#tangents of the non-math variety

[vaguely-in-vogue]

Everyone around me (funny thing to say on a non-physical platform, but I digress°) is talking about GOS2 and its characters, themes, plot, setting, and the ending, but I'm still stuck in S1-land. I entered* the fandom right before S2 aired---intentionally---and it still feels like I'm sorting through the S1 fics^, some of 'em written in 2019 right after S1 aired, trying to play catch-up and look through the old metaposts as the fandom buzzes about S2 and potentially S3. Which is to say most of braincells are stuck contemplating Aziraphale and Crowley in Alternate Universe form or as they inevitably hit their post-Armageddon happy-ending, or else as they romp through history as pining messes; all of this rather than canon. I wonder if that's why while the Good Omens fandom is still trying to "recover from the heartbreak", I've been sat here trying to recreate the depth of emotional intensity most other people are experiencing.

°I am not digressing. A lack of a good system for footnotes is not going to stop the roiling waters of my extremely weird mind, Tumblr.

*That's a bit dramatic, "enter." Really, I just shuffled through a side door and found myself in this massive state. I managed to locate a small outhouse and ducked inside. It's connected to everywhere else via these thin hallways, and sometimes it's hard to get back; eventually I find a lovely bungalow and it seems quite a manageable place, only there are mirrors absolutely everywhere, and it's so crowded and at the same time someone has hung art all over the walls and you just get so distracted staring at them you forget there are other people around, people who actually have ideas about this art, house, fuck, this whole state, but you're enamoured by this Rembrandt and don't know how to express it, and that's okay too. Okay, that's even more dramatic.

^which all have their own specific plot beats and happy endings and call-backs to canon

[forestwhisper3]

Finally finished catching up on One Piece and was starting to look into the stuff for the new movie when I found out about Uta.

Or more specifically, her fruit.

(Slight spoilers for One Piece Film: RED, so read on at your own discretion)

Seriously, why does this stuff keep happening? Why do I keep getting weirdly close with canon stuff? First with Peony in my pokemon fic, and now with this?

There’s a reason why I’ve tagged the picrew images of Ran with the fanfic name Crescendo. I was intending to give her a devil fruit. The Uta-Uta no Mi to be exact. And now this movie has Shanks’s daughter having it and I can’t decide whether to be weirded out that this fruit is associated so closely with him or upset that the idea for this fruit was used (seriously, with how many endless possibilities there are for devil fruits I still choose one that ends up in canon).

I actually sort of hit a few things with the fruit’s power too. The Wiki article says it can teleport peoples’ consciousness to a virtual space, where they can manipulate reality to their will and also control the real-world bodies of those trapped in it.

Before I found all this out, this was how I imagined the powers of the Uta-Uta no Mi. Granted, I was still working out the details, but this was what I had by the last time I worked on it (straight from my word document):

Uta Uta no mi- song fruit

Can produce effects with songs.

Stage 1: mood alteration

Stage 2: hypnotic effects/persuasion

Stage 3: control of the body (much like the dance island)

Awakened: Can hear the "song" (soul?) inside of living things; gains the ability to alter the world around them.

Pros: Wide variety of uses. Can affect large groups of people at the same time.

Cons: Limited by the imagination of the user and lyrics of the song. Can't affect the user, whether it's beneficial or not. User needs to be able to speak. Can be resisted if the one hearing it has a will stronger than the user's. The more powerful the effect intended, the more energy is used (i.e. things like drastically affecting the weather/environment or bringing someone back from the brink of death will significantly weaken her and she'll need some time to recover).

So...yeah. In a way, I sort of had similar ideas to what ended up being the actual powers of the Uta-Uta no Mi. I still kind of like mine better, so I still might end up going with that, but I guess it’s going to have to be non-canon now.

...And now I’m imagining that, in canon, Ran dies after Uta is born and Shanks gets ahold of her fruit to give to their daughter. Might make for a nice canon meets AU side story, at any rate.

Although I’m still on the fence of Uta being born in the fic. If I did the math correctly, Shanks would have been eighteen when she was conceived.  While I did plan on him and Ran having a child, it wasn’t going to be until they were both a bit older than that. Plus, if Ran is there, then Uta won’t get the fruit and that makes the whole movie (which I still need to see) obsolete, right?

Anyway, I guess that’s about all I have to say on that. Thanks for listening to my half rant, half confused tangent. Here’s a short clip (still being refined) on how I planned on Ran getting the Uta-Uta no Mi:

========

"Is this-?"

"A devil fruit," Roger confirmed, his expression one of the most serious I'd ever seen from him. "I want you to have it."

"What-...What does it do?"

"It's the song-song fruit. Officially, there's not a lot known about it, but there are rumors..."

"Rumors?"

"That it could hold the key to life and death."

My eyes widened, and my heart was pounding frantically against my chest when I looked up at him. He nodded, and I felt tears flood my eyes.

"There's not enough time for me to figure out if it's true," Roger continued softly. "We both know my days are numbered. But you...I know you can do it. Look after them for me, Ran."

"Roger...I-I-..."

He smiled warmly. "I know."

Before I knew it, I had wrapped my arms around him, my hands clutching tightly to his shirt as sobbed into his chest.

"It's not fair!" I choked out. "Why-...why does it have to be you, Roger?! You should be able to see the future with us- to see the man your son becomes."

Roger returned the embrace, and it was only because he did that I was able to feel how shaky his next breath was.

"Will you tell me about him?"

Not all of it, I thought. He was in enough pain thinking about his own death- I didn't need to add anyone else's.

"His name will be Ace, and his greatest treasure will be those he calls his family."

========

Bonus clip- Shanks realizes/accepts his feelings and the seeds of them begin to grow in Ran (WIP):

"Shit! Ran!"

The panic in Captain's voice was the first sign that something was wrong.

The second was when she didn't immediately come up for air.

He didn't bother waiting for the third before he was tossing Cap- his hat aside and jumping over the ship's railing into the water below.

Shanks's first love was the sea. The beauty. The danger. The freedom. It called to him in a way that he knew he would never be able to settle down on land. But...there was something else that has slowly been claiming its own stakes in there too.

Or rather, someone.

He hadn't really noticed it- not at first, anyway. His first impression of her hadn't exactly been the greatest, though he could now admit that that was more his fault than hers. He'd just been upset at missing out on a party. But the more he spoke with her...the more he got to know her...

She was like the sea.

Full of mystery and adventure...

Kind to those who respected her and unforgiving to those who didn't...

...and so beautiful he could gaze at her for hours.

Even now, as she drifted unconsciously in the water, she was beautiful. Her pink hair, darkened to a coral hue, fanned around her like streams of silk, and her skin was like porcelain.

It was when he thought that not even a mermaid's beauty could compare to her at that moment that he finally accepted that he'd fallen. Hard.

However, it was only after he'd brought her back to the surface that it really hit him. The way his heart was still thundering in his chest from residual fear as she began to cough, the way his breath seemed to leave him as her eyes- sea blue eyes -focused on him with confusion, then realization.

"Shanks...you-"

"You okay?"

The question came out just as breathless as he felt holding her so close to him. She just stared for a long moment before she finally looked away.

"Y-Yeah."

========

Leave it to Shanks to wax poetic about the things he loves, ahaha. Anyway, hope you enjoyed the little clips. I feel a little better about this whole thing now that I’ve had the chance to vent a bit. I leave you now with a new picrew of Ran.

“Sorry for not saying it before, but thank you, Shanks. For saving me.”

*Shanks then proceeds to turn redder than his hair*

These two are going to be so flippin cute, I swear. I actually kind of want to start this fic now.

(Made with this picrew: https://picrew.me/image_maker/1705444)

...Later!

[wozziebear]

These and other surprising examples made it clear that mathematicians needed to prove that dimension is a real notion and that, for instance, n- and m-dimension Euclidean spaces are different in some fundamental way when n ≠ m. This objective became known as the “invariance of dimension” problem.

Finally, in 1912, almost half a century after Cantor’s discovery, and after many failed attempts to prove the invariance of dimension, L.E.J. Brouwer succeeded by employing some methods of his own creation. In essence, he proved that it is impossible to put a higher-dimensional object inside one of smaller dimension, or to place one of smaller dimension into one of larger dimension and fill the entire space, without breaking the object into many pieces, as Cantor did, or allowing it to intersect itself, as Peano did. Moreover, around this time Brouwer and others gave a variety of rigorous definitions, which, for example, could assign dimension inductively based on the fact that the boundaries of balls in n-dimensional space are (n − 1)-dimensional.

Although Brouwer’s work put the notion of dimension on strong mathematical footing, it did not help with our intuition regarding higher-dimensional spaces: Our familiarity with three-dimensional space too easily leads us astray. As Thomas Banchoff wrote, “All of us are slaves to the prejudices of our own dimension.”

Suppose, for instance, we place 2^n spheres of radius 1 inside an n-dimensional cube with side length 4, and then put another one in the center tangent to them all. As n grows, so does the size of the central sphere — it has a radius of √n − 1. Thus, shockingly, when n ≥ 10 this sphere protrudes beyond the sides of the cube.

The surprising realities of high-dimensional space cause problems in statistics and data analysis, known collectively as the “curse of dimensionality.” The number of sample points required for many statistical techniques goes up exponentially with the dimension. Also, as dimensions increase, points will cluster together less often. Thus, it’s often important to find ways to reduce the dimension of high-dimensional data.

The story of dimension didn’t end with Brouwer. Just a few years afterward, Felix Hausdorff developed a definition of dimension that — generations later — proved essential for modern math. An intuitive way to think about Hausdorff dimension is that if we scale, or magnify, a d-dimensional object uniformly by a factor of k, the size of the object increases by a factor of k^d. Suppose we scale a point, a line segment, a square and a cube by a factor of 3. The point does not change size (3^0 = 1), the segment becomes three times as large (3^1 = 3), the square becomes nine times as large (3^2 = 9) and the cube becomes 27 times as large (3^3 = 27).

One surprising consequence of Hausdorff’s definition is that objects could have non-integer dimensions. Decades later, this turned out to be just what Benoit B. Mandelbrot needed when he asked, “How long is the coast of Britain?” A coastline can be so jagged that it cannot be measured precisely with any ruler — the shorter the ruler, the larger and more precise the measurement. Mandelbrot argued that the Hausdorff dimension provides a way to quantify this jaggedness, and in 1975 he coined the term “fractal” to describe such infinitely complex shapes.

To understand what a non-integer dimension might look like, let’s consider the Koch curve, which is produced iteratively. We begin with a line segment. At each stage we remove the middle third of each segment and replace it with two segments equal in length to the removed segment. Repeat this procedure indefinitely to obtain the Koch curve. Study it closely, and you’ll see it contains four sections that are identical to the whole curve but are one-third the size. So if we scale this curve by a factor of 3, we obtain four copies of the original. This means its Hausdorff dimension, d, satisfies 3^d = 4. So, d = log3(4) ≈ 1.26. The curve isn’t entirely space-filling, like Peano’s, so it isn’t quite two-dimensional, but it is more than a single one-dimensional line.

A Mathematician's Guided Tour Through Higher Dimensions

https://www.quantamagazine.org/a-mathematicians-guided-tour-through-high-dimensions-20210913/ Comments