The Self-Reference Engine Introduction Thread (Actually a cosmology discussion)

[PrinceofPein]

The biggest question is about the level of the multiverse
Ultima said that the multiverse is high 1-A because in the English version we learn that it is necessary to use a progression of large cardinal numbers to number all the universes but in the Japanese version there is a statement that says that this progression will wait for "the extreme top of the large cardinal numbers" but we are not sure what level would give this statement, according to Doctor 129 the statement is precise but previously Cat said that mathematically it is not coherent

So we just need to know what the level of the multiverse is using the statement about the extreme top of the large cardinal numbers, the higher levels will be easy to evaluate then

About the characters that could have their own pages:

• The Giant Corpora will adapt to the level of the multiverse
• The alien from Alpha Centauri and the Laplace's Demon would adapt to certain upper layers of the knowledge hierarchy
• No known character adapts to other higher hierarchies
• SRE will fit at the extreme top of the whole cosmology

So then contention here is that we either follow the English version that is coherent or we follow the Japanese version that is not coherent?

My answer is, the verse is not officially translated, so I will go with the Japanese version whatever it gives.
Drop the quote here let me see what it gives.

 

[Jibz]

I havent cared enough to keep up with the thread is there an issue with the English version?

 

[Cat275]

I havent cared enough to keep up with the thread is there an issue with the English version?

Just check the translations, this bassically gives a summary.

 

[Jibz]

Just check the translations, this bassically gives a summary.

If i ask a question. Either give an answer or dont reply. Dont say “check yourself”.

 

[Cat275]

Alright mate.

 

[EndlessWords]

So then contention here is that we either follow the English version that is coherent or we follow the Japanese version that is not coherent?

My answer is, the verse is not officially translated, so I will go with the Japanese version whatever it gives.
Drop the quote here let me see what it gives.

I did not say that the Japanese version is inconsistent but according to Cat the statement about the extreme top of the large cardinal numbers does not work but he said he was neutral on the subject
In the English version we talk about a progression of large cardinal numbers:

Or else, it could be that when the Z to Z Theorem ultimately appears, and truth is once again upended, this disturbance will simply blow over. It’s fun to think that after that, without theorems or anything like them, the null set may appear, or a Null Set ø Theorem based on that, and from this Null Set ø Theorem the Von Neumann Ordinals: the {ø} Theorem, the {ø ,{ø}} Theorem, the {ø ,{ø, {ø}}} Theorem.

Given a choice, I would choose to be involved with this last. The ø Theorem points toward the Transfinite Number ω Theorem, which could lead to the ω + 1 Theorem, the ω + 2 Theorem, 2ω Theorem, ω*ω Theorem, etc., etc., a progression of large cardinal numbers.

Here is Doctor 129's explanation of the Japanese version:

in original text

ωのω乗理論等々、巨大基数の階梯を登っていく

mean after past ω^ω，this sequence will be continued to the ladder of large cardinals，and will climb the ladder of large cardinals

so， what i want to say is in the original text ，the author said directly，

here is a one-to-one correspondence between the ladder of large cardinals and the number of different cosmologies

And actually， after this the author said directly

階梯の極限の極限の高みから、

from the the highest point of this ladder

so this sequence will be continued to the highest point of large cardinals ladder

I think main problem is a lot of information is lost during translation which lead to misunderstanding

So the English version talks about a progression of large cardinal numbers without mentioning anything else but in the Japanese version we learn that this progression reaches the extreme height of the scale of large cardinal numbers

 

[EndlessWords]

Looks like the author now has trivialism, dialethism or something. ;-;

This is quite different than a infinite large cardinal hierarchy simply because some large cardinals surpass a infinite hierarchy and even have something either as big or bigger than it.
(Like axiom 13 which states there is always a bigger 13, or the hyper-hyper-mahlo to even bigger hyper-mahlo's or something like Reinhardt which is equivalent to 0=1 or V→V which puts the set theoretic universe into itself or maybe just V or L as itself (or combined, V=L), but the case here is that even 1 cardinal can have something more than a infinite hierarchy or even limit a entire infinite hierarchy to more of a single large cardinal, this is clearly not simillar, as many large cardinals have different nature's and function to other large cardinals.)

I was talking about infinite hierarchies because in fiction many infinite hierarchies have a last layer so I was thinking that a last layer to a hierarchy of large cardinal numbers would not be so confusing
You are right in saying that the great cardinals have different natures and functions but the explanation about the "anything goes" concept change your mind or not really?

 

[Antvasima]

The main problem here appears to be that adding such an extremely high-powered verse based on unofficial translations that are unclear or possibly inaccurate seems unwise.

 

[Cat275]

I was talking about infinite hierarchies because in fiction many infinite hierarchies have a last layer so I was thinking that a last layer to a hierarchy of large cardinal numbers would not be so confusing

Alright well let me remind you that some of the large cardinals has a hierarchy of themselves, so it's really hard to picture one compared to something that is just a infinite hierarchy.

You are right in saying that the great cardinals have different natures and functions but the explanation about the "anything goes" concept change your mind or not really?

The anything goes concept helps solving inconsistencies but also helps making one nonetheless it's bassically trivialism.

This is like a op version of ultimate L and 0=1 really helps on proving everything:

Trivialism - Wikipedia

en.m.wikipedia.org

I'm still neutral on the matter though.

 

[EndlessWords]

Alright well let me remind you that some of the large cardinals has a hierarchy of themselves, so it's really hard to picture one compared to something that is just a infinite hierarchy.

I see!

The anything goes concept helps solving inconsistencies but also helps making one nonetheless it's bassically trivialism.

This is like a op version of ultimate L and 0=1 really helps on proving everything,

I didn't know the concept of trivialism but it is really interesting, I didn't imagine that there was such a thing in SRE but when I think about it it explains a lot of things

I'm still neutral on the matter though.

Ok thanks for your opinion

 

[MrOMG]

Bump

 

[Antvasima]

The main problem here appears to be that adding such an extremely high-powered verse based on unofficial translations that are unclear or possibly inaccurate seems unwise.

So is there any way to resolve this problem quoted above?

 

[MrOMG]

Bump

 

[Timeless]

Should we get Ultima back to in the thread

 

[Antvasima]

Should we get Ultima back to in the thread

Well, I still haven't received a proper response to my last post.

What does Ultima currently need to evaluate here exactly?

 

[Ultima_Reality]

Yeah I guess I might as well tie up this dusty old thing already.

In any case, to clarify, before anything else: I am not sure why people are going around saying the book isn't officially translated, because it very much is.

- We know that the Giant Corpora of Knowledge evolve on a structure called "hierarchy of intelligence" but according to my understanding it is part of the multiverse and does not extend above, so also High 1-A

- The multiverse and the hierarchy of intelligence are only a step in the infinite hierarchy of logic, each layer in the hierarchy of logic is only a dream in the layer above, so the hierarchy of logic would be High 1-A

I should note, also, that as far as I am aware there is no evidence that the hierarchy of knowledge/intelligence and the logical hierarchy are different things. This excerpt, for one, makes it fairly obvious that they are the same thing, especially when you take its context into account (The Giant Corpora are going through an extended existential crisis after finding out the existence of entities up to 30 layers of existence above themselves):

“The pressure of knowledge,” Kircher said, just as the words sprang to his mind. “They believe, naively, that they are advancing under their own steam. Wouldn’t it be more accurate to say, though, that they are just going with the flow? Through something akin to the power generated at the interstices, between the levels of logic. Between the small degree of freedom and the large degree of freedom, in contact with the hyle of the universe, an entropic force is generated. In the direction of the large degree of freedom.”

In Kircher’s imagination, at the very end of the levels of logic there is a vast desert, stretching endlessly in all dimensions.

They are all now moving determinedly toward that desert, while continuing to disperse, physically. Whatever power they might have to resist that vastness is terribly feeble.

Regardless, though, what exactly are the remaining issues there? Most of this thread seems like fairly disjointed discussion about large cardinals, with some derailment here and there, so, hard to get anything from the above.

I'm probably making sandboxes for the verse profiles in a bit, by the by. Starting with the Giant Corpora of Knowledge, since they're the most feat-heavy characters in the book.

 

[Antvasima]

Yeah I guess I might as well tie up this dusty old thing already.

In any case, to clarify, before anything else: I am not sure why people are going around saying the book isn't officially translated, because it very much is.

Okay. That is probably fine then. Thank you for helping out.

 

[EndlessWords]

Regardless, though, what exactly are the remaining issues there? Most of this thread seems like fairly disjointed discussion about large cardinals, with some derailment here and there, so, hard to get anything from the above.

I would like to know if this information would not bring anything to cosmology

I'm probably making sandboxes for the verse profiles in a bit, by the by. Starting with the Giant Corpora of Knowledge, since they're the most feat-heavy characters in the book.

All right, I'll follow that

 

[Antvasima]

So what are the conclusions here so far?

 

[EndlessWords]

So what are the conclusions here so far?

Ultima will start making a sandbox for the character profiles starting with the Giant Corpora of Knowledge who are the characters we see the most in the story
I guess that the Giant Corpora of Knowledge will be high 1-A at most
If the Alien from Alpha Centauri has a profile it would also be high 1-A but 30 layers above
If the demons have profiles then they will be up to an infinite number of layers high 1-A
Nemo Ex Machina will be tier 0

I don't know if the information I sent above changes anything about the verse or not

 

[Antvasima]

Okay. I suppose that we should wait for Ultima then.

 

[Timeless]

What about the cardinal hierarchy? Is it part of the bad translation or something else?

 

[Ultima_Reality]

I would like to know if this information would not bring anything to

Ah, I see. Yeah, reading Ant's conversation with this user, that's... immensely clearer than the translation, which gives off the impression that it's referring to the series of ordinals it lists as "a progression of large cardinal numbers." Given that Doctor 129 seems to be, from what I understand, a native Japanese speaker, and how much more sensible that phrasing of the text is, I'd say they're probably right, especially given how SRE's author is an actual mathematician who'd certainly know better than to imply something as completely wrong as the above.

Considering "the extreme heights of the [large cardinal] ladder" is mentioned as existing in the verse, from a glance, that statement would probably be fairly high into 0 (Granted, there's the fact large cardinal axioms are mostly not ordered in terms of size, but in terms of "A implies B," but then a statement this strong would include the ones that'd result in a Tier 0 rating, anyway, those being the ones we are presently aware of)

In fact, given the main theme of the book, it seems like the author is playing with the idea that, technically, the "strongest large cardinal axiom" would be just an inconsistent statement, since by the principle of explosion, anything whatsoever can be derived from a contradiction, and so such a statement would be at the apex by virtue of implying any other (Which a mathematician by the name of Akihiro Kanamori illustrated by putting the statement "0 = 1" at the tip-top of a diagram depicting the hierarchy), so, the cosmology extending that far probably isn't unprecedented, at least.

So, yeah, fairly crazy stuff, so much so that I'd frankly want a second opinion here, to make sure I'm not getting ahead of myself.

 

[KingPin0422]

After reading the conversation between Ant and the other person, I'm inclined to agree with the conclusion that Ultima reached. The question is, where does the Self-Reference Engine scale in relation to the 0=1 axiom?

 

[EndlessWords]

Ah, I see. Yeah, reading Ant's conversation with this user, that's... immensely clearer than the translation, which gives off the impression that it's referring to the series of ordinals it lists as "a progression of large cardinal numbers." Given that Doctor 129 seems to be, from what I understand, a native Japanese speaker, and how much more sensible that phrasing of the text is, I'd say they're probably right, especially given how SRE's author is an actual mathematician who'd certainly know better than to imply something as completely wrong as the above.

Considering "the extreme heights of the [large cardinal] ladder" is mentioned as existing in the verse, from a glance, that statement would probably be fairly high into 0 (Granted, there's the fact large cardinal axioms are mostly not ordered in terms of size, but in terms of "A implies B," but then a statement this strong would include the ones that'd result in a Tier 0 rating, anyway, those being the ones we are presently aware of)

In fact, given the main theme of the book, it seems like the author is playing with the idea that, technically, the "strongest large cardinal axiom" would be just an inconsistent statement, since by the principle of explosion, anything whatsoever can be derived from a contradiction, and so such a statement would be at the apex by virtue of implying any other (Which a mathematician by the name of Akihiro Kanamori illustrated by putting the statement "0 = 1" at the tip-top of a diagram depicting the hierarchy), so, the cosmology extending that far probably isn't unprecedented, at least.

So, yeah, fairly crazy stuff, so much so that I'd frankly want a second opinion here, to make sure I'm not getting ahead of myself.

I agree that the wording given by Doctor 129 makes much more sense.
Your explanation agrees with Doctor 129 and yes the author of the book uses the concept of "anything goes", this universe was even crazier than I thought.
In short I also agree with this conclusion!

After reading the conversation between Ant and the other person, I'm inclined to agree with the conclusion that Ultima reached. The question is, where does the Self-Reference Engine scale in relation to the 0=1 axiom?

Looking at the graph posted by Ultima I would say that Self-Reference Engine would be scale at least here
Which would give a level 0 above Manifold pre-downgrade but I could be wrong

 

[Antvasima]

@Ultima_Reality @KingPin0422

Did you read my entire message wall conversation with the native Japanese speaker who had read the book in question, or just a partial screencapture?

You can both ask questions directly to them here if you wish:

Antvasima

vsbattles.fandom.com

 

[Ultima_Reality]

After reading the conversation between Ant and the other person, I'm inclined to agree with the conclusion that Ultima reached. The question is, where does the Self-Reference Engine scale in relation to the 0=1 axiom?

As far as I see, the numerical progression that reaches through the ladder of large cardinals would be restricted to the multiverse, as explained in the OP. Although I am uncertain if the "all possible stories" refers to the multiverse as a whole, or if that too is just a part of the collection that the Self-Reference ENGINE comprises.

Regardless, here is the sandbox draft for the Corpora's profile.

 

[Ultima_Reality]

Did you read my entire message wall conversation with the native Japanese speaker who had read the book in question?

And I did, yes.

 

[Antvasima]

Okay. That is good then.

So what tiering should we preferably apply here, and what is the reasoning for it?

 

[Ultima_Reality]

So what tiering should we preferably apply here, and what is the reasoning for it?

The slightly-less-compacted TL;DR is:

Individual Corpora of Knowledge are High 1-B, since they became one with and administer every single natural phenomenon in their home universes, which are infinite-dimensional spaces (With objects in the 3-dimensional subset inhabited by humans, like stars, actually being cross-sections of objects residing in that higher realm)

The full extent of the multiverse itself, as far as I see, is 0, since there is a one-to-one correspondence between a portion of the number of universes there is and the full collection of all cardinal numbers, with this explicitly reaching up to the ladder of large cardinals. The "extreme heights of it," in fact, past which everything breaks down into arbitrary nonsense, since spacetime has been fragmented so badly that "everything follows," even things like a sentence and its negation being true at once.

This doesn't scale to the individual factions of Corpora, but it does scale to the full might of their collective, since they explicitly hold dominion over the entire multiverse, and the narration at one point says that, if the need arose, they could burn all universes as fuel to augment themselves and tear through existence.

Then there's infinite layers above that. And the Self-Reference Engine containing it all as the collection and teller of all possible stories.

There's more detail to the higher stuff, but it's been elaborated in the OP already, so any curious onlooker can refer to it.

 

[KingPin0422]

If at all possible, it wouldn't be a bad idea to get another translator to double-check this stuff, would it? The native Japanese speaker gave some pretty compelling stuff, but just in case...

 

[Ultima_Reality]

Oh, I absolutely agree. This stuff is a bit high into the Tiering System, so, gotta make sure it's rock-solid.

 

[Timeless]

How do you view a sandbox without having the link?

 

[Setsuna_tenma]

How do you view a sandbox without having the link?

Just look at ultima recent contributions in his profile

 

[Antvasima]

The slightly-less-compacted TL;DR is:

Individual Corpora of Knowledge are High 1-B, since they became one with and administer every single natural phenomenon in their home universes, which are infinite-dimensional spaces (With objects in the 3-dimensional subset inhabited by humans, like stars, actually being cross-sections of objects residing in that higher realm)

The full extent of the multiverse itself, as far as I see, is 0, since there is a one-to-one correspondence between a portion of the number of universes there is and the full collection of all cardinal numbers, with this explicitly reaching up to the ladder of large cardinals. The "extreme heights of it," in fact, past which everything breaks down into arbitrary nonsense, since spacetime has been fragmented so badly that "everything follows," even things like a sentence and its negation being true at once.

This doesn't scale to the individual factions of Corpora, but it does scale to the full might of their collective, since they explicitly hold dominion over the entire multiverse, and the narration at one point says that, if the need arose, they could burn all universes as fuel to augment themselves and tear through existence.

Then there's infinite layers above that. And the Self-Reference Engine containing it all as the collection and teller of all possible stories.

There's more detail to the higher stuff, but it's been elaborated in the OP already, so any curious onlooker can refer to it.

Okay. That seems to make sense to me. Thank you for the explanation.

If at all possible, it wouldn't be a bad idea to get another translator to double-check this stuff, would it? The native Japanese speaker gave some pretty compelling stuff, but just in case...

Oh, I absolutely agree. This stuff is a bit high into the Tiering System, so, gotta make sure it's rock-solid.

That is probably a good idea. Feel free to request help with this in our official translation requests wiki management forum thread.

 

[Ultima_Reality]

That is probably a good idea. Feel free to request help with this in our official translation requests wiki management forum thread.

Done so.

 

[Antvasima]

Thank you.

 

[MrOMG]

Here is my interpretation at this point. For the beginning of hierarchies leading to other hierarchies, in which the multiverse of Giant Knowledge Corps is nothing more than one rung in the Ladder of Hierarchies. And the number of hierarchies should be equal to the number of Theories, and all this is due to the evolution of evolution itself, because of which the history of Self Reference Engine tries its best to complicate its structural complexity, and according to the idea such a huge number of Theorems arose precisely due to the evolution of history and space. Well and an infinite chain of stories, in which the story of Self Reference Engine is no more than one group, and there are an infinite number of the same stories about Self Reference Engine, and due to the fact that there are all kinds as well as impossible (it is doubtful) stories, then there must surely be stories that must surpass the story of Self Reference Engine, I would not be surprised if there is a story called "this is the story that surpassed the story of Self Reference Engine". This would create a sort of hierarchy of stories. And at the very top, beyond everything and everything Nemo Ex Machina who created it all, and of course surpasses it.

 

[Ultima_Reality]

And the number of hierarchies should be equal to the number of Theories, and all this is due to the evolution of evolution itself, because of which the history of Self Reference Engine tries its best to complicate its structural complexity, and according to the idea such a huge number of Theorems arose precisely due to the evolution of history and space.

I am not sure that the number of hierarchies there are is necessarily the same as the progression of large cardinal numbers, since the latter specifically enumerates a subcollection of the multiverse generated by the Event, which higher planes of the logical hierarchy are completely above. So much so that Alpha Centauri's race saw the whole thing as more of a nuisance than anything, and explicitly didn't fix it themselves because "their hands were too big" for such work:

“Right now, we are faced with a critical situation. We are hurrying down the path, but the truth is, the space-time structure your calculations have created is interfering with our existence.”
Having first been called computers and then interference, the giant corpora boiled over with rage, escalating their state of war readiness to DefCon One. Now they understood what the old man was trying to say. He wants to alter our space-time root and branch, to secure a right-of-way for a road to just-over-there.
“Under ordinary circumstances, we should be able to avoid conflicts like this. For example, by having you move that way just a bit, for a little while. Then you could come back later.”
This was something the giant corpora of knowledge did on a routine basis, so they were easily able to grasp the idea. But the truly depressing thing now was that it was completely unclear to the corpora just what sort of metaphor was being employed. According to the conventional wisdom shared by the giant corpora of knowledge, a change in the past was merely a change in the past. Something had was something lost; if it was then restored to something had, that would just be the same as before—something had. For a being from thirty levels higher up the hierarchy of knowledge, that should be simple stuff.
“But your computers are attaching very gnarly roots to space-time, making them difficult to uproot. Our hands are too big for such work.” So saying, the old man scratched his head and bowed it low.
Unsure whether they were being praised or mocked, the giant corpora of knowledge wavered in their judgment.
“Just imagine a tree suddenly growing smack in the middle of where you want to put a road. You would get rid of it, wouldn’t you? If you do a bad job of it, some of the roots might be left behind. If you take your time, and do the job carefully, it is possible to pull up the tree without damaging the roots. Unfortunately, though, we don’t have that much time remaining.”
The giant corpora of knowledge began to protest, saying you can make as much time as you want. If you’re not willing to go to that much trouble, you must be out to hurt us.
“This is a problem whose complexity is far beyond your comprehension of the very notion of complexity, and as such it is difficult to explain.”

 

[MrOMG]

I am not sure that the number of hierarchies there are is necessarily the same as the progression of large cardinal numbers, since the latter specifically enumerates a subcollection of the multiverse generated by the Event, which higher planes of the logical hierarchy are completely above. So much so that Alpha Centauri's race saw the whole thing as more of a nuisance than anything, and explicitly didn't fix it themselves because "their hands were too big" for such work:

Well, such a thing to remember, where did such a huge number of theorems come from, why did the number of theorems not end at infinity, why did it advance even further, reaching the top of the progression of large cardinal numbers, it is all because of the evolution of evolution itself. It seems that because of the Event somehow history began to strive to complicate its structure, becoming recursive at all levels, first there was one universe with 3 dimensions, then multiverse with an infinite number of dimensions, then began to appear higher dimensions, in which some whales and turtles live, the appearance of the hierarchy of knowledge, well then further hierarchies, it was even said that meeting a being from a higher level hierarchy is not a new Event, but a continuation of the current Event, referring to the fact that these hierarchies appeared because of the Event, that is, from one ordinary 3-dimensional universe/common story that tried hard to complicate itself. In short, everything is recursive on all levels, because of the evolution of evolution itself.