The Human Experience Is So Crazy. At Any Time I Want, For Free, I Can Comprehend The Beauty And The Horror

31 VII 2022

finally posting after the exams are over, it was the longest session I have ever experienced, a month of exams. I passed everything and it was a good semester, actually my grades are better than ever before, which comes off as a surprise, I can't believe that it's anything other than luck

now what am I going to do for the holiday huh

next semester I am going to take three courses: analytic functions, commutative algebra and a mix-course of category theory, sheaf theory and homological algebra. then I plan to take algebraic topology, algebraic geometry, number theory and some more abstract algebra, along with writing a bachelor's thesis. this is probably going to be the hardest year so far, I don't know how I am going to survive this, I'm so scared

I was asked to give some lectures on geometry during a math summer camp for people who want to participate in the math olympiad. it's a great opportunity for me to practice giving lectures, as that's what I plan my job to be. moreover, it is my dream to be so good at math that I could prep people for the olympiad, hence that's a fraction of that dream coming true

the problem is I don't know geometry lol last time I did any was like four years ago in high school

thus I play with triangles everyday

other than that I must prepare a talk for a conference, I chose to do one on the knot theory, Seifert surfaces specifically. I started reading about it some time ago and it seems super cool

untangling knots is a perfect thing to do for fun

my plan for the holiday outside of these side-quests is to learn as much as possible for the courses that I'll be taking. the problem with them (besides analytic functions) is that they will be quite technical, detailed and dry, as they are supposed to give the tools necessary to study algebraic topology and geometry. that does sound dreadfully boring, no? that's what scares me, because when I am not interested in what I'm trying to learn everything becomes twice as hard. I asked here and there for advice and people told me to read about algebraic geometry in tandem with commutative algebra, since many constructions have beautiful interpretations and motivations there. sounds like exactly what I need

my bachelor's thesis will be on algebraic or differential topology probably, but I don't know exactly what I want to write about. I was thinking about vector fields on manifolds or de rham cohomology, but the thing with the proseminar on geometric topology (mine) is that it's been planned to give the introduction to the currently researched topics and offer opportunities to work with fresh conjectures and theorems. at least that's how it was described. allegedly geometric topology has this property that undergrads can contribute to the development of new theory, which is very surprising to me ngl, I would guess that this is highly unlikely with any kind of math nowadays and yet here we are

in conclusion, I'm excited but scared

I think "high value person" can be interpreted as "someone who is liked by everyone and perfectly adheres to social norms" but also as "someone who wants to find their core values and to this end tries many different approaches" and many other things. some of the things listed are pretty good, such as "take care of themselves" or "doesn't equate their worth to sex", some are unnecessary: "perfected first impressions" or "ALWAYS well-dressed". naah, who cares lol

the thing with self-improvement or other forms of conscious existing (I just invented this term, by that I mean something like chosing which parts of oneself to keep and which to change) is that one must start somewhere. it's nice, in general, to have social relationships, sex life or hobbies and I see this list as a guideline for increasing the probability of achieving those and other things in a certain way

in my opinion it's really important to keep in check with oneself, ask if the cost of being likeable and elegant is worth it. some people derive pleasure from wearing nice clothes and make-up, I am not one of them and for me that would be too much of a sacrifice. I guess most people would hate to have my lifestyle: I basically do math all day. it is my decision to so, it's fun, and I hate it when someone assumes that it's bad just because they wouldn't enjoy it

hence I see this controversial list as goals of someone who genuinely wants to be perfect. and yeah I do think that most of those things are completely unnecessary, I don't consider this set of characteristics as a "high value person" but maybe some people do. a part of self-improvement for me was realizing that I don't care about most things and this post reminded me that there might exist people who care about everything. have they not yet realized that they actually don't care? idk, maybe they do care

but yeah if someone came to me and said that this list objectively defines a high value person then I would laugh lol I will respect everyone's values if they respect mine

I have a bunch of followers and mutuals that I never even talked to and I know some of you guys are very into math too, so let's get to know each other, shall we?

if you feel like you'd enjoy talking to me then go ahead, write me a message! I just realized I never said something like this and I would really love to have conversations with like-minded people

if this feels familiar, you can reblog this post to invite people to talk to you

Every now and then I remember that Malbolge exists and I get to spend the better part of an hour cry-laughing at the world’s worst programming language

already starting off strong, but it gets worse

Wow! Sounds easy and intuitive to use! What’s the “crazy operation” you ask? We’ll get to that later. For now let’s see what a program in this language looks like :)

Thanks! I hate it!

it’s so difficult to work with that the first program was written by another brute force search program

mmmmm delicious base-3 arithmetic, what could go wrong? (For reference, that means this program forgoes the usual “0/1″ values of binary code in favor of a much more fun “0/1/2″ set of values)

ah.

Here’s how the language actually figures out what to do. It’s got 8 “simple” commands that can be executed easily by *checks notes* running the code itself through the modulo operation and taking the result.

As a bonus, on top of all that every single character in your code will now alter what every single other character does. So I hope you’re alright with cracking a cipher every time you add a new letter to your program!

oh god oh fuck.

behold, Malbolge’s primary arithmetic operation and what you’ll be using for most of your math while programming with it :)

This looks specifically designed to be the least logical math operation you could make, and knowing what the rest of Malbolge is I’d wager that’s precisely what happened. I never want to ever use this and it’s my favorite thing I’ve ever seen.

https://en.wikipedia.org/wiki/Malbolge

Anyways here’s the wiki page if you wanna read through it more deeply, I’m gonna sit here holding in my laughter staring at the hello world program again.

[ID: a figure in a textbook that has curved arrows to look like vectors in a field. The figure caption reads, "Is this a vector field? No. It's a picture" /end]

Hello, lovelies! I’ve gotten a couple of asks about studying so I decided to condense them into one post for you guys! I’m trying to hit a bunch of different topics so if you need an even more specific post you can send an ask! Without any further ado, have some tips! My studyblr is @spacey-scholar​

Prep

First, you always need a good base for your day! Especially if you’re studying a lot.

Make a good full breakfast! Ex. Eggs and Toast, Smoothie and fruit, Pancakes and a cup of juice. 

How’s your hygiene? Do you need to shower, brush your teeth, wash your face, condition your hair? Do it! You’ll be distracted if you feel messy!

Get dressed like it’s a normal day. Staying in PJ’s is okay! But being ready for the day seriously helps focus!

Likewise, your space should be clean. A clean space is a clean mind! Remove dishes, trash, scrap paper, and extra items. Wide down your desk, organize your pens and books. Your space should feel like your space!

Now make a list of what you need to get done! What needs to be done Now, what needs to be done Soon, and what needs to be done Later? 

Order your list how you want your day to go, and don’t put super-tough subjects back to back, or subjects that are similar exercises i.e. reading thirty pages of two different books back to back is no fun.

The Studying

It’s important to buckle down with No Distractions! If you find yourself distracted put your phone away! If you need your phone, put it on Do Not Disturb until you’re done. I also do this at night for better sleep. 

Pick the best technique for you, Pomodoro, reward-based, group studying, etc.

Play music but only if it will not distract you! If you sing along or daydream it’s the wrong music! Classical, Lo-fi, and White noise are all good! My Spotify Here has some good ones.

Use a nice journal (I don’t mean expensive!) and pens/pencils you enjoy using. I like to have a specific journal and color dedicated to each subject. 

Take notes on recorded lectures and classes, if you’re doing online classes right now try to screen record or record the audio! That way if you space out you can play it later and take notes, and you can absorb the lesson better instead of being distracted.

Don’t worry about your notes, stationary, pictures, being beautiful and your grades being perfect. Life doesn’t always look the way it does on Instagram. And the people who spend hours trying to get a good photo of their coffee are not studying! 

Use flashcards! Quizlet is good if you need premade ones! If you can save up and buy them, Barrons AP Flash Cards are the best in my opinion. Very clean, not too long, very durable, and cover all subjects.

Feeling Distracted 

If you catch yourself drifting off and getting into your head, get up and take a quick walk, stretch, or energizer. 

It’s okay if this happens, don’t guilt yourself! practice affirmation. The best and smartest still get distracted. 

If you are drifting, why? Are you hungry? Tired? Thirsty? Bored? Get a snack and some water, take a break and rest, find a way to make your studying more enjoyable. 

Remember that Motivation and Discipline are different things. Sometimes we just won’t be motivated, we won’t want to do it and it will be rather frustrating. But the cure to this is not shaming its discipline. Remind yourself “This may be hard, and I may not want to do this, but I want to reach my goals and If this is what It takes I will make it happen. 

Always do just one more page of you’re tired. One at a time and oh you did it! Maybe just one more? One more? Eh, one more just to finish the train of thought, Oh just- I’m done? Nice!

If you really can’t focus just move on and come back to this subject, you can always ask for help.

Supplementary Things

There are so many apps you can use to study, for free! My favorites are Tide, Quizlet, Focus Keeper, Forest, Flora, Egenda, SpanishDict, Photomath, and Kahn Academy. 

You can also join a study group! You may know one, but if you don’t, there are a lot of online ones! I’m in a study Discord and have been for a while! it helps a lot and motivates me to finish my work!

You can make a studyblr, but don’t do it just for the aesthetics! It’s about studying, and sometimes that gets messy! Sometimes we fail a test, we spill our tea on our notes, we cry because we don’t understand the formula. That’s the part you don’t see!

Having cute stationery can really help, as well as nice organizers and decorations for your space! I don’t have much money so I get a lot of stuff on Amazon or FB Marketplace.

Health

Remember that no matter what you are good enough. It’s okay if you fail, it’s okay if you struggle.

It’s also okay if your path doesn’t go the way you expected! Maybe you go to a different school than expected! Or choose a trade instead! Maybe you take a gap year! Maybe your passion changes! Maybe it changes six times!

Your health is always more important than your school. If you are in pain, mentally or physically, if you are anxious, exhausted, burnt out, talk to your teachers about it! You matter more than a grade.

Your best is good enough! And your best doesn’t look the same as someone else’s best! Don’t compare!

Now go get out there and study!

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

being a humanities major who’s friends with stem majors is so funny because you’ll ask your friends what they’re doing today and they’re like “UGH it’s so stressful i have to stabilize the reactor core for my nuclear power midterm and then i have to build the supercomputer from i have no mouth yet i must scream for my electrical engineering homework :/ what about you” and you’re like “oh well i have to read a fun little book and write an essay about gender.” and they still think you have it worse

saving this for self-care and for anyone who might need this

also, I can add: squint your eyes hard and then looking at something far away. it's supposed to help your eyes relax and a bonus simple grounding exercise!

from my personal experience, once you start paying attention to how different it feels on your eyes to look at something far away as opposed to something close, you can relax your eyes without needing an object to look at. now when I'm going to bed I imagine a tree far away and I feel my eyes relaxing, it helps with me fall alseep faster. it might be a placebo ofc, I know nothing about eyes, but it is still a good trick for falling asleep regardless of the supposed effect of it on the eyes

We need like “unclench your jaw” posts but for eye strain. Like

Go look at something 20ft away for 20 seconds.

yes, this, but also among other stem courses in a typical school, math is taken the most seriously. idk about other countries, but in poland in highschool people study chemistry, biology, physics and geography only if they decide to take the advanced final exams in these subjects. with math, everyone has take the standard level exam, so it can't be ignored like other subjects

up to highschool everyone has to complete their share of stem courses, but with the subjects other than math, the teachers often allow students to pass by memorizing the theory or by making some extra projects to earn points. with math you can't do that. when someone struggles with physics, the teacher sometimes says "alright, next year you won't have to study physics, so just learn those formulas and definitions and write them down on a test and I will let you pass". in math this is not an option, the student will have to take n more years of math courses

also, math mainly requires learning new skills, not just new information. many people never memorize the "dry theory" in highschool, because you have access to a reference table of formulas during exams and your job is only to know where to use those formulas – no need to memorize anything. but this does not come naturally to everyone and I think a huge part of the problem is teaching people how to work on their problem solving skills. I tutored a few students who believed they were bad at math and their mindset was "I can solve this type of problem because I know how to substitute into this formula, but when the problem is slightly different I panic, because the teacher never showed us how to solve it", which can be fixed by practicing a wider variety of problems and practicing the awareness of one's thinking process

people do not understand that problem solving is a skill on its own and I blame schools for that, because what we are offered is the image of math being about re-using the same kind of thinking processes but with different numbers. heck, when I was in elementary school I thought this is what math is about and I hated it because it's so boring and repetitive. I can imagine, when someone believes that this is what math is supposed to be and then they see the "more real math", which is about creativity, they panic (and rightfully so, they've been lied to)

my unpopular opinion is that not everyone can be good at this, just like I will never be good at understanding literature – my brain just sucks at processing this kind of stuff and I have aphantasia which doesn't help at all. but what makes it even worse for those people is the belief that it should be about repeating the same patterns over and over, so when they see that it's something completely different, it must be very frustrating – the reality is inconsistent with their beliefs

I am sure it doesn't cover the entirety of the "oof I always hated math" phenomenon, but it certainly does explain some of it, especially in the context of the education system in my country

As I said in a previous post, I have deep sympathy for the frustration of people who are good at math when they see math so almost universally hated by children and adults

And again and again, they try to explain that math is very much within everyone's reach and can be fun and, at least in western countries, education was to blame, messing up this very doable and fun thing by teaching it wrong

But I still gotta wonder - why math? If it is really just education messing this up, why does it mess up so much with math, specifically? I'm sorry but I still cannot shake the sense that even if it's just bad teaching, math is especially vulnerable to bad teaching.

Or is it maybe just that math is the only truly exact science, so there is no margin of error, so unlike every other field where you can sortof weasel around and get away with teaching and retaining half-truths and oversimplifications and purely personal opinions, math is unforgiving with the vague and the incorrect?