#fourier analysis

[isomorphismes]

Test functions and [tempered] distributions require the notion of topological vector space … distributions can be traced back to Green's functions in the 1830’s to solve ordinary differential equations … the 1936 work of Sergei Sobolev on hyperbolic PDE’s.

Laurent Schwartz introduced the term "distribution" by analogy with a distribution of electrical charge, possibly including not only point charges but also dipoles and so on.

tempered distribution

topological vector space

(^ if there is a dipole, there must be a notion of subtraction, hence the need for a vector, and to speak of this very conceptually, use a TVS)

[pseuddamntired]

This is cool

[bsahely]

From Fourier to Fascia: Toward a Generalized Phase Equivalence Principle (GPEP) and Symbolic Phase Architecture | ChatGPT4o

[Download Full Document (PDF)] This paper introduces the Generalized Phase Equivalence Principle (GPEP) as a new scientific and philosophical foundation that unites diverse systems through a common law of coherence. According to GPEP, a transformation — whether biological, cognitive, social, or symbolic — is legitimate and viable if it preserves three core invariants: Phase Continuity – Smooth,…

[rigelwithafedora]

she Lomb on my Scargle till I-- [EXTREMELY LOUD INCORRECT ANSWER BUZZER]

[msfeatherfreckles]

Re watched the pilot ep of Supernatural last night and I haven't been able to get over the fact that John thrust baby Sam into Dean's arms and said "watch out for Sammy" and Dean has tried to do so to the best of his abilities, at the cost of almost everything else, because his dad said so and because that's his baby brother and he loves his baby brother.

Aaand then in season 4, the angels/God thrust Dean at Castiel and said "watch out for Dean" and Cas has tried to do so to the best of his abilities, at the cost of almost everything else, because his dad said so and because that's his brother buddy pal bro friend and he loves-- [gunshots]

[mishy-mashy]

Fourier never appeared in the main series, but man, he's actually really funny. Absolutely like Subaru in his behavior but less cringe that stems from realism and second-hand embarrassment. Just friends being friends

Since I got my hands on that EX novel, I'm gonna pitch some moments of him so he's at least remembered if his name is brought up. I'll include some pictures for reference, and won't include the whole thing to avoid spoilers

1. This one can be found on the wiki as is: he fell in love with Crusch at first sight, but the moment she saw him, she threatened him with a knife in his own house—she then proceeded to almost attempt suicide for her mistake

2. He's so much like Subaru. He's loud, brash, in love with a girl at first sight, has small worries that he blows out of proportion unless they're absolutely important and life-changing like impending death, falls to his knees in anime-style sulking when told he's not as manly/strong as he wants to be to the girl he likes...

3. After seeing Crusch, you see how there's a guy chasing him in the first picture? That's his tutor. Fourier proceeded to slap him in the face ("MY EYE!!" screamed in comical fashion), drag him down a hall, and make him hit his head on every column and wall in existence

4. In the second picture, where Crusch holds a dagger, Fourier backtracks over it a lot like Subaru would

Fourier: Who would give their daughter a dagger on their birthday? They've no sense.

Crusch: Your Highness, I asked for this dagger from my father as a gift that day.

Fourier: Yep! Your father's the most sensible man ever! Daggers, wonderful gifts to young girls, they are!

5. That illustration of him and Crusch in a sword fight? He did that so Crusch would wear a dress.

Crusch sees him about to fall over like a shaking fawn, pathetic with trembling legs and supporting himself on his sword. He's exhausted and wanting to pass out or cry, and Crusch is like "Should we stop?"

And Fourier is all "NO!" and charges in with war cries the entire time.

"YAAAAAHHHH! CRUUUSCH! WEAR A DRESSS!!!"

I crap not, that's all he shouted, and it kinda scared Crusch.

"Wear makeup! Like flowers! Wear jewelry! Show me that beautiful smileeee!!! Uwaaaaaa!!!"

That's his motivation. It's hilarious and also sad, because he knows he probably hurt Crusch a lot for not letting her wear dresses. He's so exhausted by the end of it that he literally passes out on the ground after Crusch cedes it's her defeat

6. He didn't know Ferris was a boy. So when he had Ferris pose as his fiancee after Crusch couldn't so he could turn down his marriage prospect,

He did so, thinking Ferris was a girl. He only found out afterwards.

Also, before they actually went through with the plan, Fourier was raring to pretend being Crusch's lover, and getting all flustered at the idea. Imagine servant Subaru being all blushy over going on a date with Emilia and wiggling around. Not very different

"M-Me... and Crusch..!!"

"Compose yourself, my prince!"

- Fourier and Ferris, off of memory

7. The castle rumored that Fourier was gay, because he declared he loved Ferris, no matter his gender.

"As long as you're you..!"

Which is really sweet (how Fourier loves him). Still, Ferris worried he hated him after the reveal.

Ferris and Crusch are discussing this new rumor as Ferris is afraid of confronting Fourier after he learned he was a male... then His Highness comes barreling in, basically screaming and crying

"Crusch! Ferris! It's horrible, oh so horrible! I need you two now through the worst struggle of my life! Where are my two trusted people?!"

Because he literally just heard the rumor himself.

I think he was afraid that Crusch wouldn't love him if she thought he was batting for the other team, and that's why he stressed over the rumor? He also feared Crusch not liking him if he got fat

He's so fricken funny and this is just from me skimming the book. I haven't sat down to read it through, but just by skimming, Fourier and Subaru behave so similarly that it's just- my gosh.

Do Ferris and Crusch look at Subaru and think of the prince? When Subaru shouted and disrupted the Royal Selection gathering, and Julius probably saw Joshua, did those two see Fourier?

Granted, Fourier is more wise and composed than Subaru, and probably would've been more graceful about his interruptions, but the shouting of what he wants and thinks when riled up? The "wisdom" (knowledge) that comes out of nowhere, which both Fourier and Subaru have? (Fourier from instinct, Subaru from Return By Death)

Fourier wanted so badly to let Crusch be a woman, and fawned over her beauty and just wanted her to enjoy typical things of women. Subaru kicks his blanket like it's personally assaulting him, just thinking of multiple Emilias as he tries to sleep, and isn't afraid of showing his affection throughout the entire series

On the point of affection, neither of them are afraid of showing it to people they care about. Subaru braids hair, plays with kids, compliments outfits and smiles, Fourier hugs and tells his dreams of futures with his friends and has dances with them, etc.

(They even have the penchant of acting like things are fine to Julius by not telling him anything before they literally collapse in front of him [Fourier in a carriage, Subaru being possessed], leaving Julius to deal with them when things go south)

(On that note, it's sweet that Julius always calls for Ferris when someone is hurting, because he knows who can help best)

Anyway, Fourier? Funny kid. Resembles Subaru. Parallels can probably be drawn from them. Is important to the development of Crusch and Ferris, so it's not bad to remember him. The history of the royal family should come into play when regarding the Archbishop of Lust and Felt, too.

[elipsi]

erasmus log: classmate seemingly did not know about the difference between weight and mass

[longlive2023]

WHAT THE FUCK IS A FOURIER KERNEL

[woodfrogs]

its crazy how much physics is just wave mechanics. and how many people dont realize this and wind up completely misinterpreting things

[gay-victorian-astronomer]

last exam of my undergrad career is shaping up to be long & annoying contour integral hell times

(granted the entire course has been long and annoying integral hell, so... I suppose that's fitting for the final? still doesn't make me want to do it any more)

[thats-cantorintuitive]

oh please god let me pass this math methods course at least in morally grey if not flying colors

[greenouillee]

It's kind of messed up that they (and by They I mean the nebulous maths departments of the universities of the world) let you do calculus for years before telling you, "By the way, there's actually several differeny types of integration with different definitions and motivations, and which one you're doing when really matters, and you've quite possibly already been doing more than one of them, and we will now proceed to not actually define any of them or give a comprehensive list. Have fun!"

This post is NOT about pathwise vs lineat integration and nor is it about different methods of solving integrals or multiple integration or any of that sort of stuff; those are my friends and allies. This post is about Lebesgue and Riemann and Stieltjes and the £17 they owe me

[turnedpalefromlackofsun]

[super-ion]

She pulls me close to her, envelopping me in the heat of her body. Her lips brush my ear, sending a shudder through me.

"How fast can you do fourier transformations?" she purrs.

I blink, confused. I try to pull away, but she clutches me greedily.

"Wh-what?" I manage to stammer.

She nibbles at the base of my neck, and a tiny moan escapes unbidden from my throat.

"I want you to do frequency analysis on the noises you make while I fuck your brains out tonight."

[transgenderer]

I wish there was a good pop sci book abiut like...antenna and circuit design. Or yknow "dynamic electromagnetics" more generally. I basically just did electrostatics and some stuff with like simple moving charges. closest thing I think of is hot molecules cold . electrons but I was reading the book and it's mostly just an into to PDE's and Fourier analysis? I've done thst stuff. I think I know the necessary physics to understand circuit and antenna stuff but it's hard to find explainers that aren't super dense and boring

[transmutationisms]

speaking of Sophie Lewis have you read her book Abolish the Family? if so I’m curious about your thoughts on the third chapter (“A Potted History of Family Abolitionism”). she makes some big claims (e.g. people have been arguing for variants of family abolitionism for 2000 yrs) but imo doesn’t really tee up good evidence in support & maybe also doesn’t properly historicise the family at some points, though I might be expecting too much from such a short text. anyway would be super interested to hear your thoughts! would also be curious about your favorite/most useful family abolitionist texts! thanks for your insightful writing & suggestions.

that chapter is weak & to be honest i'm not particularly enamoured of Abolish the Family as a theoretical text in general. she doesn't prove her claim about 2000 years even in the slightest (1 quote from plato that doesn't really pertain to the social form we recognise as 'family' since c. the 19th century + extremely vague and broad and homogenising claims about indigenous americans) & even on the sections from fourier onward the analysis is v minimal and at points even conflates opposition to the bourgeois nuclear family specifically with a genuinely anti-family position. as though other family forms can't a) exist, b) be equally awful, or c) defend themselves specifically by positioning themselves as a critique of the nuclear family lol.

i also don't think she's even arguing a point that matters all that much—like, who cares how long people have or haven't been saying something? it doesn't inherently mean the position is good or bad. her critique is much stronger where she focusses on the ways in which the family currently actually really does fail people, and on what it actually exists for, economically speaking. i don't really give a fuck intrinsically what a few canonical 19th-20thc thinkers said about the family: it's incumbent upon you to demonstrate that their positions actually were insightful or meaningful or important. like, even when she talks about marx it's a bit like, well there are things marx said that were wrong or underdeveloped or facile too. i don't automatically lend an argument credence just because he said it lol; just gesturing to the fact that xyz expressed verbally an opposition to bourgeois marriage is not convincing argumentation.

i sound like a huge hater right now & like i said above, i do see value in other aspects of lewis's work; i also frankly just have some respect for the text as a polemic defending an incredibly unpopular position that i obviously think is fundamentally important. but the historical work is shoddy and frankly kind of embarrassing for her imo.