Bsdndprplplld - You Can't Comb A Hairy Ball

13 X 2022

I dedicated the weekend to meeting with people from the machine learning club, helping my friend through her analysis homework and studying category theory for one of my subjects. then I did mostly the complex analysis homework

here are some wannabe aesthetic notes

my main goal at the time was to truly understand yoneda's lemma and the main intuition I have is that sometimes we shouldn't study the category C, but thw category of all functors from C to Set

after studying for a few hours I can say that the concept became a bit more intuitive

one of the problems in my "putnam homework" was to calculate the product of all differences of distinct n-th roots of unity – or so I thought. for a few days I believed that my solution doesn't work. I ended up with a disgusting fomula interating cosines of obscure angles but the visual intuition is neat, especially for an odd n. aaand that's no surprise since it turns out I'm fucking illiterate. not distinct roots, just differences of distinct roots, so that the whole thing is symmetric and there is no distinction of n odd vs n even

anyway I finally solved it, so that's nice!

I completed 5 out of 10 problems, which was my goal, so I should stop now and do my commutative algebra homework. there is one more exercise I want to solve:

the complex polynomial P with integer coefficients is such that |P(z)| ≤ 2 ∀z∈S¹. how many non-zero coefficients can P have?

I'm almost there with it and it's really cool

ofc the opportunity to include pretty drawings in my homework couldn't be wasted

during my category theory tutorial the professor asked me to show my solution on the blackboard. I was kinda stressed because now is the first time when I have my lectures and tutorials in english and on top of that this is a grad course. that whole morning I was fighting to stay awake, after the blackboard incident I didn't have to anymore

this is what I did

this week is likely to be the hardest out of many proceeding ones, because I won't have the weekend for studying (it's my grandma's birthday) so I need to use the maximum of my time during the week and get as much done as possible. I still need to do two homeworks, and study the theory. I am trying to learn how to prioritize and plan things, this is still a huge problem for me

I found an interesting youtube channel: Justin Sung. he talks about how to study/ how to learn and I like what he says, because it just makes so much sense. it's been a while since I started suspecting that methods such as flash cards or simple note-taking don't work and his content explains very well why they indeed might not work. it's very inspiring to see a professional confirm one's intuition

I love reading stuff on abstract geometry because there'll be some extremely complicated construction of abstract polytopes that takes up like two full pages

and the first example is this

and you're like "wow that's a cube :)"

and then the next example is this

7 XI 2022

I think I found an advisor and a topic for the bsc thesis! or rather they found me

one of the teachers that prepares us for writing our theses approached me and started asking about homology I mentioned during our presentation, he wanted to know what courses I took and how familiar I am with that stuff. I told him that I know a bit about homology only from self-study but I enjoyed everything from algebraic topo so far and I would be happy to write about something from that. "ok then I'll find the right topic for you" was his response. then he suggested I read Groups of Homotopy Spheres by Milnor and Kervaire and write about surgery theory. I was sold the moment I heard that name, it's almost as funny as writing about the hairy ball

so there she is, very high level, very complicated. I barely skimmed the first half of that 34-page paper, it's gonna take a lot of work before I learn the basics necessary to even comprehend what is going on. it feels good to be noticed tho, I'm so happy to start writing asap

other than that my mood hasn't been in a great place, because commutative algebra is super hard and I am struggling to find the right resources to study. the last thing we did was tensor product and I've been procrastinating actually studying it by making pretty notes lol

I found a textbook that seems decent. the theory is very thoroughly explained here and there are plenty of exercises ranging from easy to difficult ones

recently I've been trying a new method of tracking, which is instead of writing to-do lists, I write down what I did each day, here is what it looks like for now:

I find it much less anxiety-inducing than the to-do approach because I know damn well what I need to do and writing down what I actually completed feels much better than crossing things off of the list

this week I hope to study the tensor product, representable functors (yoneda is still not done with me) and probably start the complex analysis homework. if I have time I will study the prerequisites for the Milnor's paper

2 IV 2023

oh god the programming task for today was so annoying. I was supposed to process the MIT database with ECG records, and the annotation part of it was hell. after three hours I finally did it but the anger I felt at that time put me seconds away from throwing my laptop out of the window lmao

a recent success is that I calculated the rank of the module that I am working with, the problem is almost solved! when I told my advisor about it he looked so happy, he said that maybe he should start looking for another problem for me to ponder, it was so satisfying. I have a thing for mentors. at each point in my life for which I had a mentor who would teach me my special interest the progress I was making improved significantly and those were always the happiest times of my life. I am not sure if my advisor will stay with me to further show me a way into the research, but it certainly feels like a possibility

today I did some algebraic topology and differential geometry, I'm trying not to fall behind with the material even when I don't feel like studying

next week the easter starts, so I will probably have to visit my family. it's an interesting feeling to see my sister all grown up, there is still the image in my head of when she was barely a teenager and we didn't have much to talk about. now she is almost 18 and the significance of the age difference is nearly gone. when she start university it will be even less noticeable as she will understand what I mean by "fuck my life it's exam session season" lol

for about a week I've been trying to eat more healthy food, it's going fine so far. my biggest problem is that I'm eating way too much sugar but undereating in the general sense at the same time. I'm trying to incorporate more fruits and vegetables into my diet, as well as different kinds of nuts. it's so important to be properly nourished for math and yet I neglect it so much

yesterday I had a conversation with my friend and he said that his vision for doing math is working on some huge open problem such as RH. obviously you do you, but this sounds like such a depressive idea to me lol. chances of solving something like this are almost non-existent, that's such a waste of time to work on something like this for 10, 20, 50 years and make no progress. I mean, it certainly would feel nice to prove or disprove something like RH, but I'm perfectly fine with reading papers and answering all the questions I can anwer, which might not be huge and famous but I'm pretty sure creating those small pieces of theory will be useful to somebody one day

in a way. over the last two years or so. mathematics has become the altar at which I pour out my private grief, and transmute it to something like solace. it does not particularly matter to me if I am ever any good at it. what matters is that the effort I apply to it is rewarded by understanding. I have no natural aptitude for it; I am climbing this hill because it was the steepest and least hospitable to me. there is less agony in the gentler slope, but less valor

that sounds a bit like mystery flesh pit national park

I’m Christian and respect the order of creation as God intended it but I’m not gonna lie if I could take a massive vat of agar and grow an alive shopping mall made out of red blood and meat and feed it living human bodies to make it expand larger with more shops and amenities, Without hesitation, Without question I would do exactly that

One of my favorite thing I’ve learned about animals studies is that you should avoid using colorful leg bands when you’re banding birds because you can accidentally completely skew the data because female birds prefer males with colorful bands

Apparently if you put a red band on a male red wing blackbird his harem size can double

So like you can completely frick up the natural reproduction of a group of birds by giving a guy a bracelet so stylish that females CANNOT resist him

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.

Nothing but respect for this mathematician's webpage