I think levels are only exponential in the sense that a fixed size level gap is equally bad no matter how high you are, in terms of raw energy output they grow much faster. Cultivation stages, by contrast, actually do follow an exponential progression, so I wouldn't expect to ever get to an infinite power output.
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Even Further Beyond [Complete]
- Thread starter Rihaku
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You should not pay much attention to Cantor's metaphor for God, no one else does.
Aabcehmu
Confusion as a Natural State of Being
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You may want to note the paranthetical. "Absolutely infinite" is not actually a property of all (or any) infinities.
What would say is infinite? Would you say that, for example, the cardinality of all natural numbers is infinite? What about the cardinality all real numbers? What about the cardinality of all real functions?
If any of those sound 'infinite' to you, or, hell, if literally any set of things at all sounds infinite to you, then you must recognize that transfinite things are infinite.
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The blurb in Vagabonds is hardly sufficient evidence for Cultivation being able to increase one's level without limit.
Your numbers aren't great here, and I don't see any evidence that our Stage growth should be expected to be exponential in time. Here's a couple references regarding the combat-type Cursebearer that give some bounds on the level vs Stage relation around the Low Titan tier which shows that a Titan is far higher level than 140.
If you break into transfinite numbers then your growth is not properly described as exponential unless you're also having transfinite time pass. You can never double your way into a number larger than all finite numbers; you have to transcend your way there. If we're going to get math-y in describing things then the layman's use of exponential has got to go.
The one caveat here is we have things like Immortal Awakening and Titanic Ascension that may be gamechangers and cause it to no longer be merely exponential. Note that Kong at least claims to have infinite worlds within him, for instance.
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Worth noting that Rihaku-type exponential growth seems to lend itself to qualitative shifts, like we would see (apparently) from Cursebearer progression or like we have seen (Dao Cleaving, Titanic Ascension) from Cultivation, when is starts giving conceptual silliness. But anything which breaches finiteness is effectively the same, I don't really see any distinction between being larger than any finite value and being infinite unless you're a mathematician linking infinity to God any you accidentally blundered your way into a proof that there are multiple infinities. Actual exponential power growth, like both Cultivation and levels are described as, should stay finite, though they clearly don't, presumably because of the more qualitative shifts.
I'm not actually sure of that, because of the aforementioned capacity to use things like Reality Masks (I expect we would get different types of those as we got farther along, so long as we did research). They seem like they could plausibly offer actually transfinite power, though who knows. I'm also not sure they follow actual exponential growth, because a 2-3 Stage gap is enough to ignore any number of your lessers, and an exponential gap wouldn't let there be any such number (though the number required would be something absurdly large).
Huh. That's odd, I guess the ratio must be less than that. Either way, it was supposed to be a conservative estimate, so that's fine. Exponential with time comes form a relatively trivial application of All Paths combined with Monster Vault to provide enemies of Stage equal to our effective Stage, then Necromancer to eat them, ~doubling each time. Of course, this needs a monster vault, but given enough effort I'm pretty sure we can find some way to make one. (That's the main issue I was talking about, with obvious solutions to try, in rough priority order to my mind, as follows: 1) Find a way to create a second copy of Grands. 2) Use our Essence Grand for it and EFB it. 3) Throw a (True, probably) Magnum Opus at the problem, they're supposed to be more versatile than the Diagram. 4) Actually put some thought into it and see what we think of.)
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Even with the monster vault our cultivation time each Stage was still increasing at a decent pace, though we certainly didn't have enough data to know if it would be properly characterized as exponential.
Concerning creating a Monster Vault, we shouldn't need the capability to create a second copy of Grands; the Essence version of a pocket dimension ought to be a different spell as far as I know and not cause any such issue. An Artifact to make it actually a good Monster Vault may prove a serious problem while the Fates remain undefeated, however, so given the scant amount of time remaining before Zang Kong awakens I don't expect the creation of such a Vault to be within the scope of this quest even without talk of a Magnum Opus, Truespell slot, or EFB.
I do however disagree concerning the effects of essence draining the Doombeasts, as it creates enemies of equal combat power which needn't have equal essence.
My plan is resurrection so we can resurrect the l8ch and don't bother to do research some diagram ourselves.
That anti social nerd Lich should have some juicy diagram not in their 5000 years of research.
Also Bae probably help us a lot in research fate diagram and positive influence on vengeance heroic passion to pull through.
Yeah, these were proposals for ways to get one before Zang Kong. Duplicating the Grand, or finding some way to get an Essence Grand which is close enough to give a similar effect but far enough to not count as the same for Artifact-creation purposes, is the hard part of doing it that way.
I mean, I guess the enemies who we can refine to be exactly like the enemies from the Overgrowth won't be consumable like Overgrowth monsters? That seems unlikely, though. This is all based on the fact that we can usefully consume Overgrowth beasts, which seem to operate like Jotunheim Beasts in that they both fundamentally operate on Essence (as both produce Cultivator-usable treasures), so presumably we can usefully consume Jotunheim beasts. It's possible they could be designed to have most of their power in bonuses rather than Stages, but we get at least some control over their construction, so we can just not set them up like that.
That only gives us twice as much Essence as we have, nowhere near what I want. My goal is to make an enemy who has as much Essence as we have effective Stages, like the Monster Vaults seem to do (because they can produce proportional Treasures). If we can do that and use Necromancy essence consumption to steal all its stages, we gain as many stages as we have bonus stages each iteration. Now, using All Paths we can get one bonus effective stage per Stage by being Stageless, and thus for each Stage we gain we can increase our number of bonus stages by 1.
Overall, then, this gives us about twice as many Stages as we had each time we do it, thus allowing for the exponential growth of our exponential power (that is, of Stages, which themselves grow exponentially) we would need to catch up to levels of the relevant beings in this multiverse. Essentially, I want our power to grow as 2^^n, not just 2^n, because 2^n means we take approximately forever to catch up to people who have been pulling off exponential growth for millions of millenia longer than we will have. Doubling our Essence each iteration only gets 2t power in time t, which is exponentially below what I want even though it is exponential itself. (Obviously my bases might be wrong, kindly ignore that. The principle should hold whether the base is 1.1 or 1,000, though at the upper end of that we'll catch up a bit faster --- not much faster if we're doubly exponential, though, doubly exponential is an absurdly prompt growth rate.)
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Rihaku
The Internet
Why would such a thing have essence?
Because the gain is exponential rather than linear!
Shard
One and Many
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Huh, specifically exponential instead of tetratational or pentational? Interesting.
Wonders if attributes follow that as well.
What would Nameless Yong's current level be under the Cursebearer system?
I'd just assume it was because there actually are relevant bounds to power, otherwise the Accursed would have had Graham's number or BB-20 (or 200, but it really really doesn't matter at that point), or if we want to get really bad, TREE(7) (again, you could use 3 or 20 equally well, they're all horribly intractable and really solidly larger than anything computable is going to practically get, unless I misread my math). If we want functions which grow quickly, they're all over.
The fact that the Accursed only has doubly exponential power means he's actually an achievable goal, for the proper definitions of achievable --- if anyone were to do something like septuply exponential, much less uncomputable values, it's just hopeless rather than a value people can theoretically reach via some horrifically unbounded infinite loop. Very few infinite loops are actually going to grant uncomputable levels of power.
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Ehh I think it's more that this is a better way to communicate what's meant and sufficiently large to convey the point. Keep in mind that it's not truly exponential - leveling up accounts for paradigm shifts like infinite quantities of energy. An actually exponential level meaning would imply some function relating things like amount of force created to level and hence give an infinite level around where this system gives one million as a level.
I definitely don't think we're meant to perceive the Accursed's power as an achievable goal.
I'm still not convinced there's some level at which you suddenly achieve a discontinuity and can suddenly exert transfinite quantities of force, I would expect that to be the result of a perk you could just only get once you were high enough level. The levels, in other words, seem like they would still be exponential in power, it's just that some perks transcend that.
But either way, I think the Accursed having a finite-number-like (in a way TREE(4) isn't) level means he's just asking to meet the Lord British Postulate, I would say. I don't expect it to be a reachable goal for anyone, but it's a goal, which we wouldn't be able to have if he had a more untouchable value.
Also that potential isn't infinite. Like, the difference between me and the Sun is probably (in absolute terms) less than the difference between a level 600 and level 601, but that doesn't mean if I trained really hard I'd be able to punch out the Sun. It was notable that a Potential-type Cursebearer could just keep levelling up, but that isn't the case for most beings.
That's somewhat of a fair point, but almost all of Rihaku's protagonists have workarounds for that. Odyssial/Ulyssian, for instance, had a Solar Exaltation, and those things are made to have endless potential (not that they necessarily succeed, but they can probably be made to). Arthur had both Chrysopoeia access (via the fealty to Imperia, but will) and the Ordinal Spiral, plus whatever else Vitalism and the Strategist could have gotten him. Hadrian had epic spell research and the obvious access to leveling, and as an epic wizard his levels could well have had exponential-ish value.
To bring this home, Nameless also has a way around this — the Beyonded Daos offered reduced bounds on progression, with FB being a definitionally endless path and All Paths being the step Beyond even that. He has a quite solid reason to just keep progressing forever, even if he can't get the same constant-ish time per improvement Seram (Cursebearer) could. The lack of a Dao quite plausibly allows for this sort of endless advancement, and clever usage of our other capacities should hopefully allow us to make up for the decreasing rate of advancement.
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I don't really agree about the discontinuity. I think you're taking too simple a view of levels and the stats of the Gamer expressed progression-Cursebearer. I think there's likely a soft cap on gaining Strength stat via increasing one's ability to exert finite force and further that it would converge to some value. In that case, one would eventually reach a point where to gain more than one point of Strength one must gain a qualitative boost to the expression of that strength or transition to capabilities involving infinite energy.
I think you're dramatically overstating the accessibility of the Accursed there. Imagine if Yong Shen were on our world and did not wish to be disturbed. Should he exert himself in the slightest towards such, we would have no hope whatsoever at disturbing him. That's a difference of less than a thousand levels, so if you imagine a being as much above Yong Shen as Yong Shen is above you, then you'd need more than 7e31 such escalations to have the Accursed be the next step. Over the course of the entire quest, we are still working on our second such escalation and are starting to run out of 'easy' options.
It's no more 'a goal' than gathering every neutron in our universe in one place with your bare hands is 'a goal'.
I will note that Odyssial eventually hit the limits of the Solar Exaltation, and had to figure out a way around them.
It's possible? In that case, I feel like Cultivation (maybe with a proper Beyonding, of course) should be able to make the same leap, because it's supposed to scale in the same way as Strength up to that point — where else would it go from there? It doesn't stop gaining in power, after all.
And that is why I don't think we have any shot without something which lets us escalate exponentially, and if we try we seem to have ways to generate such exponential stage gain. I quite agree that the Accursed can't be reached conventionally (that is, via actually gaining power only exponentially, no faster — so, linear gains of level/stage), but his level is computable and nowhere near the power level you would expect if he was doing something to get exponentially exponential gains. As such, I think his level being a value I can construct a halfway plausible way to reach has got to be a challenge, at least in part, even if it isn't one Rihaku will ever let us succeed at.
Yeah, that was the "can probably be made to" part.
Anyway, I'm getting to bed now. In the morning I'll probably be less bull-headed about incorrect interpretations of Rihaku's metaphysics.
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Rihaku
The Internet
The issue is that some are thinking of exponentiation only in the first value.
It would be more correct to say that the level system abstracts exponentiation across the entire gamut of conceptual escalation. For example, in the Nasuverse there is "raw physical power," and "conceptual power." In Exalted there might be physical, conceptual, and perfected power. A Cursebearer's progression represents higher levels of power first in the physical realm, then the conceptual, then the realm beyond, then the realm beyond that, and so on and so forth... that would be "2nd derivative" of escalation. Then there is the "3rd derivative" of escalation whereby the rate at which additional realms are breached accelerates with level density. Then the 4th derivative, etc... it might be called an infinite singularity husk of sorts.
It would be more correct to say that the level system abstracts exponentiation across the entire gamut of conceptual escalation. For example, in the Nasuverse there is "raw physical power," and "conceptual power." In Exalted there might be physical, conceptual, and perfected power. A Cursebearer's progression represents higher levels of power first in the physical realm, then the conceptual, then the realm beyond, then the realm beyond that, and so on and so forth... that would be "2nd derivative" of escalation. Then there is the "3rd derivative" of escalation whereby the rate at which additional realms are breached accelerates with level density. Then the 4th derivative, etc... it might be called an infinite singularity husk of sorts.
So progression is exponential in the sense that it's proportional to it's own derivative?
Interesting about combat type is level 438 and Jotarun of Yore need level 500 except for specialize build to defeat him.
That mean Jotarun is on city busting power that can outwit sign of sword combat type cursebearer.
...Yeah he is deserve Title for " Hero out of legend" that actually more hax than the heroine.
That mean Jotarun is on city busting power that can outwit sign of sword combat type cursebearer.
...Yeah he is deserve Title for " Hero out of legend" that actually more hax than the heroine.