This is such a relief. I couldn't see how Keris was going to escape this on her own.
Ascensions and Transgressions: the Tales of Keris Dulmeadokht (Exalted game)
- Thread starter Aleph
- Start date
The epilogue was fun in several ways, not the least of which confirming my guess about Ipithymia being a better occultist than she lets on.
Also, hinting that a future Infernal Liaisons may involve Keris, Lilunu, and Ligier.
Which is a combination that makes me concerned that Adorjan will poke her head in Lilunu to see what the fuss is. Unfortunately, she doesn't have Eko's foibles about lewdness, funny as it would be to scare off the yanyan murder wind in that fashion.
Also, hinting that a future Infernal Liaisons may involve Keris, Lilunu, and Ligier.
Which is a combination that makes me concerned that Adorjan will poke her head in Lilunu to see what the fuss is. Unfortunately, she doesn't have Eko's foibles about lewdness, funny as it would be to scare off the yanyan murder wind in that fashion.
And so the hints of Lilun resembling Ruvellia bear further fruit.
Five Calibrations Pass - Late Earth 775
- Location
- The sixth circle of Hell (second on weekends)
- Pronouns
- She/Her
Oh jesus. Okay, so fair warning, Late Earth 775 is a fucking massive chapter. We couldn't really cut it down, there were just too many plot points that needed wrapping up in Hell, and too many consequences to show - both to Keris's mental state in the aftermath of The Golden Coin and to her relationships, alliances and spoils. This season has been, if perhaps not the chronological or wordcount midpoint of Kerisgame as a whole, then at least, I feel, the narrative midpoint; the halfway point of the five-year lead-up to the all-important vote, the game-changer in a bunch of major relationships, the conclusion of a few plot threads that we've been leading up to and the start of a fair few new ones.
I hope you've enjoyed everything so far, and I very much hope you enjoy everything to come as we continue with Ascensions and Transgressions! But not for a while, because for the next few updates we're going back to Calesco to wrap up her Water and catch her up to the end of Earth.
I hope you've enjoyed everything so far, and I very much hope you enjoy everything to come as we continue with Ascensions and Transgressions! But not for a while, because for the next few updates we're going back to Calesco to wrap up her Water and catch her up to the end of Earth.
That armour is really neat, and I look forward to seeing what Style Keris comes up with for it.
Very nice to see Lilinu being more proactive, and Eko getting a chance to work on her own.
Very nice to see Lilinu being more proactive, and Eko getting a chance to work on her own.
Well, this just got very recursive really fast.
Yeah, Ligier would be the munchkin, wouldn't he?
Did Keris just turn that poor innocent imouto-chan into a depraved yandere?
Khereon Ul: "See, this is why I'm friends with her!"
Oh, and Keris had a Limit Break and smashed up an arena and probably traumatized a demon lord in the process. That also happened.
I am not sure if she actually turned into anything yet. Her final chunk in Golden Coin sounded to me as if she is still larval-ish and needs to eat Keris to complete her change.
Since that groups gimmick is that everyone on the brink of ascending beyond Balanado she would probably grab a domain outside of the harem genre and use her new freedom to eat him as well.
- Location
- United States
- Pronouns
- She/Her
Is Ney about to get involved in the plot? Is he going to ascend from "fan-favorite guest star from three seasons ago" to "main cast member?" If so, I'm very excited. I really like Ney, and I always thought it was a shame how he disappeared after the Malra arc, despite how large he looms in Keris' thoughts. Granted, it made sense for him to disappear, he lives halfway across Creation from where Keris lives, but it still felt like such a waste. I'll be glad if he somehow worms his way into more regular appearances in the story.
Chloe Sullivan
Subdefective
- Location
- 1630 Revello Drive, Sunnydale CA
Lilinu is performing not even that specutacturlay for something Ligier crafted himself.
Keris may be loyal to Lilinu, bu Keri's does not have an unbiased view of her either . Lilinu was probably always a bit more savvy that Keris recognized.
To Follow A Star - Chapter 4
- Location
- The sixth circle of Hell (second on weekends)
- Pronouns
- She/Her
Calesco's adventures continue in To Follow A Star 4, as she resolves her investigation in Triumphant Air, sets off on her trip northeast and encounters some obstacles along the way.
Including, in sharp contrast to last episode, The Best Roll Ever as Calesco got 11 sux on 16 dice and Fari got 10 sux on 11. You'll know the bit I mean. It's hard to miss.
Including, in sharp contrast to last episode, The Best Roll Ever as Calesco got 11 sux on 16 dice and Fari got 10 sux on 11. You'll know the bit I mean. It's hard to miss.
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Fari is going to become something interesting by the end of this.
This latest chapter provided a pretty anti-climatic ending to a plot that would have culminated in the destruction of an entire Direction. Does it really make sense for there to be an immediate and decisive victory after merely giving an ally proof the of Realm's misdeeds? I was expecting some kind of epic struggle of subterfuge and manipulation that would eventually force the Realm navy to abandon their exploitation of the Magma-Centipede eggs. This could easily have been the central focus for the rest of the side-story.
Is this plot now completely resolved or can we expect to see it return? It would make sense for Ana to call upon Calesco for further help after her attempts to expose the Realm Navy's actions are thwarted by corruption in the Immaculate Order or treachery by her fellow local nobles.
Is this plot now completely resolved or can we expect to see it return? It would make sense for Ana to call upon Calesco for further help after her attempts to expose the Realm Navy's actions are thwarted by corruption in the Immaculate Order or treachery by her fellow local nobles.
I don't think the magma centipede egg plot has reached an ending at all. sure, the local immaculates should now have evidence that the Steel Dragon Society has been harvesting the eggs, along with a large supply of said eggs, but the centipedes are still pissed, the Navy still needs to be handled so that they don't, say, kill everyone involved to cover up their crimes, and Ana's stuck right in the middle of all this with Cally faaaar away. I would be quite surprised if this was the last we heard of this.
- Location
- The sixth circle of Hell (second on weekends)
- Pronouns
- She/Her
Here's the additional thing that's lurking in the undertow of this plot.
Nobody actually knows about Krastion. If they did, believe me, this whole plotline and the entire culture of Triumphant Air would be very, very different. But she's so old, and her slumber has been so long, that human history has forgotten her. As far as the monks who are in the know are aware, the danger is "merely" that there are a lot of magma centipedes under the island and they get pissy when disturbed.
The scope of this story of egg-thievery is not so large, and much as Keris is the Catwoman to Ney's story, Calesco was only ever a dark and mysterious love interest who is implied to have some interesting backstory to explore in future arcs and somehow knows way more than she should and turns up out of the blue to put the protagonist onto the trail of what she's looking for before bowing out of the plot. As with a lot of Kerisgame stuff, the joke is that we're seeing a standard heroic story, just from the point of view of one of the characters who usually just shows up in places and knows things they shouldn't because the plot needs them to.
Ana will be continuing her protagonist-y adventure of going up against the Steel Dragon Society to expose their wicked deeds and getting them officially censured and probably arguing the abbess into some face-punching and drawing some heat from the Navy for exposing them to another scandal on top of that one from five years ago where a bunch of their retired veterans turned out to be part of a sinful Yozi cult worshipping the mad green sun and the demon sea. We may see some hints of it as she complains in dreams to Calesco about what's currently going on.
(If she knew about Krastion, her love for her island would remove any and all chances of her leaving it; her convictions and Justice virtue would compel her to stay and throw the rest of her life into safeguarding her home.)
But while that will be happening largely offscreen as we follow Calesco to the Scavenger Lands, make no mistake - this wasn't the end of the Krastion plotline. It was the first hint at it, which in future stories will come back and shock everyone as it turns out that the egg-smuggling business on Triumphant Air was in fact the first clue to the presence of a lurking apocalypse.
Nobody actually knows about Krastion. If they did, believe me, this whole plotline and the entire culture of Triumphant Air would be very, very different. But she's so old, and her slumber has been so long, that human history has forgotten her. As far as the monks who are in the know are aware, the danger is "merely" that there are a lot of magma centipedes under the island and they get pissy when disturbed.
The scope of this story of egg-thievery is not so large, and much as Keris is the Catwoman to Ney's story, Calesco was only ever a dark and mysterious love interest who is implied to have some interesting backstory to explore in future arcs and somehow knows way more than she should and turns up out of the blue to put the protagonist onto the trail of what she's looking for before bowing out of the plot. As with a lot of Kerisgame stuff, the joke is that we're seeing a standard heroic story, just from the point of view of one of the characters who usually just shows up in places and knows things they shouldn't because the plot needs them to.
Ana will be continuing her protagonist-y adventure of going up against the Steel Dragon Society to expose their wicked deeds and getting them officially censured and probably arguing the abbess into some face-punching and drawing some heat from the Navy for exposing them to another scandal on top of that one from five years ago where a bunch of their retired veterans turned out to be part of a sinful Yozi cult worshipping the mad green sun and the demon sea. We may see some hints of it as she complains in dreams to Calesco about what's currently going on.
(If she knew about Krastion, her love for her island would remove any and all chances of her leaving it; her convictions and Justice virtue would compel her to stay and throw the rest of her life into safeguarding her home.)
But while that will be happening largely offscreen as we follow Calesco to the Scavenger Lands, make no mistake - this wasn't the end of the Krastion plotline. It was the first hint at it, which in future stories will come back and shock everyone as it turns out that the egg-smuggling business on Triumphant Air was in fact the first clue to the presence of a lurking apocalypse.
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The Phoenixian
The Glacier Witch
- Location
- My own little world
My only observation on the matter, is that for all the Magmga-Centipede arc was cut short --- from a "full knowledge overview of all the situation's potential" perspective --- the way in which it was did feel natural to both the internal mini-arc itself, and Calesco's situation. She is just here on a stop from a voyage, after all. There's always pressure to get a move on eventually.
Well, however it shakes out, I'm sure it won't end with;
Definitely won't result in Keris struggling with having to be forced out into the open to contest the Dead for control of the Anarchy with her own force of demons, all the while the rest of Creation descends into chaos between the post eruption Winter, various degrees of supernatural nastiness with increased ability to be a problem, and likely the Realm Civil War kicking off when the Dynasty gets too heated talking about how to resolve this problem.
Definitely probably won't happen.
Definitely won't result in Keris struggling with having to be forced out into the open to contest the Dead for control of the Anarchy with her own force of demons, all the while the rest of Creation descends into chaos between the post eruption Winter, various degrees of supernatural nastiness with increased ability to be a problem, and likely the Realm Civil War kicking off when the Dynasty gets too heated talking about how to resolve this problem.
Definitely probably won't happen.
3e writeup - Orvenkeruby
I've been writing a lot of First Circle Demons recent for a game I've been running in the Kerisgame server. One of my players recently had the wonderful idea of inviting a bunch of Orvenkeruby and Tidal Raiders into the Dreaming Sea to harass the Sorcerer-ruled nation of Ysyr.
Naturally I had to give this my full support, and so with advice/explanation on their themes and how they're intended to function compared to other spirits from @EarthScorpion and @Aleph, have some Orvenkeruby, fully statted and ready to form a sentai team with YOUR PCs! <3
Naturally I had to give this my full support, and so with advice/explanation on their themes and how they're intended to function compared to other spirits from @EarthScorpion and @Aleph, have some Orvenkeruby, fully statted and ready to form a sentai team with YOUR PCs! <3
Orvenkeruby, the Wave Charmers
Essence: 2; Willpower: 5; Join Battle: 5 dice
Personal Motes: 70
Health Levels: -0x2/-1x2/-2x2/-4/Incap.
Actions: Feats of Derring-Do: 9 dice; Feats of Strength: 8 dice (may attempt Strength 3 feats); Resist Poison/Illness: 6 dice; Senses: 8 dice; Social Influence: 8 dice; Stealth: 7 dice; Threaten: 7 dice; Tracking: 8 dice
Appearance 4, Resolve 3, Guile 3
Combat
Attack (Hammer): 8 dice (Damage 15)
Attack (Grapple): 7 dice (7 dice to control)
Combat Movement: 9 dice
Evasion 3, Parry 3
Soak/Hardness: 4/0 (more if they've gotten their hands on armor)
Special Qualities
Orven Tokusentai!: Orven work best as teams, and struggle to fight alone. When an Orven fights alongside at least two others of its kind, or within a group containing at least two people for whom the Orven holds a Major or better positive intimacy for, waive the Initiative cost of their Charms, and reduce the difficulty activation of all gambits involving or benefiting other Orven or the subjects of their ties by two.
Excessively Familiar Attitude: The nature of the keruby remains a mystery, but by all appearance they were made to be friends and companions, and happily offer their impudent services to others. A kerub may spend 1m and make a verbal offer of service or companionship, even one as simple as "I guess I'll tag along". If accepted, the kerub is treated as a familiar in all ways, and gains the Hurry Home Charm as if they were Sorcerously bound. Keruby bound to mortals add three to the difficulty of any attempt to turn them from their bonded friend, and magic which can banish demons has no effect on them. A pacted kerub always has at least positive minor intimacy towards their master, though the form this intimacy takes will vary based on their personality, breed and history. Pacted characters count as Orvenkeruby for the purposes of their Charms.
**Merits**
Distract: The Orven can make distract gambits to assist its allies. If it makes a successful gambit from stealth, the bonus it provides increases by two dice. Orven may train to use this to benefit non-Orven allies as if it were learning a latent ability.
Pack Hunting: When the Orven attacks an enemy, it adds one automatic success to the attack roll for each allied Orven in close range to that enemy, to a maximum of three successes. On a decisive attack, it may also pay a point of Willpower to add that many dice to the raw damage of the attack, representing its allies joining in the attack.
Offensive Charms
Not Today Intervention (8m,3i; Reflexive; Instant; Uniform; Essence 1): The Orven may use this Charm when witnessing someone targeted by a violent attack, flashing into action and leaping to clash the attack with one of their own, rolling Join Battle if they have not already done so, and gaining an automatic success on the attack roll (or (Essence) automatic successes if defending another Orven or someone for whom they hold a Major tie). They may intervene from out to Medium range, though doing so at the maximum distance imposes a -2 penalty to their defense until their next turn. The Orven may not use this Charm in combat if they have already acted unless defending another Orven.
Justice Bears A Sting (4m,2i, Supplemental, Instant, Decisive-only): When the Orven attacks while upholding an intimacy related to justice or righteousness, when opposing someone who has done something clearly dishonorable or abhorrent, or when avenging or defending another Orven, they may use this Charm, converting a die from their damage pool to an automatic success and marking their opponent as someone to be targeted by other Orvenkeruby, giving their allies an automatic success to all attack rolls and rushes performed against the target.
Defensive Charms
Armored To Save The Day (5m, Simple, Indefinite): The Orvenkeruby shapes their outfit into armor, gaining +5 soak and the appearance of wearing some form of pearlescent armor, though without any mobility penalty. If the Orven finds actual armor that they prefer, the cost of this Charm becomes 4m,3i, requires a miscellaneous action that may explicitly be flurried with combat and movement actions, and lasts until their next turn.
We're Strongest Together Approach (7m,2i, reflexive, until next turn, Perilous): The Orven stands up and declares their friendship to be more than a match for their adversaries. Until their next action, the allies of the Orven add (Orven's Essence) to their soak and hardness. This hardness does not stack with Hardness gained from armor other than spells such as Invulnerable Skin of Bronze, and does not stack with other forms of magic that grant hardness other than other Orvenkeruby using this Charm. If the Orven attacks or moves on the same turn they use this Charm, they take a -2 penalty to all attack and movement actions, and a -1 penalty to defense from their distraction.
Misc Charms
Hurry Home (10m,1wp, Simple, instant): The Orvenkeruby may Hurry Home to anyone they have made a pact with via Excessively Familiar Attitude.
Materialize (35m, 1wp; Simple; Instant): The Orvenkeruby flow like pearlescent water into a material shape.
Gleeful Hand of Orven (1m; Simple; One scene; Essence 1): All the keruby have the capacity to animate a small amount of their linked phenomenon, water and pearlescent material for the Orven, allowing them to play pranks and interact with the world even when they are immaterial. Once per scene, the kerub may create an animated doll from a source of the appropriate phenomenon, which lasts for a scene. This doll is material, and has no soak, one health level (meaning a solid slap will make it fall apart) and rolls 1 die for all Physical actions that require strength. Otherwise, it uses the kerub's traits.
Essence: 2; Willpower: 5; Join Battle: 5 dice
Personal Motes: 70
Health Levels: -0x2/-1x2/-2x2/-4/Incap.
Actions: Feats of Derring-Do: 9 dice; Feats of Strength: 8 dice (may attempt Strength 3 feats); Resist Poison/Illness: 6 dice; Senses: 8 dice; Social Influence: 8 dice; Stealth: 7 dice; Threaten: 7 dice; Tracking: 8 dice
Appearance 4, Resolve 3, Guile 3
Combat
Attack (Hammer): 8 dice (Damage 15)
Attack (Grapple): 7 dice (7 dice to control)
Combat Movement: 9 dice
Evasion 3, Parry 3
Soak/Hardness: 4/0 (more if they've gotten their hands on armor)
Special Qualities
Orven Tokusentai!: Orven work best as teams, and struggle to fight alone. When an Orven fights alongside at least two others of its kind, or within a group containing at least two people for whom the Orven holds a Major or better positive intimacy for, waive the Initiative cost of their Charms, and reduce the difficulty activation of all gambits involving or benefiting other Orven or the subjects of their ties by two.
Excessively Familiar Attitude: The nature of the keruby remains a mystery, but by all appearance they were made to be friends and companions, and happily offer their impudent services to others. A kerub may spend 1m and make a verbal offer of service or companionship, even one as simple as "I guess I'll tag along". If accepted, the kerub is treated as a familiar in all ways, and gains the Hurry Home Charm as if they were Sorcerously bound. Keruby bound to mortals add three to the difficulty of any attempt to turn them from their bonded friend, and magic which can banish demons has no effect on them. A pacted kerub always has at least positive minor intimacy towards their master, though the form this intimacy takes will vary based on their personality, breed and history. Pacted characters count as Orvenkeruby for the purposes of their Charms.
**Merits**
Distract: The Orven can make distract gambits to assist its allies. If it makes a successful gambit from stealth, the bonus it provides increases by two dice. Orven may train to use this to benefit non-Orven allies as if it were learning a latent ability.
Pack Hunting: When the Orven attacks an enemy, it adds one automatic success to the attack roll for each allied Orven in close range to that enemy, to a maximum of three successes. On a decisive attack, it may also pay a point of Willpower to add that many dice to the raw damage of the attack, representing its allies joining in the attack.
Offensive Charms
Not Today Intervention (8m,3i; Reflexive; Instant; Uniform; Essence 1): The Orven may use this Charm when witnessing someone targeted by a violent attack, flashing into action and leaping to clash the attack with one of their own, rolling Join Battle if they have not already done so, and gaining an automatic success on the attack roll (or (Essence) automatic successes if defending another Orven or someone for whom they hold a Major tie). They may intervene from out to Medium range, though doing so at the maximum distance imposes a -2 penalty to their defense until their next turn. The Orven may not use this Charm in combat if they have already acted unless defending another Orven.
Justice Bears A Sting (4m,2i, Supplemental, Instant, Decisive-only): When the Orven attacks while upholding an intimacy related to justice or righteousness, when opposing someone who has done something clearly dishonorable or abhorrent, or when avenging or defending another Orven, they may use this Charm, converting a die from their damage pool to an automatic success and marking their opponent as someone to be targeted by other Orvenkeruby, giving their allies an automatic success to all attack rolls and rushes performed against the target.
Defensive Charms
Armored To Save The Day (5m, Simple, Indefinite): The Orvenkeruby shapes their outfit into armor, gaining +5 soak and the appearance of wearing some form of pearlescent armor, though without any mobility penalty. If the Orven finds actual armor that they prefer, the cost of this Charm becomes 4m,3i, requires a miscellaneous action that may explicitly be flurried with combat and movement actions, and lasts until their next turn.
We're Strongest Together Approach (7m,2i, reflexive, until next turn, Perilous): The Orven stands up and declares their friendship to be more than a match for their adversaries. Until their next action, the allies of the Orven add (Orven's Essence) to their soak and hardness. This hardness does not stack with Hardness gained from armor other than spells such as Invulnerable Skin of Bronze, and does not stack with other forms of magic that grant hardness other than other Orvenkeruby using this Charm. If the Orven attacks or moves on the same turn they use this Charm, they take a -2 penalty to all attack and movement actions, and a -1 penalty to defense from their distraction.
Misc Charms
Hurry Home (10m,1wp, Simple, instant): The Orvenkeruby may Hurry Home to anyone they have made a pact with via Excessively Familiar Attitude.
Materialize (35m, 1wp; Simple; Instant): The Orvenkeruby flow like pearlescent water into a material shape.
Gleeful Hand of Orven (1m; Simple; One scene; Essence 1): All the keruby have the capacity to animate a small amount of their linked phenomenon, water and pearlescent material for the Orven, allowing them to play pranks and interact with the world even when they are immaterial. Once per scene, the kerub may create an animated doll from a source of the appropriate phenomenon, which lasts for a scene. This doll is material, and has no soak, one health level (meaning a solid slap will make it fall apart) and rolls 1 die for all Physical actions that require strength. Otherwise, it uses the kerub's traits.
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- Location
- Graveyard of Forgotten Thoughts
But @Aleph, that's pop culture topology. And also not completely correct.
I will try to provide a better introduction to Topology, clarify the Topological concept of equivalent objects, demonstrate how topological spaces are often nothing like Euclidean spaces, and finally provide an example of two topological spaces that are topologically identical but cannot be transformed from one to another without doing one of the forbidden transformations.
To begin with, Topology is quite simply a generalization of the concept of "open sets" in Euclidean spaces, in much the same way Algebra is the generalization of the concepts of "addition and multiplication". The general idea is that an open set contains some neighbourhood around each of its points.
A topological space is defined by associating a set S with a collection T of its subsets that fulfills certain requirements
Recall that in Algebra, two groups are considered equivalent if there is a way to identify their elements such that the structure induced by the operator is preserved (in technical terms, "there exists an [/i]invertible homomorphism[/i] between the two groups"). In Topology, two topological spaces are considered equivalent if there is a way to identify the elements of the underlying sets such that the open sets also end up identified between the two (technical lingo, "there exists a bijective function that is open and continuous").
Some topological spaces can be very different from Euclidean spaces. For example, for some, nothing analogous to the concept of distance can be constructed. To illustrate this, we need to define a metric, which is the generalization of the concept of distance.
The collection of subsets of S that can be written as unions of open balls in S under metric d is a topology on S, and is called the topology on S induced by d. A topology that can be induced by a metric is called a metrizable space. One example, of course, is the topology on the Euclidean space of dimension n, induced by Euclidean distance; the open sets are the ones we are familiar with.
Here's a simple topological space that isn't metrizable.
Even in the familiar Euclidean spaces, two objects (viewed as subspaces - that is, topological spaces with topology inherited from the larger space they are found in) can be topologically equivalent without one being deformable into the other without tearing, etc.
I must also point out that it's kind of desperately wishful thinking on Keris's part that just because two shapes are topologically equivalent meant the transformation would have been done without any tearing, gluing, and the like.
So I guess Sasi was lucky, in a very loose sense of the word.
...
Look, there's a reason Eko's my favourite character. Don't judge me.
I will try to provide a better introduction to Topology, clarify the Topological concept of equivalent objects, demonstrate how topological spaces are often nothing like Euclidean spaces, and finally provide an example of two topological spaces that are topologically identical but cannot be transformed from one to another without doing one of the forbidden transformations.
To begin with, Topology is quite simply a generalization of the concept of "open sets" in Euclidean spaces, in much the same way Algebra is the generalization of the concepts of "addition and multiplication". The general idea is that an open set contains some neighbourhood around each of its points.
A topological space is defined by associating a set S with a collection T of its subsets that fulfills certain requirements
- Both S and the null set are in T
- Membership in T is closed under arbitrary union (see the neighbourhood thing mentioned above)
- Membership in T is closed under finite intersection
Consider S = {1,2}.
Exercise 2: Prove that the open sets on the real numbers, as usually defined, fulfills the three requirements
- { {}, {1,2} } is a Topology on S (this is the trivial topology on S)
- { {}, {1}, {2}, {1,2} } is a Topology on S (this is the discrete topology on S)
Exercise 2: Prove that the open sets on the real numbers, as usually defined, fulfills the three requirements
Recall that in Algebra, two groups are considered equivalent if there is a way to identify their elements such that the structure induced by the operator is preserved (in technical terms, "there exists an [/i]invertible homomorphism[/i] between the two groups"). In Topology, two topological spaces are considered equivalent if there is a way to identify the elements of the underlying sets such that the open sets also end up identified between the two (technical lingo, "there exists a bijective function that is open and continuous").
Example: Let S = ℝ∪{∞}. Let the open intervals on S be the usual open intervals on ℝ along with subsets of the form
{∞} ∪ (-∞, -a) ∪ (a, ∞)
where a is a real number. Define T as the collection of all subsets of S formed by arbitrary unions of such open intervals.
Then T is a topology on S and furthermore the topological space (S, T) can be identified with an open circle.
Sketch of proof for the second claim: Assume without loss of generality that the circle has circumference 4 and is centered at the origin (note that the arc in each quadrant has length 1). we'll equate the bottom of the circle with the origin in S, and the top of the circle with ∞. The part of the circle in the third quadrant corresponds to (-1, 0) in S, and similarly the part of the circle in the fourth quadrant corresponds to (0, 1) in S.
The parts of the circle in the first and second quadrants are respectively mapped to 1/d and -1/d in S, where d is the distance between a point and the top of the circle as measured along the arc of the circle.
{∞} ∪ (-∞, -a) ∪ (a, ∞)
where a is a real number. Define T as the collection of all subsets of S formed by arbitrary unions of such open intervals.
Then T is a topology on S and furthermore the topological space (S, T) can be identified with an open circle.
Sketch of proof for the second claim: Assume without loss of generality that the circle has circumference 4 and is centered at the origin (note that the arc in each quadrant has length 1). we'll equate the bottom of the circle with the origin in S, and the top of the circle with ∞. The part of the circle in the third quadrant corresponds to (-1, 0) in S, and similarly the part of the circle in the fourth quadrant corresponds to (0, 1) in S.
The parts of the circle in the first and second quadrants are respectively mapped to 1/d and -1/d in S, where d is the distance between a point and the top of the circle as measured along the arc of the circle.
Some topological spaces can be very different from Euclidean spaces. For example, for some, nothing analogous to the concept of distance can be constructed. To illustrate this, we need to define a metric, which is the generalization of the concept of distance.
A metric on a set S is a function d: S x S -> ℝ with the following properties for all elements x, y, and z in S
- d(x, y) ≥ 0, with equality if and only if x = y
- d(x, y) = d(y, x); this is the reflexive property
- d(x, y) + d(y, z) ≥ d(x, z); this is the triangle inequality
Here's a simple topological space that isn't metrizable.
The trivial topology on {1, 2} that we saw back in Example 1 is non-metrizable. As a reminder, the only open sets under the trivial topology are the whole set {1, 2} and the null set {}.
We will prove that this topological space is non-metrizable by contradiction. Suppose there exists a metric d on {1, 2}. Then there exists a real number x > 0 such that d(1, 2) = x, due to the first property of metrics. Choose some real number a such that 0 < a < x.
Then the open ball of radius a about 1 is just {1}. Furthermore, this ball is an open set per definition of induced topologies. But {1} is not an open set in this topology. Contradiction!
We will prove that this topological space is non-metrizable by contradiction. Suppose there exists a metric d on {1, 2}. Then there exists a real number x > 0 such that d(1, 2) = x, due to the first property of metrics. Choose some real number a such that 0 < a < x.
Then the open ball of radius a about 1 is just {1}. Furthermore, this ball is an open set per definition of induced topologies. But {1} is not an open set in this topology. Contradiction!
Even in the familiar Euclidean spaces, two objects (viewed as subspaces - that is, topological spaces with topology inherited from the larger space they are found in) can be topologically equivalent without one being deformable into the other without tearing, etc.
Consider the Möbius strip with 1 twist and the Möbius strip with 3 twists. It's clear that the parts away from where the edges are glued together are unaffected. To verify that there is no topological change where the edges meet: make a Möbius strip with 1 twist, draw a ball whether the edges would have been glued together; take it apart and add two more twists, then verify that there is still a ball where the edges meet.
Then actually glue the edges together and see if you can reduce the number of twists without tearing the loop.
Remark: All Möbius strips with odd number of twists are topologically equivalent. And all "Möbius strips" with even number of twists are topologically equivalent.
Then actually glue the edges together and see if you can reduce the number of twists without tearing the loop.
Remark: All Möbius strips with odd number of twists are topologically equivalent. And all "Möbius strips" with even number of twists are topologically equivalent.
I must also point out that it's kind of desperately wishful thinking on Keris's part that just because two shapes are topologically equivalent meant the transformation would have been done without any tearing, gluing, and the like.
We will use a well known example from Algebra for this one. We will transform a circle into itself, in a way that involves making a (countably) infinite number of tears, and remove one of the original points in the process.
Let S be the unit circle. Pick out the points at n radians, for n=1,2,3,...; take out the point at 1 radian and rotate all of the others clockwise by 1 radian. The point that was originally at 2 radians ends up at 1; 3 ends up at 2; etc. All of the points we had picked out end up covered because if n is a natural number, then so is n+1.
Let S be the unit circle. Pick out the points at n radians, for n=1,2,3,...; take out the point at 1 radian and rotate all of the others clockwise by 1 radian. The point that was originally at 2 radians ends up at 1; 3 ends up at 2; etc. All of the points we had picked out end up covered because if n is a natural number, then so is n+1.
...
Look, there's a reason Eko's my favourite character. Don't judge me.
Kali speaks wisdom. Hanily, have you forgotten the face of your mother?Early Earth 775 said:
And wow, the only demon lord level beings near the twins were Hermione, who's severely restricted; Kalaska, who's not exactly close to...well, anyone; and Seresa, who's not a combatant and whose presence in Zen Daiwye was unplanned for in any case. In this, the devouring of Keris's principle of "Looking After My Babies" makes itself felt.
Haneyl: At least Oula's well practiced at taking in demon lord essence.
---
On to Late Earth 775.
Lilunu kicking Ligier out of her game for munchkining before he even joined was pretty funny. It kind of expands on the revelation in The Golden Coin that Ligier has his own angle on [strike]Ruvelia[/strike] Lilunu. There seems to be a contradiction between his pleasure at Lilunu asserting herself and his role in the binding of Lilunu's Defying Soul, but perhaps he did it to keep Lilunu safe until she is strong enough to make the Blue Glass Maiden choke on her own laws.
I'm not sure that Keris's children haven't already been forced to confront their bans. One may for example draw some parallels between Eko's situation and Sisim's. Like the Innocent Demon that was, the Joyful Wind had to give up her ability to forget "the sickening perversities of the world", an ability that was arguably more integral to Eko than it ever was to Sisim. Yet Eko's change was much more subtle, to the degree that her bestie doesn't seem to have noticed it. Keris's progeny souls were raised like people, so they tend to respond to human-ish problems like people.
Finally, I've been wondering whether Asarin could theoretically leave Elloge's soul hierarchy altogether if there existed a primordial who resonated more strongly with her. Perhaps one who knows what it is like to strive for power that seems to be beyond the reach of her inborn talents; who strives to hold to principles even when all her peers see it as obstinate childishness; who responds to the clash between her morals and her heart with violent rage.
Remember, the core of Eko's nature wasn't her prudishness. She's an embodiment of Keris's "Be Loved" principle, as interpreted through the lens of Adorjan's murder-murder fight-fight Charms, and thus her prudishness was a secondary consequence of the fact she wants to support and love people, but hurts anyone she gets close to.
By contrast, the role-narrative in Balando's nature that Sisim filled was very specific, and Keris punched her straight in the contradictions of her genre archetype. And so she shattered and reformed in a new shape which hadn't been broken in the same way.
(Now, yes, on the flip side Keris's souls are better at working things through, but for example, Haneyl literally had to use her Terrestrial sorcery sacrifice to "give up on" getting the Szoreny charms back, because she's Keris's possessiveness and greed and she had to break her own nature - albeit using the sorcery pathway - to let go of that one thing.)
- Pronouns
- They/Them
In my head-canon, if Ligier just finally gave up and sought out fetish-death, Malfeas would reform into a form with two fetich souls once more. All that keeps the Yozi chained is the stubborn pride of their king.
I'm pretty sure the Unconquered Sun, Luna, all five Maidens of Destiny, and then all of the gods, Solars, Lunars, Sidereals, Dragon-Blooded, Autochthon and Gaia would have considered "what if the Ebon Dragon sics his souls on Ligier in order to escape" or "What if Malfeas compels Ligier to kill himself".
They seem like smart cookies.
pheonix89
Wants to be Seven Of Nine
- Location
- North American Plaguelands
- Pronouns
- She/Her
It doens't create an escape.
Fetich death and the accompanying reformation is not an out.
For Malfeas it doesn't.
But a) there are other Yozi and b) Malfeas can get pretty self-destructive even when the other Yozi aren't egging him on.
The possibility gets considered.
- Location
- The sixth circle of Hell (second on weekends)
- Pronouns
- She/Her
No, it just... doesn't. The Surrender Oaths are baked into the Yozis. Fetich death is no escape. If you kill the Demon City, if you slay the Endless Desert, if you murder the Demon Sea; the form of their prison will change, but imprisoned they will stay.