Ma sì, vantatevi del fatto che non vi va di fare un cazzo, che non vi piace studiare; crogiolatevi nella vostra obesa ignoranza, nella vostra assenza totale di ideali- in qualsiasi ambito e di ogni matrice. Continuate pure a credere che il mondo giri attorno a voi, che in America vi aspettino per diventare il nuovo Steve Jobs e che leggere un libro ‘non serva a niente’. Un sogno deve essere impregnato di caparbietà e non di arroganza.
“It’s common for men to demonstrate mild (or strong) disdain for how much women care about fashion or how much money women spend on clothes. But they are mostly just demonstrating a complete lack of awareness of a semiotic system that women are required to participate in, in order to accrue both economic and social benefits, which men are largely exempt from.”
Graduate Level Mathematics Appears in Gravity Falls... Holy Shit
If you’re a viewer of Gravity Falls, you’ve likely paused the opening theme near the end in order to get a glimpse of the lovely triangle thingy that appears for a few frames. If you manage to pause correctly, what you will see is this:
While the image in the center, and the symbols in the circle are clearly the thing that draws the eye of the viewer most, take a look in the upper right corner. What do you see?
Matrices. The bane of every high school student who went past the first year of algebra. I was looking at this today (since my life is apparently now consumed by this show), and noticed that the symbols and patterns of the matrices were familiar for some reason.
I looked up how well the page had been interpreted/translated, and the only explanation I found for the matrices were: Geometric Transformation. That’s all well and good, but there was something still not clicking. I determined that I needed a better look at the full matrix equation (you can tell there’s some missing from the top of the previous image, if you look closely).
So, I found an image of the page (from S1E19, taken from the Gravity Falls Wiki) which showed the other portions of the matrices:
Here we have the full matrix equation. It turns out that what we can see in the title card is the final form of the equation itself, which is an expanded form of a column vector with components [hx, hy_z, h, 1]. Suddenly, it hit me:
This is something I learned about in a 6000 level Stat course last semester!
This is not a random “geometric transformation.” This is a projective transformation from 2D to 3D! These transformations preserve the connections between points, but can stretch and warp the connective lines beyond recognition.
If I were to extrapolate this identification into an implication about Bill Cipher, the lovely triangle in the center, I would think it implies three things, one of which is confirmed:
1) Bill can project into minds, and possibly into 3D in general. [Confirmed by S1E19]
2) Bill is trapped in 2D space in general. The summoning described in the ring (which is not fully deciphered/understood in the context of the show) will permanently project him into 3D space/the “real” world (of the show).
3) Bill can alter his form, but will overall stay contained by the form of a triangle (projective transformations can stretch and warp the lines that connect the three points).
I am super, super excited to see this, and was a bit shocked to find a graduate level mathematics reference/clue hidden in a 1-frame image in the opening theme of a children’s television show.
tl;dr - There’s another clue in the title card of Gravity Falls, and it depends on an understanding of a particular topic of graduate-level mathematics.
“my mother tells me:
women fall in love with love and men fall in love with women.
we were summer sweat at the knees and pomegranates staining our elbows all the way to our mouths. she tells me i have fallen in love with a concept. a matrix full of infinite quivering promises -
multiply the rows of secrets by the columns of
sandcastles we’d watch fall behind us.
rome was not built in a day, but pompeii was destroyed in a minute.
i know the way fire often means subtraction. but i was never the scientist. that was you, baby.
that was all you.”
there was never enough room on the postcard for this. (A.B.)
“Quando l’immaginazione-l’idea che qualcosa possa realizzarsi- si unisce a un’emozione che dà vita a una possibilità, si crea la realtà. La manifestazione inizia con la nostra disponibilità a creare uno spazio fra le nostre certezze destinato a qualcosa che si suppone non esista.”
After Derek wrote about vintage leathers yesterday, we joked about dressing appropriately for your personality—that is, what if you look like a dork? Leather jackets seeped into casual men’s wardrobes by their association with specialized, hide-bustin’ activities like racing motorcycles or piloting jet aircraft, and although today they’re socially acceptable for everyone from rebellious teens to cool uncles, some jackets will make you feel like a poseur and probably look like one, too. The matrix above plots some well-known leather jacket designs on axes of how cool they are right now vs. how wearable they are for the average guy (like most people, I see myself as a reasonable average, which is both absurd and somewhat valid). In approximately clockwise order:
1. Undercoverism knit sleeve biker jacket—A typical “grail item” of internet hype hounds, this jacket looks fantastic on a hanger but is probably best left there. It presaged the recent trend of remixing garment archetypes. It was made for Undercover’s fall 2009 season in a range of sizes, from XS to S.
2. Rick Owens scuba jacket—Here’s your Put This On Rick Owens reference of the day (if I were Jesse I’d be courting Rick as a sponsor). Asymmetrical cuts and intentionally overlong/bunchy sleeves put most Ricky O out of the comfort zone for a lot of men.
3. Schott Perfecto—The “Marlon Brando’s smoldering look” of leather jackets. Some say bigger dudes can’t wear a Perfecto; thousands of well-fed bikers disagree.
4. Eastman Leathers A-1—The A-1 is a no-nonsense classic leather jacket that fits and flatters a lot of builds. You don’t have to ride a bike to back it up, and it matches favorably with denim or dressier stuff.
5. Schott cafe racer—A biker jacket with fewer baubles, plus the word cafe which just seems soft. Slipping down the cool scale in favor of the Perfecto recently.
6. Bill’s Khakis G1—The classic Air Force jacket. Good for almost everyone, best for Top Gun dads.