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So I was wondering if this could qualify 'Possible Tier 1-A' for Downstreamers (https://vsbattles.fandom.com/wiki/Downstreamers)
[Anna's face worked. "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 a truism that all logically possible universes must exist. The universe, this universe, is described - umm, that's 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."]
Explains that in infinite ensemble universes, all universes that follows formal systems, must already exist. I presume this would automatically include universes with infinite dimensions (hilbert space), universes that follow string theory, and numerous others. Since all mathematical structures are basically formal systems. That's including hilbert space which is part of quantum mechanics. That, is called Level IV Multiverse.
And I got this explanation from another site :
[Level IV multiverse contains universes with different structures of mathematics than ours, contains sets, structures, or systems that exist beyond spacetime, duality, or existence and nonexistence, contains universes with different fundamental laws of physics than ours, contains universes with different laws of logic or metaphysics than ours, contains universes with wholly alien or incomprehensible concepts, or contains impossible worlds.]
Dunno if that interpretation is true or not but if it is, Any kind of systems, even at metaphysical levels can be radically different for all universes.
And [exist beyond spacetime, duality, or existence and nonexistence] are characteristics reserved for transduality characters.
And Downstreamers created infinite amount of this Level IV Multiverse :
[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.]
A manifold = infinite ensemble of universes.
So the assumption that they made 'Impossible Universes' may actually be true. But that'd contradict 'possible universes' statement since its not explicitly stated that DS made 'impossible worlds'. Its just 'all formal systems that are internally consistent describe possible universes that exist'.
Ehm, basically Manifoldverse probably has a Composite Hierarchy. All kind of cosmologies are a go.
And Downstreamers transcend such Level IV Multiverse. By surviving its collapse. Able to comprehend it as a whole and by embodying said Multiverse at the same time.
This Multiverse idea shares a parallel with Plato's realm of ideas. Where all things in our material world are just shadows cast by true Ideal things (I presume this 'Ideas' would mean 'concepts'). The difference is said 'Ideas' are replaced with 'mathematical structures' or 'abstract mathematics'.
From wiki :
[Abstract mathematics is so general that any Theory Of Everything (TOE) which is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of.]
Basically, it contains every cosmology imaginable and… unimaginable (if I understand it right).
Said 'true mathematical structures' are described as aspatial, atemporal, unchanging and archetypal according to wiki. It could be said they're 'Concepts', the true form of things. And Downstreamers are described to fully comprehend whole Manifold and embody it (which should contain said Concepts).
[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 the entire universe, arbitrarily well ― or rather She must exist, as Babo put it.
"The God of the Manifold," Manekato said dryly.]
Of course, this quote contradicts the whole 'incomprehensible concepts' thing, so there might be something missing here.
Okay, Downstreamers being able to comprehend it as a whole might mean they see the Manifold as eternal and unchanging. From Tegmark's 'The Mathematical Universe' :
[Recall that a mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would therefore correspond not to a single frame of it but to the entire videotape.]
So, what do you guys think?
[Anna's face worked. "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 a truism that all logically possible universes must exist. The universe, this universe, is described - umm, that's 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."]
Explains that in infinite ensemble universes, all universes that follows formal systems, must already exist. I presume this would automatically include universes with infinite dimensions (hilbert space), universes that follow string theory, and numerous others. Since all mathematical structures are basically formal systems. That's including hilbert space which is part of quantum mechanics. That, is called Level IV Multiverse.
And I got this explanation from another site :
[Level IV multiverse contains universes with different structures of mathematics than ours, contains sets, structures, or systems that exist beyond spacetime, duality, or existence and nonexistence, contains universes with different fundamental laws of physics than ours, contains universes with different laws of logic or metaphysics than ours, contains universes with wholly alien or incomprehensible concepts, or contains impossible worlds.]
Dunno if that interpretation is true or not but if it is, Any kind of systems, even at metaphysical levels can be radically different for all universes.
And [exist beyond spacetime, duality, or existence and nonexistence] are characteristics reserved for transduality characters.
And Downstreamers created infinite amount of this Level IV Multiverse :
[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.]
A manifold = infinite ensemble of universes.
So the assumption that they made 'Impossible Universes' may actually be true. But that'd contradict 'possible universes' statement since its not explicitly stated that DS made 'impossible worlds'. Its just 'all formal systems that are internally consistent describe possible universes that exist'.
Ehm, basically Manifoldverse probably has a Composite Hierarchy. All kind of cosmologies are a go.
And Downstreamers transcend such Level IV Multiverse. By surviving its collapse. Able to comprehend it as a whole and by embodying said Multiverse at the same time.
This Multiverse idea shares a parallel with Plato's realm of ideas. Where all things in our material world are just shadows cast by true Ideal things (I presume this 'Ideas' would mean 'concepts'). The difference is said 'Ideas' are replaced with 'mathematical structures' or 'abstract mathematics'.
From wiki :
[Abstract mathematics is so general that any Theory Of Everything (TOE) which is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of.]
Basically, it contains every cosmology imaginable and… unimaginable (if I understand it right).
Said 'true mathematical structures' are described as aspatial, atemporal, unchanging and archetypal according to wiki. It could be said they're 'Concepts', the true form of things. And Downstreamers are described to fully comprehend whole Manifold and embody it (which should contain said Concepts).
[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 the entire universe, arbitrarily well ― or rather She must exist, as Babo put it.
"The God of the Manifold," Manekato said dryly.]
Of course, this quote contradicts the whole 'incomprehensible concepts' thing, so there might be something missing here.
Okay, Downstreamers being able to comprehend it as a whole might mean they see the Manifold as eternal and unchanging. From Tegmark's 'The Mathematical Universe' :
[Recall that a mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would therefore correspond not to a single frame of it but to the entire videotape.]
So, what do you guys think?
