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
EEEEGH MY KEYBOARD JUST TURNED INTO A BADGER!!11asdaghf
At least it's a QWERTY badger, from the looks of it...
your subjective experience has an equal chance of continuing down any branch
And just what does that mean?
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.
The OP was careful, it seems, to avoid that issue. (Infinite set agnosticism?)
In any case, our perceived history matches the Born rules too well for it to be reasonable that "probabilities are meaningless", so either the universe is OK with measures on infinite sets or it's somehow finite after all. (I incline strongly toward the former hypothesis, for reasons of mathematical elegance— thoroughly finitary versions of Hilbert spaces are hack-ish.)
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...
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 ...
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.
I'm going to assume it all adds up to normality and live as though I only exist in a single world. :P
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?
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.
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?
Some universes are predictable. Others are predictable until tomorrow, and after that, chocolate bars turn into hamsters.
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.
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?
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...
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...
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.
I don't find it to be emotionally dangerous. Rather, it resolves multiple emotional dangers from earlier surprises.
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].
"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.
Modal realism by itself seems no more shocking than superintelligence and the Singularity (i.e., SL4):
I didn't get which version of 'you exist multiple times' you use.
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&...
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:
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.
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.
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.
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.