Manifold : Possibly having Woodin Cardinals (Tier 0 Upgrade)

[Threemagi]

To elaborate ImNot4nUser, yeah, Downstreamers or Old Ones created the whole thing.

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-

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?

To redesign an infinite ensemble of universes: what terrible responsibility, what arrogance...

(Random fact : 'World Engines' books are actually part of Manifold series, despite the different naming.)

 

[Planck69]

Tier 0 looks fine to me.

 

[Antvasima]

Hmm, good point actually. Tier 0 does seem justified then, but I'd still like to see if DT has any counterarguments.

@DontTalkDT

We would appreciate further input from you here, as it is about a possible tier 0 upgrade.

 

[DontTalkDT]

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.

But... our real world also has the concept of the woodin cardinal? Like, that the idea/concept exists doesn't mean that anything that idea/concept physically describes exists (which, in case of a cardinal, means that anything physical exists in these amounts)

You speak about "a multiverse where all mathematical possibilities are true" but in which way is that established? Remember I don't know the verse at all. Like, is it a space where every mathematical idea is represented in some way, but that way is not necessarily a reflection of what it describes (e.g. a cardinal being represented as a building) or is there also some different kind of space where it is stated for every mathematical concept to appear in a concrete physical way portraying exactly its properties (i.e. which is described in a fashion s that we can infer from the fact that cardinality exists, that it contains something that cardinality many times)?

 

[KingPin0422]

But... our real world also has the concept of the woodin cardinal? Like, that the idea/concept exists doesn't mean that anything that idea/concept physically describes exists (which, in case of a cardinal, means that anything physical exists in these amounts)

False equivalence. We haven't proven that the real world is a mathematical multiverse, wherein "mathematical existence equals physical existence," as Tegmark himself put it. Then again, that itself relies on the Manifold being a mathematical multiverse in the first place... which leads into the next part.

You speak about "a multiverse where all mathematical possibilities are true" but in which way is that established? Remember I don't know the verse at all. Like, is it a space where every mathematical idea is represented in some way, but that way is not necessarily a reflection of what it describes (e.g. a cardinal being represented as a building) or is there also some different kind of space where it is stated for every mathematical concept to appear in a concrete physical way portraying exactly its properties (i.e. which is described in a fashion s that we can infer from the fact that cardinality exists, that it contains something that cardinality many times)?

That's a good question. To answer this, I have gathered some quotes both from this blog (such as it is) and from the resources provided in this thread, with the relevant parts highlighted in bold:

'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.'

"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."

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."

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.

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.

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.

I don't know this verse either, but with these quotes at hand, I'm pretty strongly convinced that the Manifold is a true mathematical/type IV multiverse, and since the mathematical possibilities include Woodin cardinals, it follows that something, somewhere, in the Manifold physically corresponds to them. What do you think, though?

 

[Threemagi]

@KingPin0422 Thank you for helping out copying these quotes. I just started doing it but it seems I have been nijaed.

To elaborate, "mathematical logic underlay all things" is from Manifold Space novel.

"All logical system of mathematics must exist" is from Manifold Time novel.

And lastly, the quote I posted previously "physical laws are guided by mathematical which is evidently inherent in reality " is from Ultima novel.

 

[KingPin0422]

Thanks! I added the Ultima quote and updated the other two quotes with their sources.

But anyway, all that's left is to get DontTalk to respond. I think I made a pretty good argument, so let's see if it convinces him, since he admits that he doesn't know the verse.

 

[Threemagi]

Thanks! I added the Ultima quote and updated the other two quotes with their sources.

But anyway, all that's left is to get DontTalk to respond. I think I made a pretty good argument, so let's see if it convinces him, since he admits that he doesn't know the verse.

You are welcome.

Your argument is simple and easy to understand for sure.

It was my mistake not to add relevant quotes from previous books on the OP since I thought it will just clutter my OP and I kinda assumed everyone is already familiar with Manifold.

Maybe I should add it now...

 

[Ovy7]

Honestly, Derp's post convinced me even more that Tier 0 is legit. The Manifold universe seems clearly build with the concept of the Type 4 Multiverse, also called the Ultimate Assemble or The Mathematical Universe (how Tegmark calls it), and it also mentions large cardinals like Wooding, which, by the definition of the Type 4, should represent an actual structure in the grand cosmology.

I 100% agree with the upgrade, no doubt about it.

(I also recomend the book "Our Mathematical Universe" by Tegmark, for anyone who might be interested in this concepts).

 

[Threemagi]

Ultimate Assemble

Insert Avengers Assemble joke here : "Baxterverse... Assemble!"

Which considering the context of this thread, it kinda seems fitting.

Ultimate Ensemble. Most ambitious crossover event in history, lol.

Even then, just a subset may be enough to contain many events of Baxter stories...

"There are infinite number of possible universes in the manifold," Anna said.

"Of those only a subset - nevertheless infinite itself - are capable of supporting self-aware substructures.

Hm, is this what they call 'Aleph-0'? (infinite^infinite)

 

[Antvasima]

Thank you for helping out here DontTalk.

 

[Hmesko]

@Threemagi Yes. Cantor defined an infinite set that way. An infinite set can have proper subsets equinumerous to the whole thing. For example (Infinity/ 2) is still infinite.

 

[Hmesko]

@Threemagi This isn't unique to ALEPH0 though. All infinite sets have this property.

 

[Threemagi]

@Hmesko Ah, thank you for the info. I thought Manifold's infinity is 'special' or something since I was under the impression that 'normal [infinite set] has [finite subset]'.

 

[DontTalkDT]

False equivalence. We haven't proven that the real world is a mathematical multiverse, wherein "mathematical existence equals physical existence," as Tegmark himself put it. Then again, that itself relies on the Manifold being a mathematical multiverse in the first place... which leads into the next part.

That's a good question. To answer this, I have gathered some quotes both from this blog (such as it is) and from the resources provided in this thread, with the relevant parts highlighted in bold:











I don't know this verse either, but with these quotes at hand, I'm pretty strongly convinced that the Manifold is a true mathematical/type IV multiverse, and since the mathematical possibilities include Woodin cardinals, it follows that something, somewhere, in the Manifold physically corresponds to them. What do you think, though?

That is pretty strong evidence, although I'm not actually quite sure whether quite this is the desired interpretation there.

These quotes specifically state that there is a universe corresponding to every formal system. A formal mathematical system is not the same as a mathematical object, though.
A formal system is an abstract structure used for inferring theorems from axioms (i.e. assumption) according to a set of rules.
Or, in other words, a formal system is an entire kind of mathematics, while woodin cardinal would be one object in one formal system. Basically, for every formal system there are (up to) infinite mathematical objects.

And, while there is a universe for each formal system, that every mathematical object of that system exists in the most literal way is questionable.
ake our universe as an example. Our universe actually (at least in a certain sense) needs infinite-dimensional spaces to be described. That's because things like the wave functions which model quantum behaviour build such a space. Of course, this isn't a physical infinite-dimensional space. Still, if you tried to simulate our universe, you likely couldn't avoid using such concepts.
In other words, the formal system responsible for a regular universe like ours, could contain aspects that are necessary to describe our reality but not have these aspects physically present in it.
Even more, it could contain things that must logically exist at a mathematical level as consequence of the rules of the reasoning of the logical system, yet don't have physical relevance. The ZFC-Axioms, on which the logical system modern mathematics is founded, are all necessary for the systems of mathematics we currently believe describes our reality best. None of them is unnecessary. Yet, as a consequence of its rules, many mathematical objects that are irrelevant to the description of our reality exist too.

Of course, stronger yet than the idea of a universe for every formal system, is the idea of every logically possible universe. Strictly speaking, that would include the idea of a universe with a large cardinal number of dimensions.

I guess I can be convinced of a "possibly" or "likely" rating here, but for more I think a more explicit mention of a wodin cardinal many something as physical stuff would be necessary (even if it were just as logically possible).

 

[Threemagi]

@DontTalkDT Thank you for reading through all that.

I see that Woodin Cardinal can exist as one of concepts making up a formal system. But WC itself doesn't necessarily need to exist physically even though it does have consequence to other physical things existing.

So.. Possibly/Likely Tier 0, huh...

 

[Darksmash]

I think a likely rating could be a good compromise here

 

[Threemagi]

So, I assume we should throw away "1-A" and straight up remove them from Category:Tier 1?

 

[Rikimarox2]

I also agree with Tier 0 FRA. I'm honestly more for straight up tier 0, rather than possibly/likely given Pins arguments.

 

[Rabbit2002]

If Manifold becomes Tier 0, it will be the Strongest on Wiki, if something is stronger it's just Math verse (Suggs is a bunch of nonsense and stupid that can't be compared or understood)
Woodin cardinal is actually so much larger than Mahlo cardinal (Baseline Tier 0) that it far exceeds the smallest Level whose number of Layers above Baseline Tier 0 is equal to the number of 11C beings combined to equal that degree, literally

 

[Ultima_Reality]

I guess I can be convinced of a "possibly" or "likely" rating here, but for more I think a more explicit mention of a wodin cardinal many something as physical stuff would be necessary (even if it were just as logically possible).

That sounds a bit too nitpicky, in my opinion. The disjunction here seems to be that you are treating the "All logically possible universes exist" statement as something separate from the implication that mathematics governs reality, and thus that Manifold takes place in a Type IV Multiverse, when they are just informing the same thing and building upon a single context. In fact, your examples and other similar arguments seem to be directly addressed by the text itself, in this case; for instance, they refer to the phase space that models the possible states of the universe as a literal greater set in which it is embedded:

This is the Fermi Paradox — right, Malenfant? If the aliens existed, they would be here. I heard you lecture on that so often I could recite it in my sleep. But I agree with you. It’s powerful strange. I’m sure Fermi is telling us something very profound about the nature of the universe we live in.

It is as if we are all embedded in a vast graph of possibilities, a graph with an axis marked time, for our own future destiny, and an axis marked space, for the possibilities of the universe. Much of your life has been shaped by thinking about that cosmic graph. Your life and, as a consequence, mine. Well, on every graph there is a unique point, the place where the axes cross. It’s called the origin.

Which is where we’ve finished up, isn’t it, Malenfant? And now we know why we were alone… But, you know, one thing you never considered was the subtext. Alone or not alone — why do we care so much? I always knew why. We care because we are lonely.

“Malenfant, perhaps there are a cluster of alternate universes with identical histories up to the moment of some key event in the evolution of humanity — and differing after that only in the details of that event, and its consequences.” Nemoto waved her hands vaguely, as if trying to indicate three-dimensional space around her. “Imagine the possible universes arrayed around us in a kind of probability space, Malenfant. Do you see that universes differing only in the details of the evolution of mankind must somehow be close to ours in that graph?”.

Further in the blog, a few quotes even have the characters talk about the solution space of a given function as being a real thing, too, and in this case, what they are referring to is the solution space of the universal wave function:

"So where does the message come from in the first place? The information in it, I mean. If you're just copying what you received— "

Cornelius stopped tapping and sighed. "That's a deeper question, Malenfant. At any point in time, at any now , there are infinite numbers of pasts that could have led to the present state, and the infinite number of possible futures that flow from it. This is called the solution space of the universal wave function. Somewhere out in that solution space some equivalent of me figured out and wrote down the message, and sent it back with a Feynman radio. "

So, as far as I'm concerned, a solid 0 is more than fine here.

 

[Threemagi]

Strongest

... Till it inevitably got downgraded (that seems to be the common fate of such verses). Which I'll give... few months, probably. Lol.

@Ultima_Reality Thank you for reading through the quotes on that blog, and for giving your thoughts on the matter.

I want to add origin to each one of those quotes (you posted) but I myself am not sure.
But afair :
1. Is from Manifold Space
2. Is from Manifold Origin
3. Is from Manifold Time

Well, just in case if people want to know where those quotes came from.

 

[Ultima_Reality]

... Till it inevitably got downgraded (that seems to be the common fate of such verses). Which I'll give... few months, probably. Lol.

Manifold, as far as I can ascertain, is not a weeb verse, so you should be fine in that regard.

 

[Delta333]

Manifold, as far as I can ascertain, is not a weeb verse, so you should be fine in that regard.

DC exists

 

[Darksmash]

DC exists

TIL that DC is a weeb verse

 

[DontTalkDT]

That sounds a bit too nitpicky, in my opinion. The disjunction here seems to be that you are treating the "All logically possible universes exist" statement as something separate from the implication that mathematics governs reality, and thus that Manifold takes place in a Type IV Multiverse, when they are just informing the same thing and building upon a single context. In fact, your examples and other similar arguments seem to be directly addressed by the text itself, in this case; for instance, they refer to the phase space that models the possible states of the universe as a literal greater set in which it is embedded:





Further in the blog, a few quotes even have the characters talk about the solution space of a given function as being a real thing, too, and in this case, what they are referring to is the solution space of the universal wave function:



So, as far as I'm concerned, a solid 0 is more than fine here.

The fact that I'm considering "all logically possible universes" as separate from "every formal system corresponds to one universe" is the reason why I'm fine with a likely/possibly in the first place. As I said in my last post, every formal system describing one universe doesn't really imply every mathematical object being given physical reality. EVery logically possible ones would at least in theory indicate that for most of the... physically ore plausible ones. Such as things existing cardinal numbers of time.

The solution space you bring up clearly isn't a physical manifestation of the infinite-dimensional wave function space, though. That's just the all possible futures/pasts that many Tier 2 verses have, too.

 

[Ultima_Reality]

The fact that I'm considering "all logically possible universes" as separate from "every formal system corresponds to one universe" is the reason why I'm fine with a likely/possibly in the first place.

The solution space you bring up clearly isn't a physical manifestation of the infinite-dimensional wave function space, though. That's just the all possible futures/pasts that many Tier 2 verses have, too.

Sure, and my point is that there is no reason to consider them as separate to begin with, because they are clearly meant to complement one another. Couple that with all of the statements regarding mathematical existence being more fundamental than physical existence and defining it at the core, and you have a pretty clear picture of what it's meant to be, in my opinion. You seem to be looking at the quotes in strict isolation instead of looking at the background context each of them are informing.

DC exists

You got me.

 

[DontTalkDT]

Ok. If the other knowledgeable people here think so to, then go ahead.

 

[Threemagi]

Okay, I assume there's no more hestitation towards Straight up Tier 0?

Changes :
Tier 1-A to Tier 0

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 and possibly greater Baxter multiverse connected with Manifold, which when combined, make up 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."

Is there any other 'secondary superpowers' that need to be changed?
Or maybe Transduality still Type 3?
Beyond Dimensional Existence still Type 2?

 

[deonment]

I mean is there a reason for said transduality rather than just being tier 0, because if so it depends on the evidence for it, otherwise they shouldn't get it

 

[Threemagi]

Okay, less trouble for me then.

 

[Antvasima]

Thank you for working out an agreement here. This revision can probably be applied then.

 

[Ovy7]

Can i ask a question please?

Exactly how much transcendence above baseline tier 0 will they have when the manifold's tier 0 upgrade is complete? How much above WoD and TP will they be?

Hmm, really really really high. Like, stupidly, amazingly, mindbogglingly high. So high that saying that baseline tier 0 would be like tier 11-C for Manifold would be extreme downplay.

I'll quote Rabbit, who also made a really good example for how high this is:

Woodin cardinal is actually so much larger than Mahlo cardinal (Baseline Tier 0) that it far exceeds the smallest Level whose number of Layers above Baseline Tier 0 is equal to the number of 11C beings combined to equal that degree, literally

 

[HalilAssassino]

Hmm, really really really high. Like, stupidly, amazingly, mindbogglingly high. So high that saying that baseline tier 0 would be like tier 11-C for Manifold would be extreme downplay.

Oh, man. Literally craziness. Thank you Ovy7

 

[Rikimarox2]

Also, please, for the love of all that is holy, add scans when you make the changes. The old profile lacked any sort of scan.

 

[Ovy7]

The Downstreamers' profile does link to the Cosmology Blog IIRC.

 

[Antvasima]

So, just out of curiousity, are Woodin cardinals somewhere on a Suggsverse level? However, no derailments or other nonsense after this question please.

 

[QuasiYuri]

So, just out of curiousity, are Woodin cardinals somewhere on a Suggsverse level? However, no derailments or other nonsense after this question please.

"Every universe within the Metaverse is absolutely boundless and it is so boundless that it transcends the greatest inaccessible cardinal."
Guess it doesnt go above first floor..?

 

[Antvasima]

Okay.

 

[KingPin0422]

So, just out of curiousity, are Woodin cardinals somewhere on a Suggsverse level? However, no derailments or other nonsense after this question please.

I mean, ehh... Suggsverse is wildly inconsistent cosmology-wise. It has regular universes using a literal copy-and-paste of both the Mathiverse's in-verse description and our justification of its rating, but then much higher levels are apparently much less impressive. The Metaverse, for example, only describes exceeding inaccessible cardinals, which very well can be lowballed to baseline tier 0. I believe there is an even higher level of the First Floor that directly references proper classes, too, but I'd have to look. Point is, accurately tiering Suggsverse is nigh-impossible, which is why no one on any battleboard site does it.

Hmm, really really really high. Like, stupidly, amazingly, mindbogglingly high. So high that saying that baseline tier 0 would be like tier 11-C for Manifold would be extreme downplay.

I'd also like to add that the Goddess of the Manifold would scale even higher. The Old Ones' manifold is just one thread in the greater tapestry of a "manifold of manifolds," which the Goddess scales to. In other words, the ontological difference between the Goddess and the Old Ones is equal to the ontological difference between the Old Ones and regular humanity. Of course, we don't treat these sorts of levels of transcendence as impressive anymore, but if you think about the example that was given to illustrate the Old Ones' scale and then extend that to the Goddess, then maybe...