#math with vectors

[er-cryptid]

Vectors with i and j [Ex. 3]

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[lipshits-continuous]

Something about maths that'll never not amaze me is how sometimes you'll read a certain topic and it'll be kinda out of reach, like you kinda get the idea but the details go over your head. But then a few months later you'll come back to it and somehow it makes so much more sense. Maybe it's cause you've realised something that makes it click or sometimes you'll have learnt other things and it'll put it in a new perspective. And it's honestly one of the best feelings

[why-the-heck-not]

maybe maybe a mistake taking astronomy; idk why I thought I'd suddenly be a physics mastermind just bc I have more motivation for it now. It's the first week and I have no actual clue what I'm doing (or more accurately: should be doing. Mostly so far it's been lots of staring and muttering of "what the fuck" in regular intervals)

[team-chaotix-week]

*Screenshot taken from IDW Sonic #17*

[shitpostingkats]

Some fun findings in my Barian Emperor deep dive

Zexal cannot for the life of them decide if they want Dumon to be Greek, English, French, or Norse. The folklore taxonimist part of my brain finds this inordinately funny.

They want SO bad for Nasch's empire to be some Mycenaean/Classical Era kingdom, but totally bungles it by having Dumon be there. This is also inordinately funny to me.

Squinting our eyes a little and giving the series a lot of creative license, Alito seems to be the oldest of the Barian emperors, then a huge gap of a couple centuries, and then the death order would logically go Mizar, then Marin, Vector, Nasch, Dumon, and finally, Girag.

Mizar, in his past life, carried around, and presumably knew how to use, a sword. I had completely forgotten about this.

[moonlight-n-moondust]

day 69/100

AHAHAHA we've reached the holy (or not so holy) number

finished ucat revision (5x VR, 5x SJ)

finished phy pract paper from yest

finished vectors 1 add pract

was a pretty light day as most shit was already done atp

CLEARED TODOLIST FULLY SO LESSGO BABY

ripping it was like asmr ffs

the 100 dop challenge is transforming into someone i can learn to be proud of

makes me really happy because im finding less excuses to procrastinate

was able to chill with some netflix hehe

unfortunately, the grind starts again this week

drafted my new todo list and allocated tasks for each day

as usual, my printer never fails to clown around smh

~2 hours 25 min on ypt~

[im-tired1124]

So it’s been a solid 366 days since I last drew a full-body lineup of the castoff cast, and wowee has my art style changed to an unrecognizable extent and also hasn’t changed at all

2/10/24 version for reference

[then-ponder]

Time to start a wrestle with the mathematicians

[smath-or-pass]

Vectors

[bubbloquacious]

So say you have the set of all lines in a plane through some point p, and you have a different line k not through that point, then all but one of the lines (the parallel one) through p intersects k in a unique point. And if you're in the projective plane, then even the parallel line will intersect k in a point at infinity. But, if you cycle through all the lines in such a way that the intersection point 'travels around' k once, then the lines through p will have 'flipped around' only half a turn. So what that comes down to is that the line bundle over the real projective line is an open Möbius strip.

[lisaof2evils]

behold

tensor

[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)

[lipshits-continuous]

So at the moment, we're studying smooth manifolds in Riemannian Geometry before we actually get to do any Riemannian Geometry specifically. However, this means I've seen a lot of the stuff already because I'm reading Intro to Smooth Manifolds by Lee. At least that's what you'd think right? No it turns out my lecturer is using different notation for certain things and he's defining the tangent space via curves instead of derivations. Which ultimately means I have to remember two lots of constructions simultaneously and not accidentally use the stuff I've learnt in Lee in my Riemannian Geometry assignments/exam at the end

[why-the-heck-not]

truly my best brain time is in the middle of the night caffeine & sugar rush. I think I just understood math, like some part of the general pattern of math if that makes sense. something clicked somewhere in my brain and I felt it

[fuck-i-like-too-much-stuff]

Being at tuition with the assholes from non med is basically reminding yourself that you in fact are better than them and not just because you had the backbone to choose humanities instead of succumbing to parental/societal pressure but also because your entire personality is not the fact that your stream "has it harder" for absolutely no reason.

[unnonexistence]

kicking my feet and giggling thinking about vector spaces