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.
(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:
The fact that the universe apparently exists, and is apparently consistent with MWI, seems to indicate that an MWI universe is at least possible.
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).
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.
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.
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.
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.
At this point, we’re mostly both working with different implicitly-modified versions of the original problem, and so if we really wanted to get anywhere we’d have to be a lot more specific.
My original point was that a factor of MWI in the original problem might be non-negligible, and should have been considered. I am acting as the Devil’s Concern Troll, a position which I claim is useful even though it bears a pretty low burden of proof. I do not deny that there are gaping holes in my argument as it relates to this post (though I think I am on significantly firmer ground if you were facing Galaxy Of Computronium Woman rather than Matrix Lord). But I think that if you look at what you yourself are arguing with the same skeptical eye, you’ll see that it is far from bulletproof.
Admit it: when you read my objection, you knew the conclusion (I am wrong) before you’d fully constructed the argument. That kind of goal-directed thinking is irreplaceable for bridging large gaps. But when it leads you to dismiss factors of 3^^^3 or a googolplex as petty matters, that’s mighty dangerous territory.
For instance, if MWI means someone like you is legion, and the anthropic argument means you are more likely to be that someone rather than a non-MWI simulated pseudo-copy thereof, then you do have a pertinent question to ask the Matrix Lord: “You’re asking me to give you $5, but what if some copies of me do and others don’t?” If it answers, for instance, “I’ve turned off MWI for the duration of this challenge”, then the anthropic improbability of the situation just skyrocketed; not by anything like enough to outweigh the 3^^^^3 threat, but easily by enough to outweigh the improbability that you’re just hallucinating this (or that you’re just a figment of the imagination of the Matrix Lord as it idly considers whether to pose this problem for real, to the real you).
Again: if you look for the weakest, or worse, the most poorly-expressed part of what I’m saying, you can easily knock it down. But it’s better if you steel-man it; I don’t see where the correct response could possibly be “Factor of 3^^^3? Hadn’t considered that exactly, but it’s probably irrelevant, let’s see how.”
On an even more general level, my larger point is that I find that multiplicity (both MWI and Tegmark level 4) is a fruitful inspiration for morals and decision theory; more fruitful, in my experience, than simulations, Omega, Matrix Lords, and GOCW. Note that MWI and TL4, like Omega and GOCW, don’t have to be true or falsifiable in order to be useful as inspiration. My experience includes thinking about these matters more than most, but certainly less than people like Eliezer. Take that as you will.
But what if you can’t make a good decision theory that works the same with or without MWI?
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.
The fact that the universe apparently exists, and is apparently consistent with MWI, seems to indicate that an MWI universe is at least possible.
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?
This contradicts the premise that MWI is untestable experimentally
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.
It is also consistent with Christianity and invisible pink unicorns
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.)
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”.
My understanding of QM is quite good for someone who has never done the actual math
And my violin skills are quite good for someone who has never done the actual playing.
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.
Different parts of what? Of equations? They are all equally real: together they form mathematical models necessary to describe observed data.
Which is why we’re using terms like “reality fluid”.
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 a related degree, if that’s what you are asking.
ψ
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.
Precisely; the issue is far from settled. That clearly doesn’t mean “any handwavy speculation is as good as any other” but it also doesn’t mean “speculation can be dismissed out of hand because we already understand this and you’re just wrong”.
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.
But what if you can’t make a good decision theory that works the same with or without MWI?
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.
The fact that the universe apparently exists, and is apparently consistent with MWI, seems to indicate that an MWI universe is at least possible.
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?
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.
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.
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.
As for the second, well, substances are kind of made of colossal numbers of events in a convenient pattern such that it’s useful to talk about the pattern. Like, I’m not falling through my chair over and over and over again, and I anticipate this continuing to be the case… that and a bunch of other things lead me to think of the chair as substantial.
substances are kind of made of colossal numbers of events...
Right, but I’m not something that happens. The continuation of me into the next second might be something that happens, and so we might say that this continuation have more or less reality fluid, but I don’t know that the same can be said of me simpliciter. You might think that I am in fact something that happens, a series or pattern of events, but I think this a claim that would at least need some working out: one implication of this claim is that it takes time (in the way a motion takes time) to be me. But this is off the QM (maybe off the scientific) path, and I should say I very much appreciate your time thus far. I can’t take it personally if you don’t want to join me in some armchair speculation.
But it seems problematic to say that I am my thoughts. I seem to persist in time despite changes in what I think, for example. Afew days ago, I thought worlds were ‘generated’ on the MWI view. I now no longer think that. I’m different as a result, but I’m not a different person. I wasn’t destroyed, or remade. (I don’t mean this to be a point specifically about human personal identity, this should apply to animals and plants and maybe blocks of wood too).
To reiterate my concern in the grandparent, if my thoughts are a process that takes time (as they seem to be), and I am my thoughts, then it takes time to be me. Being me would then be something interruptible, so that I could only get half way to being me. This is at least odd.
I don’t mean to suggest that this is a knock down argument or anything, it’ not. It’s little more than an armchair objection on the basis of natural language. But it’s the sort of thing for which this theory should have an answer. We might just discover that the temporal persistance or identity of macroscopic objects is a physically incoherent idea (like identity based on having a certain set of atoms). But if we do discover something radical like that, we should have something to say to ward off the idea that we’ve just misunderstood the question or changed the topic. Again, thanks for your indulgence.
You are a 4-dimensional region of spacetime. What you normally call ‘you’ is a mutually-spacelike-separated cut of this 4-dimensional region, but the whole reason for calling this slice special is because of causal chains that have extent in time. For instance, your hand is considered yours because your brain can tell it what to do*. That causal chain takes time to roll out.
if each of us had a partner and could control the other’s hands, the terms would probably soon switch so that your hands are the pair on their body, not the pair on your own body.
Do you think there is a meaningful distinction to be drawn between the kinds of things I can talk about via mutually-spacelike cuts (like arrangements, shapes, trombones, maybe dogs) versus the kinds of things I cannot talk about via mutually-spacelike cuts, like the motion of a fast-ball, Beethoven’s Ode to Joy, or the life of a star? Processes that take time versus...I donno, things?
I ask because natural language and my everyday experience of the world (unreliable or irrelevant though they may be to the question of physical reality) makes a great deal of fuss over this distinction.
There is a distinction, and you just gave it—some things are defined by their processes, and some things are not. Imagine instantaneously reducing something to an arbitrarily low temperature and leaving it that way forever as a substitute for stopping time, and see if the thing still counts as the same thing (this rule of thumb is not guaranteed to apply in all cases).
A frozen human body is not a human. It’s the corpse of a now-defunct human (will stay this way forever, so no cryonic restoration). So, the life—a process—is part of the definition of ‘human’. BUT since it was done instantaneously you could say it’s a corpse with a particular terminal mental state.
A trombone or triangle that’s reduced to epsilon kelvins is just a cold trombone or triangle.
A computer remains a computer, but it ceases to have any role-based identities like ’www.lesswrong.com′ or 230.126.52.85 (to name a random IP address). But, like the corpse, you can say it has a memory state corresponding to such roles.
Very interesting answer, thank you. So, for those things not defined by processes, is it unproblematic to talk about their being more or less real in terms of reality fluid?
Well, we haven’t exactly nailed down the ultimate nature of this magical reality fluid, but I don’t think that whether you define an object by shape or process changes how the magical reality fluid concept applies.
if my thoughts are a process that takes time (as they seem to be), and I am my thoughts, then it takes time to be me. Being me would then be something interruptible, so that I could only get half way to being me.
What’s this “me” thing? Your thoughts are most likely reducible to an arrangement of neurons, their connections and electric potentials and chemical processes (ion channels opening and closing, Calcium and other ions going in and out of dendrites, electric potential rising and falling, electric impulses traveling back and forth, proteins and other substances being created, deposited and removed, etc.) Some of these processes are completely deterministic, others are chaotic, yet others are quantum-random (for example, ion channel opening and closing is due to quantum-mechanical tunneling effects). In that sense, your thoughts do take time, as it takes time for chemical and electrical effects to run their course. But what do you mean by “it takes time to be me”?
Let’s drop the talk of people, that’s too complicated. Really, I’m just asking about how ‘reality fluid’ talk gets applied to everyday things as opposed to ‘happenings’. The claim on the table is that everyday things (including people) are happenings, and I’m worried about that.
Suppose ‘being a combustion engine’ meant actually firing a piston and rotating the drive shaft 360 degrees. If that what it meant to be a combustion engine, then if I interrupted the action of the piston after it had only rotated the drive shaft 180 degrees, the thing before me wouldn’t be a combustion engine. At best it would be sort of half way there. The reason being that on this account of combustion engines, it takes time to be a combustion engine (specifically, the time it takes for the drive shaft to rotate 360 degrees).
If we did talk about combustion engines this way, for example, it wouldn’t be possible to point to a combustion engine in a photograph. We could point to something that might be a sort of temporal part of a combustion engine, but a photograph (which shows us only a moment of time) couldn’t capture a combustion engine any more than it could capture a piece of music, or the rotation of a ball, or a free throw or anything that consists in being a kind of motion.
But, at least so far as I know, a combustion engine, unlike a motion, is not divisible into temporal parts. If all happenings take time and are divisible into temporal parts, and if combustion engines are not so divisible, then combustion engines are not happenings. If they’re not happenings, how does ‘reality fluid’ talk apply to them?
EDIT:
yet others are quantum-random (for example, ion channel opening and closing is due to quantum-mechanical tunneling effects).
Really? That’s fascinating, I have to look that up.
a combustion engine, unlike a motion, is not divisible into temporal parts
A combustion engine is deterministic. The behavior of a combustion engine is defined by the underlying physics. If properly designed, tuned and started as prescribed, it will cause the drive shaft to rotate a number of turns. A complete specification of the engine is enough to predict what it will do. If you design something that gets stuck after half a turn, it’s not what most people would consider a proper combustion engine, despite outward appearances. If you want to use the term “reality fluid”, then its flow is determined by the initial conditions. You can call this flow “motion” if you like.
I think you think I’m saying something much more complicated than what I’m trying to say. Nothing I’m saying has anything to do with prediction, design, determinism, (not that I know of, anyway) and I’m certainly not saying that ‘reality fluid’ moves. By ‘motion’ I mean what happens when you throw a baseball.
The distinction I’m trying to draw is this: on the one hand, some things take time and have temporal parts (like a piece of music, a walk in the park, the life-cycle of a star, or the electrochemical processes in a neuron). Call these processes. These are opposed, on the other hand, to things which so far as I can see, don’t have temporal parts, like a trombone, a dog, an internal combustion engine, or a star. Call these fubs (I don’t have a good name).
If reality fluid is a way of talking about decoherence, and decoherence talk always involves distinctions of time, then can we use reality fluid talk to talk about how real fubs are? We could if all fubs were reducible to processes. That would be a surprising result. Are all fubs reducible to processes? If so, is this an eliminative reduction (fundamentally, there are no fubs)? If not...well, if not I have some other, even weirder questions.
You seem to have a philosophical approach to this, while I prefer instrumental reductionism. If a collection of “fubs” plus the rules of their behavior predict what these fubs do at any point in time, why do you need to worry about some “temporal parts”? If you take an MP3 file and a music player and press “start”, you will have music playing. If this time stuff sounds mysterious, consider Eliezer’s timeless picture, where these fubs are slices of the flow. You can generalize it somewhat to quantum things, but there will be gaps (denied by handwaving MWIers, explicit in shut-up-and-calculate), hence the probabilistic nature of it.
You seem to have a philosophical approach to this, while I prefer instrumental reductionism.
We share the impression that the right answer will be a reductive, empirically grounded one. We might differ on the instrumentalism part: I really do want to know what the furniture of the universe is. I have no intended use for such knowledge, and its predictive power is not so important. So far as I understand instrumentalism, you might just reply that I’m barking up the wrong tree. But in case I’m not...
But let me ask this question again directly, because I think I need an answer to understand where you’re coming from: are fubs (everyday objects like tables and chairs and people, or if you like elementary particles or whatever) reducible to processes at some level of physical explanation? Or is the whole idea of a fub incoherent? Is the question somehow incoherent? Or would you guess that when we arrive at the right physical theory, it will include reference to both processes (like decoherence, motion, heating, etc.) and fubs?
are fubs (everyday objects like tables and chairs and people, or if you like elementary particles or whatever) reducible to processes at some level of physical explanation?
Hmm, I’m not sure how to avoid repeating myself. I’ve already said, and so has Luke_A_Somers, that “fubs” are 3d spatial slices of 4d spacetime regions. If this statement does not make sense to you, we can try to dissect it further. is there a particular part of it that is problematic?
I’ve already said, and so has Luke_A_Somers, that “fubs” are 3d spatial slices of 4d spacetime regions.
Ah! I didn’t catch that. Thanks. Suppose a man-made satellite (Fubly 1) is released into (non-geosynchronous) orbit around the earth directly over Phoenix, Arizona. Each time it orbits the earth, it passes over Phoenix, and we can count its orbits this way. One orbit of Fubly 1 is extended in time in the sense that it takes one month (say) to get around the whole planet. In any time less than one month, the orbit is incomplete. So the orbit of Fubly 1 is temporally divisibile in the sense that if I divide it in half, I get two things neither of which is an orbit of Fubly 1, but both of which are parts of an orbit of Fubly 1.
Now, Fubly 1 itself seems different. Suppose Fubly 1 only completes one orbit and then is destroyed. Supposing it’s assembled and then immediately released, the spaciotemporal region that is Fubly 1 and the spaciotemporal region that is the orbit of Fubly 1 have the same extension in time. If I divide the spaciotemporal region of the orbit in half, time-wise, I get two halves of an orbit. If I divide the spacio-temporal region of Fubly 1 itself, I don’t get two halves of a satellite. Fubly 1 can’t be divided time-wise in the way its orbit and its lifespan can. Does that make any sense? My question, in case it does, is this ’Is the distinction I’ve just made likely to be meaningful in the correct physics, or is this a mere artifact of intuition and natural language?
Fubly 1 can’t be divided time-wise in the way its orbit and its lifespan can.
It’s already the result of such a division. As for orbits and lifespans, they are not physical objects but rather logical abstractions, just like language is (as opposed to the air released from the mouth of the speaker and the pressure waves hitting the ear of the listener).
If you mean that Fubly 1 is a given 3d slice, can Fubly 1 persist through time? I mean that if we take two temporally different 3d slices (one at noon, the other at 1:00PM), would they be the same Fubly 1? I suppose if we were to call them ‘the same’ it would be in virtue of a sameness of their 3d properties, abstracted from their temporal positions.
I don’t know what sameness is, sorry. It’s not a definition I have encountered in physics, and SEP is silent on the issue, as well. I sort of understand it intuitively, but I am not sure how you formalize it. Maybe you can think about it in terms of the non-conservation of the coarse grained area around the evolved distribution function, similar to the way Eliezer discussed the Liouville theorem in his Quantum Sequence. Maybe similar areas correspond to more sameness, or something. But this is a wild speculation, I haven’t tried to work through this.
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.
But you’re assuming a theory in which “reality fluid” is conserved.
Well, yes, I’m assuming that QM is correct. That’s kind of the point: we’re talking about predictions of QM.
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.
No… why do you think that you would be able to feel it? It seems to me rather like the argument that the Earth can’t be moving since we don’t feel a strong wind.
An important part of QM being a linear theory is that it is 100% independent of overall amplitude. Scale everything up or down by an arbitrary (finite nonzero) factor and all the bits on the inside work exactly the same.
So, whether something likely happens or something unlikely happens, the only difference between those two outcomes is a matter of scale and whatever it was that happened differently.
QM has no “reality fluid”. The whole point of calling it “reality fluid” is to remind yourself that it’s standing in for some assumptions about measure theory which are fuzzy and unproven.
My own (equally fuzzy and unproven) notion about measure theory is that anything which has nonzero amplitude, exists. Yes, you can then ask why probabilistic predictions seem to work, while my measure theory would seem to suggest that everything should be 50⁄50 (“maybe it happens, maybe it doesn’t; that’s 50/50”). But I believe that there is some form of entropy in the wave function, and that probable outcomes are high-entropy outcomes. No, I obviously don’t have the math on this worked out; but neither do you on the “reality fluid”.
I could easily be wrong. So could you. Probably, we both are. Measure theory is not a solved problem.
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.
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.
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:
The fact that the universe apparently exists, and is apparently consistent with MWI, seems to indicate that an MWI universe is at least possible.
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).
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.
At this point, we’re mostly both working with different implicitly-modified versions of the original problem, and so if we really wanted to get anywhere we’d have to be a lot more specific.
My original point was that a factor of MWI in the original problem might be non-negligible, and should have been considered. I am acting as the Devil’s Concern Troll, a position which I claim is useful even though it bears a pretty low burden of proof. I do not deny that there are gaping holes in my argument as it relates to this post (though I think I am on significantly firmer ground if you were facing Galaxy Of Computronium Woman rather than Matrix Lord). But I think that if you look at what you yourself are arguing with the same skeptical eye, you’ll see that it is far from bulletproof.
Admit it: when you read my objection, you knew the conclusion (I am wrong) before you’d fully constructed the argument. That kind of goal-directed thinking is irreplaceable for bridging large gaps. But when it leads you to dismiss factors of 3^^^3 or a googolplex as petty matters, that’s mighty dangerous territory.
For instance, if MWI means someone like you is legion, and the anthropic argument means you are more likely to be that someone rather than a non-MWI simulated pseudo-copy thereof, then you do have a pertinent question to ask the Matrix Lord: “You’re asking me to give you $5, but what if some copies of me do and others don’t?” If it answers, for instance, “I’ve turned off MWI for the duration of this challenge”, then the anthropic improbability of the situation just skyrocketed; not by anything like enough to outweigh the 3^^^^3 threat, but easily by enough to outweigh the improbability that you’re just hallucinating this (or that you’re just a figment of the imagination of the Matrix Lord as it idly considers whether to pose this problem for real, to the real you).
Again: if you look for the weakest, or worse, the most poorly-expressed part of what I’m saying, you can easily knock it down. But it’s better if you steel-man it; I don’t see where the correct response could possibly be “Factor of 3^^^3? Hadn’t considered that exactly, but it’s probably irrelevant, let’s see how.”
On an even more general level, my larger point is that I find that multiplicity (both MWI and Tegmark level 4) is a fruitful inspiration for morals and decision theory; more fruitful, in my experience, than simulations, Omega, Matrix Lords, and GOCW. Note that MWI and TL4, like Omega and GOCW, don’t have to be true or falsifiable in order to be useful as inspiration. My experience includes thinking about these matters more than most, but certainly less than people like Eliezer. Take that as you will.
I think we’re talking past each other, and future discussion will not be productive, so I’m tapping out now.
(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?)
ψ
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.
Precisely; the issue is far from settled. That clearly doesn’t mean “any handwavy speculation is as good as any other” but it also doesn’t mean “speculation can be dismissed out of hand because we already understand this and you’re just wrong”.
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)
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?
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.
Your first paragraph is correct.
As for the second, well, substances are kind of made of colossal numbers of events in a convenient pattern such that it’s useful to talk about the pattern. Like, I’m not falling through my chair over and over and over again, and I anticipate this continuing to be the case… that and a bunch of other things lead me to think of the chair as substantial.
Right, but I’m not something that happens. The continuation of me into the next second might be something that happens, and so we might say that this continuation have more or less reality fluid, but I don’t know that the same can be said of me simpliciter. You might think that I am in fact something that happens, a series or pattern of events, but I think this a claim that would at least need some working out: one implication of this claim is that it takes time (in the way a motion takes time) to be me. But this is off the QM (maybe off the scientific) path, and I should say I very much appreciate your time thus far. I can’t take it personally if you don’t want to join me in some armchair speculation.
Your thoughts are things that happen. Whatever’s doing those is you. I don’t see the problem.
But it seems problematic to say that I am my thoughts. I seem to persist in time despite changes in what I think, for example. Afew days ago, I thought worlds were ‘generated’ on the MWI view. I now no longer think that. I’m different as a result, but I’m not a different person. I wasn’t destroyed, or remade. (I don’t mean this to be a point specifically about human personal identity, this should apply to animals and plants and maybe blocks of wood too).
To reiterate my concern in the grandparent, if my thoughts are a process that takes time (as they seem to be), and I am my thoughts, then it takes time to be me. Being me would then be something interruptible, so that I could only get half way to being me. This is at least odd.
I don’t mean to suggest that this is a knock down argument or anything, it’ not. It’s little more than an armchair objection on the basis of natural language. But it’s the sort of thing for which this theory should have an answer. We might just discover that the temporal persistance or identity of macroscopic objects is a physically incoherent idea (like identity based on having a certain set of atoms). But if we do discover something radical like that, we should have something to say to ward off the idea that we’ve just misunderstood the question or changed the topic. Again, thanks for your indulgence.
You are a 4-dimensional region of spacetime. What you normally call ‘you’ is a mutually-spacelike-separated cut of this 4-dimensional region, but the whole reason for calling this slice special is because of causal chains that have extent in time. For instance, your hand is considered yours because your brain can tell it what to do*. That causal chain takes time to roll out.
if each of us had a partner and could control the other’s hands, the terms would probably soon switch so that your hands are the pair on their body, not the pair on your own body.
Do you think there is a meaningful distinction to be drawn between the kinds of things I can talk about via mutually-spacelike cuts (like arrangements, shapes, trombones, maybe dogs) versus the kinds of things I cannot talk about via mutually-spacelike cuts, like the motion of a fast-ball, Beethoven’s Ode to Joy, or the life of a star? Processes that take time versus...I donno, things?
I ask because natural language and my everyday experience of the world (unreliable or irrelevant though they may be to the question of physical reality) makes a great deal of fuss over this distinction.
There is a distinction, and you just gave it—some things are defined by their processes, and some things are not. Imagine instantaneously reducing something to an arbitrarily low temperature and leaving it that way forever as a substitute for stopping time, and see if the thing still counts as the same thing (this rule of thumb is not guaranteed to apply in all cases).
A frozen human body is not a human. It’s the corpse of a now-defunct human (will stay this way forever, so no cryonic restoration). So, the life—a process—is part of the definition of ‘human’. BUT since it was done instantaneously you could say it’s a corpse with a particular terminal mental state.
A trombone or triangle that’s reduced to epsilon kelvins is just a cold trombone or triangle.
A computer remains a computer, but it ceases to have any role-based identities like ’www.lesswrong.com′ or 230.126.52.85 (to name a random IP address). But, like the corpse, you can say it has a memory state corresponding to such roles.
Very interesting answer, thank you. So, for those things not defined by processes, is it unproblematic to talk about their being more or less real in terms of reality fluid?
Well, we haven’t exactly nailed down the ultimate nature of this magical reality fluid, but I don’t think that whether you define an object by shape or process changes how the magical reality fluid concept applies.
Alright, thanks for your time, and for correcting me on the MWI point. I found this very interesting and helpful.
What’s this “me” thing? Your thoughts are most likely reducible to an arrangement of neurons, their connections and electric potentials and chemical processes (ion channels opening and closing, Calcium and other ions going in and out of dendrites, electric potential rising and falling, electric impulses traveling back and forth, proteins and other substances being created, deposited and removed, etc.) Some of these processes are completely deterministic, others are chaotic, yet others are quantum-random (for example, ion channel opening and closing is due to quantum-mechanical tunneling effects). In that sense, your thoughts do take time, as it takes time for chemical and electrical effects to run their course. But what do you mean by “it takes time to be me”?
Let’s drop the talk of people, that’s too complicated. Really, I’m just asking about how ‘reality fluid’ talk gets applied to everyday things as opposed to ‘happenings’. The claim on the table is that everyday things (including people) are happenings, and I’m worried about that.
Suppose ‘being a combustion engine’ meant actually firing a piston and rotating the drive shaft 360 degrees. If that what it meant to be a combustion engine, then if I interrupted the action of the piston after it had only rotated the drive shaft 180 degrees, the thing before me wouldn’t be a combustion engine. At best it would be sort of half way there. The reason being that on this account of combustion engines, it takes time to be a combustion engine (specifically, the time it takes for the drive shaft to rotate 360 degrees).
If we did talk about combustion engines this way, for example, it wouldn’t be possible to point to a combustion engine in a photograph. We could point to something that might be a sort of temporal part of a combustion engine, but a photograph (which shows us only a moment of time) couldn’t capture a combustion engine any more than it could capture a piece of music, or the rotation of a ball, or a free throw or anything that consists in being a kind of motion.
But, at least so far as I know, a combustion engine, unlike a motion, is not divisible into temporal parts. If all happenings take time and are divisible into temporal parts, and if combustion engines are not so divisible, then combustion engines are not happenings. If they’re not happenings, how does ‘reality fluid’ talk apply to them?
EDIT:
Really? That’s fascinating, I have to look that up.
A combustion engine is deterministic. The behavior of a combustion engine is defined by the underlying physics. If properly designed, tuned and started as prescribed, it will cause the drive shaft to rotate a number of turns. A complete specification of the engine is enough to predict what it will do. If you design something that gets stuck after half a turn, it’s not what most people would consider a proper combustion engine, despite outward appearances. If you want to use the term “reality fluid”, then its flow is determined by the initial conditions. You can call this flow “motion” if you like.
I think you think I’m saying something much more complicated than what I’m trying to say. Nothing I’m saying has anything to do with prediction, design, determinism, (not that I know of, anyway) and I’m certainly not saying that ‘reality fluid’ moves. By ‘motion’ I mean what happens when you throw a baseball.
The distinction I’m trying to draw is this: on the one hand, some things take time and have temporal parts (like a piece of music, a walk in the park, the life-cycle of a star, or the electrochemical processes in a neuron). Call these processes. These are opposed, on the other hand, to things which so far as I can see, don’t have temporal parts, like a trombone, a dog, an internal combustion engine, or a star. Call these fubs (I don’t have a good name).
If reality fluid is a way of talking about decoherence, and decoherence talk always involves distinctions of time, then can we use reality fluid talk to talk about how real fubs are? We could if all fubs were reducible to processes. That would be a surprising result. Are all fubs reducible to processes? If so, is this an eliminative reduction (fundamentally, there are no fubs)? If not...well, if not I have some other, even weirder questions.
You seem to have a philosophical approach to this, while I prefer instrumental reductionism. If a collection of “fubs” plus the rules of their behavior predict what these fubs do at any point in time, why do you need to worry about some “temporal parts”? If you take an MP3 file and a music player and press “start”, you will have music playing. If this time stuff sounds mysterious, consider Eliezer’s timeless picture, where these fubs are slices of the flow. You can generalize it somewhat to quantum things, but there will be gaps (denied by handwaving MWIers, explicit in shut-up-and-calculate), hence the probabilistic nature of it.
We share the impression that the right answer will be a reductive, empirically grounded one. We might differ on the instrumentalism part: I really do want to know what the furniture of the universe is. I have no intended use for such knowledge, and its predictive power is not so important. So far as I understand instrumentalism, you might just reply that I’m barking up the wrong tree. But in case I’m not...
But let me ask this question again directly, because I think I need an answer to understand where you’re coming from: are fubs (everyday objects like tables and chairs and people, or if you like elementary particles or whatever) reducible to processes at some level of physical explanation? Or is the whole idea of a fub incoherent? Is the question somehow incoherent? Or would you guess that when we arrive at the right physical theory, it will include reference to both processes (like decoherence, motion, heating, etc.) and fubs?
Hmm, I’m not sure how to avoid repeating myself. I’ve already said, and so has Luke_A_Somers, that “fubs” are 3d spatial slices of 4d spacetime regions. If this statement does not make sense to you, we can try to dissect it further. is there a particular part of it that is problematic?
Ah! I didn’t catch that. Thanks. Suppose a man-made satellite (Fubly 1) is released into (non-geosynchronous) orbit around the earth directly over Phoenix, Arizona. Each time it orbits the earth, it passes over Phoenix, and we can count its orbits this way. One orbit of Fubly 1 is extended in time in the sense that it takes one month (say) to get around the whole planet. In any time less than one month, the orbit is incomplete. So the orbit of Fubly 1 is temporally divisibile in the sense that if I divide it in half, I get two things neither of which is an orbit of Fubly 1, but both of which are parts of an orbit of Fubly 1.
Now, Fubly 1 itself seems different. Suppose Fubly 1 only completes one orbit and then is destroyed. Supposing it’s assembled and then immediately released, the spaciotemporal region that is Fubly 1 and the spaciotemporal region that is the orbit of Fubly 1 have the same extension in time. If I divide the spaciotemporal region of the orbit in half, time-wise, I get two halves of an orbit. If I divide the spacio-temporal region of Fubly 1 itself, I don’t get two halves of a satellite. Fubly 1 can’t be divided time-wise in the way its orbit and its lifespan can. Does that make any sense? My question, in case it does, is this ’Is the distinction I’ve just made likely to be meaningful in the correct physics, or is this a mere artifact of intuition and natural language?
It’s already the result of such a division. As for orbits and lifespans, they are not physical objects but rather logical abstractions, just like language is (as opposed to the air released from the mouth of the speaker and the pressure waves hitting the ear of the listener).
If you mean that Fubly 1 is a given 3d slice, can Fubly 1 persist through time? I mean that if we take two temporally different 3d slices (one at noon, the other at 1:00PM), would they be the same Fubly 1? I suppose if we were to call them ‘the same’ it would be in virtue of a sameness of their 3d properties, abstracted from their temporal positions.
I don’t know what sameness is, sorry. It’s not a definition I have encountered in physics, and SEP is silent on the issue, as well. I sort of understand it intuitively, but I am not sure how you formalize it. Maybe you can think about it in terms of the non-conservation of the coarse grained area around the evolved distribution function, similar to the way Eliezer discussed the Liouville theorem in his Quantum Sequence. Maybe similar areas correspond to more sameness, or something. But this is a wild speculation, I haven’t tried to work through this.
Well, thanks for discussing it, I appreciate the time you took. I’ll look over that sequence post.
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.
Well, yes, I’m assuming that QM is correct. That’s kind of the point: we’re talking about predictions of QM.
No… why do you think that you would be able to feel it? It seems to me rather like the argument that the Earth can’t be moving since we don’t feel a strong wind.
An important part of QM being a linear theory is that it is 100% independent of overall amplitude. Scale everything up or down by an arbitrary (finite nonzero) factor and all the bits on the inside work exactly the same.
So, whether something likely happens or something unlikely happens, the only difference between those two outcomes is a matter of scale and whatever it was that happened differently.
QM has no “reality fluid”. The whole point of calling it “reality fluid” is to remind yourself that it’s standing in for some assumptions about measure theory which are fuzzy and unproven.
My own (equally fuzzy and unproven) notion about measure theory is that anything which has nonzero amplitude, exists. Yes, you can then ask why probabilistic predictions seem to work, while my measure theory would seem to suggest that everything should be 50⁄50 (“maybe it happens, maybe it doesn’t; that’s 50/50”). But I believe that there is some form of entropy in the wave function, and that probable outcomes are high-entropy outcomes. No, I obviously don’t have the math on this worked out; but neither do you on the “reality fluid”.
I could easily be wrong. So could you. Probably, we both are. Measure theory is not a solved problem.
QM may not have ‘reality fluid’, but the thing we’re tongue-in-cheek calling ‘reality fluid’ is conserved under QM!
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.