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Manifold : Possibly having Woodin Cardinals (Tier 0 Upgrade)

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Threemagi

He/Him
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0. 'Manifold or Baxter (Greater) Multiverse Contains All Logical System of Mathematics'

Aka it is a 'Type 4 Multiverse' or something like that.

Manifold (Also wider Baxter Multiverse) is governed by deeper source than physical laws. Namely, mathematics and logic, both are underlyings of reality on Manifoldverse.
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. .
Its here explicitly said that complexity itself did not originate or created from most fundamental of physical laws. But all is originating from even deeper and more primal source, that is mathematical logic that underlay all things.
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
How the existence of one mathematical structure caused the existence of physical structures like stars. And since said mathematical structure existed everywhere, (all over Manifoldverse) so can complexity like Life exist all over the Manifold of Manifolds because it would be consequence of mathematical.

In other words, mathematical concepts take the role of 'base'.
From the beginning, even when the universe was still very young, there was life. Life self-organised, from collections of more or less
simple chemicals, blindly following the laws of chemistry and physics, guided by mathematical rules evidently inherent in reality.
The statement above is said by omniscient narrator. It also confirms that the cosmos is made out of mathematics. Because math is inherent in reality. Because previously it is said that it is more fundamental than physical laws.
Manifold Time said:
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.
And the meat of the argument. There are all kinds of formal systems, system of mathematics, therefore, there must be universes corresponding said formal systems...

Because in Manifold Space quote above, it is already said that real existence is mere side effect of mathematical concepts existing.
Manifold Origin said:
"A manifold of manifolds."

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

Mane held up her hands.
In which there are further recursions to the structure.
I mean, there is nothing preventing Type 4 Multiverse containing another Type 4, ad infinitum, right?

1. 'Oceans inside larger ocean, continuing to infinity'
The We Who Sing said:
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.
'Ocean' refers to universe before 'age of matter'. Where lifeforms are like fluid plasma.
This one short story most likely connected to Manifold. There is mention of Reid Malenfant in the story and it is packed inside Phase Space.

2. Woodin Cardinal
'A Journey to Amasia', short story.
A Journey to Amasia said:
'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.'
Mathematical superspace, all possible structures, yada yada.

One of many structures is called 'Woodin cardinals'. An inaccessible cardinal, apparently.
Old post that I found said:
0=1 > 10-13 > N-Huge > Superhuge > Huge > Almost Huge > Vopenka > Extendible > Supercompact > Strongly Compact > Woodin > Strong > Measurable > Strongly Ramsey > Ramsey > w1-iterable > Strongly Unfodable > Indescribable > Weakly Compact > Inaccessible Cardinal
Maybe it has something to do with 'hierarchies of infinities'?

Connection to Manifold is through short story 'Spindrift'. 'Spindrift' is one of short stories in Phase Space. And the 'life all around us' seems to hint on the Dreamers (which is from Ultima and Proxima novels. Possibly is also organelles appearing in Dante Dreams (short story packed into Phase Space)).
In which 'A Journey to Amasia' characters both made appearances in Proxima/Ultima & Dante Dreams in Phase Space.
Phase Space said:
Or (Malenfant wrote to Michael) perhaps there is life all around us, even now. Perhaps there is life in the stars, the clouds, the rocks under your feet. But we just can’t see it. Wouldn’t that be strange?

3. Summary
I am under the impression that 'Inaccessible Cardinal' (which Woodin belongs to) warrants new rating/tiering. So is this true? Would this warrant an upgrade? Or would this just an additional supporting quotes for 1-A?

This would affect Downstreamers and that one God, yes.
 
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Woodin cardinals are unanimously agreed to be one of the largest classes of large cardinals, exceeding Mahlo cardinals (the baseline for tier 0) by several orders of magnitude. Feel free to consult Cantor's Attic for more information on that.

In any case, I decided to read the source material where you got the Woodin cardinal line from (speaking of which, it would help your credibility if you posted scans or at least cited sources instead of just quoting the text). Taking note of the fact that the city here is a representation of the Ultimate L and is described as if it's a reflection of it (evidenced by the city's buildings representing the existence of Woodin cardinals according to the Briton), I can see an argument for scaling to Woodin cardinals. For that matter, the references to a "mathematical superspace, which may, or may not, be an expression of all the variants of mathematics that can logically exist" reminds me of this statement from Manifold: Origin. It's comparatively far more limited in scope, but the general idea should be the same, I think.

The other important detail is that the end of this short story directly parallels parts of Dante Dreams:

The study, the building around them, the cavern, all of it folded away like a cheap stage set, revealing an underlying darkness. Philmus could still see Boyle, the Briton, lit by an unreal light. But there was no structure beyond the three of them and their relative positions. She felt as small as an electron, as huge as a galaxy. Boyle grabbed her hand.
And the three of them, like birds hovering beneath the domed roof of a cathedral, ascended into the Empyrean.
They passed into a layer of darkness, like a storm cloud. The hemispheres of the 3-sphere—the Earth and its nested spheres, the globes of the angels—faded like stars at dawn.

But Himmelfarb’s eyes glowed brightly. And then, space folded away. Philmus could still see Boyle, Himmelfarb, the priest’s shining eyes. But she couldn’t tell how near or far the others were. And when she tried to look away from them, her eyes slid over an elusive darkness, deeper than the darkness inside her own skull.

There was no structure beyond the three of them, their relative positions. She felt as small as an electron, as huge as a galaxy. She felt lost.

And Philmus saw light, a new light, just a point, and yet it filled space and time. It unfolded like a flower blooming, and particles and lines billowed out and rushed past her face in an insubstantial breeze. Some of the lines tangled, but still the unfolding continued, in a fourth, fifth, sixth direction, in ways she could somehow, if briefly, comprehend.
Philmus saw light, like the image of God at the centre of the angels’ spheres. It was a point, and yet it filled space and time. And then it unfolded, like a flower blooming, with particles and lines (world lines? quantum functions?) billowing out and rushing past her face, in an insubstantial breeze. Some of the lines tangled, and consciousness sparked—trapped in time, briefly shouting its joy at its moment of awareness—before dissipating once more. But still the unfolding continued, in a fourth, fifth, sixth direction, in ways she could somehow, if briefly, conceive.

So, if there was ever any doubt about the canonicity of this short story, this should clear it up.

The only objection I can think of that could be raised here is that merely referencing large cardinals does not mean scaling to their size, but then there's an as-of-yet unpublished character profile (here) that's been accepted to be tier 0 simply because inaccessible cardinals are evoked as something that the character encompasses and exceeds, and this short story does seem to strongly imply that the Old Ones' manifold similarly includes Woodin cardinals in its scope.

In summary, yeah, I think that this upgrade is legitimate at a not-so-quick glance. (And to think that I wanted to downgrade the Old Ones before!) Still, just to be extra certain, I'll go and contact a few people who I think are knowledgeable on the verse to provide some input - an upgrade this massive should be handled with care.
 
I share similar thoughts with KingPin0422, from reading over the evidence like scans.
On the topic of inaccessible cardinals, currently without many clarifications if an inaccessible cardinal is larger than a Mahlo cardinal, we default to High 1-A regarding such hierarchy, in the current tiering system. So, I don't think White Light's case would be much of an issue.
 
This is quite explicit, so I agree. Only counter argument could be questioning whether that story applies to Manifold or not I guess
 
@KingPin0422 Ah you are doing job for me of providing scans. Sorry, and thank you.

Regarding "mathematical superstructure", There is also supporting statement on Ultima regarding "Manifold is made of math" which is said in the very first book : Time.
Ultima said:
From the beginning, even when the universe was still very young, there was life. Life self-organised, from collections of more or less
simple chemicals, blindly following the laws of chemistry and physics, guided by mathematical rules evidently inherent in reality.
^ 'Omniscient narrator' said that mathematical rules is inherent in reality. 2nd book 'Space' said the same thing too.
(On no, I am doing it again. Sorry, I have no time to post scan ovo)

So they may very well be referring to same multiverse, yes. (Baxterverse... lol)
Thus can be appicable to relevant factions.

@Darksmash True. KingPin however has helpfully added supporting quotes for connecting the story.

Anyway, I now use this chance to 'bump!'. And maybe brainstorming on what to revise on the pages.

Summary :
The revision, it'd be High 1-A then. Maybe Goddess thing can have Tier 0?
 
It would just be tier 0, from Woodling cardinal hierarchy being included in Ultimate Manifold. So, they both would be Tier 0.
I thought you can't have multiple Tier 0s in one verse? Or is that old news?

So, the thing that's needed to change is just AP details, I assume.

So : AP (Can create Ultimate Manifold/Mathematical superspace which contains all the variants of mathematics that can logically exist, including Woodin Cardinals, which exceeds Mahlo Cardinal by several orders of magnitude)

Do I need to call more people in this thread?
 
It is an old standard that was revised and removed. So, High 1-A would not be right.
Ah, thank you for the info.
I agree with High 1A
I am under the impression that KingPin is agreeing for Tier 0. So is Elizhaa.

Because it seems Woodin>>>Mahlo ('Baseline' Tier 0).

And I checked that Cthulhu gods are all Tier 0.

So it seems entire 'race/civ' (in this case : Old Ones) of Tier 0 is allowed.

Hence, maybe the revision is to be Tier 0.

Just in case if someone want to ask of my AP revision plan :
(The Old Ones' capability, which includes the effortless manipulation of the fabric of existence, is nearly boundless, and they are capable of creating infinitely-layered multiverses that contain an equally infinite number of multiverses within them. The Manifoldverse itself consists of an infinite hierarchy of infinite multiverses. In Manifoldverse, there exist at least one realm which is beyond the structure of spacetime, where mathematical concepts such as; "add" and "substract" lose all meaning, and in which the notion of dimensionality is meaningless. Manifoldverse is mathematical superspace which consists of an infinite number of infinite multiverses, encompassing all forms/variants of mathematics and formalisms; Type IV Tegmark Multiverse, Woodin's Constructible Multiverse (Ultimate L) which includes Woodin Cardinals, which in turn exceeds Mahlo Cardinal (Standard for Tier 0) by several orders of magnitude. The Old Ones themselves exist at the top of this endless hierarchy, far beyond the applications of normal space and time, and maybe one with an "Ultimate Manifold", that encompasses all other manifolds in the tapestry of existence. Superior to all physical laws as they can be described, they have a near complete understanding of existence itself, allowing them to modify a few rules governing how the entirety of the verse works, such as likely changing the type of the multiverse, which enables them to create "infinite possibilities for life and mind")
New changes marked by bolded. I also linked the scans KingPin so graciously provided.
 
I added 'Tier 0' to title to give clear objective of the thread. (And sense of 'dangerousness', I guess.)

6 users agreed so far.
 
If someone who read the short story can confirm it being a legit thing and not just an entity's name or the place being something else, it sounds like it could possibly work.

Justification sucks tho.
 
At a glance, it sounds like there is a space in which something represents (/is an expression of) a cardinal, but not that there is a something (i.e. anything) that exists this cardinality many times. It is the latter that is the requirement for it to be relevant to tiering, however.
 
If someone who read the short story can confirm it being a legit thing and not just an entity's name or the place being something else, it sounds like it could possibly work.
My post from before addresses this adequately, I think. The city depicted in the short story, although belonging to a simulation, is described as if it's a microcosmic image of the Manifold - namely, its buildings are said to symbolize the existence of Woodin cardinals in the greater mathematical superspace which is believed (and essentially proven by other stories) to express all possible mathematical structures.
Justification sucks tho.
How's this, then?

The Old Ones' capability, which includes the effortless manipulation of the fabric of existence, is nearly boundless, and they are capable of creating infinitely-layered multiverses that contain an equally infinite number of universes within each layer. They are one with the "Manifold," a mathematical superspace encompassing all forms/variants of mathematics identified with Woodin's constructible multiverse (Ultimate L) which includes Woodin cardinals. The Old Ones themselves have a near complete understanding of all of existence, allowing them to easily create "endless possibilities of life and mind."

It could use some more work that's probably beyond me right now (I'd have to actually read the Manifold books, for one), but I think it's good enough for the time being, unless you have some objections to parts of it.
At a glance, it sounds like there is a space in which something represents (/is an expression of) a cardinal, but not that there is a something (i.e. anything) that exists this cardinality many times. It is the latter that is the requirement for it to be relevant to tiering, however.
As before, the city itself is a simulation, but it is stated to be a representation of the Ultimate L, which in turn is described as a "mathematical superspace which may, or may not, be an expression of all the variants of mathematics that can logically exist" - an obvious reference to Max Tegmark's type IV multiverse theory. Said space is also figuratively called "a jungle in which hierarchies of infinities tower like prehistoric beasts," so at the very least, we know that some notion of higher infinities is included in the Manifold's scope.

As for why I think Woodin cardinals do physically exist somewhere in the Manifold, well, it's as simple as the city's buildings being stated to represent those cardinals, the city itself being a reflection of the Manifold, and this unpublished profile being accepted by Ultima and other experts as tier 0 because of statements of the cosmology encompassing all infinities and one other statement of inaccessible cardinals. For that last part in particular, I'd argue that this profile has similar enough context to Manifold's case to be comparable (even if it's not exactly the same), so if you're against this revision, then you have to prove that either:
  1. I'm wrong and the two cases are contextually too different to be compared.
  2. The White Light's inaccessible cardinals statement is unusable for scaling.
 
As before, the city itself is a simulation, but it is stated to be a representation of the Ultimate L, which in turn is described as a "mathematical superspace which may, or may not, be an expression of all the variants of mathematics that can logically exist" - an obvious reference to Max Tegmark's type IV multiverse theory. Said space is also figuratively called "a jungle in which hierarchies of infinities tower like prehistoric beasts," so at the very least, we know that some notion of higher infinities is included in the Manifold's scope.

As for why I think Woodin cardinals do physically exist somewhere in the Manifold, well, it's as simple as the city's buildings being stated to represent those cardinals, the city itself being a reflection of the Manifold, and this unpublished profile being accepted by Ultima and other experts as tier 0 because of statements of the cosmology encompassing all infinities and one other statement of inaccessible cardinals. For that last part in particular, I'd argue that this profile has similar enough context to Manifold's case to be comparable (even if it's not exactly the same), so if you're against this revision, then you have to prove that either:
  1. I'm wrong and the two cases are contextually too different to be compared.
  2. The White Light's inaccessible cardinals statement is unusable for scaling.
If I have an opinion I don't really care which other verses would be affected as consequence. That said, I don't really know White Light, although I think I do remember a somewhat similar debate about it. Or, at least, I remember this not being the first debate where I say that just having something represent a cardinality doesn't mean high tiers.

Anyways, the fact that a cardinal exists as a building (or as 'prehistoric beasts' i.e. probably dinosaurs) is exactly the problem I have with the argument. It doesn't seem to be that the cardinality exists as there being that number of something or there being a space with that many dimensions or anything of that nature. Instead, mathematical objects, even such as cardinalities, are represented as physical objects.
It's like in mathematics a cardinality can be said to exist (in some philosophical opinions in form of some metaphysical object) and be represented by a symbol written on a piece of paper, but that doesn't mean any physical thing corresponds to it and wouldn't affect the size of real life.

So, I stay at my opinion that just materializing the idea of a cardinal as a building doesn't imply the physical existence of anything that amount of times and hence not a higher tier. Either you would have to show that something actually exists in these amounts or, alternatively, that the buildings corresponding to higher cardinals are bigger/on higher levels of reality than buildings of lower cardinals, with an infinite gap corresponding to the gap between the cardinal sizes.
 
DontTalk makes sense to me as usual.
 
Tally Votes

Agree : 8
(KingPin0422, Elizhaa, Guardian_Doge, Darksmash, Setsuna_tenma, Delta333, catzlaflame, Maginova_stella)

Disagree (aka Depends wether "its real or not") : 3
(QuasiYuri, DontTalkDT, Antvasima)

As DontTalk said, you can see that as just "unconfirmed hypothesis" (albeit the whole idea is supported by the verse mechanics).

(Thank you KingPin0422 for vouching for the verse though. Reading the relevant Manifold's wall of text must take some effort)

The supporting statements for Mathematical multiverse came from in universe conversations (in 1st and 2nd books), that is confirmed by omniscient narrator later. Honestly, this seems to be Baxter's style. In universe 'speculations' seems to be confirmed sooner or later by omniscient narrator.

However, I see that Baxter likes to add more confusion by representing concept as physical construct. Which adds more layer of ambiguity to it. Might as be as wortless as piece of paper indeed.. unless Baxter releases new book and confirm the speculation by using omniscient narrator, (as always).

Summary :

Raised good points about the realness of the concept in the first place.

So should we leave the relevant profile pages at this state? (No changes)

Or do some compromise like adding "Possibly"?

Honestly tho, it's a waste not to include information from the new quotes, imo, even if they are currently not reliable.
So I'd want to reach the "Possibly" compromise. If possible.
 
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8 agree and 4 disagree.

Btw, I don't mind if this thread got concluded/locked and the final motion is for not upgrading.
 
Seems to be using set theory correct here. Applying it to the size of the cosmology. Where the number of universes in a multiverse correspond to a class of large cardinals.
 
Thanks for coming to the thread.

Agree : 9 | Disagree/hestitant : 4

To advance the disc.

@Antvasima @DontTalkDT So, right now I cannot yet find the evidence required to prove the real thing.

So, is the revision allowed?

Can we compromise on settling on "Possibly" using the information we currently have?

Thank you.
 
I have a message someone asked to deliver
🐧


Hi, I am the author of 2 Spacebattle threads, one for connections between Baxter's works are made, and one for The Dreamers of Proxima's feats.

https://forums.spacebattles.com/threads/dreaming-bugs-of-mars-proxima-respect-thread.916771/

https://forums.spacebattles.com/threads/a-meta-baxter-thread-about-possible-connections-but-not-definitively.962113/

I was also the one who mentioned the possible connection between the Manifold and the
Proxima series, as well as The We Who Sing's feat in another thread.

https://forums.spacebattles.com/threads/self-reference-engine-vs-downstreamers.961603/?post=78423241#post-78423241

Putting that aside, while I agree with the upgrade, I am against the grouping of the Dreamers's feat (and by extension the Proxima's cosmology) into the Manifold series. They are different series with different top tiers that should not be considered the same in anyway. Even though there are lots of connections between the 2 series, and by extension the rest of Baxter's works, it will take time to put forward enough proofs to draw a conclusive statement. Case and point, even I am not confident in arguing that the living Moon/planets in "Spindrift" are true Dreamers, since the short story lacks many pivotal elements that would mark the appearance of the Dreamers race. Furthermore, if we are talking about living planets appearing in Baxter's works, there would be nearly a dozen of them, and obviously, not all of them are Dreamers.
 
I don't think it really matters whether the building actually holds the size of a Woodin cardinal or is just a representation. What matters is that the idea of the cardinal exists in the verse.

The only reason a Type 4 multiverse isn't straight up tier 0 is because we lowball them based on the things that are shown in the verse. If for example the best things shown in the verse are simple higher dimensions then it would be low 1-A/1-A(afaik). And if it has transfinite sized hierarchies then it would hypothetically be 1-A+/High 1-A.

In this case the verse has shown to contain the concept of Woodin cardinals, hence I don't see why it wouldn't physically exist somewhere in a multiverse where all mathematical possibilities are true.
 
Hmm, good point actually. Tier 0 does seem justified then, but I'd still like to see if DT has any counterarguments.
 
Possibly would look safer imo, but I don't really have any argument besides "I feel it would be better".
 
@Orion I see... Maybe we should separate Manifold and Ultimate L/Math superspace in the justification for new AP. We just have to tweak KingPin's concise AP justification a little.
The Old Ones' capability, which includes the effortless manipulation of the fabric of existence, is nearly boundless, and they are capable of creating infinitely-layered multiverses that contain an equally infinite number of universes within each layer. They are one with the "Manifold" which contains all forms of self-consistent formal systems. They also Possibly have created AND/OR their Manifold possibly has similar vastness to mathematical superspace encompassing all forms/variants of mathematics identified with Woodin's constructible multiverse (Ultimate L) which includes Woodin cardinals, which originated from Proxima series multiverse. The Old Ones themselves have a near complete understanding of all of existence, allowing them to easily create "endless possibilities of life and mind."
Oh, and thank you for coming to this thread.

@QuasiYuri That's fair.

Downstreamers/Manifold having anything to do with Ultimate L/Proxima itself is a 'Possibly'.

But Woodin Cardinals natively existing in Manifold (not Proxima) itself is very likely, since it has that containing all formal systems statement.

So yeah, "Possible/Likely Tier 0" is probably better/best wordings here.

Okay, I think the consensus is that most have agreed... For now.

Time to wait for staff. I guess.
 
Hold on a second guys. Idk anything about about manifold. But the quotes I'm seeing here only state large cardinals including Woodin exist. Does anyone scale to this Woodin sized multiverse? As in is anybody in the verse able to affect the entire Woodin multiverse? Having such a massive cosmology wouldn't really matter in a battle setting if nobody scaled to it.
 
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