Even Further Beyond [Complete]

[George]

So here are some random math pages, speaking of ordinals:
First uncountable ordinal - Wikipedia
Epsilon numbers (mathematics) - Wikipedia
Dedekind-infinite set - Wikipedia

The Dao of Greater Increase? "I will take what you have, and go even further beyond it"? </titledrop>

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I recommend looking to cardinals and the idea of homomorphisms. Kong Zang uses the idea of an isomorphism to decide how to create a new World in his structure: he just creates a copy. Yong Shen, on the other hand uses homomorphisms: he spins off a smaller World from his Primordium that preserves the property of being part of the elemental structure of the world. So to have both power and infinite growth, we need merely pick an aspect of eastern fantasy that scales up without limit and then populate our collections of worlds by examining smaller pieces of that concept that still preserve its structure. For instance, 3 and therefore 9 as 3*3 is, to my limited knowledge, a mystical number in that culture so you could have a collection of three collections of worlds that each have three worlds and thereby harness the power of a theme that involves the number 9 at the level of a Type III Titan. So the idea would be to say that, actually, Kong Zang is skipping a step here and after becoming a Type IV Titan who contains infinite worlds he should put his world into a structure of collections and thereby increase in power in the same way that a Type I or II Titan increases by advancing a Stage. In this sense, he would be skipping straight from a Type IV Titan to a Type VI Titan or else that when he advanced to a Type IV Titan he failed to do so properly and destroyed the structure of his Dao and that actually a 'proper' Type IV Titan would be collections of infinite collections of worlds rather than just an infinite collection of worlds.
That is, one can posit that a Titan with a collection of two Worlds that are different from each other is stronger than a Titan with two identical worlds, and then we could use abstract algebra to find a highly advanced yet also mystically significant structure to construct a Dao around and thereby harness more power at a given stage than Kong Zang. Homomorphisms come into this by telling us how to organize our collections and how to make sure a collection is a valid part of the whole - or rather, how to take the whole and identify an appropriate portion of it to make into a distinct collection.

 

[Alratan]

One thing we should consider in he search for a Dao is that scaling may not be the only useful metric to judge them on.

There may be an analogue to the quality as well as the quantity of inner worlds.

If we look at the Dao as the implementation of an algorithm to solve the problem that is existence, then simply getting bigger doesn't necessarily help, if all it does is throw more 'processing power' at a question. What we want is something that does better with the same amount of resources, so is efficient as well as scaling.

We should look for something that elegantly solves problems with minimum work, rather than brute forces them with computational power.

As an example, and this is possibly how Yong Liefang has explored his father's Dao, is that the Yong arts give dominion over all things beneath the tallest mountain. That includes all Cultivators, and all of humanity (and the remains of all previous Magical styles). Kong Zhang himself may still dwell beneath that mountain, so all his infinitude of worlds are still encompasses by Yong Sheg's Primordium.

 

[RedV]

Final Sanctum

Hab 2
Access 5
Sign 5
Size 3
Sec 5

And transition back to a flexible Hab 4 / Size 5 build upon going Further Beyond. This would give you access to basically the full array of combat Vault functions, giving you some combat-speed Utility effects that don't require direct Diagram casting. You have the bodily strength of a Titan but no Reality Effects so far, so this could help patch that hole in your capabilities while retaining long-term versatility. Reflect or absorb enemy attacks by opening portals in front of them, soft-teleport by opening Sign-augmented access portals around a battlefield, etc. High Access is also really nice if you end up making Artifact weapons/armor later. With more work you could even do crazy shit like using the Time sign to freeze an enemy's intercepted attack inside to save for later.

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Rihaku, could this be used as a seed Vault to create scaling monsters and release them outside later? Or can monsters made in the Vault not be released outside it?

I'd like to try for something like that- Typhon from TCMM was interesting, as were Coldbriar's Dragons, and if Vault can do something like release the monsters it breeds within itself out into the world it could be fun.

 

[Shard]

Tangential, I wonder what the Ordinal Spiral offered at level 14-20, and whether it extended out infinitely; Did our ability to use Shield and Seeker come from using the Shadow of the Ordinal Spiral?

 

[Rask]

That's a lot of functions for 1 vault guys. It's probably not impossible to get all of them, but it would be.. suboptimal.

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The requirements for the Monster Vault are fairly harsh. I just checked Rihaku's earlier posts on the Vault, and I found this.
Sign/Realm 7 occasionally spawns weak monsters with weak but relevant Priceless Treasures; Sign/Realm9 spawns appropriately challenging Monsters that drop Priceless Treasures of roughly equivalent power. This means the Monster Vault definitely needs the 9 rating, leaving not much else for a secondary role.

It's 15 points to get Hab, Sign, and Size to 5. Sign 9 can probably come from the artifact (in the example monster vault, it also reduces Hab to 3 for non-monsters). Leaves 5 points to be distributed between Acc and Sec, or 9 for an FB vault. With potentially reduced habitability, it's not really good as an empire phylactery. Monster Vault + Combat Vault might be an option still, if we don't care about someone potentially breaking in. (Or monsters breaking out? Is that possible?)

Requirements for effective Monster Vault
Hab: 5(+)
Acc: ?
Sign: 9
Sec: ?
Size: 5(+)


The combination of effective monster+combat vault is only available with the Proto-Arcology option, since both of the others have Sec at 5, which is the dump stat for the monster+combat variant.

 

[RedV]

Requirements for effective Monster Vault

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I'd prefer
Acc 5
Sign/Realm 5 (7 if FB, boost up with Artifact even more)
Hab 5
Sec 2
Size 3 (5 if FB)

For our FB Monster Vault. Size gives us plenty of space to hold 'em in, Access lets us release our little terrors on the world, Hab means they regen back in time.

We don't give a fuck about security because even if they get in, they have multiple scaling beasties and chimeras and dragons to eat them.

The low size is sad, but it just makes them even more stir-crazy and capable of hilarious destruction when released!

 

[Rotekian]

Naturalism is also capable of spawning monsters. So creating an elf habitat might well allow us to get away with passing up monster spawning. Otherwise I'm in favour of the monster spawning vault.

 

[vali]

So to have both power and infinite growth, we need merely pick an aspect of eastern fantasy that scales up without limit and then populate our collections of worlds by examining smaller pieces of that concept that still preserve its structure.

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Our concept is that of the Philosopher King, which draws its influence from Western Mysticism rather than Eastern. Hermeticism, the Kabbalah, alchemy, Gnosticism, the Philospher's stone, people like John Dee and Hermes Trismegistus; these are our themes.

I think a lot of people here are unaware that the Aleph being special is not a new idea in Western mysticism. The Aleph represents both the infinite nature and oneness of God. It is the first letter in the Hebrew alphabet, and the word for God in Hebrew, Elohim, starts with an Aleph. Aleph is the first letter of the Hebrew word emet (אֶמֶת‬), which means truth. In Jewish mythology, it was the letter aleph that was carved into the head of the golem that ultimately gave it life.

Cantor himself, the man who invented ordinals and set theory and the like, probably choose to use the Aleph to describe his new math on the nature of infinity precisely because of its divine implications. Here is an essay on God, George Cantor, and infinity.

Picking a Dao of the Aleph is like declaring ourselves God. It doesn't get bigger, or more powerful, or more mystically significant than that. There may be larger math things, but from a mystical and literary standpoint a Dao of the Aleph makes far more sense than anything else.

 

[Box Lunch]

If we look at the Dao as the implementation of an algorithm to solve the problem that is existence, then simply getting bigger doesn't necessarily help, if all it does is throw more 'processing power' at a question. What we want is something that does better with the same amount of resources, so is efficient as well as scaling.

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The Dao is a boat; an island of stability in a ocean of chaos. The Endless Sky's solution was simply to float above it all. That's certainly ingenious - in the same way that resolving a domestic dispute with double-homicide is genius. It misses the point of the Dao entirely.

 

[Rask]

I'd prefer
Acc 5
Sign/Realm 5 (7 if FB, boost up with Artifact even more)
Hab 5
Sec 2
Size 3 (5 if FB)

For our FB Monster Vault. Size gives us plenty of space to hold 'em in, Access lets us release our little terrors on the world, Hab means they regen back in time.

We don't give a fuck about security because even if they get in, they have multiple scaling beasties and chimeras and dragons to eat them.

The low size is sad, but it just makes them even more stir-crazy and capable of hilarious destruction when released!

Click to shrink...

I think both Size and Hab affect the spawn rate, which is why we don't want them to be below 5.

 

[Alratan]

I think that we may need to give up on the Monster Vault option. It compromises too much else.

We should consider that we can get other game changers at Further Beyond Vault that open up all sorts of things. Being able to use high level augmentation with unknown spells is a phenomenal benefit.

Imagine, for example, a Vault that reproduces the results of a yet unknown Essence spell to improve Cultivation or Artifice.

For even more cheese potential, Rihaku's description only said unknown spells. The Further Beyond version of Amplification is a spell that Nameless doesn't know. As Essence encompasses all of the standard signs, presumably their . What stops him having a central nexus within his Realm that produces such an effect?

Similarly, we may be able to produce a ((Even) Further) Beyond Solar Pill Furnace within a Further Beyond Vault, or a Beyond Sarcophagus.

The potential cheese options are incredibly vast. Yes, we can't take the spells out of the Vault. That doesn't stop us from benefiting from the spells in the Vault.

Simply getting a Beyond Sarcophagus would be amazing.

An Even Further Beyond Vault could well give the benefits of even more BP spent on appropriate spells.

 

[Box Lunch]

So, here's my shot at an ever-escalating Dao:

The Dao of Arabian Nights

• The Ultimate Anachronism! Though the Beast of Reason may be able to derive for himself any abstract mathematical or philosophical concept, I think it's safe to assume he's never heard of 8th-century Earth literature. This may prevent him from using specialized countermeasures against our Dao, which I can't assume is outside of his practical capacity.
• Intuitive Personal Synergy! Scheherazade was removed from her normal life and dropped into the lap of decadence, to provide amusement for a power-mad dictatorship on pain of death. Only her wits, imagination, and out-of-context perspective allowed her to survive by cobbling together familiar ideas in novel and unexpected ways. Nameless can empathize.
• The Power of Narrative! Deception isn't just misdirection: it's creating false belief. To create belief is the root of subjective reality, which is critical to the establishment of any internal world. As the only inherent limit to illusion is interest, it's entirely possible that we could expand infinitely simply by lying more.

 

[RedV]

I think both Size and Hab affect the spawn rate, which is why we don't want them to be below 5.

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Only Hab was explicitly noted as affecting spawn rate in that post you linked, I think. Besides, we can get both at 5 + Realm 7 with FB alone.

 

[Rask]

The potential cheese options are incredibly vast. Yes, we can't take the spells out of the Vault. That doesn't stop us from benefiting from the spells in the Vault.

Simply getting a Beyond Sarcophagus would be amazing.

An Even Further Beyond Vault could well give the benefits of even more BP spent on appropriate spells.

Click to shrink...

I think that's a little too optimistic. Rihaku said we may be overestimating what the Realm attribute can do.

Only Hab was explicitly noted as affecting spawn rate in that post you linked, I think. Besides, we can get both at 5 + Realm 7 with FB alone.

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Size 4 is only the size of a big mansion. This may be insufficient for fighting giant level-appropriate monsters.

 

[RedV]

I think that's a little too optimistic. Rihaku said we may be overestimating what the Realm attribute can do.

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Plus, there is a clear limit on time mods within FB Vault- 10x in either direction. We're not getting Sarcophagus out of it. If we're going for Cultivation enhancers, I prefer Chronoreactor since we can also simultaneously do other stuff while Cultivating with it, making Nameless' motivation nearly a non-issue.

Besides, entire time Vault was sold as monster factory and treasure generator. I'd prefer to have a clear goal on what to do with it.

 

[RedV]

Size 4 is only the size of a big mansion. This may be insufficient for fighting giant level-appropriate monsters.

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They can be house-sized monsters instead of giant kaiju things, then. Small size does not mean loss in deadliness- the killiest thing on this world is Kong Zang, and he's merely six feet tall!

We get size 5 with FB, also. That'll solve that particular issue.

 

[Shard]

Plus, there is a clear limit on time mods within FB Vault- 10x in either direction. We're not getting Sarcophagus out of it. If we're going for Cultivation enhancers, I prefer Chronoreactor since we can also simultaneously do other stuff while Cultivating with it, making Nameless' motivation nearly a non-issue.

Besides, entire time Vault was sold as monster factory and treasure generator. I'd prefer to have a clear goal on what to do with it.

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Palimsest Elder Beast provides Treasure Generation, Cultivation Multiplication, and Combat relevance, in addition to improving our ability to attract women to our utterly perfect form..!!

Meanwhile, people seem to want Vault to do like 6 different things now?

 

[RedV]

Palimsest Elder Beast provides Treasure Generation, Cultivation Multiplication, and Combat relevance, in addition to improving our ability to attract women to our utterly perfect form..!!

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I love Palimpsest too, but when did it begin to generate treasures?

 

[Rask]

Meanwhile, people seem to want Vault to do like 6 different things now?

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I mainly want it to be the best Monster Vault it can be. However, picking a monster Vault doesn't help us immediately - we don't have the artifact that enables the monster spawning - so I'm looking into options to have it work as a combat Vault too for convenience's sake.

I love Palimpsest too, but when did it begin to generate treasures?

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While we are capped at Peak Dao Cleaving we put cultivation progress into artifacts.

 

[Shard]

I love Palimpsest too, but when did it begin to generate treasures?

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Through Cultivation multiplying - Due to Chronoreactor we autocultivate, so multiplying cultivation speed means more cultivation base that can be burned to produce artifacts.

Titanic Grade Artifacts customized to precisely what we want.

 

[Alratan]

As an aside, thinking about how to save the elves, and to pick up on a previous advantage mentioned by Rihaku about going to Yonghai.

I speak of course, of the Legendary Pure Elven Waifu™️.

The plan here would be to marry the Elven Princess (Queen?) and get any inconvenient King to abdicate in our favour.

As King of the Elves, we can then grant land within our Vault to them as our vassals, which should hopefully make it count as both their land and our land. They can then use Naturalism on the Vault for our benefit and theirs.

We do need to consider how to sell them on this idea. One option I've considered before is whether Diminished Elven Artificers can use the Cultivation arts we developed for Xiaoling to recover Essence. It seems factually plausible, as I think we know that Xiaoling's mother would make a good test case.

We also need to sell the idea to the Ming, and this is where the Vault comes in. If we transfer the elves to the Vault, the area they used to occupy would be freed up.

If we are rescuing/evacuating the elves, we may want to tailor it to their use. For example, if we go Further Beyond, it might be possible to produce a Sign Augmentation effect based on an unknown spell that strengthens the soul, to the advantage of Binary Magicians and Cultivators alike, and apply it to the place. We may also want to see if we can collaborate with their artificers so that one of them can make a one-use artifact that interacts with the initial creation of the Vault to transfer the Elven kingdom inside it, in a way that doesn't use up our artifact slot.

 

[Shard]

We're of Titanic strength, and the 4 other Titans don't seem interesting in wiping the Elves, so if we push our weight around we can probably secure a peace treaty.

 

[Alratan]

think that's a little too optimistic. Rihaku said we may be overestimating what the Realm attribute can do.

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That reply was about Realm augmentations having to follow a theme though, and a Death theme that allowed zombie raising having other consequences.

I think we could manage an appropriate theme about empowerment.

Plus, there is a clear limit on time mods within FB Vault- 10x in either direction. We're not getting Sarcophagus out of it. If we're going for Cultivation enhancers, I prefer Chronoreactor since we can also simultaneously do other stuff while Cultivating with it, making Nameless' motivation nearly a non-issue.

Besides, entire time Vault was sold as monster factory and treasure generator. I'd prefer to have a clear goal on what to do with it.

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X10 for the entire Vault.

Also, the monster vault idea is something that's only become popular very, very recently.

Personally, using it that way when we have the Overgrowth right next door seems wasteful. Worse, it seems boring. We can create a vast, continent sized personal sub-dimension, and the bet we can do with it is produce a cheap knock-off what some one else has already achieved? That's a domain unworthy of the future Philosopher King.

Using a Vault for the purpose of the Phlactery of Empires has a lot longer track record.

We should also consider that there's a general desire in parts of he thread to incorporate/link the Vault to the Reality we form. A Monster Vault seems singularly unsuitable for that. Even the Ivory Tower would be less bad.

The Phylactery of Empires, however, would be pretty much perfect, particularly if combined with evacuating the elves there.

We're of Titanic strength, and the 4 other Titans don't seem interesting in wiping the Elves, so if we push our weight around we can probably secure a peace treaty.

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Grand Sopliphism strength, I thought?

 

[vsh]

So, interesting math fields to make Dao of. First, I wouldn't want to use a theory without a plethora of applications for Dao: that's just too self-contained to be effective. Ordinal theory is one example of that, it's just a nice construct in a set theory that's more of a result than a tool. If you want cool things to daosize, try one of those:
The Deep

Number theory
Functional analysis
Topology

The Practical

Optimization theory
Numerical analysis
Probability theory

The Meta

Mathematical logic
Category theory
Type theory

My personal favorite is number theory. Surprisingly fruitful and useful layer of math that deals with the most intuitive mathematical object there are and derives a huge and diverse number of results. Cryptography is the most iconic example but algebra and calculus have its roots there, and a lot of not really related fields like set theory or computer science use number theory to prove some of the most fundamental of the results.

 

[Rask]

Marry an elf? Scandalous! We bring shame to the Yong clan!

More thoughts on the monster Vault:

Monster Vault on 20 point + artifact build:
Hab: 5
Access: 3
Sign: 9 (5)
Sec: 2
Size: 5
It does what it's supposed to do, no more and no less.

Monster Vault on 24 point FB + artifact build:
Hab: 7
Access: 5
Sign: 9 (5)
Sec: 2
Size: 5
Lets the monster vault double as combat vault and increases the spawn rate. Worth the two BP? I'm not sure.

If all we want out of the Vault is monster spawning, the Beyond version suffices and we can take Palmipsest as Liminal instead. Dual role requires going FB and therefore the Liminal slot.