Bsdndprplplld - You Can't Comb A Hairy Ball

6 VIII 2021

went back home

sleep: good, finally, although it's already almost 3 and i'm still up so i gotta go be unconscious for a few hours soon

concentration: fine

phone time: fine

did some measure theory, only this today and i'm in love, shit's fucking amazing

tomorrow i'll probably do more measure theory and possibly some coding

september

I decided to start posting monthly, I hope it will help me keep it regular during the semester, it may also bring more structure into my posts

I gave my talk at the conference, I was surprised with the engagement I received, people asked a lot of questions even after the lecture was over. it seemed to be very successful in a sense that so many people found the topic interesting

what I need to do the most in the next 3 weeks is learn the damn geometry. sometimes I take breaks to study algebraic tolology, I did that yesterday

you guys seem to enjoy homology so here is me computing the simplicial homology groups of the projective plane. I tried to take one of these aesthetic photos I sometimes see on other studyblrs but unfortunately this is the best I can do lmao

my idea for mainly reading and taking notes only when it's for something really complicated seems to be working. I focus especially on the problem-solving side of things, because as I learned the hard way, I need to learn the theory and problem-solving separately. what I found is that sitting down and genuinely trying to prove the theorems stated in the textbook is a good way to get a grasp of how the problems related to that topic are generally treated. sometimes making one's own proof is too difficult, well, no wonder, experienced mathematicians spend months trying to get the result, so why would I expect myself to do that in one sitting. then I try to put a lot of effort into reading the proof, so that later I can at least describe how it's done. I find this quite effective when it comes to learning a particular subject. I will never skip the proof again lmao

in a month I'll try to post about the main things I will have managed to do, what I learned, what I solved, and hopefully more art projects

also a funny thing is happening

my title here on tumblr is "you can't comb a hairy ball" – hairy ball theorem, which says that whenever an n-dimensional sphere admits a continuous field of unit tangent vectors, n must be odd. I love how geometric this is, math is full of memes

anyway when I found out about it I was joking that my thesis will be on it. and now it's actually very likely that my first thesis will be about hairy manifolds, I can't wait till I can start writing

15 V 2022

I have a topology test this friday, not gonna lie I'm kinda stressed. this is my favourite subject and I am dedicating a great deal of time to learn it so if I get a low grade it undermines the efficiency of my work. everyone thinks I'm an "expert", but internally I feel like I lied to them. it's ridiculous, because I can solve all the theoretical problems fairly well but the moment I have to calculate something for a specific example of a space I am clueless. and it's about applying theory to problems, right? so what is it worth

other than that tomorrow is a participation round in the integral competition at my university. I am participating. I don't have any high hopes for this, because it's been a while since I practiced integration and I am not motivated to do so because it's not an important skill – wolfram exists. either way could be fun, that's why I decided to go there

I am dreading the fact that I'll have to sit down and learn all the material from the probability theory until the exams. I've been ignoring it completely so far, because it's boring and complicated. the last homework broke me, it's high time to get my shit together

The chili plant made a deal with their God to only be consumed by things that could spread its seeds and fly. The chili received capsaicin, making itself painful to eat for mammals, but not birds, and all was well for the chili.

Then the human shows up, tastes it, and likes the pain. So now there's this flightless fucking mammal eating the chili. Like not even a fruit bat or anything, a flightless fucking mammal chomping on the chili.

What the fucking shit, God, cried the chili, I specifically requested the opposite of this.

Now hold on, wait a moment, replied the God who talks to plants but has no idea what the fuck these apes are going to do next. It might be something cool.

And in a flash of a second, in barely fraction of the time that chili took to develop capsaicin, the humans went from walking across land bridges and rowing little boats across small waters, into building ships that could cross oceans. More humans tasted the chili, and liked the pain. They took the seeds with them, and planted it elsewhere.

See? They spread the seeds.

They're still not flying, said the chili, still feeling insulted and betrayed.

But before the conversation was over, the humans were still not done fucking around and nowhere close to finding out. The ships became machines, and another machine was invented, capable of flight. Now, not only were the humans farming chili on continents far too far away for any of the birds that originally ate it could dream of flying, but the chili flew with them to lands where it could possibly not grow, so that humans over there could also eat it and enjoy the pain.

You see? They spread your seeds and fly.

It doesn't count as keeping a promise if you only manage it by a fucking accident, said the chili, still somewhat insulted. But nonetheless, the chili thrived.

Right. So. A Tarot sequence of three cards, A -> B -> C is exact if everything you take from A as part of B is all that you leave behind when you interpret B as part of C.

For example let's look at a relationship spread:

Self -> Other -> Dynamic

Start with the Self, then identify the self with aspects of the Other; those aspects are precisely the parts of the Other that you ignore when interpreting the Other in the Dynamic. With me so far?

Let's add another link to the sequence:

Self -> Other -> Dynamic -> void

"void" has no card. It has no interpretation, consumes all, and yields nothing. All aspects of the Dynamic are consumed by the void, but when we know this sequence to be exact this tells us much:

The aspects of the Self that we see in the Other are those parts we leave behind when we see the Other in the Dynamic. The aspects of the Other that we see in the Dynamic are those parts we leave behind in the void (which is everything). So for this sequence to be exact we know that the Dynamic is fully explored by those parts of the Other than we cannot identify with the Self.

25 XII 2022

this chunk of the semester is finally over, sweet jesus I'm so exhausted. I'm getting the well-deserved rest and later catching up with all the things I put on my to-do list that I kinda learned but not really

the test I had last week went fine. frankly I expected more from it after solving more than 50 problems during my prep, but I scored 74%, which is objectively great and more than I predicted after submitting my solutions

here is my math plan for the break:

in algebraic methods I started falling behind a few weeks ago when I missed two lectures while being sick. they were about resolutions, derived functors and group homology and afterwards I wasn't really able to stay on top of my game like before. high time to get back on track. in commutative algebra I was doing ok, but there are some topics I neglected: finite and integral maps and Noether's normalization. for complex analysis everything is great until we introduced the order of growth and recently we've been doing some algebraic number theory, which btw is a huge disappointment. don't get me wrong, I understand the significance of Riemann's ζ, but the problems we did all consisted of subtle inequalities and a lot of technical details. I am doing mainly algebraic stuff to avoid these kind of things lol

when we were doing simplicial sets I stumbled upon some formulas for the simplicial set functor and its geometric realization and I thought it to be a nice exercise to probe them, so here it is:

I won't know if this proof actually works until I attend office hours to find out, but I am satisfied with the work I put into it

I already started making some notes on the derived functors

other than that I have this nice book that will help me prepare for writing my thesis, so I'd like to take a look at that too

as for the non-math plans, I am rewatching good doctor. my brain has this nice property that after a year has passed since finishing a show I no longer remember anything, the exponential distribution is relatable like that. this allows endless recycling of my favourite series, I just need to wait

I wish you all a pleasant break and I hope everyone is getting some rest like I am

Me: I should write something

me : … or I could spent 78 hours straight making a miniature library with a working LED chandelier

Real estate agent, 5 minutes into the meeting with a topologist: So, when you were talking about "contracting" a "house with two rooms",

(Points at the function I'm doing my thesis on) this is my son who has every disease

Pick a point inside a triangle and drop perpendicular projections onto the sides. These define another triangle. Repeat, with the same point but within the new triangle. Do the same thing once more. The fourth triangle now has the same angles as the first one, although it’s much smaller and it’s rotated.