If you’re a multiverse skeptic, you should know that there are many potential weaknesses in the case for parallel universes, and I hope you’ll find my cataloging of these weaknesses below useful. To identify these weaknesses in the pro-multiverse arguments, we first need to review what the arguments are.

via Are Parallel Universes Unscientific Nonsense? Insider Tips for Criticizing the Multiverse | Guest Blog, Scientific American Blog Network.

Max Tegmark seems to be everywhere these days. This is an interesting piece exploring the arguments for, and problems with, the various multiverse theories.

I have to admit that I’m a multiverse skeptic. I can appreciate that if a successful theory predicts something, we should take that prediction seriously. However, when that prediction is extraordinary, we should be cautious until we have empirical support. As Carl Sagan said, extraordinary claims require extraordinary evidence.

But Tegmark omits what I think is the biggest flaw in the multiverse, namely that there isn’t just one multiverse prediction. There are several. Each of the theories he mentions predicts a different type of multiverse. It’d be one thing if all of these theories converged on the same multiverse concept. I think I’d find that compelling. But they don’t.

I’m not closed minded about the multiverse. If someone found evidence that the multiverse was the simplest explanation for, I’d be much more willing to accept it. Until then, while it’s fascinating speculation, I’m going to keep firmly in mind that it is speculation.

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Thanks Eric.

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A very interesting article, but I would pick on a few issues.

His Level I parallel universes aren’t parallel universes as I understand them. It’s just one very large (possibly infinite) universe.

His Level III universes aren’t dependent on the Schrödinger equation, but on a particular interpretation of the Schrödinger equation. He’s being naughty here.

His Level IV universes are complete fantasy. I know that he says that “fantasy” is a a vague and unscientific criticism, but his level IV universes are precisely fantastic, so I feel justified in using the word. He is saying, as I understand it, that any universe we can imagine is just as real as the universe we live in. Worse than that, he is associating criticism of this idea with criticisms of the Level I-III multiverse theories, in an attempt to tar critics of his theory with the same brush as critics of inflation, etc. He even implies that critics of his fantasy universes are in the same boat as people who criticise the predictions of general relativity. That’s very naughty.

In fact, it’s a very naughty article all told. Is naughty a scientific word?

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Hi Steve,

It’s a short article. Read his book. He’s a lot more humble and fothcoming than you might think. He very very clearly distinguishes what is mainstream from what is controversial, and in particular emphasises that his Level IV multiverse is extremely so, to the extent that he was advised not to pursue it for fear that it might destroy his career.

The Many Worlds Interpretation is the only one which takes the Schrodinger equation at face value. The others generally do not, either positing hidden variables or objective wavefunction collapse in order to justify a unique universe.

I do think it is not fair to call the Level IV multiverse a fantasy. There are very good reasons to suspect it is true. Indeed I became convinced it was true even before I heard of Max Tegmark.

I explain why on my blog. I would genuinely be very excited if you could point out any particular flaw in my reasoning.

http://disagreeableme.blogspot.co.uk/2013/12/the-universe-is-made-of-mathematics.html

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I will take a look at your blog with pleasure, but at this point I don’t see any way even in principle of demonstrating that parallel universes exist. Of course they *could* exist – anything *could* exist outside our universe, although that is stretching the meaning of the word “exist.”

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Thanks Steve. You comment clarified some things for me. I agree on the Level I universe. It doesn’t even seem like the term “parallel” applies. I think for Level IV, I would use the term “speculative” rather than “fantasy”, since fantasy to me implies something that we know to be impossible. I don’t know if “naughty” is a scientific word, but it is a much friendlier one than others you might have used 🙂

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Hi SAP,

I disagree that the multiverse prediction is extraordinary. It’s an extremely simple idea that explains a lot. Indeed it would seem to me to be weirder if only one universe were possible. To me, it would be like if there were only one planet in the universe.

I have a post on my blog which explains why I think an infinite multitude is actually simpler than a single member of a set.

http://disagreeableme.blogspot.co.uk/2012/05/part-is-more-complex-than-whole.html

Even apart from the fact that multiverses are predicted from various theories, I think they have immense explanatory power when considered from the point of view of the anthropic principle.

I don’t see a problem with the idea that there are different kinds of multiverses. All of these multiverses are complementary. In fact, in his book Tegmark presents an interesting argument which unifies the Level I (Distant Space) and Level 3 (Many Worlds Interpretation) multiverses into one consistent whole.

Overall, I think the existence of the Level I (Distant Space), Level III (Many Worlds) and Level IV (MUH) multiverses is less extraordinary and simpler than their absence. I’m much less sure about the Level II (Endless Inflation) multiverse.

The existence of the Level I multiverse is essentially beyond doubt, I think. All that is required for this to exist is for space to extend beyond our cosmic horizon, which it certainly does and in fact seems to do for a very great (potentially infinite) distance based on measurements of the flatness of space.

The Level II multiverse is possibly correct, being predicted by some models of inflation. This is a scientific hypothesis because it could potentially be confirmed or falsified not by direct observation but by testing these various inflation models based on what we can glean about the early history of the universe.

The Level III multiverse is simply the most parsimonious straightforward interpretation of quantum mechanics there is. The traditional Copenhagen interpretation postulates the collapse of the wavefunction, without having any test for this or prediction of how it might work. It’s becoming increasingly obvious that this is a desperate post-hoc rationalisation which seeks to preserve our intuition of a single universe from what the equations actually predict. If quantum computation ever becomes a practical reality, Tegmark argues that this would be direct evidence of the multiverse, because it can be interpreted as having all the copies of a quantum computer performing the same computation with different variables in parallel, thereby covering a massive amount of ground in the time it takes for a single iteration. It’s hard to see how this could work with the other interpretations of QM. I agree though that this is perhaps not strictly science, because since all of the interpretations agree on the mathematical fundamentals of QM, it’s hard to see how one interpretation could ever be proven.

The Level IV multiverse is not scientific but neither is it nonsense, as you know I have argued on my blog.

I very much recommend that you read Tegmark’s book. I’m about halfway through it currently, and it manages to be engaging, personal and informative without ever beating you over the head with his particular world-view. Even apart from the multiverse stuff, it’s a great way to brush up on your cosmology and physics in general.

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Hi DM,

I’m familiar with the standard arguments for why the multiverse is simpler than one universe, but it just feels like just-so reasoning to me, and attempts to unify them sound almost like apologetics. It just goes to show that complexity and simplicity are matters of judgment, and some of us are going to have different intuitions about it. Whose intuition is right? Only time (maybe) will tell.

I have to admit that I don’t really understand how quantum computing is supposed to work, and I’ve been meaning to do some reading on it. It never made sense to me that, even if a qubit can be in superposition, how we can ever have access to more than one of those states? Wouldn’t the very act of accessing it cause a universe fork, wave function collapse, or whatever your favorite interpretation is? And if we can only ever have access to one, it seems like any work done by the other is lost, even if the many worlds interpretation is true. But I’m completely open that I may be missing some key fact here.

I may take a look at Tegmark’s book, but my current reading list is pretty long (and getting longer), so it may be a while. It might well move up on my list if it gets a lot of acclaim in the reviews.

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Quantum computing is based on the idea that we keep the qubits in superposition until the calculation is complete. We don’t fork the universe / collapse the wavefunction until the work is done. It’s a bit like juggling – you have to keep the balls in the air until the performance is over – if you drop one, you’ll have to start again!

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Thanks, but I’m still left wondering how we access the results of the work done on the side that doesn’t “win” on measurement. For that matter, how do we work with the qubit, manipulate it, without causing decoherence / wave function collapse / universe forking?

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The mechanics of accessing the results are complicated. Quantum computing algorithms are not like classical ones. Quantum calculations are reversible for one thing. Algorithm’s like Shor’s algorithm can be used to perform specific calculations.

Keeping the system in a coherent quantum state until the calculation is done is one of the big challenges, which is why you don’t have a quantum computer sitting on your desk. But room temperature calculations are looking promising, I believe.

That’s pretty much the limit of my expertise on the subject!

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Thanks for the explanation!

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Hi SAP,

Tegmark’s attempt to unify the Level I and Level III multiverse is interesting, but ultimately it doesn’t matter. They don’t need to be unified.

I disagree that complexity and simplicity are matters of judgement. There are mathematical ways to look at it, such as Shannon entropy, where the amount of information in a sequence is related to how much “surprise” we feel on seeing each bit.

Let me explain.

I think we intuitively feel that two universes are more complex than one, and three are more complex than two. Our intuition is correct. However it is not correct to extrapolate this to assume that unlimited universes are more complex than one. The maximum amount of entropy (complexity) is actually If each possible universe has an equal chance of existing or not existing with no rule to say which is the case. This is like tossing a fair coin, where there is one bit of information per universe to specify if it exists or not. The only way to describe this situation is to list out all the possible universes and say whether they exist or not.

As the probability moves away from 50%, the entropy goes down. If your coin is only 5% likely to show a heads, you will typically be able to express a sequence in much fewer bits than listing the whole thing out because you can just indicate the rare cases where the heads came up. The case where only one universe is impossible is exactly as complex as the case where only one universe is possible, and just as abritrary and prima facie unlikely. The case where no universes exist and the case where all universes exist are the simplest cases.

And as it turns out, both of these are compatible with the MUH. The MUH says that that the concept of existence as applied to universes doesn’t really work. They exist from one point of view but not from another. The real point is that the distinction between those that exist and those that don’t is simply incoherent. As both of the simplest cases show no such distinction, they are both compatible with the MUH.

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Thanks for the explanation. I can see an infinite number of universes being no more complex than 2 universes, but 2 through n universes still seems more complicated to me than the one we can observe.

Of course, there are aspects to reality that we can’t observe yet (or possibly ever), and those aspects might include additional universes. My understanding is that we don’t have empirical evidence to rule them out, but we also don’t have evidence to make them mandatory. (I know a lot of people feel like there’s enough in the mathematics to justify certitude. Personally, I need more than mathematical manipulations to give me certitude.)

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Hi SAP,

I’d be interested to know why you think an infinite number of universes is no more complex than two but more complex than one. I would also like to know which of 2, 1,000,000 or infinite universes is more complex/unlikely.

I agree that the MUH in particular is not science. But to me the philosophical and mathematical argument is convincing. From my point of view it can only be false if my reason has failed me in some way. And this is possible, but I see no problem in being very confident that it has not, for the same reasons that we feel confident about our capacity to reason in other contexts.

Lack of empirical evidence does not mean we ought to be squarely on the fence, as you seem to be (or perhaps leaning towards MUH-denial). We have no direct evidence for the proposition that God does not exist, but I don’t think either of us would judge the probability of God’s existence at 50%.

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Disagreeable Me, I left a comment on your blog about this. I questioned your assumption of mathematical platonism (the idea that mathematical objects have their own “existence” outside our universe. I put forward an argument for why I don’t think this can be true. Could you respond to that?

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Sorry, please ignore my latest comment. I see that you have left a detailed reply on your blog.

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Hi DM,

Well, to add a second universe requires positing a new dimension, a new parameter of existence. Once that dimension or parameter is there, once we have a second universe, then a third, fourth, etc, seems much more plausible. Actually, now that I think of it, once you have a second universe, stopping at a certain number would be an additional complication. But the whole realm of two or more universes is more complicated than just the one due to that additional dimension, parameters, or set of parameters.

The God comparison is interesting. A deistic god cannot be proven or disproven. However, the only thing it really has going for it is that a lot of people would like to see it exist. There’s nothing that makes its existence mandatory, so you’re right, I don’t regard the probability as 50%. It can’t be ruled out, but the number of possible concepts that can’t be ruled out is vast, but the number of concepts that actually exists is far smaller. The chances that one of our cherished concepts falls within the exists category is minuscule (although a small number will occasionally).

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Steve, do you have any follow up to the discussion on my blog?

Hi SAP,

I see where you are coming from now as you posit a new dimension to allow a second universe. You seem to conceptualise the current universe by analogy to a 3D Cartesian space, and the introduction of further universes as the extension of this to 4D. Points in a 3D space are defined by positional paramters (X,Y,Z), but now we need an extra parameter to locate ourselves in this larger space. Our universe would then be the set of all points for which W=0, say.

However I don’t see it like that at all. Unlike Cartesian points, universes in the MUH are not defined by their relative positions in some kind of space but by their laws of physics. In the Level IV multiverse, our universe is not above, under, before, after or beside any other. Everything required to “locate” it is there in its physics. This universe thus already has its “position” in the set of possible universes and no new dimension or parameter is required.

It seems to me that it is the case of a limited number of universes that requires another parameter. In addition to all the laws of physics, we must include a non-mathematical parameter to represent whether the universe exists or not. The only way this might not be true of a single universe scenario is if there is only one possible universe, one specific way the laws of physics could have been arranged (which could in principle be derived from the armchair). This seems highly improbable to me, to put it mildly.

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Hi DM,

You read in detail that I actually tried to avoid in my comment. It’s why I said “dimension or parameter”. However you construct it, it seems like you’re adding an extra characteristic to reality. An added attribute, dimension, parameter, characteristic, or whatever you want to call it, that by its very addition adds complexity, at least in my mind.

On your last point, in my mind, the complexity hierarchy, from high to low, is:

1. single universe

2. infinite universes (requires the extra (generic) dimension I mention above)

3. a finite number of universes (requires the extra dimension of 2. plus an additional constraint to limit the iterations)

Hope this makes sense.

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HI SAP,

Sorry for banging on about this, and sorry for apparently misinterpreting what you meant by parameter or dimension, but then I am lost as to what you do mean. What is this new parameter that is needed for two universes and not for one and what kind of value could it have?

I’m still left with the opinion that one universe requires an extra parameter that infinite universes do not. We presumably agree that there are effectively infinite possible universes, so if only one of those is actual, then does there not need to be a parameter to indicate which one of those it is?

I wonder how you feel about the question about whether it would be more surprising if it turned out that life had only arisen once in the universe or if there were countless instances of it. I personally would find the former scenario to be much more strange (infinitely more so if there is only one universe!). Do you also feel that two instances of life life arising need an extra parameter, or is this different from the universe case? If so, why?

Or we could make it more abstract. Suppose we found a very strange unique object of some kind floating in interstellar space (but that we had little reason to suspect that it was artificial). Perhaps it’s a lump of rock made of antimatter, for instance. Such a discovery would lead me to suspect that there were many other such objects in the universe. By your reasoning, this would seem to be unlikely, as it would mean the introduction of a new parameter or dimension to distinguish between them. This seems absurd to me, so I assume that this is not in fact your position, but that’s how it comes across to me.

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Hi DM,

I’m struggling to think of a way to explain the new parameter without repeating myself. Maybe this: Suppose on one hand you have X. Then suppose on the other you have a series of Xs. Isn’t the single X a simpler phenomena than the series of Xs?

On life elsewhere, when we conclude it’s probable that there’s life elsewhere in the universe, it’s because we

observelife here, weobservethat it arises from the laws of nature, weobservethat the laws of nature seem to exist everywhere, and weobservethe immensity of the universe. There’s still a logical step in our conclusion, but it seems far less tenuous.We haven’t observed another universe. We’re evoking multiverses to explain (excuse) the fact that we don’t understand this one. Again, I see the multiverse as a possible explanation, but can’t go past that until we see something that makes it mandatory, or at least compelling.

Here’s a question in the “turtles all the way down” tradition. If there were a multiverse, then why not a mult-multi-verse? Or a multi-multi-multi-verse? Where do we draw the line?

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Hi SAP,

I still don’t see the extra parameter in your series of X’s.

Is one X simpler than a series of X’s? Perhaps. It depends on questions such as whether X has any other properties or on whether the series is infinite. If X is an arbitrary integer, chosen with each integer having equal probability, then it is likely to be very large (as most numbers are), effectively infinite. As such, it would require an effectively infinite number of bits to precisely specify a single X. An infinite series of Xs however can be defined with only the axioms needed to define the integers.

On the analogy to life, I’m not exactly arguing that we ought to have precisely the same level of confidence that there is life elsewhere than that there are other universes, I’m just trying to understand how you perceive the relative complexity of the different scenarios. Perhaps you think that multiple origins for life is indeed more complex but that the evidence we have to bolster it still makes it the more reasonable position.

Do we observe that life arises from the laws of nature or do we infer that it does? Do we observe that the laws of nature are the same everywhere or do we infer that they are?

To paraphrase your comments about life, I would say that we observe that this universe exists, we infer that there is some explanation for how it is that the universe exists, and we infer that this same explanation could account for other universes. I would say it is also virtually certain that the set of logically possible universes is much vaster than what we directly observe.

But where these inferences may be less straightforward than those you make about life, I think they are bolstered by a pretty robust argument that the MUH must be true given naturalism, computationalism and Platonism.

How would you feel about a phenomenon for which we have no understanding? Such as a lump of antimatter? Would you feel an inference that there must be many such objects to be tenuous? Can you explain how your idea of the extra parameter or dimension fits in here, or indeed give any example where it would apart from universes?

“If there were a multiverse, then why not a mult-multi-verse? Or a multi-multi-multi-verse? Where do we draw the line?”

Well, in a way that’s what the MUH proposes, since the MUH encompasses lesser multiverses on multiple levels (e.g. Tegmark’s Levels I-III).

But it’s not turtles all the way down, because the MUH is so fundamentally simple. It is at core the proposition that all possible universes exist. By definition, any possible universe therefore exists inside the MUH multiverse. There can be no greater multiverse.

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Excellent book on this: “Why is there anything,” by fellow blogger, quantum physicist, and Many Worlds Theory advocate, Matthew Rave. It’s an easy read, a dialogue had between two characters, and details the argument quite convincingly.

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Disagreeable Me, when you write this:

“If X is an arbitrary integer, chosen with each integer having equal probability, then it is likely to be very large (as most numbers are), effectively infinite. As such, it would require an effectively infinite number of bits to precisely specify a single X.”

I cannot help but notice that this idea of bits used to represent X sounds like X can only exist in a physical universe (that contains bits), not in an abstract sense. In other words, numbers and other mathematical objects are instantiated.

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Hi Steve,

Bits are a mathematical concept, not a physical concept, although they do have significance for certain physical concepts such as entropy and the Holographic principle etc. Bits are relevant here because most definitions of complexity hold structures with more information (measured in bits) to be more complex.

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I’m no mathematician, but I’m comfortable with the idea of the infinite.

If X = anything you like

Then X needs no information to constrain it. It can be infinite. In fact it is.

But if X = 1 then I need to write an equation to constrain it that way. So an infinite number of objects is simpler than 1 or some other integer.

But no objects at all is the simplest possibility.

Another example. An empty page contains no information. This is the simplest configuration of the page. It contains no stories. If I write on the page, “Once upon a time a King lived in a forest,” then I have constrained the possible stories. But this is not yet an interesting story. The more information I add, the more constraints there are, until eventually I arrive at a single story. And this story will be rich, detailed and interesting. Our universe seems to me like that. So a single universe seems to be quite an unlikely occurrence. Most likely of all is the blank page.

So I can understand why (all possible universes) could be simpler than (our universe). But I don’t understand why we have any universes at all, if that is the logic.

As I say, I’m no mathematician. This is probably complete garbage.

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Hi Steve,

I would say that no objects is exactly as simple as all possible objects existing.

No objects: For all possible objects x; x does not exist.

All objects: For all possible objects x; x does exist.

The reason that all mathematical objects exist and not no mathematical objects is that it is logically impossible for no mathematical objects to exist. On a Platonist view of existence, a mathematical object exists if it can be defined consistently. It is possible to define mathematical objects therefore they exist. The laws of logic are not contingent, they are necessary, so it could not have been otherwise.

The most apt comparison to nothing existing is not the blank page, because the set of all possible states of the page includes the blank page (and there is an analogous mathematical structure, the empty set). The comparison to absolutely nothing existing would be the view that it is impossible for the page to be in a non-blank state (i.e. to compose a block of text containing more than zero characters), which is patently absurd.

By the way, I’d love to know if I have given you any reason to reconsider Platonism at all, or if you still feel comfortable dismissing Tegmark as a naughty fantasist.

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Yes, you have answered my questions well, and although I cannot say that I really believe in MUH or Platonism, I cannot say that they are clearly not true.

I think that by definition, Tegmark is a naughty fantasist, even if what he says turns out to be true! He conflates ideas that should not be conflated. Your way of reasoning is not naughty at all, but equally fantastic (fantastic can be a good or bad word, depending on your outlook).

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Thanks Steve,

Again, I’d encourage you to read his book. There’s a chance he comes across a little less naughty when he has the time he needs to explain his thinking more clearly.

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DM,

On the antimatter question, my initial thoughts would be that there may be more in the universe, but given the properties of antimatter and its reaction to matter, I would judge that it would have to be rare.

But you’re asking me about my thoughts of it existing within the universe, which is vast and observable, and equating that with the existence of other universes. If we could observe a vast multiverse and you then asked me if there were antimatter universes out there, I would give it a much higher probability than I can now, not having observed any other universes.

I also have to admit to being skeptical about Platonism, at least in any ontological sense.

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Again though, how would you use your thoughts about the complexity parameter or dimension to treat the antimatter question? Are you beginning to think that maybe that’s not the right way to think about such questions?

Yes, we can observe the universe and see that it is vast. For me, this is just like appreciating that there are many other ways the universe could be, even if we are only modestly tweaking the fundamental constants (or do you entertain the notion that there is something logically necessary about the way the constants are?). If there are many ways the universe could have been, it seems to me to be very strange that only one of those should be realised, like having only one sizeable lump of antimatter in a massive universe.

Rejecting the MUH on the grounds of not accepting Platonism makes a lot more sense to me than your arguments from complexity, although I still think it is wrong to reject Platonism!

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Hmmm. I thought I had addressed that question. Asking what the complexity of one or multiple lumps of antimatter in the universe, versus one or more universes, aren’t equivalent questions.

That said, would it be more or less complex if there were only one lump of antimatter in existence? I would think only one instance of an antimatter lump in the universe (assuming we had some way to know that) would be more complicated (probably related to our way of knowing about it).

On fundamental constants, I don’t know the reason why they are what they are. Multiverses are one possibility. Another is logical constraints of some kind. (Of course, then we’d be asking why those logical constraints? Turtles again.) Until we have reasons to isolate one particular explanation, I don’t think we should stop looking.

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Hi SAP,

If they’re not equivalent questions, that’s OK. Could you give any other example of a case where your reasoning about parameters or dimensions would apply?

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Hi DM,

Another name for what I’m talking about is Occam’s razor. Any situation where we multiply the assumptions beyond necessity would apply. So a light in the night sky is either an airplane or an alien from outer space. I’m sure you’d agree that we should assume it’s an airplane or some other mundane thing before we assume aliens, spirits, etc.

Now, I do know many people insist that multiple universes are simpler than one. But I don’t think we know enough about how this universe works yet to make firm conclusions. Maybe it is simpler, or maybe we just don’t yet understand why the laws and constants are the way they are.

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Sure, Occam’s razor is why I like the MUH. We have this concept of existence, and we have this concept of mathematical consistency. The MUH says that these are the same concept, or alternatively that we can do away with the concept of physical existence because it is meaningless.

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Disagreeable Me,

I think that’s one of the jumps I can’t make yet. Dismissing the concept of existence strikes me as violating Einstein’s advice that, “Things should be as simple as possible, but no simpler.” Our experience seems to show that existence or non-existence matters. This seems like a brute fact that we need more justification to dismiss.

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there are many great books that should be read. there are many great theory, and although they may seem sometimes ridiculous, you can not reject them before, at least not try to understand them, so you need something to read on this topic. however, in the case of this theory, one can completely abandon attempts to understand. it is a theory completely detached from reality. the problem is not that this theory doesn’t make sense. simply put, there can be no such reality. also very funny are evidence adduced to prove the existence of p.u; multiverse.

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