expect to find ourselves in will be influenced by N (the number of observers).
Hey Alex,
DeleteI think you put your finger on the core supposition which seems natural to DM and also completely right that it doesn't immediately logically follow:
"""
It seems to me that there is a subtle, but important, piece of implicit reasoning to which you subscribe (but to which I do not). That is the belief that, given the fact that there is a 50/50 chance that any random possible galaxy will be actualized, it must follow that our galaxy also has a 50/50 chance of being M or S.
However this doesn’t logically follow.
"""
Thanks Dmitriy.
DeleteI should also clarify the following statement, because it can seem confusing. When I write this:
“The former statement only entails the latter provided that we already believe that our likelihood of ending up in one galaxy is randomly determined”
I mean that our likelihood of ending up in one galaxy is determined irrespective of N. So that we are randomly selecting among all possible worlds, and not among all possible observers.
It can be simultaneously true that there is a 50/50 chance that a randomly selected possible world has an M or S galaxy, and that our own universe doesn’t have such a probability.
I agree that it doesn't logically follow. I don't think I'm assuming this.
DeleteIf there's a 50% chance that we would find ourselves in universe A, where 99% of observers see an environment like ours, and a 50% chance we would find ourselves in universe B, where only 1% of observers see an environment like ours, then it is much more likely we are in A.
Oh, to follow up on the latest comment, I do think it's probably irrespective of N. Unless N feeds into the evidence we can observe in some way.
DeleteHey DM,
ReplyDelete“If there's a 50% chance that we would find ourselves in universe A, where 99% of observers see an environment like ours, and a 50% chance we would find ourselves in universe B, where only 1% of observers see an environment like ours, then it is much more likely we are in A”
I don’t think that actually follows. In your example we’re trying to find out which universe we are more likely to be born in; so “If there's a 50% chance that we would find ourselves in universe A”
Then by default the answer must be 50%. I think what you meant to say is that if there is a 50% chance that universe A exists then etcetera...
Which of course I agree with. However, I don’t see how you can reconcile your new claim that this makes for legitimate reasoning, with your other point that there is a 50% chance of M or S existing. For you still conclude that we are not more likely to experience an M galaxy. Unless of course I am misinterpreting you.
Finally, I hope it is clear from the above not logically following, that you cannot simply rely on your claim that M and S have a 50% chance of being realized in our hypothetical aliens galaxy (which I don’t agree with) as some justification. That premise is in dispute and so needs independent justification if you’re going to continue your argument against the original EP.
That being said, there are of course many potential justifications one can make (I am actually writing up an article at the moment exploring one such avenue), but your simulation results do not constitute a justification, as they rely on an unsupported claim.
Also you can’t coherently believe both this:
Delete“Oh, to follow up on the latest comment, I do think it's probably irrespective of N. Unless N feeds into the evidence we can observe in some way.”
And your earlier point that we are more likely to be born in A on account of the greater number of observers in A who would experience what we are experiencing.
To say that our likelihood of being born in one galaxy is determined with respect to N; is the same thing as expressing what you wrote above.
Hey DM,
DeleteLet me know if I have misunderstood you. For instance, if by
“I don't think I'm assuming this.”
You meant the statement that followed your declaration (as opposed to my comment where I claimed you assumed x).
Hi Alex,
Delete> I think what you meant to say is that if there is a 50% chance that universe A exists then etcetera...
Correct, thanks for the clarification.
I think the difference between our assumptions is something more like I think the logic is the same whether we're reasoning from a first or third person perspective and Dmitriy (and perhaps you) think the logic is different.
> However, I don’t see how you can reconcile your new claim that this makes for legitimate reasoning
I think this claim is consistent with what I have claimed before. If we reason from a third-person perspective, as if we're a fisherman trying to predict whether case A or B obtains regarding the fish in a lake, then we get the result I indicated.
I'm assuming N is the same for both universes. I don't think N matters anyway, which is why I spoke in percentages. But since you do think N matters, let's say N is 100 for each universe.
If E = I see the evidence I see, and A = A exists, then
P(E) = P(A) * P(E|A) + P(B) * P(E|B) = 0.5 * 0.99 + 0.5 * 0.01 = 0.5(0.99 + 0.01) = 0.5
P(A|E) = P(E|A) * P(A) / P(E) which is 0.99 * 0.5 / 0.5 = 0.99
P(B|E) = P(E|B) * P(B) / P(E) which is 0.01 * 0/5 / 0.5 = 0.01
So I'm much more likely to be in A.
But this is still quite different from how you would analyse it, because I would get the same result even if there were a gazillion observers in A and only 100 in B. In the above calculation, all that matters is the unlikeliness of the evidence, not the number of observers.
So I'm definitely not assuming that "given the fact that there is a 50/50 chance that any random possible galaxy will be actualized, it must follow that our galaxy also has a 50/50 chance of being M or S.", but I am assuming that N doesn't matter. The justification for this assumption is that N doesn't enter into the calculations we would do to answer the question from a 3rd person perspective, and further justified by the fact that this appears to give the right results when simulated (at least when simulated as I think it should be simulated).
Whether or not there should be a logical difference from a 1st or 3rd person perspective remains to be discussed.
Hey DM,
DeleteIt’s now clear to me that Dmitriy is right, and you only meant that the proportion of observers in your preferred reference class is relevant and not the total number of observers. However, in that case your previous statement needs some qualification. You wrote:
“If there's a 50% chance that we would find ourselves in universe A, where 99% of observers see an environment like ours,”
But ‘seeing an environment like ours’ is an insufficient condition to limit the reference class from the total number of observers. That’s because every person in M or S sees/knows the same thing; that the aliens created only one galaxy, and that they flipped a coin as to whether they should pick a 42 planet or single planet galaxy. Each observer is also unsure which galaxy they belong to. Hence, we need some additional criterion for why we should restrict our reference class from the general reference class of the total number of observers.
It is this criterion which we presently lack justification for.
To add onto my last:
Delete“ The justification for this assumption is that N doesn't enter into the calculations we would do to answer the question from a 3rd person perspective, and further justified by the fact that this appears to give the right results when simulated (at least when simulated as I think it should be simulated)”
I’m not sure how the 3rd person reasoning is a justification. I agree that if we were God and choose a galaxy at random, then there is a 50/50 likelihood of there being a 42 or single planet scenario. But the whole point is that we are not God, and the ensemble is meant to model our epistemic credences. The crux of the matter is that we suffer from self-locating uncertainty and therefore *must reason from the position of the possible observer. Now whether we have some additional knowledge which warrants a restriction of our reference class, is another matter entirely.
Your last regarding the justification being your simulation correctly predicting the results: of course as you know the assumption that we have a 50/50 chance of being born in either alien galaxy is built into the simulation. In other words, your simulation assumes that we should assign our probability of birth by first constructing our world according to the results of the coin flip. So that’s hardly a justification since that was the contentious premise to start with (should we assume that our likelihood of being born is fixed to the ratio of possible galaxies?).
Hi Alex,
DeleteYes, Dmitriy interpreted me correctly.
> But ‘seeing an environment like ours’ is an insufficient condition to limit the reference class from the total number of observers.
Not in this problem. This isn't M vs S, it's a completely different scenario. A vs B is just to illustrate that I don't take for granted that our credences are identical to the probability of each universe existing. It's not supposed to be analogous to M vs S, where I agree we have no evidence.
> I’m not sure how the 3rd person reasoning is a justification.
It's a justification only under the assumption that 3rd person reasoning is applicable! This is evidently contentious but has yet to be meaningfully discussed. We're just starting to get into that.
> I agree that if we were God and choose a galaxy at random, then there is a 50/50 likelihood of there being a 42 or single planet scenario.
That's not quite what I'm saying. If we have a credence for each scenario, then one of those scenarios exists and one doesn't. God doesn't really have a choice at that point. What I'm saying is that ex hypothesi, some of the observers are actual and some are not. I don't think we should be including observers who are not actual in our self-location uncertainty. The effect of trying to take account of which observers actually exist is that we end up with the same logic as 3rd person reasoning.
Hey Alex,
ReplyDeleteI think he is saying that it is independent of N, but dependent on the fraction of those N observers that belong to the relevant reference class.
Hey DM,
ReplyDelete"My next question would be how would you simulate a single such experiment on a computer? Would you follow my steps or do something different?
My 3 steps were:
(1) Decide which possibility is actualised
(2) Build a population based on the results of (1)
(3) Sample from the population built in (2), report the result."
This question is much more ambiguous than you might take it to be I think. If for example by simulating a single such experiment on the computer you mean to basically play God and create a virtual world containing a coin flipper who in turn populates a lake with either 42 fish or 1 fish, then I would just do the first two steps of the above three.
But I think what you mean is actually something else, except I am not sure exactly what.
Hi Alex,
DeleteWhat I'm assuming is that if there is a fact of the matter about which way of reasoning is correct, we should be able to program a simulation to spit out a bunch of results, one from each trial, and then empirically determine the correct answer by looking at the frequencies in the results.
So my thought was that we could simulate being born into a given population by just selecting randomly from it according to the frequencies of different types of observers. So if the simulation is a computer game, then every time you play it you find yourself as a certain type of character in a certain type of world, for instance. This is no different than the fisherman selecting a fish.
I haven't questioned this assumption up to now, even though it works just fine for China/Chile. In China/Chile, it makes perfect sense to run such a simulation, I think, and you get the same results as in your ensemble.
You say it doesn't work for your ensemble because you seem to think it legitimate to quantify over observers who may not exist. That doesn't seem right to me. You would "do the first two steps of the above three", and perhaps wind up with a population of 10 blue fish in the lake only. Now, to me, it seems that on that run, you are certainly going to wind up being a blue fish, so the simulation should report "blue". The red fish observers don't exist, so we can't include them in our ensemble for that run.
Anyway, must think, and have stuff to do. Interesting in any case.
Hi DM,
ReplyDelete"""I think the difference between our assumptions is something more like I think the logic is the same whether we're reasoning from a first or third person perspective and Dmitriy (and perhaps you) think the logic is different."""
It is easy to see that the first and third person perspectives are quite distinct in anthropic questions, just look at the Dr. K example. He flips a coin and if tails kills 99 out of 100 sleeping patients. Clearly from his perspective the credence is 50-50 (assuming he forgot, or the process was automated and he wasn't looking), but from your perspective, if you wake up, it's 100:1 in favor of heads as we discussed before.
I don't think that's to do with perspective-taking so much as identifying yourself as special. You would have similar credences from a third person perspective if one of the patients was particularly special in some obvious way. Like if 99 of the patients were ordinary people and one patient was Tom Cruise.
DeleteAssuming that from a 3rd person perspective you can't just look and see how many survived. Because if you could you wouldn't need credences, you would just see the answer. So maybe Dr K isn't analogous to the fisherman. The fisherman/fish scenario seem to be the same apart from perspective shifts. I'm not sure about Dr K. But I may forget important details of the Dr K case so I'm not sure.
DeleteSo, if you're a Tom Cruise fan, and you're only interested in whether Tom Cruise survived, and you learn that Tom Cruise survived, then your credences are the same as Tom Cruise himself. So it seems that in some cases a 3rd person perspective can stand in for a 1st person. I think it's like this for fisherman/fish too, but I might have to offer further justification when I have time.
DeleteEven simpler, you could randomly sample one of the patients (as the fisherman randomly samples from the fish) and discover that the patient survived. At first blush, this seems to me to be the same as finding that you yourself survived. No?
DeleteHi DM,
ReplyDeleteThe crucial point in my example was this: with the exact same description of the setup given to the first and third person, their credences do not have to be the same, there is no such general principle.
Of course situations can easily be constructed, as you just did, where there credences are in fact the same. But that of course doesn't diminish the fact that there is no such general principle, so we cannot start from this principle to analyze the fish or the aliens case. As you yourself just said, and I completely agree, this would need to be justified in whatever specific case we are considering.
From the ensemble perspective, it's actually very easy to identify situations where the first and third person’s credences are the same.
DeleteIt's whenever there is a one to one correspondence between instances of the first person and the third person in the ensemble. For example, in the ensemble there are just as many Tom Cruises as there are doctors.
Hi Dmitriy,
DeleteTo be clear, my intuition is that just changing perspective while keeping all other evidence the same should not change credences.
It seems to me that in fisherman/fish, all evidence is the same. The only difference is the agent for which you're calculating credences.
In Dr K/patient, the evidence is different.
Hey DM,
ReplyDeleteWhy do you think the evidence is different in one case but the same in the other?
In both cases the first and the third person are given the same information about the setup.
You could say that in the Dr. K case, the patient has the additional evidence, beyond the information about the setup, that he exists as a conscious being, and that accounts for the difference in the credences. (By the way, I think it’s more instructive to imagine that Dr. K doesn’t just kill the other sleeping patients, he completely annihilated them from existence.)
And if that's what you would say, I would definitely agree. However, this would mean that you accept that my existence is evidence that I can use, which is what I argue in my anthropic reasoning 1 article. And then this would equally apply to the fish. So I am not sure why you think the fish case is different.
There's more to the evidence than the setup. There's who was and who was not annihilated, and whether or not they were preselected. It seems to me that Dr K and the patient have different information in this regard.
DeleteThe scenario you're hinting at is not very clear so I'm forced to guess what you mean and answer a number of different versions.
Does Dr K know who was annihilated? If so, even though he may have forgotten he flipped the coin, he knows that there is only one patient left, so he has no uncertainty.
If Dr K doesn't know who was annihilated, then how does Dr K know this in particular survived? If Dr K is randomly sampling from the patients like the fisherman and finds that the randomly sampled patient survived, then Dr K's credences would be the same as the patient.
If Dr K only knows that some patient survived, (equivalently: he knows he will be informed of the identity of only one survivor no matter how many patients survived) then the difference is that the patient is special/preselected to the patient and not to Dr K, so again the evidence is different. Some preselected special patient survived vs the identity of some survivor.
In the fisherman story, I can draw no such distinctions, because the sampled fish is special to both the fish and the fisherman.
Hey DM, I should have been more clear. The setup I had in mind, of which both the doctor and the patients are equally informed is this:
ReplyDeleteA coin was flipped, and if it lands on heads then all patients wake up, otherwise 99 patients get erased from existence and only one random patient wakes up. Let’s say whoever survives wakes up at exactly noon.
That’s the extent of it, the doctor is not informed of anything else (he, like the patients, doesn’t know the results of the coin flip, he also is not informed of who survived and who didn't), neither are the patients. Now it’s noon, what are the credences a patient and the doctor should assign? They should assign different credences.
So the information about the setup is the same for the doctor and the patients, so why do they get different answers?
If your answer is because any surviving patient has the additional evidence that he in fact is still in existence, then I agree with that. But if one’s existence is legitimate evidence for that individual, which is what I argue in the anthropic reasoning 1 article, then that applies for the fish case as well.
Hi Dmitriy,
Delete> because any surviving patient has the additional evidence that he in fact is still in existence
I think we can be more general than that.
If self-locating uncertainty can be modelled as random selection from a population, any surviving patient has the additional evidence that a randomly selected patient is still in existence. The Dr does not have this evidence, but we could imagine the Dr having such evidence if the Dr randomly chooses a patient from the population and learns that this patient is alive. Now, given that Dr K has the same evidence as the paitent, they have the same credences.
But both the fisherman and the fish already have the same evidence: that a randomly selected member of the fish population is blue (say).
> But both the fisherman and the fish already have the same evidence: that a randomly selected member of the fish population is blue (say).
DeleteSorry, this is incorrect. Neither of them know a fish is blue. This evidence doesn't enter into it, this is what they're both trying to predict.
But the point stands that they have the same evidence. The fish knows that a particular fish exists, but unlike Dr K this isn't obviously relevant as this information is used in neither your calculation nor mine.
Hi Dmitriy,
ReplyDeleteSo, just to recap and to try and justify my position.
I'm not 100% sure that we should reason the same given the same evidence from third or first person perspectives, but I would expect that there should be some reason for thinking otherwise.
Given that:
* We agree how the fisherman should analyse the setup
* We agree (I think) that the problem of credences regarding self-locating uncertainty in a population is equivalent to the problem of credences regarding sampling once at random from the population
* There seems to be no relevant evidence the fish has that the fisherman lacks or vice versa
* There has as yet been no convincing analogous proposal of a situation where the perspective of the agent matters and yet includes no new relevant evidence
* We are well acquainted with situations where self-location uncertainty most certainly does not mean all observers should be weighted equally (e.g. in Everettian quantum mechanics)
Then:
* A sensible default assumption seems to be that the logic for the fish should be the same as the logic for the fisherman
* I don't see any reason why the assumption that we should weight all observers equally from a first person perspective should trump all the above. This assumption seems to need justification or explanation of its own.
Hi DM,
Delete* We agree how the fisherman should analyse the setup
Yes.
* We agree (I think) that the problem of credences regarding self-locating uncertainty in a population is equivalent to the problem of credences regarding sampling once at random from the population
Yes and no. It seems you have a different idea what constitutes a population. In the ensemble analysis, we count only the entities in the same epistemic situation as you, the agent whose credences we're calculating. We're then assuming that you are equally likely to be one of those "clones". For you, it seems, for example sleeping, dead, or even currently non-existent patients can be part of the population.
* There seems to be no relevant evidence the fish has that the fisherman lacks or vice versa
The fish's existence / being conscious is that relevant evidence. You say my ensemble doesn't take it into account, but it most definitely does, because of what I said above (only the existing fish in the lake count as "clones", just as only existing patients do)
* There has as yet been no convincing analogous proposal of a situation where the perspective of the agent matters and yet includes no new relevant evidence
There are no such situations, on my and Alex's view.
* We are well acquainted with situations where self-location uncertainty most certainly does not mean all observers should be weighted equally (e.g. in Everettian quantum mechanics)
But they do within one quantum branch.
Hi Dmitriy
Delete> In the ensemble analysis, we count only the entities in the same epistemic situation as you
...
> For you, it seems, for example sleeping, dead, or even currently non-existent patients can be part of the population.
(I confess to some ambiguity on this latter point -- sometimes by "population" I mean all observers in some group, e.g. red fish, sometimes I mean all observers in some possible world, sometimes I mean all possible observers in the scenario. For this I can only apologise and hope that what I mean is clear in context most of the time)
I think it's the other way around -- I'm trying to count entities in the same epistemic situation as you and you are not. You know that you exist. You don't know which of the other entities exist. Only observers who exist are in the same epistemic situation as you. Other observers are not in any situation at all.
I think we agree that you need to do some weighting to take account of that, we only disagree as to how. You would do so by multiplying each group by a number representing your credence that its possible world exists exists (what I call the naive prediction). I would do this also but then divide credence in each individual by the number of individuals in that possible world (just as we do from the fisherman's perspective), because the larger the population the lower the chances of being any specific individual in the population. On this scheme, the total probability of being any individual in a possible world should equal the probability of the possible world existing in the first place, which is determined by the initial coin flip, and that seems right to me.
In particular, if we're flipping a coin, then I think that means you need to assume that you need to weight them so that 1 S observer contributes as much as all your M observers together. Otherwise I think you overweight "even currently non-existent patients".
> The fish's existence / being conscious is that relevant evidence.
How? The fish is under self-locating uncertainty. It doesn't know which fish it is. It only knows it is a fish. So all it knows is that some fish exists. The fisherman also knows some fish exists. I don't see that the fish has any more relevant evidence than the fisherman.
> There are no such situations, on my and Alex's view.
Then I think you need to have another go at explaining why the fish has more evidence than the fisherman.
> But they do within one quantum branch.
And they do within one possible world. Possible worlds are equivalent to quantum branches as far as I can see. But in the fish scenario with two coin flips we have four possible worlds. Observers in different possible worlds need not have the same weight.
Hi DM,
ReplyDelete"""I think it's the other way around -- I'm trying to count entities in the same epistemic situation as you and you are not. You know that you exist. You don't know which of the other entities exist. Only observers who exist are in the same epistemic situation as you. Other observers are not in any situation at all."""
You are pointing to the difference between our methods:
Ensemble. G copies of experiment, one "sampler".
Simulation. G copies of experiment, G "samplers", then average the results.
We should probably focus on arguments for and against our methods soon. But my point about only counting clones in the same epistemic situation as part of the population was about something else. It was about the fact that a few comments ago you were saying that we can imagine the doctor sampling a random patient to find out if that patient survived, and how this was similar to self-locating uncertainty. I am saying the difference is that in self-locating uncertainty you are a random sample from a population in the same epistemic situation, so for example all the surviving patients (either in the actual world in your method or in the whole ensemble in mine). So that population is different from the population sampled by the doctor in your account, which includes both alive and dead patients.
"""Then I think you need to have another go at explaining why the fish has more evidence than the fisherman."""
The claim isn't about who, if anybody, has more evidence. This would depend on which exact fisherman setup we are considering. Without sampling by the fisherman this is like Dr.K, the fish, just like the patient, has extra evidence, for the exact same reason. With sampling, they have different evidence. You are claiming that they are equivalent, but to demonstrate that we would need to know what the proper method to analyze anthropic scenarios is, mine (ensemble), yours (simulation or its equivalent), or some third method.
So I think it might be a good idea to just present arguments for and against our respective methods. Note a very important thing: my method is mathematically equivalent to the Self Indication Assumption, yours to the Self Sampling Assumption. So arguments for and against those would automatically be arguments for and against our methods.
Hi Dmitriy
Delete> Note a very important thing: my method is mathematically equivalent to the Self Indication Assumption, yours to the Self Sampling Assumption.
Ah, well then you've made my point.
If your argument depends on a contentious assumption that your argument does not clarify, then you should clarify it.
This has been educational for me, because I wasn't aware of these different assumptions. I should read Bostrom's book on this. So I'm happy to agree that my reasoning is contentious if you're happy to agree that yours is too. My problem then is that your ensemble argument makes it look more straightforward than it is, which I was able to spot because it's completely different from how I knew I would analyse the situation.
Oh, and I guess one other problem I have with it is that I don't accept that fine-tuning means that the ratio between the populations within a possible world should change. I think it means that the credences between possible worlds should change. Possible worlds with lots of opportunities for fine tuning are supposed to be more likely because otherwise fine-tuning is unlikely to have happened. This reasoning may depend on rejecting TER, but if we accept TER for the sake of argument, it seems clear to me that this should influence the credences going into your ensemble (the coin flip).
DeleteI've mentioned this before, and I know you don't agree because you think it's "double-dipping". But I just wanted to register this as a second problem I have with your article.
Hi DM,
ReplyDelete"If your argument depends on a contentious assumption that your argument does not clarify, then you should clarify it."
That's the thing, it doesn't depend on the SIA, it is mathematically equivalent to it. What it depends on is EP, which I think is heaps more intuitive than SIA.
Hi Dmitriy,
DeleteYour article never mentions EP or explains EP. And I'm not convinced in any case that EP is incompatible with the SSA point of view. We can discuss that if you like. But at the moment, since you defend your analysis by saying it is mathematically equivalent to SIA, I'm going to take it that it is as contentious as SIA, whether it be more intuitive or not.
The way you have analysed this problem appears just wrong from someone coming from an SSA-point of view, or someone who thinks that fine-tuning should influence credences rather than ratios. So perhaps your argument looks very simple, intuitive and straightforward to a certain audience, but to another it seems to be naive and missing the point. Now that I understand that you're coming from an SIA point of view, I actually have a lot more respect for it. I realise that some of the assumptions I'm taking for granted are open to question.
So, stating your assumptions and explaining the reasons one might have for rejecting your argument would be an improvement, even if you don't think assessing those reasons are in scope, especially since you're relying implicitly on contentious issues like SIA/TER. As it is, I reject your argument for reasons that are not even mentioned or considered in the article, which makes it look bad.
Hi Dmitriy,
ReplyDeleteOn SIA vs SSA, this article is pretty good, but suggests the problem may be that the original problem is underspecified.
https://www.quantamagazine.org/solution-sleeping-beautys-dilemma-20160129/
I wonder what you think?
I'm inclined to be a halfer, naturally, and I expect you to be a thirder. And yet in the two variations of the problem proposed by the author, as predicted by the author I analysed the first variation as a halfer and the second as a thirder. I wonder would you be the same?
But the crucial difference is just that in the first variation, only one experiment is conducted, and in the second variation, many are conducted. This seems to agree with what I was saying about it mattering whether there is only one chance for S vs M to be decided or many. When there's only one trial ever, we should be halfers, and when there's many, we should be thirders. Is this a path towards reconciling the two views? That would be nice, but probably not...
Hi DM,
ReplyDeleteI would never claim my article couldn't benefit from improvements, but I have to disagree with most of your criticisms. The main reason is that the article advertises itself as being a "shorter and sweeter" version of my main multiverse article. In that article, I provide a more detailed explanation of the assumptions behind the ensemble method along with some defenses.
But even that longer article isn't meant to be a full defense of EP, that would be a topic for the whole Anthropic Reasoning series. Instead, it's mostly an application of the ensemble method to analyze a specific debate. It's also a popular level article. Still, it does make a quick case for the ensemble method, with the hope that many people, especially ones already familiar with how ensembles work in other applications, will find it intuitive and unobjectionable. But I am not under any illusion that I have provided some kind of knock down defense that should convince most skeptics. Even when I finish the Anthropic Reasoning series I don't expect that a skeptic would be rationally compelled to accept my conclusions, I can only expect to show what intellectual price he or she would be committed to paying for rejecting them.
That's not a problem with my arguments though, that's how philosophy works, there are very few knock down proofs in philosophy. In other words, the fact that this article, the longer one, or any other relies on some assumptions that can be rationally denied is not an indication of weakness - because virtually every argument in philosophy does.
So I would say I agree with you that it's a good idea for me to write a more complete defense of EP, and I definitely plan to do that, it's just that I disagree that it's a problem with this article, or the main multiverse one for the reasons above. I will think about how to improve both of them though to make the logic clearer. The discussion with you and Alex has helped me understand much better what parts might be unclear to people and what objections they might have.
And just a couple of points of clarification:
"But at the moment, since you defend your analysis by saying it is mathematically equivalent to SIA, "
I don't defend it this way, that wasn't supposed to be an argument for EP. As I mentioned, it's really the other way around, I think EP is miles more plausible than SIA, so it's actually an argument for SIA. My point was that whatever other arguments exist for SIA (which I haven't used to defend my analysis yet) would also, due to the mathematical equivalence, automatically be arguments for the ensemble analysis.
"The way you have analysed this problem appears just wrong from someone coming from an SSA-point of view, or someone who thinks that fine-tuning should influence credences rather than ratios. "
My argument is about credences, the whole point of the ensemble argument is that, if EP is true, we can use ratios to derive credences. I make that clearer in the main multiverse article.
> My argument is about credences, the whole point of the ensemble argument is that, if EP is true, we can use ratios to derive credences. I make that clearer in the main multiverse article.
DeleteBut you set up the ensemble based on your starting credences. You even make the point that it doesn't have to be 50/50. ("It's easy to redo the math for a more general prior")
Of course I agree that fine-tuning is not going to influence the preferences of the aliens. But fine-tuning could well influence our credences regarding the preferences of the aliens, making us more likely to give a higher prior to M42.
If it's not 50/50, then presumably all sorts of considerations could go into our credences about these preferences. It's obvious to me that fine tuning should be one of them, for Bayesian reasons. I'm not sure anyone ever claimed that fine-tuning should affect the ratios in the way you're showing it doesn't, so I think you've set yourself up too easy a target to defeat.
Imagine if you had targeted another consideration. Perhaps someone believes in a multiverse for philosophical reasons independently of fine-tuning (as I do). Let's make it simple and say the reason for somebody's belief one way or another is parsimony. Now you do an ensemble analysis and show that considerations of parsimony don't influence the ratio of observers in M vs S worlds, ergo parsimony can have no influence on credences relating to M vs S. Surely you can see how daft that argument would be. So how would you distinguish your argument from that one?
Hi DM,
ReplyDeleteI decided, based on your comment, to add another section to the article clarifying the logic. I hope it's an improvement, it's less "shorter and sweeter" now but hopefully more self-contained. I can see how what I added could make things clearer for some people but more confusing for others, hopefully it's a good change on balance.
Hi Dmitriy,
DeleteIt's certainly an improvement to state the ensemble premise, thanks. I can now assess in context whether your assumption makes sense.
Unfortunately, the ensemble premise seems to me to miss the mark. There are some subtle problems with it.
"The main reason is that stipulations about what's going on in parts of reality that are so distant from us that they have no causal physical influence on us should not matter"
First, you're talking about "distant from us", but in problems self-locating uncertainty we don't know what is distant from us and what is near, so this seems confused.
I agree that what's going on in distant parts of reality can have no influence on what is happening here now. But we're not talking about causal influence, we're talking about self-location credences. The structure of our model of reality as we analyse our problem can of course matter a great deal. In particular, a model which grants the existence of a single universe/galaxy can lead to a different result than a model which assumes many.
You would at least grant this from the fisherman's perspective, it seems. If the groundskeeper ran his trials many times, continually adding fish to the same lake before the fisherman came to sample, then you would analyse the problem differently than you do the scenario with one trial only. Indeed your analysis in the many trials case would mirror your ensemble analysis, despite the fact that you're doing it from the fisherman's perspective.
So why not from the fish's? Why, from the fish's perspective, does it not matter how many trials are performed, such that you can pretend a one-trial setup is a many-trial setup, but from the fisherman's perspective the same move would be a mistake?
The ensemble premise may seem more intuitive to you than the SIA, but it seems even less plausible to me that it should work the way you're using it in this argument.
Hi DM,
ReplyDeleteLet me address your first comment first, the one with
"But you set up the ensemble based on your starting credences. You even make the point that it doesn't have to be 50/50. ("It's easy to redo the math for a more general prior")"
There seems to be some very fundamental gap between how we understand the question of interest to begin with. The question is, of course, whether fine-tuning is evidence of the multiverse, but what exactly does that mean?
I hope we can immediately agree that even if we can infer the multiverse from all of the evidence we have, including fine-tuning, that doesn't automatically mean fine-tuning is evidence of the multiverse. Why? Because maybe the specific datum of fine-tuning doesn't actually affect the strength of the inference to M.
So then what exactly would it mean for fine-tuning to be evidence of the multiverse? This may seem like a silly question given how much time we, as well as Steven, Philip, and others have already spent debating it. But actually everybody has been somewhat sloppy about the actual exact meaning of the question, which I think has contributed greatly to the overall confusion and miscommunication.
It would be good to at least settle this part once and for all. In my two multiverse articles I express a particular way the question can be mathematically formulated, but the objections you raise in your comment would only make sense, I think, if your interpretation of the question was inconsistent with mine. So let me state my mathematical formulation of the question and then ask if you agree and, if not, how you would formulate your interpretation instead.
Statement X = "fine-tuning is evidence for M" is understood to mean (or be equivalent to) the following. Let P be our estimate of the degree of fine-tuning, that is the chance for a random universe to be life-permitting. Let E be the evidence that we find ourselves to be in a life-permitting universe. Let B(P) be the Bayes factor for M vs S:
B(P) = numerator / denominator, where
numerator = given M and P, what's the likelihood of E?
denominator = given S and P, what's the likelihood of E?
Then statement X is: B(P) is larger for tiny values of P than for non-tiny values of P.
Do you agree that this is a valid mathematical translation and, if not, how you would formulate your interpretation instead?
That seems fine.
DeleteHi DM,
ReplyDeletethere seem to be a lot of threads here, it's hard to know what to address. I think the two most important points I should make are:
1. If you accept the formulation of the question expressed by statement X (B(P) is larger for smaller P), then the reason the objection I quoted doesn't work is because it's talking about prior credences in M or S, which play no role in X.
2. You are absolutely right that ultimately this boils down to SIA vs SSA. That's really the central issue, so maybe we should give our arguments for and against those. One of my arguments is based on EP, and we have implicitly discussed some others. I give a quick list of them in the Anthropic Reasoning 1 article. Perhaps you could present an argument for SSA.
Hi Dmitriy,
Delete> the objection I quoted doesn't work is because it's talking about prior credences in M or S, which play no role in X.
Easily addressed.
On my view, there are two stages to the thinking.
1) Bayesian considerations, which show fine tuning should affect credences
2) Ensemble considerations, which discover no further effects.
The posterior credences from stage 1 are the priors for stage 2.
> 2. You are absolutely right that ultimately this boils down to SIA vs SSA.
Well, perhaps. You didn't answer if it's possible to reject TER and accept SIA. If it is, then it would seem there would need to be some way to reconcile the Bayesian argument with SSA, and if not with my strategy (where the Bayesian posteriors become the sampling priors) then I don't know how. So if it's possible to reject TER and accept SIA, then this may not ultimately boil down to SIA vs SSA.
As to your argument for SIA based on EP, I had a comment on that earlier, the one with "Unfortunately, the ensemble premise seems to me to miss the mark. There are some subtle problems with it.".
I'm less interested in debating SSA vs SIA per se here because this is an old issue with many papers published and there's little prospect of resolution or our contributing much. But basically the argument in favour of SSA would be what I outlined above in my post with all the "Given that:" points in the context of fishermen and fish and concluding with "I don't see any reason why the assumption that we should weight all observers equally from a first person perspective should trump all the above."
Hi DM,
ReplyDeleteabout the part of your objection not working I'm confused by your response:
"""1) Bayesian considerations, which show fine tuning should affect credences
2) Ensemble considerations, which discover no further effects.
The posterior credences from stage 1 are the priors for stage 2."""
If your objection presupposes this, then it's not an objection to my ensemble method, because as you know it works differently than the above two step process.
Also, I am confused as to whether that two step process is equivalent to your simulation (SSA) based method, or if it's some third method distinct from both my ensemble method and your simulation method.
This overall line of inquiry seems quite murky to me.
Hi Dmitriy,
DeleteThis is compatible with your ensemble method because in your ensemble method you take priors as an input. Those priors can come from anywhere. There may be some evidence or reasoning going into deciding them. I think it would be a mistake to assume that those priors should be completely arbitrary.
Furthermore, my point is directly opposed to the conclusions of your ensemble analysis because your ensemble analysis purports to show that fine-tuning can't possibly affect credences. But it can, if fine-tuning is supposed to affect the priors feeding into the ensemble method.
> Also, I am confused as to whether that two step process is equivalent to your simulation (SSA) based method, or if it's some third method distinct from both my ensemble method and your simulation method.
The two step process is not a part of my simulation method but it is compatible with it in the same way that I say it is compatible with your ensemble analysis. My simulation takes P(A), P(B) and P(A&B) as inputs. Those inputs can be outputs from some other process such as a Bayesian analysis.
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