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This is going to be a long post, and I'm probably going to sound unreasonably angry in it, but I have been holding this in for far too long and need to get it off my chest. There are certain types of multiverses that I have seen wanked to absolute absurdity, the most egregious example being the Level III Quantum Multiverse, but I have also seen this for the Level IV Multiverse as well as a few others.
Specifically, there is a video by Kristian Kember () that wanks the Level III and Level IV Multiverses to ridiculous levels. He also wanks the Holographic Multiverse, but that isn't the focus of this rant, since I don't really see the Holographic Multiverse being used all that much in powerscaling debates. I seek to debunk the common arguments for the wanked scaling of the Level III Multiverse, as well as debunk Kember's arguments for his scaling of the Level IV Multiverse.
So, lets start with the Level III Multiverse. The common argument is that the Level III Multiverse is High 1-B because "the wave function rotates in infinite-dimensional Hilbert Space". I have seen multiple powerscaling Youtubers promoting this view. The problem is that the people who espouse this idea glance over a crucial detail; Hilbert Space is an abstract space.
IT'S NOT REAL.
It's just a tool for us to describe quantum states using mathematics. That's it. That's all it is.
We describe quantum states using vectors called kets. Since a quantum object can exist in a superposition of infinite different quantum states, this means infinitely many orthogonal vectors, and so we need an infinite-dimensional Hilbert Space to describe them all. But quantum states are not actually vectors in reality, we simply describe them that way because it makes the math easier to work with. The wave function is also not real as far as we know, it's exactly that; a function that describes the probability distribution of quantum states. So saying "the wave function rotates in infinite-dimensional Hilbert Space" doesn't ******* mean anything, because wave functions, kets, and Hilbert Spaces aren't actually things that exist in reality, they're just mathematical tools to describe reality.
I believe the reason this misconception has persisted for so long is due to an equivocation fallacy. For many powerscalers, the word "dimension" immediately activates the dimensional scaling monkey brain, and they start going off on absurdities like this, and it spreads like wildfire because it seems to make sense intuitively, it doesn't seem like an equivocation fallacy at first glance, but you understand that it is once you realize what's really going on. I myself have been guilty of this on occasion.
Now, before I talk about Kristian Kember's scaling of the Level IV Multiverse, I want to make clear that you are NOT to spread hate towards this man. I shouldn't even have to say this, but some people are actually insane and viciously attack anyone who disagrees with them. This is not what I intend to do, I simply wish to address something that's been bothering me. I don't think that Kember is a bad person or bad powerscaler, I actually agree with a lot of his takes, such as Platonic concepts being Outerversal, and he accurately scales most of the other types of multiverses in his video. I respect him as a person and as a powerscaler, I simply wish to address a point of disagreement between the two of us.
That being said, Kember's scaling of the Level IV Multiverse makes absolutely no ******* sense and I'm going to explain why.
For one, he completely misunderstands the Holographic Principle. I know I said the Holographic Multiverse wasn't going to be the focus of this post, but understanding it, REALLY understanding it, will be important later.
Kember's interpretation of the Holographic Principle is that the holographic surface (what we'll call the "boundary") is external to physical reality, and is therefore 1-A. He supports this position by using Brian Greene's paper on the subject, where he compares it to Plato's analogy of the cave, and thus, according to Kember, equating it to Platonism.
However, this is not how a holographic universe would actually function. A holographic boundary is usually described as a surface one dimension LOWER than the reality we experience, what we'll call the "bulk". In the context of a 3D universe, the boundary would then be 2D. The bulk, what we experience as reality, is likened to a "hologram" being projected from the boundary, which is described as "infinitely far away" from us. The boundary encodes the bulk. What this means is that, according to the Holographic Principle, what we perceive as a 3D universe is actually just 2D. The 3rd dimension is an illusion, it doesn't actually exist. The implication of this is that in most cases, the Holographic Principle is actually a DOWNGRADE for a verse's cosmology, which may be why it isn't used very often in powerscaling.
The most famous formulation of the Holographic Principle, Juan Maldacena's AdS/CFT correspondence, frames it in the context of string theory, where the bulk is 10D superstring theory, and the boundary is a formulation of quantum field theory in 3+1 dimensions. This kicks string theory all the way down from 10D/11D to 4D/5D.
(I should note, however, that this does not mean string theory HAS to only be 4D/5D. String theory does not need the Holographic Principle in order to function, nor does the Holographic Principle need string theory to function. Indeed, I haven't heard of any verse that uses string theory that even mentions the Holographic Principle. String theorists just like the idea of AdS/CFT correspondence because it connects string theory to the tried and true quantum field theory, thus strengthening string theory's legitimacy as a Theory of Everything.)
When Brian Greene brings up Plato's analogy of the cave in his paper, he does it not to equate the Holographic Principle with Platonism, but to say that the Holographic Principle is the INVERSE of Plato's cave. The shadows on the wall ARE the true reality, everything else we perceive as "real" is just an illusory projection.
This does NOT mean the Holographic Multiverse is 1-A, however. Calling it a "multiverse" at all is actually somewhat inaccurate, but the reason for it is that there are two different "universes" playing out; the one on the boundary, and the one in the bulk. However, these two "universes" are not actually separate from each other in any meaningful way; they describe the same structure, just formulated in different ways. If you destroy a planet in the bulk, you do so on the boundary as well, the only difference is what it looks like and how the physics of the interaction is formulated. If a black hole exists in the bulk, then it also exists on the boundary, the only difference is that on the boundary (according to AdS/CFT correspondence) it just looks like a hot soup of particles. If you destroy the space-time continuum of the bulk, then you also destroy the boundary, clearly not an Outerversal feat, but merely a Universal+ feat (If we assume 3 dimensions of space and 1 of time, of course).
The reason I point this out is that Kember goes on to say that since the Holographic Multiverse is Outerversal (which I've just proven it's not), and since the Level IV Multiverse necessarily contains the Holographic Multiverse (true), then the Level IV Multiverse must be at least above baseline Outerversal. The entire previous section was devoted to debunking this point.
There's another point I want to bring up. Although Kember doesn't really focus on this in his video, it still bothers me greatly, so I just want to say that THE LEVEL IV MULTIVERSE IS NOT THE SAME THING AS MODAL REALISM. Tegmark describes the Level IV Multiverse in his paper as a version of Modal Realism formulated in mathematical terms, but this does NOT mean they are the same thing. The Level IV Multiverse is framed in terms of mathematical structures, while Modal Realism is framed in terms of possible worlds. Essentially, the Level IV Multiverse contains all that is mathematically possible, while Modal Realism contains all that is logically possible.
This distinction is important because, while possible worlds absolutely can contain Outerversal realms (nothing logically contradictory about them), mathematical structures cannot, as I'm about to prove.
1-A, or Outerverse level, is defined on the VS Battles Wiki as so:
Thus, the argument Kember uses in his video as well as his previous video on the topic () would make sense for Modal Realism, but it doesn't check out in the context of the Type IV Multiverse.
I am aware that Kember made his video before the definition of Outerversal was updated on the VS Battles wiki, but he does explicitly describe an Outerversal realm in terms of the External Reality Hypothesis, as a structure that cannot be described or formulated in terms of our reality, which is the same idea as the current VS Battles definition, so the argument still stands.
This argument applies to the Simulated Multiverse as well, which I haven't mentioned until now. While the Level IV Multiverse is framed in terms of mathematical structures, and Modal Realism is framed in terms of possible worlds, the Simulated Multiverse is framed in terms of simulations (wow shocker), those being programs on a computer. Therefore, the upper limit of the Simulated Multiverse is computability; what can in principle be "computed" by a Turing machine. The Simulated Multiverse would therefore contain all that is computably possible; all possible functions that could in principle be calculated by a Turing machine. This is essentially equivalent to Max Tegmark's Computable Universe Hypothesis, a reduced version of the Mathematical Universe Hypothesis which suggests that only computable functions exist in reality, rather than all mathematical structures. You could even argue that the Simulated Multiverse and the CUH describe the same thing, just formulated differently.
Kember argues the size of the Simulated Multiverse to be extremely large, absurdly far into High 1-A, and you can probably already see the issue with this scaling. Since both computable and non-computable functions are necessarily mathematical structures, the Simulated Multiverse must be smaller than the Type IV Multiverse. Indeed, the Type IV Multiverse must necessarily contain the Simulated Multiverse. Additionally, the Simulated Multiverse runs into the same wall that the Type IV Multiverse does. The problem isn't that "Outerversal" isn't computable, the problem is that framing "Outerversal" in terms of a function at all doesn't even make sense. If it could be framed in terms of a function, it wouldn't be Outerversal. Therefore, Kember cannot use the Simulated Multiverse to support his scaling of the Level IV Multiverse either.
So where do these different multiverse models actually scale then?
As for the Type III Multiverse, since the different "worlds" are technically all part of the same universe, it might actually be reasonable to scale it merely to Low 2-C. However, I understand this may be controversial, so I would be willing to concede 2-B, 2-A, or even Low 1-C scaling.
The Holographic Universe would, in most contexts, scale to 1 dimension below the perceived cosmology. A 3D cosmology, for example would be reduced to 2D, and a 5D cosmology would be reduced to 4D.
AdS/CFT correspondence would scale to 4D/5D, in spite of string theory usually scaling to 10D/11D.
The Simulated Multiverse/Computable Universe Hypothesis is an interesting one. I think it would scale to High 1-B, possibly High 1-B+. Some may choose to scale it to Low 1-A, the reason I chose not to do that is because of how Low 1-A is defined:
The Level IV Multiverse would be free of the computability limitation, so I would scale it to Low 1-A, however I could see people scaling it to baseline 1-A instead (The external reality itself, not the individual mathematical structures that reside in it, those would still be Low 1-A).
Modal Realism would scale ludicrously far into High 1-A+, since the set of all possible worlds would include all possible 1-A and High 1-A structures.
A final point I want to make is looping back to my first argument debunking the Quantum Multiverse wank. If we assume a Level IV Multiverse as well, one could argue that Hilbert Space, kets, and wave functions would all physically exist as mathematical structures, so the Quantum Multiverse goes back to being High 1-B. There are two problems with this line of reasoning:
1. Destroying the Quantum Multiverse would usually equate to destroying all the different timelines, not necessarily the mechanism behind them. Same for manipulating it.
2. Even if we assume that the character is destroying/manipulating the underlying mathematical structure, this argument accomplishes nothing, since destroying/manipulating a mathematical structure is already a Low 1-A feat by definition.
So anyways, that's my rant done. Honestly came out as less of a rant and more of a detailed explanation of where certain cosmologies scale. Huh.
Specifically, there is a video by Kristian Kember () that wanks the Level III and Level IV Multiverses to ridiculous levels. He also wanks the Holographic Multiverse, but that isn't the focus of this rant, since I don't really see the Holographic Multiverse being used all that much in powerscaling debates. I seek to debunk the common arguments for the wanked scaling of the Level III Multiverse, as well as debunk Kember's arguments for his scaling of the Level IV Multiverse.
So, lets start with the Level III Multiverse. The common argument is that the Level III Multiverse is High 1-B because "the wave function rotates in infinite-dimensional Hilbert Space". I have seen multiple powerscaling Youtubers promoting this view. The problem is that the people who espouse this idea glance over a crucial detail; Hilbert Space is an abstract space.
IT'S NOT REAL.
It's just a tool for us to describe quantum states using mathematics. That's it. That's all it is.
We describe quantum states using vectors called kets. Since a quantum object can exist in a superposition of infinite different quantum states, this means infinitely many orthogonal vectors, and so we need an infinite-dimensional Hilbert Space to describe them all. But quantum states are not actually vectors in reality, we simply describe them that way because it makes the math easier to work with. The wave function is also not real as far as we know, it's exactly that; a function that describes the probability distribution of quantum states. So saying "the wave function rotates in infinite-dimensional Hilbert Space" doesn't ******* mean anything, because wave functions, kets, and Hilbert Spaces aren't actually things that exist in reality, they're just mathematical tools to describe reality.
I believe the reason this misconception has persisted for so long is due to an equivocation fallacy. For many powerscalers, the word "dimension" immediately activates the dimensional scaling monkey brain, and they start going off on absurdities like this, and it spreads like wildfire because it seems to make sense intuitively, it doesn't seem like an equivocation fallacy at first glance, but you understand that it is once you realize what's really going on. I myself have been guilty of this on occasion.
Now, before I talk about Kristian Kember's scaling of the Level IV Multiverse, I want to make clear that you are NOT to spread hate towards this man. I shouldn't even have to say this, but some people are actually insane and viciously attack anyone who disagrees with them. This is not what I intend to do, I simply wish to address something that's been bothering me. I don't think that Kember is a bad person or bad powerscaler, I actually agree with a lot of his takes, such as Platonic concepts being Outerversal, and he accurately scales most of the other types of multiverses in his video. I respect him as a person and as a powerscaler, I simply wish to address a point of disagreement between the two of us.
That being said, Kember's scaling of the Level IV Multiverse makes absolutely no ******* sense and I'm going to explain why.
For one, he completely misunderstands the Holographic Principle. I know I said the Holographic Multiverse wasn't going to be the focus of this post, but understanding it, REALLY understanding it, will be important later.
Kember's interpretation of the Holographic Principle is that the holographic surface (what we'll call the "boundary") is external to physical reality, and is therefore 1-A. He supports this position by using Brian Greene's paper on the subject, where he compares it to Plato's analogy of the cave, and thus, according to Kember, equating it to Platonism.
However, this is not how a holographic universe would actually function. A holographic boundary is usually described as a surface one dimension LOWER than the reality we experience, what we'll call the "bulk". In the context of a 3D universe, the boundary would then be 2D. The bulk, what we experience as reality, is likened to a "hologram" being projected from the boundary, which is described as "infinitely far away" from us. The boundary encodes the bulk. What this means is that, according to the Holographic Principle, what we perceive as a 3D universe is actually just 2D. The 3rd dimension is an illusion, it doesn't actually exist. The implication of this is that in most cases, the Holographic Principle is actually a DOWNGRADE for a verse's cosmology, which may be why it isn't used very often in powerscaling.
The most famous formulation of the Holographic Principle, Juan Maldacena's AdS/CFT correspondence, frames it in the context of string theory, where the bulk is 10D superstring theory, and the boundary is a formulation of quantum field theory in 3+1 dimensions. This kicks string theory all the way down from 10D/11D to 4D/5D.
(I should note, however, that this does not mean string theory HAS to only be 4D/5D. String theory does not need the Holographic Principle in order to function, nor does the Holographic Principle need string theory to function. Indeed, I haven't heard of any verse that uses string theory that even mentions the Holographic Principle. String theorists just like the idea of AdS/CFT correspondence because it connects string theory to the tried and true quantum field theory, thus strengthening string theory's legitimacy as a Theory of Everything.)
When Brian Greene brings up Plato's analogy of the cave in his paper, he does it not to equate the Holographic Principle with Platonism, but to say that the Holographic Principle is the INVERSE of Plato's cave. The shadows on the wall ARE the true reality, everything else we perceive as "real" is just an illusory projection.
This does NOT mean the Holographic Multiverse is 1-A, however. Calling it a "multiverse" at all is actually somewhat inaccurate, but the reason for it is that there are two different "universes" playing out; the one on the boundary, and the one in the bulk. However, these two "universes" are not actually separate from each other in any meaningful way; they describe the same structure, just formulated in different ways. If you destroy a planet in the bulk, you do so on the boundary as well, the only difference is what it looks like and how the physics of the interaction is formulated. If a black hole exists in the bulk, then it also exists on the boundary, the only difference is that on the boundary (according to AdS/CFT correspondence) it just looks like a hot soup of particles. If you destroy the space-time continuum of the bulk, then you also destroy the boundary, clearly not an Outerversal feat, but merely a Universal+ feat (If we assume 3 dimensions of space and 1 of time, of course).
The reason I point this out is that Kember goes on to say that since the Holographic Multiverse is Outerversal (which I've just proven it's not), and since the Level IV Multiverse necessarily contains the Holographic Multiverse (true), then the Level IV Multiverse must be at least above baseline Outerversal. The entire previous section was devoted to debunking this point.
There's another point I want to bring up. Although Kember doesn't really focus on this in his video, it still bothers me greatly, so I just want to say that THE LEVEL IV MULTIVERSE IS NOT THE SAME THING AS MODAL REALISM. Tegmark describes the Level IV Multiverse in his paper as a version of Modal Realism formulated in mathematical terms, but this does NOT mean they are the same thing. The Level IV Multiverse is framed in terms of mathematical structures, while Modal Realism is framed in terms of possible worlds. Essentially, the Level IV Multiverse contains all that is mathematically possible, while Modal Realism contains all that is logically possible.
This distinction is important because, while possible worlds absolutely can contain Outerversal realms (nothing logically contradictory about them), mathematical structures cannot, as I'm about to prove.
1-A, or Outerverse level, is defined on the VS Battles Wiki as so:
I bolded an extremely important part of this definition. The definition of Outerversal is that it completely transcends all quantification. There is no number, no equation, indeed no mathematical structure that can describe it. "Outerversal" is not a concept that can be formulated in the language of mathematics, the very definition makes such a thing both impossible and nonsensical.
Thus, the argument Kember uses in his video as well as his previous video on the topic () would make sense for Modal Realism, but it doesn't check out in the context of the Type IV Multiverse.
I am aware that Kember made his video before the definition of Outerversal was updated on the VS Battles wiki, but he does explicitly describe an Outerversal realm in terms of the External Reality Hypothesis, as a structure that cannot be described or formulated in terms of our reality, which is the same idea as the current VS Battles definition, so the argument still stands.
This argument applies to the Simulated Multiverse as well, which I haven't mentioned until now. While the Level IV Multiverse is framed in terms of mathematical structures, and Modal Realism is framed in terms of possible worlds, the Simulated Multiverse is framed in terms of simulations (wow shocker), those being programs on a computer. Therefore, the upper limit of the Simulated Multiverse is computability; what can in principle be "computed" by a Turing machine. The Simulated Multiverse would therefore contain all that is computably possible; all possible functions that could in principle be calculated by a Turing machine. This is essentially equivalent to Max Tegmark's Computable Universe Hypothesis, a reduced version of the Mathematical Universe Hypothesis which suggests that only computable functions exist in reality, rather than all mathematical structures. You could even argue that the Simulated Multiverse and the CUH describe the same thing, just formulated differently.
Kember argues the size of the Simulated Multiverse to be extremely large, absurdly far into High 1-A, and you can probably already see the issue with this scaling. Since both computable and non-computable functions are necessarily mathematical structures, the Simulated Multiverse must be smaller than the Type IV Multiverse. Indeed, the Type IV Multiverse must necessarily contain the Simulated Multiverse. Additionally, the Simulated Multiverse runs into the same wall that the Type IV Multiverse does. The problem isn't that "Outerversal" isn't computable, the problem is that framing "Outerversal" in terms of a function at all doesn't even make sense. If it could be framed in terms of a function, it wouldn't be Outerversal. Therefore, Kember cannot use the Simulated Multiverse to support his scaling of the Level IV Multiverse either.
So where do these different multiverse models actually scale then?
As for the Type III Multiverse, since the different "worlds" are technically all part of the same universe, it might actually be reasonable to scale it merely to Low 2-C. However, I understand this may be controversial, so I would be willing to concede 2-B, 2-A, or even Low 1-C scaling.
The Holographic Universe would, in most contexts, scale to 1 dimension below the perceived cosmology. A 3D cosmology, for example would be reduced to 2D, and a 5D cosmology would be reduced to 4D.
AdS/CFT correspondence would scale to 4D/5D, in spite of string theory usually scaling to 10D/11D.
The Simulated Multiverse/Computable Universe Hypothesis is an interesting one. I think it would scale to High 1-B, possibly High 1-B+. Some may choose to scale it to Low 1-A, the reason I chose not to do that is because of how Low 1-A is defined:
The Simulated Multiverse would not meet this qualification, since uncountable infinities are non-computable. It would not be able to contain dimensional spaces with greater than countably infinite dimensions.
The Level IV Multiverse would be free of the computability limitation, so I would scale it to Low 1-A, however I could see people scaling it to baseline 1-A instead (The external reality itself, not the individual mathematical structures that reside in it, those would still be Low 1-A).
Modal Realism would scale ludicrously far into High 1-A+, since the set of all possible worlds would include all possible 1-A and High 1-A structures.
A final point I want to make is looping back to my first argument debunking the Quantum Multiverse wank. If we assume a Level IV Multiverse as well, one could argue that Hilbert Space, kets, and wave functions would all physically exist as mathematical structures, so the Quantum Multiverse goes back to being High 1-B. There are two problems with this line of reasoning:
1. Destroying the Quantum Multiverse would usually equate to destroying all the different timelines, not necessarily the mechanism behind them. Same for manipulating it.
2. Even if we assume that the character is destroying/manipulating the underlying mathematical structure, this argument accomplishes nothing, since destroying/manipulating a mathematical structure is already a Low 1-A feat by definition.
So anyways, that's my rant done. Honestly came out as less of a rant and more of a detailed explanation of where certain cosmologies scale. Huh.
