#ring theory

[dat-physics-gal]

0 does not have a unique additive inverse, thus it has no multiplicative inverse. By definition. Unless you're in a ring where the additive identity isn't unique, i guess? Dunno if there is one of those, but it wouldn’t surprise me if someone found a way to make that work.

I think 0÷0 is literally just 0 because like you have of you have nothing.. And divide it by nothing, you still have nothing. People are just overreacting

[nabi-unveiled]

I'm gonna need one of these powerful, royal men to carry poison in their ring...

or use it as a secret key to some special chamber...

or something.

Otherwise, what's the point of the frequency we have close-ups of these big ass rings?

I know it's about their position, and I know they're color-coded. So are their suits. So are their lapel pins. The point stands -> we're getting a lot of close-ups of the rings/hands.

Interestingly, blue shark guy HAS a ring. But I don't remember a close up of it. I could have missed it though. I was working simultaneously. His hand with the ring definitely doesn't show in this scene where the other two rings were prominently featured. And he wears his on the left hand instead of right like everyone else.

Really, I'm just wishing. It'd be fun for them to do something at least vaguely interesting with them.

I started to reblog, but I'm just going to edit. For those curious, here are shots from episode 2:

Phoenix Clan wears their ring on on the third finger of their right hand. It says "adorned with gems", but really their flag is adorned with flowers. I'm just not certain exactly which flower yet. However, rising from the ashes can always mean a lot, and has strong implications for our princess that wasn't initially allowed to compete.

Ava wears gloves in the first throne room scene in episode 3. Her hands are uncovered and ring free in the second when she declares her intention to join the competition.

Venomous Snake Clan wears their ring on the fourth finger of their right hand JUST like the King. This is also the clan with the thorny rose that deals in diamonds. For the record, this snake can represent danger and authority. BUT it can also be considered a good omen in some cultures including at least some parts of Thailand. It's typically based on how they are treated. Which could have interesting implications for Prince Ramil.

For the record, Ramil wears multiple rings in both throne room scenes in episode 3. One on the second finger of his left hand. One on the middle finger of his right hand.

Shark Clan, guardian of the seas, doesn't wear his ring on the right hand. I think it's on the third finger of his left hand. They also have precious pearls and an asterism (star pattern) associated with a protective crocodile that represents "doing good in life" within their flag.

However, his ring is almost always hidden.This could be that he's humble/not flaunting his power OR it could mean that he has a hidden agenda.

And our Golden Horse Clan with crossed swords wears his ring on his pointer finger. Obviously, a fight for power is incoming. And as I don't trust the King AT ALL. I would wager they've used violence in the past. Khanin will also be fighting to keep his own identity and probably clashing with tradition.

Khanin did not wear a ring in either throne room scene in episode 3.

🤔 Does how they wear their rings mean anything? I don't know. But it might.

[indigovigilance]

Angel Pinky Rings

I'm going to get strangely obsessed with finger jewelry for a moment.

Please do not ask Neil Gaiman to confirm or deny.

Before the Beginning, Aziraphale doesn't have a ring:

...then after the Beginning, he does:

...which he wears continuously for the rest of the story:

Archangel Michael

doesn't have a ring in Book of Job:

and then they do:

Uriel does:

...even Saraqael does:

...and Sandolphon:

...but not the Supreme Archangel

not in Book of Job:

and neither before Armageddidn't:

nor after:

...and not the 37th Order Scrivener:

Originally I thought the rings might denote rank, but Gabriel not having a ring throws a wrench in that.

Left vs. Right

Every angel that wears a ring wears it on their left hand (everyone except Saraqael wears it on their pinky, who wears it on their ring finger) except for Aziraphale, who consistently wears his pinky ring on his right hand. Furthermore, the style of each ring appears to be unique; we don't usually get a very good look at them (or at least I don't, I have kind of crappy hardware) but the differing styles seem to be meaningful to the individual. Putting it on the left may indicate that it has a negative connotation; the fact that Aziraphale's ring is on the right sets him apart.

Protecting the Ring

Additionally, all the angels that have rings, when they fold their hands, tend to cover up their ring-bearing hand, almost protectively:

Semi-Rational Theory

The rings are vessels of memory: they are only worn by angels who have transgressed against God's will, and are worn forever after as a symbol of the covenant made between the Creator and the Servant. They dump the memories of their transgressions into the ring so that their minds are made clean, but carry the mark of their prior sin with them for the rest of time. Much like a rainbow, it serves as a promise that the transgressor will never transgress again. The angels protect it because, consciously or not, they know that this ring contains a part of themselves, and it is both precious and shameful.

Absolutely Irrational Theory

Aziraphale wears his ring on his right hand because it doesn't fit on his left. That's because it's not actually his ring; it is Angel!Crowley's, and he is keeping it safe for them. Crowley and/or Aziraphale might not even know anymore that that is what it is, but by some pact between them made before the Fall, it is in Aziraphale's stewardship to keep safe until such time as Crowley can safely have his memories restored.

Again: Please do not ask Neil Gaiman to confirm or deny.

EDIT: MAGGIE HAS A PINKIE RING

This bish is sus AF

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If you would like to reblog, please reblog from this repost with additional content and references.

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To read more of my original content on erasure theory:

Jimbriel, Satan, the Book of Life, and what it means for Crowley

The Erasure of Human!Metatron

Baraqiel and Azazel

or, my first and my most popular post to date:

A Nightingale Sang in 1941

[algebraic-dualist]

New favourite rings

[more-mathematics-mor-lam]

Getting all wound up on localization

[homomorphichomosexual]

A ring without a multiplicative identitiy is called a rng. I now propose that a gay without a asshole should be called a gy. I hope for everyone sake this notation needn't be used

[mitchell-nihil]

i'm so obsessed with ring theory in writing. it's so useful and helps me think of how to organize some things, AND it really does make everything feel like it has a purpose. if someone's cat dies at the start, sure maybe that kicks off the plot but them getting a new cat at the end makes it feel like there was another level of purpose. this works better with things not so consequential, though. just making it feel like every action was thought through and was going to be paid off

[freckliedan]

I refuse to believe you were wrong about ring theory actually

thank you. i do also <3

[endofunktor]

So you can forget that a unital ring is unital.

Denote Ring the category of unital rings and Rng the category of (general) rings. Then this should constitute a forgetful functor

S : Ring → Rng.

Can this functor be adjoint? What does it yield?

[idk-anymore-mydudes]

[nabi-unveiled]

Ring Theory Continued: Episode 7

Ep 3 Ep 4 Ep 5 Ep 6

Short ring theory summary -> Right hand = power game; Left hand = personal game. Second finger is love/protection of a loved one. Third finger is good/neutral (or at least pretending to be). Fourth finger is no bueno. Pinkie is Chakri 🥰/support.

This week was VERY interesting for ring tracking in The Next Prince. There was a lot to track with several new players to the game.

In disappointing news...our coach Joe? Doesn't wear a ring.

So does that mean the ring theory has collapsed? Or does it mean that he wasn't actually behind the poisoning?

Hard to say. We know he was put in place by Prince Rachata. That man's ring has never changed (right hand, fourth finger). He's always been in it for the power, and he's not hiding any of his negative energy.

But his personal butler has a personal agenda based on love (left hand, second finger)? Shocking I dare say.

Joe is definitely suspicious and booked it after the poisoning happened. But it's pretty hard to keep tabs on a prince you killed.

And we already know there are consequences when a prince comes to harm in your care. He'd have a good reason to run scared.

Hmm. Something to think about. Anyways, Prince Tharin's ring hasn't changed. He still has a personal game supporting Khanin.

There are other suspicious people around...like the King's butler. He also wears his ring on his fourth finger. Is that because he has his own agenda? Or because he's supporting the King's evil plans?

Also hard to say. The King definitely has his own evil agenda still.

But seemed rather remorseful about Khanin's poisoning. His ring may have been there, but his sleeves ALMOST covered it up whereas butler's stayed in full view.

Who do I not suspect? Ramil. He may not sound too distraught.

But both him and Paytai are still ringless. They're being honest with each other at least. I do think Ramil would take it as a personal insult if Khanin bowed out by dying. He wants to beat Khanin himself.

In other news, Chakri was fully back in his support role this episode. His ring flashed SO MANY times. We've never had as many good looks at Chakri's ring as we did this episode. He was the MVP supporting Khanin in every way possible, and Khanin is back to appreciating that support.

The one exception? When Chakri walked in ringless on the kiss at the beginning. Khanin wasn't seeing that as very supportive at all.

I might've wished that Charan would have worn a ring when he went to confront Joe, but he stayed ringless as always. Ever sincere and open in his intentions. I do find it interesting that he's one of the only guards that doesn't wear gloves.

Khanin is always ringless when alone with Charan.

But Khanin does still play the game at some points. Both when he confronted the King directly...

And tried to figure out ways around the system, his ring switched to the right hand. He had good intentions and was trying to push for power at that point.

But by later in the episode, he was back to it being personal (left hand).

He had accepted that he had no power in this situation. "I've never had this feeling before."

Khanin, I'm sure Ramil and Ava could've clued you in on that.

Speaking of Ava, she popped off and was very blunt with her dad while wearing gloves that only partially covered her hands and were made of leather.

But she was back to covering her hands when she went to check on Khanin and accepted that she wasn't really allowed to be there.

The interesting thing to me? Her companion wears a ring. ON HER THUMB. What does that mean? Because it means she's serving a different role than we've seen before, and it's a power game.

As for our final royal... Prince Calvin wore his rings the same as last episode.

He has a personal game of love (with Jay) and he has a power game that seems to be for the good.

And Jay? Well, he decided to wear two rings on the right hand. One on his second finger and one on his middle. But...I still haven't figured out why he has power.

Is he a hidden heir to the blue shark kingdom? Is he the "power of the people"? Because we do know that he's actively involved in protests. I kind of like the latter idea.

But I'm not sure. Especially because between coffee and passing out the sandwiches, he decided to shift his game...and wear both rings on the same finger.

And he maintains that placement into the next meal too. Is he just shifty and not to be trusted?

I still don't trust the shark clan, and Jay is very much a part of that clan. Plus, why was he in this city? Which friend did he go to see?

Perhaps, if he is helping the shark clan's agenda, he really thinks he is doing good but will realize later that it's not as good as it appears? Maybe he will later switch allegiance because of Calvin.

Or could this indicate shifting priorities? Focusing more on love than the good of the people?

Hmm...let me go ponder.

[redwitchrune]

finished reading the star wars ring theory essay and. ohhh my god. i fucking love this. genuinely worldview changing. what a wonderful six movies and a wonderful essay

[algebraic-dualist]

Given a category C and an object A define a witness for A of length n as a sequence of objects S_1, S_2, ..., S_{n+1} and morphisms f_1 : S_1 -> S_2, f_2 : S_2 -> S_3, ..., f_{n} : S_{n} -> S_{n+1} such that 1. each f_i is a monomorphism but not an epimorphism. 2. S_{n+1} is isomorphic to A Define the dimension of A as the maximum number n such that there exists a witness for A of length n.

For finite-dimensional vector spaces this works nicely: given a vector space V generated by e_1, e_2, ..., e_n we can build a sequence of increasing subspaces < > -> <e_1> -> <e_1, e_2> -> ... -> <e_1, e_2, ..., e_n> = V showing dim(V) \ge n. It's not very hard to see that this is best you can do, so dim(V) = n. Unfortunately, this doesn't work well in the land of Z-modules, because we have shit like ... -> p^n Z -> p^(n-1) Z -> \cdots -> p^2 Z -> p Z -> Z so sadly we don't get the righteous conclusion that dim(Z) = 0, but rather it turns out dim(Z) = infinity.

[theladyfromplanetx]

More "Ring Theory".

The Phantom Menace vs. A New Hope

[selfimmolate444]

when i do a proof n i use zorns lemma (or equivalent statement) i feel like such a real mathematician. and the use is always so quiet. it feels so sophisticated it feels like real pure maths