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homunq comments on Pascal's Muggle: Infinitesimal Priors and Strong Evidence - Less Wrong
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I find it truly bizarre that nobody here seems to be taking MWI seriously. That is, it's not 1 person handing over $5 or not, it's all the branching possible futures of those possibilities. In other words, I hand over $5, then depending how my head radiates heat for the next second there are now many copies of me experiencing $5-less-ness.
How many? Well, answering that question may require a theory of magical reality fluid (or "measure"), but naively speaking it seems that it should be something more akin to 3^^^3 (or googolplex) than to 3^^^^3. So the problem may still exist; but this MWI issue certainly deserves consideration, and the fact that Eliezer didn't apparently consider it makes me suspicious that he hasn't thought as deeply about this as he claims. Even if throwing this additional factor of 3^^^3 into the mix doesn't dissolve the problem entirely, it may well put it into the range where further arguments, such as earthwormchuck163's "there aren't 3^^^^3 different people", could solve it.
Any reasonably useful decision theory ought to work in Newtonian worlds as well.
Damn right! I wish I could trade some of my karma for extra upvotes.
(This comment was originally written in response to shminux below, but it's more directly addressing nshepperd's point, so I'm moving it to here)
I understand that you're arguing that a good decision theory should not rely on MWI. I accept that if you can build one without that reliance, you should; and, in that case, MWI is a red herring here.
But what if you can't make a good decision theory that works the same with or without MWI? I think that in that case there are anthropic reasons that we should privilege MWI. That is: 1. The fact that the universe apparently exists, and is apparently consistent with MWI, seems to indicate that an MWI universe is at least possible. 2. If this universe happens to be "smaller than MWI" for some reason (for instance, we discover a better theory tomorrow; or, we're actually inside a sim that's faking it somehow), there is some probability that "MWI or larger" does actually exist somewhere else. (You can motivate this by various kinds of handwaving: from Tegmark-Level-4 philosophizing; to the question of how a smaller-than-MWI simulator could have decided that a pseudo-MWI sim would be interesting; and probably other arguments). 3. If intelligence exists in both "smaller than MWI" domains and "MWI or larger" domains, anthropic arguments strongly suggest that we should assume we're in one of the latter.
(And to summarize, in direct response to nshepperd:)
That's probably true. But it's not a good excuse to ignore how things would change if you are in an MWI world, as we seem to be.
If your decision theory doesn't work independently of whether MWI is true or not, then what do you use to decide if MWI is true?
And if your decision theory does allow for both possibilities (and even if MWI somehow solved Pascal's Mugging, which I also disagree with) then you would still only win if you assign somewhere around 1 in 3^^^3 probability to MWI being false. On what grounds could you possibly make such a claim?
I'm not saying I have a decision theory at all. I'm saying that whatever your decision theory, MWI being true or not could in principle change the answers it gives.
And if there is some chance that MWI is true, and some chance that it is false, the MWI possibilities have a factor of ~3^^^3 in them. They dominate even if the chance of MWI is small, and far more so if the chance of it being false is small.
Wait, so you're saying that if MWI is true, then keeping $5 is not only as good as, but outweighs saving 3^^^3 lives by a huge factor?
Does this also apply to regular muggers? You know, the gun-in-the-street, your-money-or-your-life kind? If not, what's the difference?
No. I'm saying that if there's (say) a 50% chance that MWI is true, then you can ignore the possibility that it isn't; unless your decision theory somehow normalizes for the total quantity of people.
If you've decided MWI is true, and that measure is not conserved (ie, as the universe splits, there's more total reality fluid to go around), then keeping $5 means keeping $5 in something like 3^^^3 or a googleplex or something universes. If Omega or Matrix Lord threatens to steal $5 from 3^^^3 people in individual, non-MWI sim-worlds, then that would ... well, of course, not actually balance things out, because there's a huge handwavy error in the exponent here, so one or the other is going to massively dominate, but you'd have to actually do some heavy calculation to try to figure out which side it is.
If there's an ordinary mugger, then you have MWI going on (or not) independently of how you choose to respond, so it cancels out, and you can treat it as just a single instance.
But if Pascal's Mugger decides to torture 3^^^3 people because you kept $5, he also does this in "something like 3^^^3 or a googleplex or something" universes. In other words, I don't see why it doesn't always cancel out.
I explicitly said that mugger stealing $5 happens "in individual, non-MWI sim-worlds". I believe that a given deterministic algorithm, even if it happens to be running in 3^^^3 identical copies, counts as an individual world. You can stir in quantum noise explicitly, which effectively becomes part of the algorithm and thus splits it into many separate sims each with its own unique noise; but you can't do that nearly fast enough to keep up with the quantum noise that's being stirred into real physical humans.
Philosophy questions of what counts as a world aside, who told you that the mugger is running some algorithm (deterministic or otherwise)? How do you know the mugger doesn't simply have 3^^^3 physical people stashed away somewhere, ready to torture, and prone to all the quantum branching that entails? How do you know you're not just confused about the implications of quantum noise?
If there's even a 1-in-a-googolplex chance you're wrong about these things, then the disutility of the mugger's threat is still proportional to the 3^^^3-tortured-people, just divided by a mere googolplex (I will be generous and say that if we assume you're right, the disutility of the mugger's threat is effectively zero). That still dominates every calculation you could make...
...and even if it didn't, the mugger could just threaten 3^^^^^^^3 people instead. Any counter-argument that remains valid has to scale with the number of people threatened. Your argument does not so scale.
(Moved my reply, too)
This contradicts the premise that MWI is untestable experimentally, and is only a Bayesian necessity, the point of view Eliezer seems to hold. Indeed, if an MWI-based DT suggests a different course of action than a single-world one, then you can test the accuracy of each and find out whether MWI is a good model of this world. If furthermore one can show that no single-world DT is as accurate as a many-world one, I will be convinced.
It is also consistent with Christianity and invisible pink unicorns, why do you prefer to be MWI-mugged rather than Christ-mugged or unicorn-mugged?
No it doesn't. DT is about what you should do, especially when we're invoking Omega and Matrix Lords and the like. Which DT is better is not empirically testable.
Yes, except that MWI is the best theory currently available to explain mountains of experimental evidence, while Christianity is empirically disproven ("Look, wine, not blood!") and invisible pink unicorns (and invisible, pink versions of Christianity) are incoherent and unfalsifiable.
(Later edit: "best theory currently available to explain mountains of experimental evidence" describes QM in general, not MWI. I have a hard time imagining a version of QM that doesn't include some form of MWI, though, as shminux points out downthread, the details are far from being settled. Certainly I don't think that there's a lot to be gained by comparing MWI to invisible pink unicorns. Both have a p value that is neither 0 nor 1, but the similarity pretty much ends there.)
You ought to notice your confusion by now.
What is your level of understanding QM? Consider reading this post.
Re DT: OK, I notice I am confused.
Re MWI: My understanding of QM is quite good for someone who has never done the actual math. I realize that there are others whose understanding is vastly better. However, this debate is not about the equations of QM per se, but about the measure theory that tells you how "real" the different parts of them are. That is also an area where I'm no more than an advanced amateur, but it is also an area in which nobody in this discussion has the hallmarks of an expert. Which is why we're using terms like "reality fluid".
And my violin skills are quite good for someone who has never done the actual playing.
Different parts of what? Of equations? They are all equally real: together they form mathematical models necessary to describe observed data.
Eliezer is probably the only one who uses that and the full term is "magical reality fluid" or something similar, named this way specifically to remind him that he is confused about it.
I have actually done the math for simple toy cases like Bell's inequality. But yeah, you're right, I'm no expert.
(Out of curiousity, are you?)
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I have a related degree, if that's what you are asking.
I'm yet to see anyone writing down anything more than a handwaving of this in MWI. Zurek's ideas of einselection and envariance go some ways toward showing why only the eigenstates survive when decoherence happens, and there is some experimental support for this, though the issue is far from settled.
Suppose 3^^^3 copies of you are generated in the first second after you decide. Each one will have $5 less as a result of your decision. (for the sake of argument, lets say your responsibility ends there) Let's take a dollar as a utility unit, and say that by giving the matrix lord $5 you produce 5x3^^^3 disutility points across future worlds. But since everyone is producing copies at roughly the same rate (I think), any utility gained or lost is always multiplied by 3^^^3. This means that you can just cancel the 3^^^3 business out: for everyone you benefit, the positive utility points are also multiplied by 3^^^3, and so the result is the same.
Why was this downvoted? Because everyone knows that Matrix Lord simulations don't actually follow MWI, they just seem to for the poor deluded scientists trapped inside? Sure, I know that. But I was just saying, what if they did. Riddle me that, downvoter person!
Seriously: I've now posted variants of this idea (that MWI means we are all legion, which makes threats/promises involving simulations significantly less scary/enticing) at least 5 or 6 times, between here and Quora. And it's downvoted to oblivion every time. Now, obviously, this makes me question whether there's something stupid about the idea. But though I'm generally acknowledged to be not a stupid guy, I can't see the fatal flaw. It's very tempting to think that you cats are all just too mainstream to see the light, man. That kind of thinking has to overcome a large self-servingness penalty, which is why I state it in ridiculous terms, but unless someone can talk me down here, I'm close to embracing it.
So: what is so very wrong about this thought? Aside from the fact that it embraces two premises which are too unconventional for non-LW'ers, but reaches a conclusion that's too mainstream for LW'ers?
And please, don't downvote this comment without responding. I'm happy to take the karma penalty if I learn something, but if all you get for being wrong is downvoted, that's just a dead end. So, to sweeten the pot: I will upvote any even-minimally-thoughtful response to this comment or to the one above.
I didn't downvote, but I couldn't see what MWI actually changed about the problem. The simulations are also subject to MWI, so you're multiplying both sides of the comparison by the same large number. Hmm. Unless the simulations are implemented on quantum computers, which would minimize the branching. It's not clear to me that you can mimic the algorithm without having the same degree of total decoherence.
No, the simulations are not subject to MWI. I mean, we don't know what "matrix lord physics" is, but we have his word that there are 3^^^^3 individuals inside those simulations, and presumably that's after any MWI effects are factored in.
If instead of Matrix Lord, we were just facing Galaxy Of Computronium Woman, we'd be even better off. She can presumably shift any given bit of her galaxy between quantum and normal computation mode, but it doesn't help her. If GOCW is in normal computation mode, her computations are deterministic and thus not multiplied by MWI. And if she's in quantum mode, she only gets a multiplier proportional to an exponential of the number of qubits she's using. In order to get the full multiplier that ordinary made-of-matter you are getting naturally, she has to simulate everything about the quantum wave function of every particle in you and your environment. We don't know how efficient her algorithms are for doing so, but presumably it takes her more than a gram of computronium to simulate a gram of normal matter at that level of detail, and arguably much more. Obviously she can do hybrid quantum/conventional tricks, but there's nothing about the hybridization itself that increases her multiplier.
So you're saying, what if MWI is just a local phenomenon to our world, and doesn't apply to these 3^^^^3 other simulations that the matrix lords are working with, because they aren't quantum in the first place?
I agree that in the case of a mere galaxy of computronium, it's much less credible that one can simulate an extremely high number of people complex enough that we wouldn't be able to prove that we aren't them. In the former case, we've got much less information.
Unlike Eliezer, I very publicly do not privilege MWI on this site, but let's assume that it's "true" for the sake of argument. How many (subtly different) copies of you got offered the same deal? No way to tell. How many accept or reject it? Who knows. If there are 3^...^^3 copies of you who accepted, then the matrix lord has a lot of money (assuming they care for money) to do what it promised. But what if there are only 3^^^3 (or some other conveniently "small" number) of you who accept? Then you are back to the original problem. Until you have a believable model of this "magical reality fluid", adding MWI into the mix gives you nothing.
(Note: this comment now moved to respond to nshepperd above)
Isn't the thought that even if only one Homunq is offered the deal and accepts, the next few seconds will generate [insert some large number] of worlds in which Homunq copies have $5 less because of that one original Homunq's decision? I don't think Homunq means to refer to preexisting other worlds (which couldn't be affected by his actions), but to the worlds that will be generated just after his decision.
They aren't generated. The one world would be split up among the resulting worlds. The magical reality fluid (a.k.a. square amplitude) is conserved.
I strongly disagree that you can make that assumption; see my comment on your larger explanation for why.
Okay, thanks. But I don't know what magical reality fluid is, so I don't really understand you.
Before I answer, I'd like to know how much you do understand, so I can answer at an appropriate level. Is this a 'I don't know what's going on here' question, or is it a statement that you understand the system well enough that the basics no longer are convincingly basic?
The former, mostly. I've read the sequences on this point and done a little side reading on my own, but I don't understand the math and I have no real education in quantum physics. In other words, I would really appreciate an explanation, but I will also entirely understand if this is more work than you're prepared to put in.
To condense to a near-absurd degree:
QM indicates that if you take any old state of the universe, you can split it up any way you feel like. Take any state, and you can split it up as a sum of 2 or more other states (A = B + C + D+ E, say). If you then 'run' each of the parts separately (i.e. calculate what the future state would be, yielding B', C', D', E') and then combine the results by adding, it's the same as if you ran the original (A' = B' + C' + D' + E').
This is because QM is a linear theory. You can add and subtract and rescale entire states and those operations pass right through into the outcomes.
This doesn't mean that you won't get any surprises if you make predictions based on just B, C, D, and E individually, then add those together. In general, with arbitrary B, C, D, and E, combining them can yield things that just don't happen when you'd expect that they would based on the parts individually (and other things that happen more than you'd expect, to compensate).
Decoherence tells you how and when you can pick these B, C, D, and E so that you in fact won't get any such surprises. That this is possible is how we can perceive a classical world made of the quantum world.
One tiny and in no way sufficient part of the technique of decoherence to require that B, C, D and E are all perpendicular to each other. What does that do? You can apply the Pythagorean theorem. When working with vectors In general, with A being the hypotenuse and B, C, D, and E the perpendicular vector components, we get AA = BB + CC + DD + EE (try doing this with three vectors near the corner of a room. Have a point suspended in air. Drop a line to the floor. Construct a right triangle from that point to one of the walls. You'll get AA = WW + ZZ, then split W into X and Y, for AA = XX + YY + ZZ)
Anyway, what the Pythagorean theorem says is that if you take a vector and split it up into perpendicular components, one thing that stays the same is the sum of the squared magnitudes.
And it turns out that if you do the math, the mathematical structure that works like probability in QM-with-decoherence is proportional to this squared magnitude. This is the basis of calling this square magnitude 'reality fluid'. It seems to be the measure of how much something actually happens - how real it is.
Thanks, that's really quite helpful. I take it then that the problem with Homunq's objection is that all the subsequent 'worlds' would have the same total reality fluid as the one in which he made the distinction, and so the 'splitting' wouldn't have any real effect on the total utility: $5 less for one person with reality R is the same disutility as $5 less for a [large number of] people with reality R/[large number]?
But maybe that's not right. At the end, you talked about 'how much reality fluid something has' as being a matter of how much something happens. This makes sense as a way of talking about events, but what about substances? I gather that substances like people don't see much play in the math of QM (and have no role in physics at all really), but in this case the questions seems relevant.
Good explanation. But you're assuming a theory in which "reality fluid" is conserved. To me, that seems obviously wrong (and thus even more obviously unproven). I mean, if that were true, my experiences would be getting rapidly and exponentially less real as time progresses and I decohere with more and more parts of the wave function.
I acknowledge that it is difficult to make probability work right in MWI. I have an intuitive understanding which feels as if it works to me, that does not conserve "reality fluid"; but I'm not so unwise as to imagine that a solid intuition is worth a hill of beans in these domains. But again, your theory where "reality fluid" is equal to squared amplitude seems to me probably provably wrong, and definitely not proven right. And it was not the assumption I was working under.
Right, I should have been clearer. What I meant is that s/he is privileging one aspect of MWI from unimaginably many, and I simply pointed out another one just as valid, but one that s/he overlooked. Once you start speculating about the structure of Many Worlds, you can come up with as many points and counterpoints as you like, all on the same footing (of the same complexity).
I don't think I had overlooked the point you brought up: I said "...naively speaking it seems that [MWI] should be something more akin to 3^^^3 (or googolplex) than to 3^^^^3. So the problem may still exist..."
As to the idea that everything is just a hopeless mess once you bring MWI into it: that may indeed be a reason that this entire discussion is irresolvable and pointless, or it may be that the "MWI" factors precisely balance out on either side of the argument; but there's no reason to assume that either of those is true until you've explored the issue carefully.
As I said, I don't think MWI leads to really large numbers of copies; back-of-the-envelope calculations suggest it should be "closer to" 3^^^3 or googlplex than to 3^^^^3. So yes: I tried to indicate that this idea does NOT solve the dilemma on its own. However, even if 3^^^^3 is so big as to make 3^^^3 look tiny, the latter is still not negligible, and deserves at least a mention. If Eleizer had mentioned it and dismissed it, I would have no objection. But I think it is notable that he did not.
For instance: Say that there earthwormchuck163 is right and there are fewer than 3^^^^3 intelligent beings possible before you start to duplicate. For instance say it's (x^^^x)^y, and that due to MWI there are (x^^^x) copies of a regular human spawned per fortnight. So MWI is reducing Matrix Lord's threat from (x^^^x)^y to (x^^^x)^(y-1). Doesn't seem like a big change; but if you suppose that only one of them is decisive for this particular Matrix Lord threat, you've just changed the cost/benefit ratio from order-of-1 to order-of-1/(x^^^x), which is a big shift.
I know that there are a number of possible objections to that specific argument. For instance, it's relying on the symmetry of intelligence; if Matrix Lord were offering 3^^^^3 paperclips to clippy, it wouldn't help figure out the clipperific thing to do. The intent is not to make a convincing argument, but simply to demonstrate that a factor on the order of x^^^x can in principle be significant, even when the threat is on the order of 3^^^^3.