#tensors

[xypheris]

Me, at the start of the semester:

Yeah, I’ve got this. I know my stuff, I’m ready to crush it.

Midterm week:

Rips out hair

Why does everything keep turning into a tensor? Who even asked for a tensor?!

[dnieperrobot69420]

Taking a slight tangent from classical optics, I decided to delve more into non-linear optics.

As someone who never had to use Gaussian form of Maxwell's equations, never used Tensors, and had never used Einsteins notation for summation; let me just say the algebra of the book proved to be a hard nut to crack!

What am I learning about? Anisotropy! Who knew that the direction at which you observe/propagate through a material such as a crystal plays a role in the material properties you will experience!!

I still don't believe you can determine eigenvalues and eigenvectors for an arbitrary 3x3 permittivity matrix (I need to use numerical examples to really see it) and that there exists rotational matricies that let us make the math all neat and proper.

But, slowly and with growing pains, I am continuing to slowly tread the waters of this fascinating topic!

[studywith-minmin-shelved]

[12/26/23] Day 8: Tensors and Cheesecake

I went to a cafe with my dad to work today. Had a great Frappuccino and a mindblowing cheesecake for lunch. It paired well with a light reading of Part I of Zee's QFT in a Nutshell.

Today's crowning achievement is that I finally get what a tensor is, hallelujah. No thanks to my physics education; everyone was so vague about it! Things are slowly falling into place when it comes to tensor calculus since I don't want to know it like a mathematician. Just enough to get a handle on things.

Meanwhile, I just couldn't make it through another QFT lecture today. Didn't manage time well and ended up so sleepy that I quit twelve minutes in. Oh well, difficult things take time.

[dandelionsandderivatives]

Overtures of friendship were received well. Tensions remain high; however, we have hopes of establishing a healthy working relationship with the tensors.

why are tensors like this

[turbofanatic]

Floyd was such a good design I’ve decided to recycle him for Living Creatures. I never managed to show his monster form in Sanguine Tensor anyways (it would have taken ten comics to get there! What was I thinking?). Now he’s a weird posthuman dragon thing. Anyways, here’s when he gets his ass wrecked by Lioness. Literally. She cuts his ass off. I’m so sorry Floyd.

[duct-taped-shoes]

For Go Skate Day this year I put together the set up I wanted when I first started skating

[proof-by-intimidation]

Ok this is like an itch in my brain, even though I think it's true, I am getting confused the more I look at it.

Suppose B,M, N, P are A-modules. Suppose I know that the sequence

is exact in the category of A-mod. Then is it also exact in the category of B-mod?

[questioning-my-identity-element]

as someone with a passing knowledge of knot theory & a dilettante interest in math I'm really interested in the behavior/rules of those graphs, could you talk a little more about them?

this is my first ask! and it's on my research!!! i still do research in this area. i am getting my phd in topological quantum computation. i saw someone else talk about categorical quantum in response to the post. as i understand, this is a related but distinct field from quantum algebra, despite both using monoidal categories as a central focus.

if you're familiar with knot theory, you may have heard of the jones polynomial. jones is famous for many things, but one of which is his major contributions to the use of skein theory (this graphical calculus) in quantum algebra, subfactor theory, and more.

For an reu, i made an animation of how these diagrams, mostly for monoidal categories, work:

https://people.math.osu.edu/penneys.2/Synoptic.mp4

to add onto the video, in quantum algebra, we deal a lot with tensor categories, where the morphisms between any two objects form a vector space. in particular, since these diagrams are representing morphisms, it makes sense to take linear combinations, which is what we saw in the post. moreover, any relationships you have between morphisms in a tensor category, can be captured in these diagrams...for example, in the fusion category Fib, the following rules apply (in fact, these rules uniquely describe Fib):

thus, any time, these show up in your diagrams, you can replace them with something else. in general, this is a lot easier to read than commutative diagrams.

[chelledoggo]

my overreactive tensor tympani muscle when i hear a loud, harsh, high pitched noise

[chazza-studies-mphys]

screenshots from two of today’s lecture slides, presented without comment:

[remnantglow]

the thing about the black tides of heaven by neon yang is that while i absolutely understand why not everyone would vibe with it - it compresses so much story into so few pages - it's just SO dear to me. like there's just something so so so compelling to me in a novella about characters who are twins, one of whom is a literal prophet with the world's worst case of main character syndrome, and then making the story about the Other One. that and the transgenderisms

[studywith-minmin-shelved]

[01/04/23] Day 17: Worry Less, Math More!

No QFT or Application stuff today but I had a lot of fun doing tensor calculus in the cafe today!

I have been thinking about a certain conversation I had with a TA recently, so I sat down to work through the algebra proof and finally figured out what he said actually meant. It was kind of embarrassing because I was trying to answer a different question and was talking myself in circles.

It’s kind of funny how I’m treating abstract algebra as a hobby now!

[locally-normal]

Maybe I should stop telling people I'm an algebraic topologist and just say I do homotopical algebra. It's truer I think. But less well known. Which is weird because everyone knows about homotopy theory.

I guess the brave new algebra program was only fully realized fairly recently.

[turbofanatic]

Sanguine Tensor needed a new character for various plot related reasons so I’m retrofitting an older character into that role. So here’s revamped Maulissa!

She got MURDERED and it was AWFUL and then came back kinda wrong due to carbon plague and captured and used by the government and got rescued by a weird lady with holes in her and a robot cat that keeps ranting about the booj-wah and nothing fits anymore and everything is terrible! She has a 4 year old son who thankfully is being taken care of by her sister and he's very chill about the whole thing. Mommy threw a truck at the cops and he thought that was great! She was a kindergarten teacher and just wants things to be normal again and it is not happening! What even is a booj-wah?!

Initially her resurrection due to carbon plague messed with her digestive system and she just has a toothy maw in her chest with horribly corrosive chemical. Her original mouth is gone and she just has a weird air filter instead. In a weird inversion of Zmeyevich she gets a secondary power set in the form of hyperspace worms. These turn her into a meat TARDIS with a weird subspace internal factory and she can “copy” the macro scale characteristics of anything she eats. And she’s capable of eating nearly anything. The copied objects are made of carbon allotropes and generally have superior strength/toughness/sharpness compared to the original.

They always come out covered in spit. It’s gross.

So in addition to be very strong and fast she can puke up ridiculously sharp swords. And every once in a while she can puke up something that’s doesn’t 100% seem to obey physics and confuses spectrometers.

She has to hang out with supervillians and they won't shut up about science. Please help her.

[fruitlicense]

went and saw Interstellar in IMAX on Wednesday and I’m still thinking about it. 4th time I’ve seen the film, 2nd time with a bunch of other physicists, but first time in theaters. I’m still looping the score and thinking about what it is to watch that film a little too close to the screen, when every feeling is just a little too big to hold. it’s a movie about space, about science, about love. it’s about not being able to solve something no matter how hard you try and hurting people as you try to find yourself. it’s about hurting yourself in the process and coming back from it. it’s about care and honesty and humanity and encoding all of that in numbers sent across spacetime. it’s about feeling the same smallness in the vast universe and the dark of the theater when the organ music shakes your seat. it’s about the crashing waves and the gasping breaths and the spinning ship and crying for someone you love. anyway that movie fucks me up. it’s one of the most beautiful films in the world

[stemacademics]

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