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Intro

Another one of these. Never thought I'd get into a sci-fi verse, but anyway.

Type IV Multiverse

Manifoldverse, as one would expect of a sci-fi verse, is based on the Ultimate Ensemble, that is, the mathematical universe hypothesis, where mathematics are the base/crux of all reality, being thus more fundamental than physical existence. It contains all possible mathematical permutations, and views all possible mathematical objects as real, including abstract "Platonic," ones that are aspatial and atemporal. In simple terms, mathematical existence equals physical existence, and all possible structures that exist mathematically exist physically as well.

"They are considering constraints on the ultimate manifold."

Maura suspected that she was going to struggle with the rest of this conversation. "The Manifold of what?"

"Universes. It is of course that all logically possible universes must exist. The Universe, this universe, is described--umm, thats the wrong word--by a formal system. Mathematics. A system of mathematics.

Maura frowned. "You mean a Theory of Everything?"

Anna waved a hand, as if that were utterly trivial, and her beautiful wings rustled.

"But there are many formal systems. Some of them are less rich, some more. But each formal system is logically consistent internally, describes a possible universe, which therefore exists."

~ Manifold: Time, Part 4


Some of these universes, as described by the formal systems, are rich enough to support self-aware substructures. Life. Intelligence.
~ Manifold: Time, Part 4


Mathematics are something deeper than physical laws, its the essential logic that underlays all things:

Cassiopeia had spent time trying to teach him about a phenomenon just a little beyond his own horizon — as chaos theory might have been to an engineer of, say, the 1950s. It was something to do with the emergence of complexity. The Gaijin seemed able to see how complexity, even life, naturally emerged from the simplest of beginnings: not fundamental physical laws, but something even deeper than that — as far as he could make out, the essential mathematical logic that underlay all things.
~ Manifold: Space, Chapter 10


Mathematical structures and its prime numbers exists everywhere and its what causes the existence of physical structures, like atoms, stars, life, etc:

Human scientists had a glimmering of this. His own DNA somehow contained, in its few billion bases, enough information to generate a brain of three trillion connections… But for the Gaijin this principle went farther. It was like being given a table of prime numbers and being able to deduce atoms and stars and people as a necessary consequence of the existence of the primes. And since prime numbers, of course, existed everywhere, it followed there was life and people, humans and Gaijin, everywhere there could be. Life sprouting everywhere, like weeds in the cracks of a pavement. It was a remarkable, chilling thought
~ Manifold: Space, Chapter 10


It is further proved in Manifold Origin that all possible universes must exist in the ultimate ensemble, since the mathematical universe hypothesis encompasses all branches of mathematics, which is from where universes and physical existence are born from, as already explained above:

"Infinity is significant, you see," Nemoto said, too rapidly. "There is, umm, a qualitative difference between a mere large number, however large, and infinity. In the infinite manifold, in that infinite ensemble, all logically possible universes must exist. And therefore all logically possible destinies must unfold. Everything that is possible will happen, somewhere out there. They created a grand stage, you see, Emma: a stage for endless possibilities of life and mind."
~ Manifold: Origin


And again in Phase Space:

Whatever the origin of the manifold, within it there could be an infinite number of universes. And in an infinite ensemble, everything which is logically possible must—somewhere, somehow—come to pass.
~ Phase Space


Taking into account what was said above, the cosmology technically would be High 1-A already, but I think there is more to unpack here.

1-A

The Empyrean Void is the background/canvas in which dimensional structures can be applied into it. It exists beyond the structures of space, duration, and the laws of nature. Mere dimensionality cannot cover the entire nature of the Empyrean Void.

We are outside the Primum Mobile: beyond duration, beyond the structure of space. Dante understood this place. "There near and far neither add nor subtract…
~ Phase Space: Dante Dreams


Near and far do not add or subtract there, since where God rules without mediation the laws of nature have no relevance.
~ Dante Paradiso


This is the basis of the new unified theory,' Philmus said. 'A unification of phenomena through the structure of a higher-dimensional space.'

Himmelfarb's face was turning to pixels again. 'It isn't as simple as that,' she said. 'The whole notion of dimensionality is an approximate one that only emerges in a semi-classical context—-well. I don't suppose it matters now.

~ Phase Space: Dante Dreams


High 1-A

The manifold is a mathematical superspace that contains all variants of mathematics that can possible exist. And among those, it includes Woodin cardinals as actual structures within it. And it even mentions hierarchies of infinities and set theory (because the author actually knows what he is talking about since he is a mathematician)

'Why the city in the sky?'

'Ah, my Laputas. What you see is a representation of a logical structure called the Ultimate L.'

'Logical?'

'Mathematical. A constructible universe, if you like, or multiverse. The buildings out there represent a type of entity known as Woodin cardinals. An expression of the axioms of set theory. Officer Philmus, this is a kind of mathematical superspace, which may, or may not, be an expression of all the variants of mathematics that can logically exist. Nobody knows for sure; not even I, and certainly not that arrogant brute the Archangel. Certainly one may prove profound mathematical theorems merely by exploring such a space – by looking for the edges, or internal boundaries. It is a jungle where hierarchies of infinities tower like prehistoric beasts. And it is a jungle where I hide away.'

~ A Journey to Amasia


As we established before, in a Type 4 multiverse, mathematical possibilities = physical existence, so those woodin cardinals, somewhere, exists as actual structures within the manifold itself. Overall, this and the whole Type IV shenanigans gives us a solid High 1-A cosmology. Specifically, into the 42nd layer of High 1-A (since thats where woodin cardinals reside in the hierarchy of large cardinals above Mahlo).

But there is more.

Infinite hierarchy of manifolds

'Of course,' Babo said, 'She may actually be an expression of the manifold itself—or perhaps the manifold itself, the greater structure of reality strands, is itself self-referential, in some sense conscious. Or perhaps the manifold is itself merely one thread in a greater tapestry—'

'A manifold of manifolds.'

'And perhaps there is a further recursion of structure, no end to the hierarchies of life and mind, which—'

Mane held up her hands.

~ Manifold: Origin, Part 4


What would be left if the Ocean vanished? – for the Ocean was the world. 'Perhaps there is a greater Ocean,' she said at last. 'In which our Ocean is embedded. As one becomes embedded in the three of a triple.'

'And,' Glimmer said suddenly, 'perhaps there is a greater Ocean beyond that. And then another.'

This keen, intelligent insight startled Shine. But as she tried to imagine an infinite hierarchy of Oceans, each contained within the next, she recoiled, bewildered.

~ Phase Space: The We Who Sing


Basically, a single manifold is a Type 4 multiverse as we already established before. There is an infinite hierarchy of said manifolds, in which a single one is just one thread in a greater tapestry, or, a drop in an infinite ocean.

Old Ones

The downstreamers/old ones created the manifold multiverse.

It was my mandate. It was successful, in its own terms.

This is my mandate from the downstreamers. To explore the multiverse they created. To look at all the ways life could be played out, all the possibilities inherent in it. To let it run.

'Even if people had to die to achieve that?'

The downstreamers are not destroyers of worlds. They are creators. Enrichers-

~ World Engines: Creator


I’m still blown away by what I’ve learned of the Old Ones.

The Old Ones created infinite possibility – infinite opportunities for life, for mind. What higher mission could there be?

~ Manifold: Origin, Part 4


'They made the manifold.'

"Who did?'

'The Old Ones. They constructed a manifold of universes—an infinite number of universes. They made it all.' Nemoto shook her head. 'Even framing the thought, conceiving of such ambition, is overwhelming. But they did it.'

~ Manifold: Origin, Part 4


"In the infinite manifold, in that infinite ensemble, all logically possible universes must exist. And therefore all logically possible destinies must unfold. Everything that is possible will happen, somewhere out there. They created a grand stage, you see, Emma: a stage for endless possibilities of life and mind.'

'Why did they do this?'

'Because they were lonely. The Old Ones were the first sentient species in their universe.'

~ Manifold Origin, Part 4


So they scale to High 1-A pretty much.

Goddess of Manifold

Differently from the Old Ones, while they created a single manifold, the goddess seems to encompass all of the infinite hierarchy of manifolds.

The Gaijin had a somewhat mathematical philosophy. Malenfant thought it sounded suspiciously like a religion. The Gaijin believed that the universe was fundamentally comprehensible by creatures like themselves — like humans, like Malenfant. That is, they believed it possible that an entity could exist that could comprehend the entire universe, arbitrarily well. And they had a further principle that mandated that if such a being could exist, it must exist. The catch was that they believed there was a manifold of possible universes, of which this was only one. So She may not exist in this universe. It — She — was the final goal of the Gaijin’s quest. But until the God of the Manifold shows up, there’s only us, Malenfant thought. And there is work to do. We have to fix the bugs in this universe we’re all stuck in. Hence, we throw a net around a star. Hence, my sacrifice.

~ Manifold: Space, Chapter 10


Babo shrugged massively, as Manekato groomed him. “It may yet be possible to use the world engine, if only in a limited way …”

“To do what?”

“We can explore the manifold. We can Map to other realities. Other possibilities. You don’t have to send a whole Moon to do that.”

Mane pondered. “But what is there to look for?”

“In fact there is a valid goal,” Babo said carefully.

The Astrologers, he told Manekato, believed that the universe—any given universe—was a fundamentally comprehensible system. If a system was comprehensible, then an entity must exist that could comprehend it. Therefore an entity must exist that could comprehend the entire universe, arbitrarily well—or rather She must exist, as Babo put it.

“The God of the Manifold,” Manekato said dryly.

The catch was that there was a manifold of possible universes, of which this was only one. So She may not exist in this universe. Anyhow, it—She—was to be the ultimate goal of the Daemons’ quest.

“Of course,” Babo said, “She may actually be an expression of the manifold itself—or perhaps the manifold itself, the greater structure of reality strands, is itself self-referential, in some sense conscious. Or perhaps the manifold is itself merely one thread in a greater tapestry —”

“A manifold of manifolds.”

“And perhaps there is a further recursion of structure, no end to the hierarchies of life and mind, which—” Mane held up her hands. “If we find Her: what will we ask Her?”

Babo picked his nose thoughtfully. “I asked Em-ma that. She said, ‘Ask Her if She knows what the hell is going on.’

~ Manifold: Origin, Part 4


Conclusion

  • Cosmology as a whole: High 1-A
  • The Downstreamers/Old Ones: High 1-A (42nd layer)
  • Goddess of the Manifold: High 1-A (Top of an infinite hierarchy above the Old Ones' layer)
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