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The idea that a consciousness can exist within an alternate reading frame on a system that is not conscious in my own frame, as Peer exists within the City, does significant violence to my intuitions about consciousness.

The idea that the alternate frame can be temporally discontiguous with my own... that is, that events A and B can occur in both frames but in a different order... does additional violence to my intuitions about time.

That said, I have no reason to expect my intuitions about consciousness or time to reflect the way the universe actually is. (Of course, that doesn't mean any particular contradictory theory is right.)

That said, without the possibility of intentional causal interaction with such alternate-frame consciousnesses, I'm indifferent to them: I can't see any reason why I should care whether it's true. I feel more or less the same way as I do about the possibility of epiphenomenal spirits, or epiphenomenal Everett branches: if they are in principle unable to interact causally with me, if no observation I can ever make will go differently based on their existence or nonexistence, then I simply don't care whether they exist or not.

I don't endorse that apathy, though. It mostly comes out of a motivational psychology in which believing that future events are significantly influenced by my actions is important to motivating those actions, and I don't especially endorse that sort of psychology, despite instantiating one.

I don't see the connection to Searle's CR.

The idea that a consciousness can exist within an alternate reading frame on a system that is not conscious in my own frame, as Peer exists within the City, does significant violence to my intuitions about consciousness.

How about, instead of an opaquely described "alternate reading frame", we consider homomorphic encryption. Take some uploads in a closed environment, homomorphically encrypt the whole thing, throw away the decryption key, and then start it running. I think this matches Peer's situation in all relevant aspects: The information about the uploads exists in the ordinary computational basis (not talking Dust Theory here), and there is a short and fast program to extract it, but it's computationally intractable to find that program if you don't know the secret. The difference is that this way it's much more obvious what that secret would look like.

See comment in full context

Spoiled Discussion of Permutation City, A Fire Upon The Deep, and Eliezer's Mega Crossover

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Feb 19, 2011

Permutation City is an awesome novel that was written in 1994. Even if the author, Greg Egan, used a caricature of this community as a bad guy in a more recent novel, his work is still a major influence on a lot of people around these parts who have read it. It dissolves so many questions around uploading and simulation that it's hard for someone who has read the book to talk about simulationist metaphysics without wanting to reference the novel... but doing that runs into constraints imposed by spoiler etiquette.

So go read Permutation City if you haven't read it already because it's philosophically important and a reasonably fun read.

In the meantime, if you haven't then you should also read A Fire Upon The Deep by Vernor Vinge (of "singularity" coining fame) and then read Eliezer's fan fic The Finale of the Ultimate Meta Mega Crossover which references both of them in interesting ways to make substantive philosophical points and doesn't take too long to read.

In the comments below there will be discussion that has spoilers for all three works.

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Also see discussion at http://lesswrong.com/lw/18g/the_finale_of_the_ultimate_meta_mega_crossover/

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At the risk of being shunned as something of a heretic here, I have to admit to not having cared too much for Permutation City. It had some lovely ideas, but its characters seemed too constrained by the exigencies of plot and setting, and never quite came alive for me.

I loved Fire Upon the Deep, though.

Also Deepness in the Sky, though it's not particularly about uploading, although it is a good visceral introduction to just how much benefit even a marginal increase in intelligence can provide. It is also helpful to read if you're going to get some of the crossover references in FUtD.

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I felt the same way. I feel the same way about a lot of science fiction - interesting ideas, often worth reading for the ideas alone, but falls flat on plot, or characters, or writing, or all of the above.

With Permutation City I got the sense that he was trying hard to make his characters 3-dimensional, but it didn't work for me. [SPOILER WARNING] For example, one supporting character spent most of the novel trying to overcome the guilt of murdering a prostitute. The idea is promising, but the execution was irritating.

(In fact, I have a theory that some popular works of genre fiction - I would include thrillers and romances as well as sci-fi - are popular because of their flaws. For example, when reading The Da Vinci Code, you don't have to worry about any interesting characters or beautiful prose distracting you from the puzzles and conspiracies.)

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I so rarely encounter good characters even in non-sci-fi that the book better be based on a damn interesting premise or it will be a total waste.

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For example, one supporting character spent most of the novel

Yeah, I felt like that character and all his scenes could have been cut entirely without damaging the book.

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Yeah. Other than Inoshiro from Diaspora, Egan's stories have stayed with me because of the philosophy and scientific imagination, not because I felt strongly about the characters.

What did you make of the Dust Hypothesis? It appeared to offer a vivid demonstration of the most extreme possible form of the substrate independence thesis you can have, while still having actual substrate that a person can point to and say "This implements or records a simulation of X"... but it smelled fishy to me for roughly the same reasons that I reject Searle's Chinese Room arguments and I'm curious if I was alone in this.

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The idea that a consciousness can exist within an alternate reading frame on a system that is not conscious in my own frame, as Peer exists within the City, does significant violence to my intuitions about consciousness.

The idea that the alternate frame can be temporally discontiguous with my own... that is, that events A and B can occur in both frames but in a different order... does additional violence to my intuitions about time.

That said, I have no reason to expect my intuitions about consciousness or time to reflect the way the universe actually is. (Of course, that doesn't mean any particular contradictory theory is right.)

That said, without the possibility of intentional causal interaction with such alternate-frame consciousnesses, I'm indifferent to them: I can't see any reason why I should care whether it's true. I feel more or less the same way as I do about the possibility of epiphenomenal spirits, or epiphenomenal Everett branches: if they are in principle unable to interact causally with me, if no observation I can ever make will go differently based on their existence or nonexistence, then I simply don't care whether they exist or not.

I don't endorse that apathy, though. It mostly comes out of a motivational psychology in which believing that future events are significantly influenced by my actions is important to motivating those actions, and I don't especially endorse that sort of psychology, despite instantiating one.

I don't see the connection to Searle's CR.

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The initial few 'thought experiments' in Permutation City cheat the same way the Chinese Room does. A program capable of simulating "Durham having just finished counting to 7 and about to say 8" must have, in some way, already simulated Durham counting to 7. Similarly, Searle's Giant Lookup Table must have come into being somehow.

You could make a similar case that choosing the right permutation of dust to create a universe requires complete knowledge of that universe. In this case, that knowledge is coming from the author.

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Ah, I see. Sure, agreed.

Though I guess a lot depends on whether the computation* of Durham counting to 8 requires the computation of Durham being aware of having counted to 7. If it doesn't, then the program can produce the following sequence: x7 = Durham->countTo(7); x8 = Durham->countTo(8); Durham->awareOf(x8); Durham->awareOf(x7); with the result that Durham goes "8, 7" without any cheating.

The question of whether Durham experiences "7,8" or "8,7" is less clear, though.

I'm more comfortable talking about computation rather than simulation here, because I'm not at all convinced that there's any difference between a real counting-to-7 and a simulated counting-to-7. I don't think the distinction actually matters in this context though.

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With thanks to HonoreDB, yes, the structure must have a source. And also, as with the Chinese Room, there is a sleight-of-concept going on where something that looks like a human (Searle's paper manipulator and Egan's Durham) is not the actual "brains" of the system (which are really the symbol manipulation rules with Searle, or the dust/translator combination with Egan) that we're truly analyzing.

I agree with you that if there is not stateful process to worry about, but merely the instantiation of a trivially predictable "movie-like image of counting the number 8" then the dust hypothesis might make sense... but I suspect that very few of the phenomena that we care about are like this, nor do I think that such phenomena are going to be interesting to us post-uploading. I can't fully and succinctly explain the intuition I have here, but the core of the objection it is connected to reversible computing, computational irreducibility, and their relation to entropy and hence the expenditure of energy.

From these inspirations, it seems likely to me that "the dust" can only be said to contain structure that I care about if the energy used to identify/extract/observe that structure is less than what would have been required for an optimally efficient computational process to invent that structure from scratch. Thus, there is probably a mechanically rigorous way to distinguish between hearing a sound versus imagining that same sound, that grows out of the way that hearing requires fewer joules than imagining. If a dust interpretation system requires too much energy, I would guess either than it is mediating a scientifically astonishing real signal (in a grossly inefficent way)... or you're dealing with a sort of clever hans effect where the interpretation system plus its battery is the real source of the "detected patterns", not the dust.

Using this vocabulary to speak directly to the issues raised in the article on strong substrate independence, the problem with other quantum narratives (or the bits of platospace mathematicians spend their time "exploring") is that the laws of physical computation seem such that our brains can never hear anything from those "places", our brains can only imagine them.

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Yes, that seems like a reasonable way to state more rigorously the distinction between systems I might care about and systems I categorically don't care about.

Though, thinking about Permutation City a bit more... we, as readers of the novel, have access to the frame in which Peer's consciousness manifests. The residents of PC don't have access to it; Peer is no easier for them to access than the infinite number of other consciousnesses they could in principle "detect" within their architecture.

So we care about Peer, and they don't, and neither of us cares about the infinite number of Peer's peers. Makes sense.

But there is a difference: their history includes the programming exploit that created the space in which Peer exists, and the events that led to Peer existing within it. One can imagine a resident of PC finding those design notes and building a gadget based on them to encounter Peer, and this would not require implausible amounts of either energy or luck.

And I guess the existence of those design notes would make me care more about Peer than about his peers, were I a resident of PC... which is exactly what I'd predict from this theory.

OK, then.

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Searle's Giant Lookup Table must have come into being somehow.

That's not due to Searle - you're talking about Ned Block's "Blockhead".

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Hm. The Chinese Room seems to be different in my head than on wikipedia. I guess I assumed that writing a book that covers all possible inputs convincingly would necessarily involve lots of brute force.

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Well, the man in the Chinese Room is supposed to be manually 'stepping through' an algorithm that can respond intelligently to questions in Chinese. He's not necessarily just "matching up" inputs with outputs, although Searle wants you to think that he may as well just be doing that.

Searle seems to have very little appreciation of how complicated his program would have to be, though to be fair, his intuitions were shaped by chatbots like Eliza.

Anyway, the "Systems Reply" is correct (hurrah - we have a philosophical "result"). Even those philosophers who think this is in some way controversial ought to agree that it's irrelevant whether the man in the room understands Chinese, because he is analogous to the CPU, not the program.

Therefore, his thought experiment has zero value - if you can imagine a conscious machine then you can imagine the "Systems Reply" being correct, and if you can't, you can't.

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searle is an idiot, the nebulous "understanding" he talks about in the original paper is obviously informationally contained in the algorithm. the degree to which someone believes that "understanding" can't be contained in an algorithm is the degree to which they believe in dualism. just because executing an algorithm from the inside feels like something we label understanding doesn't make it magic.

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The idea that a consciousness can exist within an alternate reading frame on a system that is not conscious in my own frame, as Peer exists within the City, does significant violence to my intuitions about consciousness.

How about, instead of an opaquely described "alternate reading frame", we consider homomorphic encryption. Take some uploads in a closed environment, homomorphically encrypt the whole thing, throw away the decryption key, and then start it running. I think this matches Peer's situation in all relevant aspects: The information about the uploads exists in the ordinary computational basis (not talking Dust Theory here), and there is a short and fast program to extract it, but it's computationally intractable to find that program if you don't know the secret. The difference is that this way it's much more obvious what that secret would look like.

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Yeah, I basically agree, and that does less violence to my intuitions on the subject... still more evidence, were it needed, that my intuitions on the subject are unreliable.

Indeed, I'm not even sure how relevant the computational intractability of breaking the encryption is. That is, I'm not actually sure how Peer's situation is relevantly different from my own with respect to someone sitting in another building somewhere... what matters about both of them is simply that we aren't interacting with one another in any important way.

The degree to which the counterfactual story about how we might interact with one another seems plausible is relevant to my intuitions about those consciousnesses, as you say, but it doesn't seem at all relevant to anything outside of those intuitions.

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Mitchell_Porter

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If by simulationism we mean the belief that the simulation of an entity causes an instance of the entity to exist, then that is dualism. We can all agree that simulations can be carried out in media which, physically, are wildly different. Simulationism then tells us that the real entity, the one being simulated, comes to identically inhabit all those physically different simulators. And then, in Egan's novel, we have only a partial simulation: the model of Permutation City is run for just a few ticks of the clock and then turned off, but it is assumed that it will continue to exist - platonically? - because of its internal logic.

I see people trying to resolve the illogicality of this - the whole Permutation-City universe gets to exist, even though only a few moments of it get simulated - by appealing to the sort of existence that mathematical entities have. The idea is that the being of mathematical entities doesn't depend on particular instances of people talking about them or computers calculating them, they just exist independently of all that; and the same thing goes for possible worlds. But in that case, you should abandon simulationism - where, to repeat, simulationism is being defined as the belief that the act of simulation causes the simulated entity to exist locally. In this second approach to the problem inspired by mathematical platonism, the possible worlds don't owe their actuality to the fact that they get simulated somewhere, they all exist platonically and independently. So why go on thinking that the simulation of Permutation City involves Permutation City actually existing, however briefly, in the universe where the simulation is occurring?

But all that is just one symptom of the same overall situation of self-concealed ignorance, which leads so many scientifically educated people to not see the problems of "consciousness", and to not understand where this whole "qualia debate" comes from. I may literally have said it a hundred times by now: The standard contemporary scientific way of looking at consciousness is dualistic. It's not a dualism of substance, where you have ordinary matter, and then a soul as well; it's dualism of properties. You have the physical properties, the properties that are actually present in our physical theories, and then you have everything that actually makes up experience - the flow of time, the sense of self, the basic perceived qualities of the world like color. And to see the world in terms of the science that we have right now is to just combine in your imagination the stream of experiences that you actually have, with an imagined play of atoms in space, or fluctuating quantum fields, or whatever avantgarde scientific metaphysics captures your fancy.

A switch to "mathematical" or computational platonism also does absolutely nothing to reinstate the excluded qualities of the experienced world into the official scientific ontology. If, having mulled it over, you were to decide that reality is really a set of equivalence classes of universal Turing machines, when it comes to interpreting your actual experience, you will again have to become a dualist. Only now, instead of imagining that your sensations and thoughts correspond with the flow of ions through membranes - that is, pairing in your imagination your sensations and thoughts as directly but subjectively perceived, with imagined microscopic biophysical processes - you will be imagining that they correspond to abstract state transitions in an abstract state machine. Either way, the disjunction between what is imagined to be the fundamental character of reality and what is experienced to be the character of reality, at least locally, by you - either way the disjunction remains and remains unaddressed.

Simulationist philosophy is the same exercise applied to computers, though from the other direction. Instead of starting with conscious experience and trying to identify it with a physical process, one starts with physical processes and tries to identify them or associate them with the existence of simulated entities or a simulated world.

I sometimes feel like I'm being cruel in pointing all this out, because the right answers are not known, and they are not going to be figured out by people just thinking casually about the problem. I can't tell you the big truth about reality, but I can tell you the little truth about your situation, which is that all the available maps are wrong. Quantum mechanics is the same story; I don't know the explanation of QM, but I can say that MWI is false because relativity is true, and MWI requires objective simultaneity. The ontological truth behind quantum mechanics will only be figured out by people who have extensive technical acquaintance with the subject, and most likely it will require extensive immersion in the most advanced physical theories, because that's how physics is: everything interlocks, and the deep answers are found at the highest levels. I would say the same thing about consciousness, and incidentally about the relationships between computation, consciousness, matter, and reality. The right answer is not yet known, not at all, and it will be found only by sustained and dedicated attention to fact, including "subjective facts" about the world as it is actually experienced, and not just the world as it is imagined by people who have mathematical and formalistic skills.

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Interesting. Easily enough ideas here for a top-level post (certainly for the discussion area.)

I don't know the explanation of QM, but I can say that MWI is false because relativity is true, and MWI requires objective simultaneity.

Not really. I suspect that what you're referring to as "MWI" contains the idea that, in addition to a wavefunction evolving unitarily under the Schrödinger equation, there are also ontologically primitive "branches" (or "worlds") which "split". I think this is obviously wrong. (However, note that the SEP article only says that it's "unclear" how to formulate it in such a way as to be compatible with SR). "Branches" are just patterns that emerge when you zoom out to the macro-scale, in much the same way as fluids with thermodynamic attributes such as temperature and entropy only make sense at the macro-scale. In fact, there's a close connection here - the fact that branches "split" but do not "merge" and the second law of thermodynamics are two manifestations of a single underlying principle.

So why go on thinking that the simulation of Permutation City involves Permutation City actually existing, however briefly, in the universe where the simulation is occurring?

I would interpret the statement "Permutation City actually exists in universe U, which is simulating it" along the following lines: "There is a system in U whose components are causally related to one another in such a way as to be isomorphic to the primitive constituents of Permutation City and their causal relations." (Yeah yeah, at some point I might be called on to explain what I mean by "causal relations" and "primitive constituents", and these are thorny questions, but let's save them for another day.)

So for me "Permutation City actually exists in universe U, which is simulating it" means no more and no less than "Universe U is simulating Permutation City." Or perhaps clearer: once it's established that U is simulating V, there's nothing more to be said about whether V exists in U.

Of course, you won't be happy with this - you want to say (a) that there's either something it's like or nothing it's like to be a simulated human and (b) that actually there's nothing it's like - simulated people are "zombies".

I may as well give the Standard Reply from my camp, though you've heard it all before: "If 'something it's like' is interpreted in the informal everyday sense where 'access consciousness' and 'phenomenal consciousness' are not conceived of as separate, then yes absolutely there's something it's like. Moreover, to the extent that the question carries ethical 'weight', again the answer must be yes. But when you try to do fractional distillation, separating out the pure P-consciousness, and ask whether simulated people are P-conscious, then the question loses all of its meaning."

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Mitchell_Porter

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I suspect that what you're referring to as "MWI" contains the idea that, in addition to a wavefunction evolving unitarily under the Schrödinger equation, there are also ontologically primitive "branches" (or "worlds") which "split". I think this is obviously wrong.

As it is the Many Worlds Interpretation, I think it is reasonable to expect there to be worlds in the resulting ontology.

But if you wish to defend a worldless version of MWI which just contains "a wavefunction evolving unitarily under the Schrödinger equation", feel free to explain how that is compatible with special relativity.

note that the SEP article only says that it's "unclear" how to formulate it in such a way as to be compatible with SR

It's also unclear where the emperor's clothes are.

"Branches" are just patterns that emerge when you zoom out to the macro-scale

Patterns of what? Macro-scale of what?

"If 'something it's like' is interpreted in the informal everyday sense where 'access consciousness' and 'phenomenal consciousness' are not conceived of as separate, then yes absolutely there's something it's like. Moreover, to the extent that the question carries ethical 'weight', again the answer must be yes. But when you try to do fractional distillation, separating out the pure P-consciousness, and ask whether simulated people are P-conscious, then the question loses all of its meaning."

Congratulations, it looks like you're pioneering a whole new stage in the appropriation of names for consciousness by people who claim it doesn't exist. The only reason we have talk about "qualia" is because simpler words like "sensation" have been appropriated to designate material events in the nervous system. One needs to be able to talk about subjective sensation itself - the thing we actually experience - and not just the physical events in the nervous system which are supposed to be its material correlate.

Until now, I have never seen anyone simultaneously deny the existence of phenomenal consciousness (yet another name for subjectivity, i.e. actual consciousness, consciousness as it actually experienced) while affirming that "what it's like to be an X" has some meaning. Until now, that second expression has been still another name for subjectivity, consciousness experienced from the inside. But apparently, not any more. What on earth it does mean, coming from you, I have no idea.

My head just spins trying to understand what's going on in yours. You espouse a physical ontology in which there are no "worlds", or in which the existence of a world is somehow an approximate thing, a matter of opinion or perspective, even though you're in a world. And, you say there are no facts about consciousness - there's no fact about whether a simulated person is conscious or not, there's no fact about whether you're conscious or not. It's just crazy, and yet I assume that awareness of the world's existence and awareness of your own existence does play a role in the functioning of your mind.

So the question is, how can an intelligent and self-aware person adopt a philosophical ideology which explicitly denies the most epistemologically elementary facts there are?

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As it is the Many Worlds Interpretation, I think it is reasonable to expect there to be worlds in the resulting ontology.

Allow me to refresh your memory of what I said previously. "Not really. I suspect that what you're referring to as "MWI" contains the idea that, in addition to a wavefunction evolving unitarily under the Schrödinger equation, there are also ontologically primitive "branches" (or "worlds") which "split"."

You ignored one of the words - do you see which one?

But if you wish to defend a worldless version of MWI which just contains "a wavefunction evolving unitarily under the Schrödinger equation", feel free to explain how that is compatible with special relativity.

This is standard stuff.

Patterns of what? Macro-scale of what?

Again, this is elementary. I suggest you read that MWI FAQ. You'll find more authoritative sources if you look around, but it's a good place to start.

Congratulations, it looks like you're pioneering a whole new stage in the appropriation of names for consciousness by people who claim it doesn't exist ... But apparently, not any more. What on earth it does mean, coming from you, I have no idea.

Are you unfamiliar with analytic functionalism? Of course you're not. Then why are you pretending to be?

The idea that one can coherently conceive of "phenomenal consciousness" separately from structure and function (and vice versa) is precisely the intuition that leads people to think that zombies are conceivable. The denial that zombies are conceivable is one of the standard positions in the philosophy of mind. Spare me your disingenuous and patronising tone of 'mind-boggled befuddlement'.

You espouse a physical ontology in which there are no "worlds"

I didn't say that, I said there were no ontologically primitive worlds, which only leaves open a yawning chasm of logical room for "ontologically non-primitive worlds". Do you think that "temperature" not being ontologically fundamental disqualifies all statements of the form "the temperature of this gas is ..."?

or in which the existence of a world is somehow an approximate thing, a matter of opinion or perspective,

Is the temperature of a gas a matter of opinion or perspective? Is it approximate? Well ultimately yes it is "approximate", though there isn't much to be said for calling it a "matter of opinion" is there?

even though you're in a world.

The notion of "you" is as "approximate" as the notion of "'world".

Here's something I find mind-boggling: Why does your side always conflate "fuzzy around the edges" with "non-existent". For instance, Dennett in Time and the Observer makes a powerful case for denying that our consciousness consists of a linear sequence of "moments" such that for each moment there is unique, well-defined 'fact of the matter' as to what you're conscious of at that moment. Perhaps I'm not speaking for all of you here, but why do many of you think that conceding this point entails denying that consciousness exists? Does observing that the "temperature of a single gas molecule" makes no sense entail that temperature doesn't exist?

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The distinctive unifying idea of special relativity is that the geometry of the universe is that of Minkowski space. The reality of things is a four-dimensional partially ordered set of point events which can be divided into hypersurfaces of equal coordinate time in a variety of ways. Two events may be simultaneous in one description of a physical process, but if they are spatially separated, then we can transform to another description in which they are no longer simultaneous. Simultaneity is a coordinate artefact and there is no universal time.

Wavefunctions are always defined with respect to a particular time-slicing, a particular foliation of space-time into hypersurfaces. All a Lorentz transform can do is change the tilt of those hypersurfaces with respect to the time axis of your coordinate system; you're still stuck with a particular preferred foliation as the ontological base of your wavefunction's time evolution. If you reify the wavefunction, you end up reifying your coordinate system as well.

That is the substance of MWI's problem with relativity. A physicist might call it "ontological gauge-fixing". In theories with a gauge symmetry, you're allowed to work in a particular gauge for the purposes of calculation, but the end product, the quantitative predictions, must be gauge-invariant. If they show a dependence on your choice of gauge, you've done something wrong.

Here, we're trying to construct an ontology for quantum theory. The ontological significance of special relativity for time is that universal time is a coordinate artefact, yet in MWI ontologies, we end up with an objective universal time. That's evidence of a mistake, and the mistake is that you are treating a wavefunction as an objectively existing thing, when it is just a frame-dependent tabulation of probability amplitudes.

Versions of MWI which fix a universal time and a particular Hilbert-space basis (such as position) may not be believable, but at least they are clear and explicit about what it is that is supposed to exist. When I think of supposedly more sophisticated approaches to MWI, where That Which Exists is just the universal wavefunction, in its sublime purity, beyond all specific choices of coordinate and basis, and where the contingent particularities of individual worlds are supposed to be logically implicit in its structure somehow... my overall impression is of utterly contemptible vagueness and handwaving, often suffused with a mystic adoration of the Big Psi.

Let's pretend for a moment that I don't have an issue with the idea that the world only exists "approximately", and that the ultimate objective reality is some sort of wavefunction. That's your hypothesis, fine. Can you tell me the nature of this approximateness? Are we taking some sort of limit? If so, can you be more specific? Your original words were

"Branches" are just patterns that emerge when you zoom out to the macro-scale

I asked for more details and you linked to the MWI FAQ - which I have seen many times before, and which mostly consists of word-pictures. That is not enough, although a word-picture can be a fine way to fool yourself into thinking that your ideas make sense.

I am going to pose a challenge to you. The issue which is ultimately at stake: whether a "Many Approximate Worlds Interpretation" even makes sense as a theory. However, we won't try to resolve that directly. The actual challenge is much simpler. I ask merely that you exhibit a mathematically exact definition of an "approximate world". This is theoretical physics we're discussing, it uses exact mathematics, and if the concept is genuinely relevant, it will have a mathematical formulation and not just a verbal one.

Since these approximate worlds are supposed to be contained implicitly within the universal wavefunction, that is the relationship which I am expecting to see formally elucidated. I don't expect to see statements about a theory of everything; supposedly all of this can be explained at the level of nonrelativistic quantum mechanics. I just want to see an exact statement of what the relationship between world and wavefunction is supposed to be.

If you want to point to a particular proposition in a paper somewhere, fine. Just give me more to work with than shapeless verbal formulations!

There are many other things to discuss in your comment, we can return to those later. You should also feel free to delay responding to what I said about relativity if doing so would interfere with this challenge. What I want from you now, more than anything else, is an exact definition of what a "world" or an "approximate world" is, stated in the same mathematical language that we use to talk about everything else in quantum theory. If you can't tell me what you mean, we have nothing to talk about.

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I appreciate that you chose to "raise the bar" here.

That is the substance of MWI's problem with relativity.

I agree that when we're seeking to 'interpret' a theory like QFT, which is Lorentz-invariant, we ought to postulate an ontology which respects this symmetry. However, from a certain perspective, I think it's obvious that it must be possible to paint a mathematical picture of a Lorentz-invariant "many worlds type" theory.

Let's assume that somehow or other, it's possible to develop QFT from axiomatic foundations, and in such a way that when we take the appropriate low-velocity, low-energy limit, we recover "wavefunctions" and the Schrödinger equation exactly as they appear in QM. As far as I know, QFT and (non-relativistic) QM are, broadly speaking, cut from the same cloth: Both of them make predictions through a process of adding up quantum amplitudes for various possibilities then interpreting the square-norms as probabilities. Neither of them stipulate that there is a fact of the matter about which slit the electron went through, unless you augment them with 'hidden variables'. Neither of them can define what counts as a "measurement". In both theories, the only strictly correct way to compute the probabilities of the results of a second measurement, in advance of a first, is to do a calculation that takes into account all of the possible ways the first measuring device might 'interfere' with the stuff being measured. In practice we don't need to do this - in any remotely reasonable experiment, when some of the degrees of freedom become entangled with a macroscopic measuring device, we can treat them as having "collapsed" and assumed determinate values. But in theory, there's nothing in QM or QFT to rule out macroscopic superpositions (e.g. you can do a "two-slit experiment" with people rather than electrons).

The reason I'm pointing all of these things out is to motivate the following claim: A 'no collapse, no hidden variable' interpretation of QFT is every bit as natural as a 'no collapse, no hidden variable' interpretation of QM. By 'natural' I mean that unless you deliberately 'add something' to the mathematics, you won't get collapses or hidden variables. (The real problem for Everettians is that (prima facie) you won't get Born probabilities either! But we can talk about that later.)

Next, I claim that a 'no collapse, no hidden variable' theory (taken together with the metaphysical assumption that 'the entities and processes described are real, not merely instruments for computing probabilities') is obviously a 'many worlds' theory. This is because it implies that the man over there, listening to a Geiger counter, is constantly splitting into superpositions. Although his superposed selves are overwhelmingly like to carry on their lives independently of each other, there's no limit to how many of them we may need to take account of in order to get our predictions right.

Finally, since the predictions of QFT are Lorentz-invariant, if it can be given a mathematical foundation at all then there must be some way to give it a Lorentz-invariant mathematical foundation.

Putting all of this together, I have my claim.

I'm "cheating" you'll say because I haven't done any hard work - I haven't told you how one can have a Lorentz-invariant ontology of things resembling "wavefunctions". Regretfully I'm not able to do that - if I could I would - but for present purposes I don't think it's necessary.

When I think of supposedly more sophisticated approaches to MWI, where That Which Exists is just the universal wavefunction, in its sublime purity, beyond all specific choices of coordinate and basis, and where the contingent particularities of individual worlds are supposed to be logically implicit in its structure somehow... my overall impression is of utterly contemptible vagueness and handwaving, often suffused with a mystic adoration of the Big Psi.

Personally I'd just say that That Which Exists is whatever it is that, when supplemented with co-ordinates and a position basis, and passing to the nonrelativistic limit, looks like a wavefunction. I don't know whether that has to take the form of a 'universal wavefunction'. (By the way, I don't think the position basis is an 'arbitrary choice' in the same way that a foliation of Minkowski space is arbitrary. This is because of the analogy with classical mechanics, where the elements of a basis correspond to points in a phase space, and changing basis is like changing co-ordinates in the phase space. But a phase space is a symplectic manifold, not an unstructured set. I'm guessing that in quantum theory too there must be some extra structure in the Hilbert space which implies that some bases (or more generally, some Hermitian operators) are "physical" and others not.)

Anyway, I don't really have any idea what a maximally elegant mathematical presentation of the Underlying Reality would look like. I just think it's misleading to use the words "MWI is inconsistent with special relativity" when what you actually mean is that "no-one has yet formulated an axiomatic presentation of QFT". Because the very moment we have the latter, we will (immediately, effortlessly) have a version of MWI that is consistent with SR, simply by making the same interpetative 'moves' that Everett made. (This is a point which the MWI FAQ tries to drive home.) And if we cannot put QFT on firm mathematical foundations then all metaphysically realistic interpretations will suffer equally badly.

Finally, let's switch briefly to the outside view. I've never before seen a critique of MWI made along the lines that it presupposes a notion of absolute simultaneity. Now that could be because I just haven't been looking hard enough (but actually I have read a fair few attacks on MWI), or not understanding what I've been reading (but I think I have, at least in outline), and it could be because almost everyone who writes about this is distracted by whatever agendas and pet theories they have, and missing the more 'obvious' line of attack right under their noses; but I think it's much more likely that you've misunderstood the relation between MWI and the QM-style wavefunction, which isn't as close as you think.

Actually, the overall impression I had prior to this conversation with you is that compatibility with SR is one of MWI's greatest strengths (especially when compared with Bohm's theory.)

Let's move on.

I am going to pose a challenge to you. The issue which is ultimately at stake: whether a "Many Approximate Worlds Interpretation" even makes sense as a theory. However, we won't try to resolve that directly. The actual challenge is much simpler. I ask merely that you exhibit a mathematically exact definition of an "approximate world". This is theoretical physics we're discussing, it uses exact mathematics, and if the concept is genuinely relevant, it will have a mathematical formulation and not just a verbal one.

I'd have to do a lot of reading before I could answer this properly. From what I've seen so far, the critical concepts seem to be einselection and decoherence. The universe can be thought of as a collection of interacting 'systems' (such that the Hilbert space of the whole universe is the tensor product of the Hilbert spaces corresponding to each system). When a system interacts with its environment, its reduced density matrix changes exactly as if the environment was performing a 'measurement' on it. However, the environment is much more likely to perform certain 'measurements' than others. Those states which are sufficiently near to being eigenstates of a 'typical measurement' thus have a degree of stability not shared by an arbitrary superposition of such states. In this way, the environment selects a so called "measurement basis" (which consists of what we can call "classical states").

A 'world' is just a component of the universe's wavefunction, when decomposed with respect to this "measurement basis". As I understand it, this notion of 'world' coincides with (or at least is closely related to) the thermodynamic concept of a 'macrostate'. In particular, one can no more (and no less) give a mathematically rigorous definition of 'world' than one can of 'macrostate'. This is just an assumption on my part, but I don't think the "measurement basis" is strictly speaking a basis - it's more like a decomposition of the Hilbert space as a direct sum of subspaces which are themselves fairly large. The indeterminacy ("approximateness") in the notion of world arises from the indeterminacy of what counts as a 'typical' interaction between systems. There may be no "fact of the matter" about whether or not two subspaces ought to be 'merged together' (i.e. whether or not a particular property somewhere between the 'micro' and 'macro' scales deserves to be called 'macroscopic enough' to make the difference between two macrostates).

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Mitchell_Porter

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Possibly I understand your outlook better now. For you, worlds are like hills in a landscape. You're on one of them, there's a local maximum, but there's no need to demarcate exactly where one hill ends and another begins. What is real is the landscape.

You don't experience a whole world, just a small part of one, so you are not epistemically compelled to think of whole worlds as sharply bounded entities. However, if you consider your own place in this ontology, you're not just near a local maximum or on a local maximum, you are a local maximum, and here you no longer have the option of indeterminacy. Your experience definitely exists - it is, after all, the only reason you know that anything exists; it is, by hypothesis, not all that exists; and so, within That Which Exists, there is a sharp and objective distinction between That Which You Experience and That Which You Do Not Experience.

It should also be apparent that you don't just exist or experience featurelessly; you are something, a particular entity, and you are experiencing something particular. This is what you are denying when you say that there are situations where there is no fact about what your state of consciousness is or even whether you have one. To which all I will say is that that is the ultimate in irrationalism. I can only guess that you are thinking of consciousness in "third person" terms, as a hypothesized entity which may or may not be posited (according to one's theoretical preference) and whose nature is a matter of definition (and therefore potentially vague or conventional), rather than as the substance of everything you know and cannot deny, unless you wish to deny reality itself.

We shall see if this latest lecture of mine on the necessity of the objectivity of your existence makes an impression. But proceeding from that premise, it follows that, if you wish to maintain that reality in its totality is something like a universal wavefunction, you must find at least one sharply delineated entity in it, because you are a sharply delineated entity that exists, and you are not identical with the whole.

P.S. On the topic of relativity and QFT: It's difficult to rigorously define the interacting field theories which physicists actually use in a self-contained way, because they probably only exist as equivalence classes of approximations to deeper trans-QFT theories (like superstring vacua). This is the contemporary understanding of the meaning of renormalization that emerged in the 1970s. You have an unknown self-contained theory whose low-energy behavior can be approximated by a finite number of parameters, and renormalizable QFTs are the language in which this approximation is expressed. They can't be axiomatized as functionals over a space of field configurations, which then get approximated by a power series of Feynman diagrams. The most you can do is develop a formal algebra of these power series themselves. For a rather technical example of this (but worth a look if you want to see the real thing), see the latest paper by Richard Borcherds.

But assuming that string theory or some other framework removes that technical obstacle, what's the status of my argument that relativity contradicts MWI? The argument does suppose that we are talking about exactly specified whole-universe worlds that "split" instantly on some hypersurface of simultaneity. I don't see how any such model can avoid the "ontological gauge-fixing" I mentioned in the previous comment. The only alternatives I can see are (1) Gell-Mann and Hartle's decoherent histories, which are self-contained (no splitting) and coarse-grained (lacking some properties by classical ontological standards), and (2) a hypothetical "blistering" model of world-splitting, where instead of being instantaneous along a preferred hypersurface, it starts at a point and a sheaf of new worlds peels away from the parent world in a local and causal way, with the blister spreading at light-speed. In this second model, one has to imagine the descendant worlds in the separating sheaf themselves beginning to blister and split even while the split that created them continues to propagate and grow, and so one has sheaves of part-worlds growing upon sheaves of part-worlds. A picture like that might be made ontologically relativistic in some complicated way. Each of these options introduces further issues, but I'll leave them alone for now unless someone takes them up.

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Thanks. This exchange really awakened me, not so much to the fact that MWI is 'wrong' (I still don't think it is), but to the enormity of the philosophical challenge one faces in justifying it.

To clarify, there are two senses in which MWI could be 'right' or 'wrong'.

(a) Do we in fact live in a multiverse?

(b) Could we have found ourselves in a multiverse? That is, in a hypothetical universe where objective physical reality is exactly as MWI theorists describe it, and supposing it contained structures that behaved like conscious observers, could we successfully predict 'what it would be like' to be those observers, and would it be 'essentially' like our own experiences (whatever we deem the 'essential' aspects of our experience to be)? (From my perspective, this is the same as asking: If you did a simulation of an MWI universe on an ordinary computer, would the 'simulated beings' have experiences like ours (in the relevant respects)?)

Leaving aside (a) for the moment, I think the 'disconnect' between our respective worldviews works out like this:

I think that, since nonrelativistic QM is a self-contained theory, if we're given a model of this theory - a 'toy universe' if you like - it must be possible to deduce a priori what conscious observers there are in this universe, if any, and what they are conscious of (albeit with my usual caveat that we shouldn't expect perfectly "sharp" answers.) If you accept this premise, then you don't need to poison the ontological simplicity of MWI by adding 'Worlds', 'Histories' or 'Minds'. All you need to do is carefully 'unpack' what's already in front of you. (The "Bare Theory" is enough, modulo a lot of analytic reasoning.)

(This presupposes the truth of analytic functionalism.)

On the other hand, I suspect you regard it as obvious - so obvious that it should go without saying - that the Bare Theory isn't enough. That the work you need to do in order to generate empirical predictions must be 'synthetic' rather than 'analytic'. That bringing 'many worlds' to life requires axioms rather than mere definitions.

Your experience definitely exists - it is, after all, the only reason you know that anything exists; it is, by hypothesis, not all that exists; and so, within That Which Exists, there is a sharp and objective distinction between That Which You Experience and That Which You Do Not Experience.

Sorry but I'm unpersuaded. I mean, when a hill gets smaller it gradually and continuously loses its identity as a 'thing', to the local topographical variations around it. Likewise, the 'boundary' of a hill is somewhat indeterminate (just as the boundary of the Sun's gravity well is somewhat indeterminate).

It should also be apparent that you don't just exist or experience featurelessly; you are something, a particular entity, and you are experiencing something particular. This is what you are denying when you say that there are situations where there is no fact about what your state of consciousness is or even whether you have one. To which all I will say is that that is the ultimate in irrationalism.

The ultimate in irrationalism? To me those conclusions look unavoidable. Don't Dennett's examples make any impression on you? Consider change blindness: you're alternately shown two slides A and B which depict the same scene, but with a significant alteration which under normal circumstances would 'leap out at you'. But because there's a short delay between presentations of A and B, the slides can be switched many times before you notice the difference. Then Dennett wants to say that there's no 'right answer' to the question of whether, prior to noticing the change, your visual phenomena included the bit of the scene that was changing.

And doesn't pointing out the inevitable arbitariness of any attempt to single out 'the first appearance of consciousness in the tree of life' cut any ice? To me it's the most obvious thing in the world that there isn't always a determinate answer to the question "is that thing conscious?" I honestly find it baffling that so many thinkers resist this conclusion.

For a rather technical example of this (but worth a look if you want to see the real thing), see the latest paper by Richard Borcherds.

Thanks for the reference - I'm always meaning to teach myself about this stuff.

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Mitchell_Porter

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User DZS has directed me to a paper which provides a relativistically covariant ontology for QFT! Consistent histories already had this, but the histories there can be arbitrarily sparsely specified. This ontology, "space-time state realism", goes to the opposite extreme and it does so very ingeniously. It uses the "Heisenberg picture" of QFT rather than the "Schrodinger picture". The Schrodinger picture is the usual one in which the state vector evolves in time and the operators do not. The Heisenberg picture is usually described as using a state vector which doesn't evolve in time and operators which do; but the important fact, for the purposes of interpretation, is that the operators are associated to space-time points and so form a manifold-like set that can be relativistically transformed.

Operators are not yet states, however. What these authors (Wallace and Timpson) do, is to define a Hilbert space for an arbitrary space-time region, and then a way to construct a state in that Hilbert space, using data about how the field operators in that region behave with respect to the unique "initial" state used in the Heisenberg picture. So in their ontology, absolutely every space-time region and subregion (every open set, maybe? haven't gone over the details) has a quantum state attached, in a way that is consistent across regions. It's very clever, and it's just enough overkill to guarantee that the true ontology is almost certainly hiding somewhere in there.

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