#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

[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.

[blueiscoool]

Archeologists Uncover Alexander the Great’s Royal Tunic in Vergina

The remains of a garment from an ancient tomb in Greece may be a tunic that was once worn by Alexander the Great, a scholar claims in a new study.

The garment was found in a tomb that many scholars believe belonged to Alexander’s father, Philip II. It's next to two other tombs thought to hold other royal members of Alexander's family.

The new study, however, claims that this particular tomb doesn't belong to Alexander's father, but to Alexander's half-brother, Philip III (also known as Arrhidaeus). The study also claims that the cotton cloth found in the tomb was once part of a tunic worn by Alexander that, after his death, was passed to Arrhideus and buried with him in this tomb.

The tunic was sacred because only Alexander the Great was allowed to wear it, said Antonis Bartsiokas, professor emeritus of physical anthropology and paleoanthropology at the Democritus University of Thrace and author of the study, published Oct. 17 in the Journal of Field Archaeology. By the time of Alexander's death, some people considered him a god, Bartsiokas said in an email.

However, not all of the scholars supported the findings, with one scholar saying that it is not a tunic at all.

A king's tomb

The garment was found in 1977 in a gold chest in a tomb near the town of Vergina (formerly the capital of Macedonia) in what is now Greece. The tomb has two skeletons that are, according to Bartsiokas, those of Arrhidaeus and his wife Eurydice.

After Alexander died in 323 B.C., Arrhidaeus became king of Alexander's empire. Historical records indicate that Arrhidaeus lived with some form of mental disability and was unable to rule. Alexander's officials and generals fought for power, and the empire disintegrated with the killing of Arrhidaeus in 317 B.C.

Bartsiokas contends that after Alexander died, this tunic was given to Arrhidaeus and, after Arrhidaeus was killed, was buried with him. In his paper, Bartsiokas cites evidence for this idea, such as the art on the tomb's walls, studies of the skeletons found in the tomb, and an analysis of ancient historical records. Bartsiokas also looked at past tests done on the garment, including energy dispersive X-ray spectroscopy, a technique that analyzes X-rays to determine what an object is made of, and fourier-transform infrared spectroscopy, which uses infrared light to analyze objects.

Alexander's tunic?

Bartsiokas contends that tests done by other scholars show that the garment was a sarapis, or a tunic. The tunic is made of three layers. Two of the layers are made of cotton that has been dyed purple. Between the two layers of cotton there is a flexible layer of a mineral called huntite. Purple was worn by kings in the ancient world, he noted, and cotton was grown in Persia, but not in Greece, during Alexander's time. Ancient historical records indicate that "cotton was introduced to Greece and Europe by Alexander’s army following the conquest of the Persian Empire," Bartsiokas wrote in his paper.

Bartsiokas also cited ancient records claiming that the king of Persia wore a tunic that used cotton and huntite and that Alexander wore a tunic like this after he conquered Persia. He noted that Philip II was not a ruler of Persia and would not have worn a tunic that used cotton or huntite.

In addition, the artwork on the wall of the tomb — an illustrated group of hunters — depicts Alexander wearing a tunic similar to the one found, Bartsiokas said, and the artwork's details suggest the artist was familiar with Persia's landscape and wildlife.

Additionally, the painting is done in a complicated style that would have taken a long time to complete, meaning the burial likely didn't belong to Philip II. That's because Philip II was assassinated in 336 B.C. and Alexander went on a military campaign shortly afterward, which means the artist would not have had time to create it before Philip II's funeral, Bartsiokas explained.

Another reason the garment didn't belong to Philip II, Bartsiokas said, is that the king suffered a wound to his right eye, but neither skeleton in the tomb has an indication of such a wound.

Controversy

Scholars had mixed reactions to Bartsiokas' paper.

Hariclia Brecoulaki, a senior researcher at the National Hellenic Research Foundation's Institute of Historical Research in Greece, said there is no evidence to support the idea that this garment was a tunic. "The textile, according to the excavators, looked more like a piece of scarf that served to wrap the bones of the deceased," Brecoulaki said in an email.

Athanasia Kyriakou, director of the Aristotle University of Thessaloniki's excavation project at Vergina, also criticized the paper. "This article is full with faulty understandings due to a lack of the relevant background," Kyriakou said in an email. Bartsiokas did not conduct tests on the materials himself, Kyriakou noted, adding that Bartsiokas "has not even seen the materials."

Other scholars were more supportive of the paper and its findings. "I am sympathetic to Antonis Bartsiokas's arguments that it belongs to Philip III," Susan Rotroff, a professor emerita of classics at Washington University in St. Louis, said in an email. "If the textile in question really is cotton, it is hard to support a date before the time of Alexander the Great."

Richard Janko, a classical studies professor at the University of Michigan, was cautiously supportive. "This is a very exciting piece of research," Janko said in an email. "The original identification of the male occupant of the extraordinarily rich Tomb II at Vergina as Philip II, the father of Alexander, is far from secure."

However, Janko noted that the cotton used to make the garment could have been imported through trade from Persia, which means that it could have been acquired and used by Philip II.

David Gill, a fellow at the University of Kent's Centre for Heritage, commended the paper's findings. "Some years ago I published the weight inscriptions from Tomb II — and I argued that they had to post-date Philip II," Gill said in an email. Several objects in the tomb, such as silver plates, have their weights inscribed on them.

He found the paper's arguments that the garment was a tunic used by Alexander the Great to be strong. "It is likely that this was an item that was worn by Alexander the Great," Gill said.