Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Shock Level 5: Big Worlds and Modal Realism

15 [deleted] 25 May 2010 11:19PM

In recent times, science and philosophy have uncovered evidence that there is something very seriously weird about the universe and our place in it. We used to think that there was one planet earth, inside a universe that is very large (at least 10^26 meters in diameter) but that the reachable universe (future light-cone in the terminology of special relativity, or causal future in the terminology of GR) was finite. Anything outside the reachable universe is irrelevant, since we can't affect it. 

However, cosmologists went on to study the process that probably created the universe, known as inflation. Inflation solves a number of mysteries in cosmology, including the flatness problem. The process of inflation seems to create an infinite number of mini-universes, or "inflationary bubbles" - this is known as chaotic inflation theory. The physical parameters and initial conditions of these bubbles are determined randomly, so every possible set of particle masses, force strengths, etc is realized. To quote from this piece by Alan Guth:

The role of eternal inflation in scientific thinking, however, was greatly boosted by the realization that string theory has no preferred vacuum, but instead has perhaps 101000 metastable vacuum-like states. Eternal inflation then has potentially a direct impact on fundamental physics, since it can provide a mechanism to populate the landscape of string vacua. While all of these vacua are described by the same fundamental string theory, the apparent laws of physics at low energies could differ dramatically from one vacuum to another.

To top this off, the dominant theory about the spacetime manifold we live on is that it is infinitely large in all directions. If you look at this picture of a reconstruction of the large-scale structure of the universe, the idea that we are living in something like an infinite volume with a finite speed-limit and a uniform random distribution of matter and energy that clumps over time becomes plausible. 

A final step along this line of increasingly large Big Worlds is modal realism, the idea that all possible worlds exist. Max Tegmark has formalized this as the Mathematical Universe Hypothesis: All structures that exist mathematically also exist physically.

If any of these theories turn out to be true, then we are living in a Big World, a cosmology where every finite collection of atoms, including you, is instantiated infinitely many times, perhaps by the same physical processes that created us here on earth. It is also the case that other life-forms might emerge and use their technological capabilities to create simulations of us. Once an alien civilization reaches the point of being able to create simulations, it can create lots of simulations - really unreasonably large numbers of simulated beings can be created in a universe roughly the size of ours1,2, Bostrom's estimate would be something like 10^50. And in other mathematically possible universes with the ability to do an infinite amount of computation in a finite time, you could be simulated an infinite number of times in just one universe. 

One (incorrect) way of interpreting it is to think of a bunch of "worlds" spread out over the multiverse, most of them uninhabited, some containing weird green aliens, and one containing you, and saying:  " Aha! I only care about this one, the others are causally disconnected from it!".

No, this view of reality claims that your current observer-moment is repeated infinitely many times, and looking forward in time, all possible continuations of (you,now) occur, and furthermore there is no fact of the matter about which one you will experience, because the quantum MW aspect of the multiverse has already demolished our intuitions about anticipated subjective experience4. Think that chocolate bar will taste nice when you bite into it? Well, actually according to Big Worlds, infinitely many of your continutions will bite the chocolate bar and find it turns into a hamster.

I once saw wormholes explained using the sheet of paper metaphor: draw two dots on a sheet of paper, reasonably far apart, imagining the paper distance between them to be an unfathomably large spatial distance, say 10^(10^100) meters. Now fold the sheet so that the two dots touch each other: they are right on top of each other! Of course, wormholes seem fairly unlikely based upon standard physics. The metaphor here is of what is called a quotient in mathematics, in particular of a quotient in topology.

But if you combine a functionalist view of mind with big worlds cosmology, then reality becomes the quotient of the set of all possible computations, where all sub-computations that instantiate you are identified. Imagine that you have an infinite piece of paper representing the multiverse, and you draw a dot on it wherever there is a computational process that is the same as the one going on in your brain right now. Now fold the paper up so that all the dots are touching each other, and glue them at that point into one dot. That is your world. 

Almost all of the histories and futures that feed into your "now" are simulations, by Bostrom's simulation argument (which is no longer shackled by the requirement that the simulations must be performed by our particular descendants - all possible descendants and aliens get to simulate us).

Future Shock level 5 is "the Copernican revolution with respect to your place in the multiverse", the point where you mentally realize that perfectly dry astrophysics implies that there is no unique "you" at the centre of your sphere of concern, analogous to the Copernican revolution that unseated earth from the centre of the solar system. It is considered to be more shocking than any of the previous future shock levels because it destroys the most basic human epistemological assumption that there is such a thing as my future, or such a thing as the consequence of my actions

Shock Level 5 is a good candidate for Dan Dennett's universal acid: an idea so corrosive that if we let it into our minds, everything we care about will be dissolved. You can't change anything in the multiverse - every decision or consequence that you don't make will be made infinitely many times elsewhere by near-identical copies of you. Every victory will be produced, as will every possible defeat. 

In "What are probabilities anyway?" Wei Dai suggests a potential solution to your SL5 worries:

All possible worlds are real, and probabilities represent how much I care about each world. (To make sense of this, recall that these probabilities are ultimately multiplied with utilities to form expected utilities in standard decision theories.)

For example, you could get your prior probabilities from the mathematization of occam's Razor, the complexity prior. Then the reason you don't worry that your chocolate bar will turn into a hamster is that the complexity of that hypothesis is higher than the complexity of other hypotheses, such as the chocolate bar just tasting like normal chocolate. But you're not saying that this scenario is unlikely to happen: it is certain to happen, but you just don't care about it. 

Wei's UDT allows you to overcome the decision-theoretic paralysis that would otherwise follow in a Big World: you think of yourself as defining an agent program that controls all of the instantiations of you, so that your decisions do matter. But remember, in order to get decisions out of UDT in a Big World, you need that all-important measure, that is a "how-much-I-care" density on the multiverse that integrates to 1.

Personally, I think that Shock Level 5 could be seen as emotionally dangerous for a human to take seriously, so beware.

However, there may be strong instrumental reasons to take SL5 seriously if it is true (and there are strong reasons to believe that it is).


1: Anders Sandberg talks about the limits of physical systems to process information.

2: Bostrom on astronomical waste is relevant here as he is calculating the likely number of people that we could simulate in our universe, which ought to be roughly the same as the number of people that some other civilization could simulate in a similar universe.

3: Not one of the originally proposed 4 future shock levels.

4: To really nail the subjective anticipation issue requires another post.

Comments (140)

Comment author: Yvain 26 May 2010 10:30:18AM *  25 points [-]

Does this theory really alter the probability that your next chocolate bar will turn into a hamster? After all, if there were only one of you, maybe there's a one in a trillion chance that one is in a simulation whose alien overlords will turn a chocolate bar into a hamster. If there are a trillion of you, and one of those trillion is in such a simulation, and your subjective experience has an equal chance of continuing down any branch, then the probability of the bar turning into the hamster is still one in a trillion. Although I've never seen a proof, intuitively you'd expect those two probabilities to be the same, or at least not be able to predict how they differ.

It all adds up to normality...except that this takes a lot of the oomph out of the project to reduce existential risk. Saving all humanity from destruction makes a much better motivator for me than reducing the percentage of branches of humanity that end in destruction by an insignificaaEEEEGH MY KEYBOARD JUST TURNED INTO A BADGER!!11asdaghf

Comment author: orthonormal 27 May 2010 02:37:09AM 22 points [-]

EEEEGH MY KEYBOARD JUST TURNED INTO A BADGER!!11asdaghf

At least it's a QWERTY badger, from the looks of it...

Comment author: CarlShulman 26 May 2010 09:12:42PM 8 points [-]

your subjective experience has an equal chance of continuing down any branch

And just what does that mean?

Comment author: Wei_Dai 29 May 2010 05:12:10AM 6 points [-]

I spent a lot of time in the late 90s trying to work out a coherent system of thinking about probabilities that involved things like "your subjective experience has an equal chance of continuing down any branch" but could not make it work out.

Eventually I gave up and went down the road of UDASSA and then UDT, but "your subjective experience has an equal chance of continuing down any branch" seems to be the natural first thing that someone would think of when they think about probabilities in the context of multiple copies/branches. I wish there is a simple and convincing argument why thinking about probabilities this way doesn't work, so people don't spend too much time on this step before they move on.

Comment author: Nick_Tarleton 29 May 2010 05:29:16AM 4 points [-]

The implied difference between making N copies straight away, and making two copies and then making N-1 copies of one of them, might be a simple convincing argument that something really odd is going on.

Comment author: Mitchell_Porter 29 May 2010 05:22:23AM 2 points [-]

I wish there is a simple and convincing argument why thinking about probabilities this way doesn't work

It doesn't? If I flip a fair coin, I can think of the outcomes as "my subjective experience goes down the branch where heads comes up" and "my subjective experience goes down the branch where tails comes up", and the principle works.

Comment author: Yvain 26 May 2010 09:57:31PM 2 points [-]

Maybe nothing - maybe the fundamental unit of conscious experience is the observer-moment and that continuity of experience is an illusion - but the consensus on this site seems to be that it's worth talking about in situations like eg quantum suicide or simulation.

Comment author: MichaelVassar 28 May 2010 04:36:26PM 2 points [-]

Maybe the inferential step would work better than the observer moment?

Comment author: Kutta 26 May 2010 01:13:24PM *  2 points [-]

reducing the percentage of branches of humanity that end in destruction by an insignificant

Well, it definitely sounds worse than simply saving the world, but the expected number of saved lives should be the same either ways.

Comment author: Yvain 26 May 2010 04:50:49PM 4 points [-]

Yes, but utility isn't linear across saved lives and maybe it even shouldn't be. I would be willing to give many more resources to save the lives of the last fifty pandas in the world, saving pandas from extinction, than I would be to save fifty pandas if total panda population was 100,000 threatening to go down to 99,950.

Now it's true that human utility is more linear than panda utility because I care much more about humans for their own sake versus for the sake of my preference for there being humans, but I still think saving the last eight billion humans is more important than saving eight billion out of infinity.

Comment author: Nick_Tarleton 26 May 2010 08:27:24PM 7 points [-]

You're an equivalence class. You don't save the last eight billion humans, you save eight billion humans in each of the infinitely many worlds in which your decision algorithm is instantiated.

Comment author: Yvain 29 May 2010 10:14:30PM 1 point [-]

Why is that significant? No matter how many worlds I'm saving eight billion humans in, there are still humans left over who are saved no matter what I do or don't do. So the "reward" of my actions still gets downgraded from "preventing human extinction" to "saving a bunch of people, but humanity will be safe no matter what".

In fact...hmm...any given human will be instantiated in infinitely many worlds, so you don't actually save any lives. You just increase those lives' measure, which is sort of hard to get excited about.

Comment author: khafra 26 May 2010 02:58:37PM 0 points [-]

Should it? It appears to me that efforts toward saving the world, if successful, only raise the odds that the branch you personally experience will include a saved world.

Comment author: MichaelVassar 28 May 2010 04:39:37PM 3 points [-]

Or from a different perspective your decision algorithm partially determines the optimization target for the updateless game-theoretical compromise that emerges around that algorithm.

Comment author: khafra 28 May 2010 05:26:42PM 0 points [-]

That's certainly a useful view of the ambiguity inherent in decision theory in MWI. Or it would be, if I had a local group to help me get a deep understanding of UDT--the Tampa chapter of the Bayesian Conspiracy has lain in abeyance since your visit.

Comment deleted 26 May 2010 11:36:44AM [-]
Comment author: Kutta 26 May 2010 01:20:49PM *  2 points [-]

It sounds a bit chicken-and-egg to me. My subjective probability estimate of simulators' motivations comes great part from the frequency and nature of observed bizarre events. Based on what I know about my universe the vast majority of my simulators don't interfere with my physical laws.

Comment deleted 26 May 2010 02:30:58PM *  [-]
Comment author: Nick_Tarleton 26 May 2010 08:30:15PM *  3 points [-]

I hear things like this a lot, but I'm not sure if I've heard a clear reason to think that the people that the simulators (of a long-running, naturalistic simulation) are interested in should be more likely to be conscious, or otherwise gain any sort of epistemological or metaphysical significance.

Comment deleted 26 May 2010 11:55:46PM [-]
Comment author: MichaelVassar 28 May 2010 04:41:09PM 4 points [-]

"interesting" is very much the wrong word though. More like informative regarding the optimization target that one cooperates by pursuing.

Comment author: Yvain 26 May 2010 04:46:04PM 0 points [-]

Isn't the measure of the set of me not in simulations (in a big world) equal to the probability that I'm not in a simulation (if there's only one of me)?

Comment author: Christian_Szegedy 26 May 2010 09:34:26AM *  7 points [-]

Shock-level-bragging is so 2003... ;) Still, in my opinion, this post contains some extremely interesting unconventional intuition, which seems to be way underrated.

In the long run, this whole mathematical multiverse idea has the potential to become much less insubstantial than it may look on superficial inspection.

There are quite a few problems with it though. For example the reliance on minimum description length does not feel like the right approach to the probability problem at that level. It may turn out to be eventually, but generally, the perceived probabilities don't come from a conscious decision to care about some abstract (and uncomputable!) complexity measure (like MDL)

No! We experience certain probabilities, because something is built into the very nature of our physics (or rather meta- or multi-physics). So, even if MDL turns out to be at the core, it must be a derived consequence, rather than just being pulled out of the hat as in the OP.

The most essential clue in the puzzle could be, if we'd manage to understand how this glue works that connects processes with phenomenologically equivalent or similar information processing structures. I can see Barbour's derivation of the general relativity as an interesting analogy. But it's obviously much harder to argue about general (approximate) isomorphisms of causality networks than measuring the similarity of mass distributions of three dimensional spaces.

Nevertheless I think the intuition multiverse ideas provide could inspire speculations in extremely exciting directions: For example: Is it conceivable that the symmetries we experience in the physical laws are plainly consequences of the natural symmetries of this observer-gluing process itself?

Comment author: Kevin 26 May 2010 09:35:49AM 8 points [-]

Just wait until you hear about shock level 7.

Comment author: Will_Newsome 26 May 2010 10:00:46AM 12 points [-]

Due to anthropic reasoning it is impossible to understand unless you have heard about shock level 8, you will never find yourself in a universe where you hear about shock level 8.

Comment author: Christian_Szegedy 26 May 2010 10:05:36AM *  14 points [-]

Q: How do you convince a singularitarian to eat shit?

A: Declare eating shit shock level 5

Comment author: Kutta 26 May 2010 01:08:50PM 5 points [-]

It's 4chan.

Comment author: Nick_Tarleton 26 May 2010 08:42:49AM *  7 points [-]

We used to think that there was one planet earth, inside a universe that is very large (at least 10^26 meters in diameter) but that the reachable universe (future light-cone in the terminology of special relativity, or causal future in the terminology of GR) was finite. Anything outside the reachable universe is irrelevant, since we can't affect it. However, cosmologists went on to study the process that probably created the universe, known as inflation.

The scientific idea of a spatially infinite universe, and the recognition that this would have weird implications, is independent of and long predates inflation. Spatial infinity is Tegmark's Level I, while eternal inflation is Level II. Eternal inflation gives rise to some more variation in physical laws than a 'normal' infinite universe, but not anything qualitatively new (if an infinite universe contains everything computable, it contains simulations of every possible set of computable physical laws). As for timing, well, see this comment by Mitchell Porter.

The role of eternal inflation in scientific Eternal inflation and its implications 10 thinking,

You've got some extraneous text there.

Comment author: Kevin 26 May 2010 06:48:40AM *  6 points [-]

In case anyone downmodded this for using the term "Shock Level 5", I agree that some of the broad or specific implications of the Tegmark Level 4 Multiverse can be called Shock Level 5.

Comment author: MichaelVassar 28 May 2010 04:45:34PM 5 points [-]

I have just tended to think of this as being how SL4 looks when you have digested it and are no longer shocked. Really though, I just think its a slightly good social rule to avoid creating self-aggrandizing terminology.

Comment author: Vladimir_Nesov 26 May 2010 12:09:02AM 5 points [-]

What you discuss is a question of decision theory, whether there is something besides the apparent environment to care about, and that hardly depends on the way physics is. One doesn't need little "exists" tags on hypotheticals in order to care about them. They probably help, but are not a defining factor, certainly not for the decision theory, before you take into account the finer details of the content of morality.

Comment author: Vladimir_M 26 May 2010 02:18:19AM *  4 points [-]

A competent and comprehensive critique of the ideas from your post would require much more thought and background reading than I've invested into it so far, but nevertheless, this key part strikes me as problematic:

[I]f you combine a functionalist view of mind with big worlds cosmology, then reality becomes the quotient of the set of all possible computations, where all sub-computations that instantiate you are identified.

To talk about a quotient set or quotient space, you need a well-defined equivalence relation. But what would it be in this instance? The set of all possible computations that "instantiate you" in any meaningful sense is necessarily an extremely fuzzy concept, for reasons I'm sure I don't need to elaborate on here. So what exactly gets to be included into "your 'now'"?

One way out of this, I suppose, would be to note that once you unwrap all the definitions, every mathematical object in ZFC is a set (of sets of sets of... -- perhaps infinite, and with empty sets as "bottom" elements), and then define "your 'now'" as the class of sets that contain subsets (or sub-sub-...-sets) that are exactly isomorphic to some "yardstick" set that represents "your 'now'." (I.e. those instances of "you" that are different in any detail at all are in a completely different class, and have no more relation to "you" than any other ones.) Similar could be done, of course, not just in ZFC but in any other theory that is sufficient to formalize standard mathematics.

Is this anywhere close to what you have in mind, or am I just rambling in complete misapprehension?

Comment author: RolfAndreassen 26 May 2010 12:25:41AM 8 points [-]

You seem to be using 'infinite' as a synonym for 'very large', which is sloppy at best and actively misleading here. MW does not of itself imply infinite copies of you, but merely very many copies. To get actual infinities requires additional assumptions which you have not supported or even mentioned. Large numbers can be compared in ways that infinities cannot; if there are really infinitely many copies of you then your decision makes no difference, but if there are merely very many, then there is a sensible way in which a good decision increases the total goodness/badness ratio of the multiverse. Confusion of these two concepts is very bad. Please stop, or back up your assertion of infinitudes.

Comment author: AlephNeil 26 May 2010 01:30:42AM 3 points [-]

Think about the wavefunction of a single electron. It specifies an amplitude for the electron to be found at any point in space. And there are continuum many such points. Now, the sense in which MWI states that there are many different 'copies' of you all simultaneously existing corresponds to the sense in which 'copies' of the electron are found (with various different amplitudes) at every point. A 'copy' of the electron = one of its possible locations.

So since there are continuum-many copies of an electron, I think it's fairly safe to assume there are at least continuum-many copies of a 'human'.

Of course, there may be a sense in which, although every possible configuration of the elementary particles in your body is assigned some amplitude, almost all of the amplitude gets 'concentrated' into a small number of 'rivers' of relatively much higher probability. For instance, the 'river of probability' for Schrödinger's cat will split into a 'live cat' branch and a 'dead cat' branch. Each branch is smeared over infinitely many configurations, and there are infinitely many configurations not belonging to either branch, which also get some non-zero amplitude, but nonetheless the two 'main branches' cover almost all of the probability mass, and thus they stand out as real patterns - as real as 'planets' or 'stones'. It is in this sense, I think, that you mean to say there may only be "finitely many" copies of a person.

But this kind of finiteness doesn't suffice to defuse the reasoning which led you to say "if there are really infinitely many copies of you then your decision makes no difference". (The resolution, of course, is to abandon that reasoning.)

Comment author: Douglas_Knight 28 May 2010 12:18:32AM 1 point [-]

Think about the wavefunction of a single electron. It specifies an amplitude for the electron to be found at any point in space. And there are continuum many such points.

It does not specify an probability for each point, but a density, which is only turned into an probability by integrating. The probability of being at a particular point is zero. More strongly, the system has countably many qubits.

Comment author: AlephNeil 28 May 2010 01:34:15PM *  0 points [-]

Sure.

So we agree: far from there being 'only finitely many copies', if there's any sense at all to be made of the 'number of copies' then it is infinite and any (or 'nearly any') possible configuration of the matter making up your body gets some non-zero density or probability depending on whether by configuration we mean a 'point' in phase space (if that's the right term...) or a little 'cube'.

Comment author: Douglas_Knight 28 May 2010 02:43:30PM *  0 points [-]

Your original post is correct. I think "continuum-many" is misleading, but I can't object much given the context. I don't remember what I was thinking.

ETA: I would think of an eigenbasis and say that there are countably many electrons, none of which is localized.

Comment author: RolfAndreassen 27 May 2010 11:13:53PM 0 points [-]

I am not certain what you mean by 'continuum-many'; it sounds as though it could be either 'infinite' or 'the large number you get from a lot of combinatorics'. However, I must point out that quantum theory has the interesting property of being quantized. (Sounds almost like a lolcat slogan. "Kwantum fyziks... iz kwantised.") A particle in a bound state does not have infinitely many degrees of freedom, and since our local spacetime is apparently closed (if only just) every particle is in a bound state, it's just not obvious.

Comment author: AlephNeil 29 May 2010 01:15:02PM 1 point [-]

I am not certain what you mean by 'continuum-many'

It refers to cardinality. You know Cantor showed that, while natural numbers and rationals can be put into one-to-one correspondence, there is no way to put the reals into one-to-one correspondence with the naturals, because there are 'too many' real numbers? Well, "continuum-many" means "the same cardinality as the real numbers".

Still, Douglas Knight makes a fair point - it is somewhat misleading to talk about continuum-many copies if each one has zero probability. In truth, I guess the concept of a 'number of copies' is too simple to capture what's going on.

As for particles being in bound states and having finitely many degrees of freedom: I'd be surprised if it altered the 'bigger picture' whereby all possible rearrangements of the matter in your body (or in the solar system as a whole, say) get some (possibly minuscule) amplitude assigned to them. (Of course, ideally it would be someone who actually knows some physics saying this rather than me.)

Comment author: RolfAndreassen 29 May 2010 09:11:33PM 1 point [-]

"continuum-many" means "the same cardinality as the real numbers".

Ok, fair enough. In that case I must merely disagree that there exist this many possible arrangements of matter; it seems to me that the arrangements are actually countably infinite.

As for particles being in bound states and having finitely many degrees of freedom: I'd be surprised if it altered the 'bigger picture' whereby all possible rearrangements of the matter in your body (or in the solar system as a whole, say) get some (possibly minuscule) amplitude assigned to them.

That's true, but the question is whether that number has the cardinality of the reals or the integers. I think it's the integers, due to the quantisation phenomenon in bound states; everything is in a bound state at some level. After my last post it occurred to me that the quantised states might be so close together that they'd be effectively indistinguishable; however, there would still be a finite number of distinguishable states. Two states are not meaningfully different if a quantum number changes by less than the corresponding uncertainty, so in effect the wave-function is quantised even in a continuously-varying number. Once you quantise it's all just combinatorics and integers.

Comment author: PlaidX 26 May 2010 07:55:08AM 0 points [-]

I don't think you're right... isn't it broken down into plank lengths or something?

Comment author: AlephNeil 26 May 2010 04:03:25PM 1 point [-]

::Shrug:: There's something important about the Planck distance, but I don't know enough physics to be able to say much more. Like Hawking radiation, It's something that only crops up when you start trying to do 'quantum gravity'.

It's tempting to imagine that the universe is something like the "Game Of Life" but with Planck sized cells, but what little I know about string theory makes this idea seem extremely naive. (And anyway, space could be both discrete and infinite.)

Comment author: Nick_Tarleton 29 May 2010 05:21:06AM *  0 points [-]

IANAPhysicist, but I'm fairly sure that space and time are entirely continuous in standard QM or QFT, though they are discrete in loop quantum gravity and possibly other theories of QG.

Comment author: Douglas_Knight 29 May 2010 05:17:34PM 1 point [-]

Standard QFT doesn't have discrete space and QCD may make sense with continuum of space-time, but models with a Landau pole, like QED and the standard model, don't make sense at small length scales. The length at which the Landau pole appears in QED is smaller than the Planck length, so no one cares about it, since they expect bad things to happen already at the Planck scale.

Comment author: Tyrrell_McAllister 26 May 2010 01:12:28AM *  3 points [-]

MW does not of itself imply infinite copies of you, but merely very many copies. To get actual infinities requires additional assumptions which you have not supported or even mentioned.

The version of "many worlds" that Roko is talking about is not that of QM. Rather, it is the one where "all structures that exist mathematically also exist physically". According to the conventional understanding of "mathematical existence", there exist infinitely many mathematical structures that contain a copy of me.

Comment author: RolfAndreassen 27 May 2010 11:14:43PM 0 points [-]

Nu. I have got to say that I don't see any good evidence for that piece of philosophising.

Comment author: Jordan 26 May 2010 12:37:21AM 3 points [-]

if there are really infinitely many copies of you then your decision makes no difference, but if there are merely very many, then there is a sensible way in which a good decision increases the total goodness/badness ratio of the multiverse.

I don't see that it matters either way, provided there is a probability distribution over the set (finite or infinite) that gives your subjective experience. Can you explain your reasoning more?

Comment author: ata 26 May 2010 12:01:37AM *  5 points [-]

And in other mathematically possible universes with the ability to do an infinite amount of computation in a finite time, you could be simulated an infinite number of times in just one universe.

Are there "mathematically possible universes with the ability to do an infinite amount of computation in a finite time"? Wouldn't that render that entire universe noncomputable, and is there any version of the mathematical universe hypothesis in which noncomputable universes are admitted?

Think that chocolate bar will taste nice when you bite into it? Well, actually according to Big Worlds, infinitely many of your continutions will bite the chocolate bar and find it turns into a hamster.

...and that's the big (apparent) problem with MUH that I'm still trying to figure out. If that line of reasoning is true, then why don't we observe arbitrary irregularities like that? I mentioned a few possible solutions around the end of my post about it, but I'm not too confident in any of them; I don't quite know how to think about this yet. (I'm still not convinced that Occam's Razor helps. Suppose we're considering ten universes: one where the chocolate bar you're about to bite into remains a chocolate bar, and nine where it turns into various things. If these were somehow the only possible universes, then you'd estimate a .9 probability of the chocolate turning into something weird, and 9 of you would be right. I don't see why using Occam's Razor to assign greater probability to simpler universes would actually work here.)

Almost all of the histories and futures that feed into your "now" are simulations, by Bostrom's simulation argument (which is no longer shackled by the requirement that the simulations must be performed by our particular descendants - all possible descendants and aliens get to simulate us).

If MUH is true, then the simulation argument doesn't matter anyway; a given universe is real and continues to be real whether or not anybody is simulating it.

However, there may be strong instrumental reasons to take SL5 seriously if it is true (and there are strong reasons to believe that it is).

What are some of those instrumental reasons?

Comment author: Jordan 26 May 2010 12:31:48AM 1 point [-]

What are some of those instrumental reasons?

Applied quantum suicide. If we are in a Big World then all we really care about is probabilities, and we can modify those probabilities by selectively removing ourselves from particular universes.

Comment author: RichardKennaway 28 May 2010 10:42:42AM 2 points [-]

Applied quantum suicide. If we are in a Big World then all we really care about is probabilities

I've never taken quantum suicide seriously, even given MWI. You speak of probabilities, but what about measures? How do I gain by ensuring that the vast majority of possible futures do not contain anything resembling me, even if the majority of those that do give me a lottery jackpot? All I'm doing if I blow myself up for failing to win the lottery is erasing the overwhelming majority of my future selves, who if asked would very likely object.

Comment author: Jordan 28 May 2010 09:45:42PM *  1 point [-]

Certainly, if you choose to care about total measure, by all means do so. Personally, I care about subjective experience, and couldn't give a blast what my total measure throughout the multiverse is (except insofar as it effects the subjective experience of other people).

Comment author: AlephNeil 26 May 2010 12:58:12AM *  3 points [-]

Applied quantum suicide.

The philosopher David K Lewis has already supplied (pdf warning) a reductio of 'quantum immortality' - the basic problem is that you're more likely to end up crippled than healthy. (And if you're crippled then you're in no position to do lots of snazzy instrumental stuff.) See page 21.

Though Lewis himself doesn't actually carry his reasoning forwards this far, we can finish off: Since the distinction between a crippled, almost-extinct mind and no mind at all is a blurry continuum, with no non-arbitrary way of measuring places along it, the event "you survive your attempted suicide" is not even well defined, and neither is "the probability that you survive", nor "the probability that you are crippled, given that you survive".

The whole notion of 'quantum immortality' is monumentally confused. Putting a gun to your head, firing and seeing whether you find yourself in a quantum miracle-world with virtually zero probability is exactly as reasonable a test of the many worlds interpretation as seeing whether a third arm spontaneously erupts from your chest.

Comment author: Jordan 26 May 2010 04:01:46AM *  8 points [-]

Putting a gun to your head, firing and seeing whether you find yourself in a quantum miracle-world with virtually zero probability is exactly as reasonable a test of the many worlds interpretation as seeing whether a third arm spontaneously erupts from your chest.

Agreed. I'd never go about it that way. If I wanted to test the many worlds interpretation I'd do the following:

Strap a few pounds of high explosives around my head and connect the detonator to a computer. Have the computer select a random number between 1 and 1000 via some unbiased quantum process. Program the computer so that if any number greater than 1 is generated the detonator is activated, otherwise have it do nothing. Run the program. Run it again. And again, until I'm satisfied the the many worlds interpretation is correct.

The important things, in my opinion, are:

  • The method of death should be faster than most thought processes. Blast velocities are typically greater than the traveling speed of action potentials. This ensures you don't accidentally observe something that commits you to a world with an almost sure probability of death (in the realm where only 'magical' quantum effects could save you).
  • The probability that the method of death fails to kill you should be thousands of orders of magnitude smaller than the probability that the method is never activated at all. In the case of my above example, the probability of finding yourself in a universe where you survived a high explosive blast at point blank range is essentially zero compared to the probability of getting 1 out of a 1000.

Note, with my above setup, it is very easy to transition from testing the many worlds hypothesis, to actually using it to your advantage. Want to factor a large number? Randomly sample the solution space on your computer, detonating only if the random sample isn't a solution. (Make sure to implement an initial fail-safe probability in case no solution exists!)

Comment author: JoshuaZ 26 May 2010 04:05:25AM 5 points [-]

Note, with my above setup, it is very easy to transition from testing the many worlds hypothesis, to actually using it to your advantage. Want to factor a large number? Randomly sample the solution space on your computer, detonating only if the random sample isn't a solution. (Make sure to implement an initial fail-safe probability in case no solution exists!)

There's an old joke about this related to the problem of sorting lists. A proposed sorting method is to take what you want, and randomly rearrange it. If that isn't sorted, destroy the universe.

Your approach seems directly inferior from a utilitarian perspective because it will lead to many universes where not only did you fail to factor it but the rest of us will miss your company (and be stuck cleaning up a large mess).

Comment author: Jordan 26 May 2010 04:25:50AM 6 points [-]

Your approach seems directly inferior from a utilitarian perspective because it will lead to many universes where not only did you fail to factor it but the rest of us will miss your company (and be stuck cleaning up a large mess).

The solution, of course, is to replace high explosives with the LHC.

Comment author: kodos96 27 May 2010 10:23:14PM 0 points [-]

Note, with my above setup, it is very easy to transition from testing the many worlds hypothesis, to actually using it to your advantage. Want to factor a large number? Randomly sample the solution space on your computer, detonating only if the random sample isn't a solution.

This is the most awesome idea I've heard all day. But you could do a lot better than factoring large numbers - you could set it up to detonate only if the random number is not the winning lottery pick!

I'll be in my basement rigging the explosives.........

Comment author: Jordan 28 May 2010 06:52:54AM 3 points [-]

But you could do a lot better than factoring large numbers

Oh yeah. You can solve any problem in PSPACE. You can basically directly sample the entire space of all programs (with bounded memory).

Screw the lottery. You could make trillions on the stock market. Afterwards sample the entire space of all love letters, send them off to famous movie stars, then detonate only if you don't get an eager response back. You might need a delegate to read the letter, as you reading it personally would shunt you into particular universes.

Comment author: kodos96 28 May 2010 07:40:25AM *  -1 points [-]

You could make trillions on the stock market. Afterwards sample the entire space of all love letters, send them off to famous movie stars

But would you really need the love letters if you had the trillions? I'd think a bank statement would suffice.

ETA: Ok, I'm confused. What's going on with the downvoting? I'm honestly not concerned at all about the karma, just mystified.

Comment author: Blueberry 28 May 2010 02:24:30PM 0 points [-]

I downvoted because of the cynicism expressed in the idea that money can buy love. It read like a bitter complaint that girls (or guys) just want money.

Comment author: RobinZ 28 May 2010 02:57:13PM 0 points [-]

More to the point, it's not well substantiated that the individuals in question would be drawn to riches - there are many people who are, but not nearly 100% of the population. I met a woman who once had a member of The Eagles chatting her up and turned him down.

Comment author: tut 28 May 2010 02:58:13PM 0 points [-]

Upvoted kodos and downvoted you because I don't see that cynicism in the grandparent.

Comment author: Blueberry 28 May 2010 03:01:27PM *  0 points [-]

Downvoted you for downvoting me for explaining why I downvoted kodos.

ETA: The cynicism was in saying that money could replace love letters. Also, the original post was about quantum suicide and using it to find the most effective love letter, and the comment about money sort of missed the point, and read like a cheap shot against love.

Comment author: AlephNeil 26 May 2010 04:31:53AM *  0 points [-]

That's exactly as reasonable a test of the many worlds interpretation as 'flipping a coin' (or a quantum version thereof) lots of times and seeing whether you get all heads.

Oh, and I don't think you've factored in Lewis' point yet. What he's saying, in essence, is that you can 'never really die'. Even when the explosion goes off, the destruction of your head will have to proceed one micro-event after another, and if any one of those micro-events should be one that would finally 'extinguish' your consciousness then your awareness will (by the logic of quantum immortality) 'jump ship' to the somewhat-less-likely world where it doesn't happen.

So you'll end up 'finding yourself' in one of the fantastically unlikely worlds where the explosive only maims you.

Comment author: Jordan 26 May 2010 04:49:46AM 5 points [-]

So you'll end up 'finding yourself' in one of the fantastically unlikely worlds where the explosive only maims you.

This is precisely what my example avoids. There are substantially more worlds where you got a 1 and there was no explosion, than worlds where there was an explosion but you somehow managed to survive.

Comment author: AlephNeil 26 May 2010 05:09:46AM 0 points [-]

Hmm. OK, you have a point there.

Still, the mere fact that if your reasoning is valid then it must also be true that (as explained above) "you can never really die" constitutes a reductio.

Alternatively, if you want to say that your consciousness really can cease as long as it happens gradually, then how can there be possibly be a principled boundary line between 'sudden enough that you'll survive' and 'not sudden enough'.

You spoke earlier of making sure that the method of death was faster than most thought processes, so as to avoid 'committing yourself' to a world where you die. But where's the boundary between 'committing yourself' and not doing so? Can you "only partially" commit yourself? How would that work?

Doesn't make sense.

Comment author: Jordan 26 May 2010 06:56:30AM 1 point [-]

Doesn't make sense.

Nope, it doesn't. Unfortunately, we don't need the many worlds hypothesis to run into this trouble. The trouble already exists in this single universe, assuming consciousness is computable. Just replace quantum world splitting with mind copying. Check out the Anthropic Trilemma.

But where's the boundary between 'committing yourself' and not doing so? Can you "only partially" commit yourself?

If I make an exact copy of you, wait X minutes, and then instantly kill one of you, how big must X be before this is murder? Beats me. I suspect there is no hard line.

Comment author: LucasSloan 27 May 2010 10:05:58PM *  1 point [-]

If I make an exact copy of you, wait X minutes, and then instantly kill one of you, how big must X be before this is murder? Beats me. I suspect there is no hard line.

I would be willing to undergo such a procedure for 10 dollars if X is a minute or less (and you don't kill me in front of me, no other adverse effects, etc.). If X is 10 minutes, probably about 100 dollars.

Comment author: AlephNeil 26 May 2010 12:11:44PM *  0 points [-]

Interesting post!

Personally I think the third option is 'obviously correct'. There isn't really such a thing as a 'thread of persisting subjective identity'. And this undermines the idea that in the quantum suicide scenario you should 'expect to become' the miraculous survivor.

All we can say is that the multiverse contains 'miraculous observers' with tiny 'probability weights' attached to them - and we can even concede that some of them get round to thinking "hang on - surely this means Many Worlds is true?" But whether their less unlikely counterparts live or die doesn't affect this in any way.

Comment author: Nick_Tarleton 28 May 2010 10:55:46AM 1 point [-]

We can modify probabilities conditional on the existence of future versions of ourselves, but those aren't necessarily the only probabilities we care about.

Comment author: rwallace 26 May 2010 07:39:06AM 0 points [-]

My antidote to this particular variety of universal acid in general and quantum suicide in particular: http://lesswrong.com/lw/208/the_iless_eye/

Comment author: loup-vaillant 27 January 2012 10:18:15PM 2 points [-]

Personally, I think that Shock Level 5 could be seen as emotionally dangerous for a human to take seriously, so beware.

Oh yes. I have already used Many Worlds Interpretation as a rationalization for not signing up for Cryonics. Arguing quantum immortality, in fact. But an uneasy sense of completely going crazy pointed out the fact that quantum suicide wouldn't be a good idea anyway, for my relative would be very sad in the universes where I don't exist.

Phew. I'm not (too) crazy. Yet.

Comment author: MichaelVassar 28 May 2010 04:36:32PM 2 points [-]

I don't find it to be emotionally dangerous. Rather, it resolves multiple emotional dangers from earlier surprises.

Comment author: rosyatrandom 26 May 2010 01:36:08PM 2 points [-]

I like the use of the quotient set here. In fact, I would go on to use it more comprehensively: not only does our observer-moment define an equivalence class, but any particular context implementing it does, too. It could be a simulation, or a simulation in a simulation in a (...), a small corner of a more general mathematical system, anything. The point is that for any and every defined part, it too will always be part of a quotient; there will always be an indistinguishability of what's happening below.

As a result of this: does it mean anything to be 'a simulation'?

My own current thinking is that the Born rule - the everydayness of everyday life - is a reflection of how consciousness must function. I am just not entirely sure how yet...

Comment author: Nick_Tarleton 26 May 2010 09:58:41AM 2 points [-]

Shock Level 5 is a good candidate for Dan Dennett's universal acid: an idea so corrosive that if we let it into our minds, everything we care about will be dissolved. You can't change anything in the multiverse - every decision or consequence that you don't make will be made infinitely many times elsewhere by near-identical copies of you. Every victory will be produced, as will every possible defeat.

I'm surprised this didn't link to Bostrom's Infinite Ethics [pdf].

Comment author: timtyler 26 May 2010 07:13:52AM 2 points [-]

"Almost all of the histories and futures that feed into your "now" are simulations, by Bostrom's simulation argument"

That isn't the conclusion to the simulation argument that Bostrom usually gives.

Comment author: CronoDAS 26 May 2010 08:23:12PM 5 points [-]

I'm going to assume it all adds up to normality and live as though I only exist in a single world. :P

Comment author: Christian_Szegedy 26 May 2010 08:47:47PM 10 points [-]

The statement It all adds up to normality. as far as I can trace back, was just a simple practical recognition that the MW interpretation of quantum mechanics was consistent with our everyday experience.

A simple, objective, true statement without any imperatives or any overreaching philosophical implications.

Unfortunately, over the time, it became a popular mantra to be repeated every time someone expresses some inconvenient sounding ontological statement that does not fit someone else's warm cozy Star Trek world view.

"It could be, but don' think about that. It always adds up to normality,. anyways... *

Isn't it?

Comment author: cousin_it 26 May 2010 02:56:49AM *  5 points [-]

But chocolate bars don't turn into hamsters. The universe is predictable. Why are we discussing this stuff when we already know it isn't true?

Comment author: Peter_de_Blanc 26 May 2010 07:37:45AM 7 points [-]

Some universes are predictable. Others are predictable until tomorrow, and after that, chocolate bars turn into hamsters.

Comment author: cousin_it 26 May 2010 11:29:52AM 0 points [-]

I'm talking about our universe. Don't try to confuse me.

Comment deleted 26 May 2010 11:41:41AM [-]
Comment author: cousin_it 26 May 2010 12:14:22PM *  5 points [-]

What makes you think so? Pure shock value?

I'm willing to (provisionally) believe in MWI, but not Tegmark's ensemble. You haven't provided any actual evidence why the latter is true, and chocolate bars indicate that it's almost certainly false. Here's the cousin_it scale of science-worthiness:

  1. This is true.

  2. This works.

  3. This sounds true.

  4. This sounds neat.

From the looks of things, you have yet to rise above level 4.

Comment deleted 26 May 2010 01:21:05PM [-]
Comment author: MichaelVassar 28 May 2010 04:48:19PM 3 points [-]

No. That's just one small part of the evidence, far from sufficient and I would say far from necessary. By itself, these ideas would cause me to say "so much the worse for chaotic inflation theory" which is, as far as I know, not terribly well confirmed (or more to the point, not terribly clear in its proper interpretation).

Comment author: cousin_it 26 May 2010 01:29:13PM *  0 points [-]

If I understand it correctly, chaotic inflation theory implies a multitude of universes with differing but stable physical laws, not a multitude of universes that evolved just like ours but will soon begin turning chocolate bars into hamsters.

Comment author: Peter_de_Blanc 26 May 2010 08:43:30PM 7 points [-]

If arbitrarily large universes exist, then there would be people with arbitrarily large computers running every possible program. From that you would get worlds in which chocolate bars turn into hamsters.

Comment author: Will_Newsome 26 May 2010 08:49:15PM 4 points [-]

Question: Tegmark, in one of his multiverse papers, suggests that ordering measure by complexity seems to be an explanation for finding ourselves in a simple universe as well as a possible to answer to the question 'how much relative existence do these structures get?' My intuition says rather strongly that this is almost assuredly correct. Do you know of any other sane ways of assigning measure to 'structures' or 'computations' other than complexity?

Comment author: JohannesDahlstrom 27 May 2010 08:59:15PM 1 point [-]

Could you elaborate? It seems to me that because there exists a much greater number of complex computations than there are simple computations, we should expect to find ourselves in a complex one. But this, obviously, does not seem to be the case.

Comment author: cousin_it 27 May 2010 12:32:16AM 0 points [-]

Doesn't follow at all. A large variety of physical laws and universe sizes doesn't imply arbitrarily large computers. It's quite possible that sentient life that can build computers exists only in universes with parameters very much like ours, and our particular universe seems to have hard physical limits on the size of computers before they collapse into black holes or whatever.

Comment author: MichaelVassar 28 May 2010 04:49:24PM *  3 points [-]

Who said anything about sentient life? Arbitrarily numerous computers should simply emerge, within this universe though not this Hubble volume, and should run every computation.

Comment author: JoshuaZ 27 May 2010 12:40:37AM 1 point [-]

our particular universe seems to have hard physical limits on the size of computers before they collapse into black holes or whatever.

There's no upper limit on the size of a computer in our universe. Black holes are only a problem if you assume a very dense computer.

Moreover, it isn't that hard to construct hypothetical rules for a universe that could easily have arbitrarily large Turing machines. For example, simply using the rules of Conway's Game of Life.

Comment author: orthonormal 27 May 2010 02:33:21AM 2 points [-]

Rather, what we know (anthropically) is that the typical observer-moment comes from an ordered history within a big, simple universe. If the universe works as we think it does (just assuming MWI, not Level IV), then there do exist Boltzmann brains in the same state as my current brain, and some of them have successor states where they do see the chocolate-hamster singularity.

But the measure of those observer-moments is dwarfed by the measure of the observer-moments in orderly contexts, or else my memories wouldn't match my experiences and my current experiences would be highly unlikely to be this low in entropy.

Comment author: thomblake 26 May 2010 03:04:32PM 1 point [-]

But chocolate bars don't turn into hamsters. The universe is predictable. Why are we discussing this stuff when we already know it isn't true?

Chocolate bars have a very low probability of turning into hamsters. A chocolate bar is one configuration of elementary particles, and a hamster is another, and there are lots of particles that may or may not be in the space of that chocolate bar at any given point in time.

Our universe is predictable, in that very low probability events happen with a very low frequency, but this does not entail that very low probability events never happen.

Comment author: John_Maxwell_IV 26 May 2010 06:09:04AM 2 points [-]

Damn, I guess God does exist.

Comment author: Wei_Dai 29 May 2010 05:56:22AM 1 point [-]

Modal realism by itself seems no more shocking than superintelligence and the Singularity (i.e., SL4):

  • Modal realism and the Singularity have followed comparable timelines of development. Modal realism was first proposed by David Lewis in 1968, the Singularity by Stanisław Ulam in 1958 and I. J. Good in 1965. The everything-list was created in 1998, SL4 in 1999 or 2000.
  • Jürgen Schmidhuber and Max Tegmark both supported versions of modal realism before (publicly) declaring themselves to be Singularitarians, so apparently the former is not more shocking to academia than the latter.

The two ideas put together might have consequences more shocking than either of them alone, but since those are still highly speculative it's probably too early to declare a shock level 5.

Comment author: ata 29 May 2010 06:08:26AM *  1 point [-]

Agreed. I didn't find modal realism terribly shocking, and I learned of it / semi-independently figured out my own version of it before I had heard of much >SL2 stuff.

Then again, I seem to have gone straight from SL1 to SL4, with no discomfort. Maybe I'm just hard to shock? Even so, putting myself in the shoes of someone who needs to gradually move up through the shock levels, I don't think modal realism would be higher than the Singularity; at most I'd put it alongside it at SL4.

Comment author: MartinB 26 May 2010 10:03:02AM 1 point [-]

I didn't get which version of 'you exist multiple times' you use.

  • multiple people that look rather similar to you
  • multiple people that share your experiences for a certain period of time (comparable to branching)
  • multiple people that would be difficult for an outsider to distinguish, but still have major notable differences (differing inside experiences)
  • multiple people that share your exact sensory experience up until now completely - which basically implies a decent copy of the whole earth, and some of the surrounding space to make it really really similar
  • atomic/quantum identical copy - which needs both a copy of the earth, and then some, but also a high level of similar quantum events.

Each of these seems less often to exist in a finite universe. In an infinite they might all just hang around. But the later seems really really unlikely to ever happen.

Comment author: Tyrrell_McAllister 26 May 2010 01:20:11AM *  1 point [-]

I'm going to repost here (with minor editing) a comment that I left in the open thread:

I'm unclear about what the statement "All mathematical structures exist" could mean, so I have a hard time evaluating its probability. I mean, what does it mean to say that a mathematical structure exists, over and above the assertion that the mathematical structure was, in some sense, available for its existence to be considered in the first place?

When I try to think about how I would fully flesh out the hypothesis that "All mathematical structures exist" to evaluate its complexity, all I can imagine is that you would have the source code for program that recursively generates all mathematical structures, together with the source code of a second program that applies the tag "exists" to all the outputs of the first program.

Two immediate problems:

(1) To say that we can recursively generate all mathematical structures is to say that the collection of all mathematical structures is denumerable. Maintaining this position runs into complications, to say the least.

(2) More to the point that I was making above, nothing significant really follows from applying the tag "exists" to things. You would have functionally the same overall program if you applied the tag "is blue" to all the outputs of the first program instead. You aren't really saying anything just by applying arbitrary tags to things. But what else are you going to do?

Comment author: orthonormal 27 May 2010 02:11:23AM *  0 points [-]

At this point, I find it less awkward to talk about the existence of mathematical structures than to talk about what it would mean to "physically exist" if that doesn't mean "instantiated in some mathematical object". We take it too much for granted.

Comment author: Kevin 26 May 2010 05:22:45AM 0 points [-]

Have you read Tegmark's papers? http://space.mit.edu/home/tegmark/crazy.html You should read The Multiverse Hierarchy if you haven't.

Comment author: Tyrrell_McAllister 26 May 2010 05:27:43AM 0 points [-]

Have you read Tegmark's papers?

No, I am going by the characterization of the hypothesis given on LW.

You should read The Multiverse Hierarchy if you haven't.

Thanks for the link :). But I confess that I was hoping that someone could at least hint at Tegmark's answers to my questions. That would help me to decide whether reading the papers is worth it.

Comment author: Kevin 26 May 2010 05:36:18AM 2 points [-]

Sorry, I'm not sure how to satisfactorily answer your questions. Don't be intimidated by the paper though; Tegmark may be the best popular science writer out there and The Multiverse Hierarchy is written for a wide audience. It is not dumbed down; it just doesn't have any math. Even the "full-strength" paper is not very mathy in the scheme of physics papers.

Comment author: AlephNeil 26 May 2010 01:44:34AM 0 points [-]

I unclear about what the statement "All mathematical structures exist" could mean,

The idea is to abolish the distinction between 'mathematical existence' and 'physical existence' or, if you like, between 'possibility' and 'actuality'. Of course all mathematical structures exist as mathematical structures. But it's not obvious (to say the least!) that all mathematical structures exist in the same sense that the physical universe exists.

Comment author: [deleted] 26 May 2010 03:48:01AM 2 points [-]

If the physical universe were a purely mathematical structure - just part of the set of all ideas, implied by some rules of mathematics, but not existing in any way that 2+2=4 does not exist - then how would we, as part of the answer to a math problem, know the difference between that and 'really existing'?

Comment author: AlephNeil 26 May 2010 04:32:55PM *  3 points [-]

just part of the set of all ideas

For a start, we'd want to abandon the idea that mathematical structures are merely "ideas". A mathematician can have an idea of a structure, but the same abstract structure can often be conceived of in many different ways, and some structures are too complicated to be conceived of at all (e.g. a non-principal ultrafilter).

implied by some rules of mathematics

A structure (like the set of natural numbers together with its arithmetical operations) is not the same thing as a proposition (like "2+2=4" or "addition of natural numbers is commutative"). Structures satisfy propositions, and it may or may not be possible to systematically investigate the propositions satisfied by a structure by setting out 'axioms' and 'rules of inference' (both of which I suppose you'd call "rules of mathematics").

but not existing in any way that 2+2=4 does not exist

Better to say "not existing in any way that the numbers themselves don't exist".

how would we, as part of the answer to a math problem, know the difference between that and 'really existing'?

The real question here is "how is it possible for a mathematical structure to contain an intelligent observer?" Once you have an intelligent observer they can in principle teach themselves logic and mathematics, which will entail finding out about mathematical structures other than the one they're inhabiting.

Comment author: torekp 27 May 2010 01:34:32AM *  1 point [-]

But it's not obvious (to say the least!) that all mathematical structures exist in the same sense that the physical universe exists.

In the New Scientist version of Tegmark's mathematical universes paper he writes "every mathematical structure ... has physical existence." But what does "physical" add? When we learn the word "physical" as children we are referring to objects we see, feel, hear, etc., and to the laws of nature that describe them. But clearly a radically different mathematical structure, i.e. different from our laws of nature, is not on the same page, so to speak.

Consider ghosts. Suppose that ghosts exist pretty much as Hollywood depicts them, and also suppose that ghost behaviors and abilities follow (highly complex) mathematical laws, albeit radically different laws from QM and relativity. (Have I just supposed two contradictory things? I'm pretty sure I haven't.) Would ghosts then merit the label "physical"? I think they'd still be paradigms of the nonphysical, and the radical difference of the correct descriptions of ghosts versus particles would be the dead giveaway.

If we remove the (apparently unmerited) label "physical" and just assert that mathematical structures exist, there won't be much disagreement.

Comment author: Tyrrell_McAllister 26 May 2010 03:02:51AM *  1 point [-]

The idea is to abolish the distinction between 'mathematical existence' and 'physical existence' or, if you like, between 'possibility' and 'actuality'.

I understand that that is the intuitive idea. But how is the hypothesis to be formulated in such a way that we could evaluate its probability, even in principle?

Comment author: AlephNeil 26 May 2010 03:48:57AM *  1 point [-]

I wrote this some years ago: Sink the Tegmark!. As you can see, I share your skepticism as to whether there's enough sense to be made of Tegmark's theory that we can derive empirical predictions from it.

Even so, you should definitely read Tegmark's original papers - he does address this question somewhat.

Comment author: thomblake 26 May 2010 03:35:21PM *  0 points [-]

the Copernican revolution with respect to your place in the multiverse

This is interesting... I saw Luciano Floridi give a talk recently where he talked about the "information revolution" and its relationship to past revolutions (borrowing from Freud's history). To summarize:

  1. Copernicus displaced us from the center of the universe
  2. Darwin displaced us from the center of the biosphere
  3. Freud revealed that we're not fully rational and transparent to ourselves
  4. The information revolution (which he identifies with Turing) revealed that we're not unique in terms of our ability to process information and be part of information-processing systems

I'd swap Turing for Weiner, but that's really an unimportant turf war.

ETA: relevant paper - www.philosophyofinformation.net/publications/pdf/tisip.pdf - pdf warning

Comment author: orthonormal 27 May 2010 02:39:14AM 0 points [-]

Whoops, formatting issue.

Comment author: thomblake 27 May 2010 02:48:32AM 0 points [-]

Thanks. I'm not sure if it's the web app or Google Chrome.

Comment author: RobinZ 27 May 2010 05:03:04AM 0 points [-]

I've seen a lot of HTML errors from the Less Wrong page on every browser I've tried.

Comment author: PeterS 27 May 2010 05:13:29AM 2 points [-]

I've noticed that too. What's odder is that they seem to come and go. I have no evidence, but I swear that sometimes I'll see a link to google in a comment on one day, and the link rendered as /">google in the same comment on another day, etc. Strange.

Comment author: jimrandomh 27 May 2010 01:22:59PM *  1 point [-]

I have noticed this too. It looks like bytes get randomly corrupted or deleted during transfer. This would indicate a hardware problem. Next time I see it, I'll 'View Source' and observe exactly what's wrong with the HTML I received.

Comment author: Douglas_Knight 26 May 2010 05:06:04AM 0 points [-]

You attribute a lot of consequences (eg, determinism?!) to this multiverse that are already consequences of much more conservative theories. The only further consequence I see you mention is the problem of finite measure.

Comment author: Sniffnoy 26 May 2010 12:35:10AM 0 points [-]

I dont think that the multiverse of MWI can be sensibly identified with Tegmark's multiverse; if we accept the latter, the former is just one of the universes that makes it up. The multiverse of MWI is one, complete, standalone mathematical structure; it is perhaps a multiverse from our usual point of view, but from the Tegmark multiverse point of view, it should be considered as just one universe, of which we only care about a small part.

Comment author: Blueberry 26 May 2010 05:59:21AM 1 point [-]

Yes. Tegmark talks about four levels of multiverses: MWI is level 3, and the mathematical universe is level 4.

Comment author: Sniffnoy 26 May 2010 10:15:29PM 0 points [-]

Oh, hah, that was pretty silly of me. I'd forgotten that distinction.

On that note, ISTM that the "levels" don't really form a total order - rather than 0-1-2-3-4, it seems more like 0-1-2-4 and 0-3-4 with 3 incomparable to 1 and 2.

Comment author: Blueberry 26 May 2010 10:28:12PM 1 point [-]

Yeah, Tegmark says that level 3 doesn't give you anything bigger than 1 and 2 together do.

Comment author: MartinB 26 May 2010 10:06:18AM 0 points [-]

The subjective experience so far doesn't imply multiple parallel worlds influencing the same person similarly (at least my own experience does not). I don't really see how that is supposed to change. I also don't particularly care about people in unreachable worlds, that are very similar to me.

Comment author: Vladimir_Nesov 26 May 2010 10:44:36AM 0 points [-]

These observations don't contradict the (general message of the) theory.