⁕ pure math undergrad ⁕ in love with anything algebraic ⁕
292 posts
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.
well, google, one of them is a giant fuckin red dog
oh, you misunderstood. when i said "applications" i didnt mean real world applications, i meant ways to use this in the context even more abstract nonsense
parents got a new cat they named lord montague and this morning i heard my dad in the other room say "i would have to advise against that decision, my lord" followed by a crashing sound
I hate it when I am blessed with a new tumblr feature without my consent
ofc that's right, thank you for fact checking!
Me duele la cabeza
i am! obsessed! with this book from the late ming dynasty about scams to watch out for (esp. if you are a traveling merchant). this guy is like, there ARE immortals who can survive without food but you WILL NOT encounter them because they live alone in the mountains and don't talk to anyone. if a monk comes to your house and claims to not need to eat, it's probably because he's secretly eating human fetuses, or something. eunuchs are invariably corrupt and the court system is useless. however, do NOT try to bribe anyone for a better SAT result for your idiot failson; this never works. nuns WILL try to seduce your wife into cheating on you. if your idiot failson does really badly on the SAT, make sure to have his father's remains buried somewhere with A+ fengshui; this is Guaranteed to work (unless your wife is cheating on you).
Me duele la cabeza
30 VIII 2023
aight it's been a while, time for an update
recently I've been doing mostly algebraic geometry, my advisor gave me some stuff to read, so I'm working through that. the goal is to familiarize myself with hilbert schemes – the topic is advanced, so there are many prerequisites coming up when I'm trying to read the book, that's kinda annoying
we are planning for my thesis to be about a certain generalization of the hilbert scheme, so basically the question is "investigate this space" and I've been having second thoughts whether I'm up for the challenge. I'm just getting to know how all that stuff works, so it's quite overwhelming to see how much I need to learn before I can do anything on my own
nevertheless, I'm pushing through as I will have to learn all of that anyway
I am working on finishing the proof from my bsc thesis and honestly I'm kinda losing hope lmao it turns out that what I probably have to do to complete it is a massive amount of extra reading and an even bigger amount of proving lemmas. the thing is that my work is about something like a generalization of results that have been proven by two people (one of which is khovanov, yes, that khovanov) and I feel it in my balls that the case I'm working on should be treated in a similar way. now the problem is that I can barely understand what they wrote for the "easier" case and I just can't see myself doing that for the more complicated one. oh and for my case I should probably use equivariant cohomology. but all I know about it is the definition, I have never even calculated anything for that + I will do a course on it this semester so it feels futile to study it now. idk I need to talk to my former advisor about this and ask him to be honest, does he even believe that this can be done?
other than that I'm applying for a scholarship. I don't think I will get it, but it is worth trying
I moved in with my boyfriend and our cat decided that my desk is way too big for one person, so now it's our desk
uni starts in a month so I should probably spend that time doing something other than math, which I will be doing all the time once uni starts, but I struggle with coming up with things to do that are not math-related. I should complete some tasks for work, but I would also like to have a hobby
there is a number of things that I could try, for instance reading, drawing, singing, grinding metas for geoguessr (apparently I'm a gamer now), but I can't commit to any of those, my interest comes in waves
maybe I could schedule about an hour per day to do one of those things so that my brain gets used to it. it is not like I can focus on math 24/7, I need to take breaks and I have days when my motivation is zero, so I just sit at my desk and watch stupid shit on youtube. but that's the point, days like that could be spent doing something meaningful and refreshing, instead I just procrastinate math lol
If you want to rizz up a mathematician, just tell them that they "proved love at first sight exists by giving an explicite example".
yea right in some parallel universe
All that I understand about algebraic geometry at my present stage of learning.
My favourite fucked up math fact™ is the Sharkovskii theorem:
For any continuous function f: [a,b] -> [a,b], if there exists a periodic point of order 3 (i.e. f(f(f(x))) = x for some x in [a,b] and not f(x) = x or f²(x) = x), then there exists a periodic point of ANY order n.¹
Yes you read that right. If you can find a point of order 3 then you can be sure that there is a point of order 4, 5, or even 142857 in your interval. The assumption is so innocent but I cannot understate how ridiculous the result is.²
For a (relatively) self-contained proof, see this document (this downloads a pdf).
(footnotes under read more)
¹ The interval does not have to be closed, but it should be connected. (a,b), (a,b] and [a,b) all work.
² Technically the result is even stronger! The natural numbers admit a certain ordering called the Sharkovskii ordering which starts with the odd primes 3 > 5 > 7 > ... , then doubles of primes, then quadruples of primes and so forth until you get no more primes left, ending the ordering in 2³ > 2² > 2. Sharkovskii's theorem actually says that if you have a periodic point of order k, then you have periodic points of any order less than k in the Sharkovskii ordering. It is frankly ridiculous how somehow prime numbers make their way into this mess.
@dimiclaudeblaigan asked for a tutorial on how to begin drawing. Good news! If you can draw a funky looking stick man, you have already started!
I think that stick people are a great starting point for artists because of the things you can learn from them that will be important later on.
If you are able to draw a circle and a couple of lines, you can easily put together a stick person.
Congratulations! You have started to draw. :)
A stick person is a very minimal artistic representation of a real life person. It is simple yet recognizable, and is widely used in art, media, and signage.
But what can a stick person teach us about drawing people that look more like… well, people? Lets have a look!
By simply adding a few more lines, we can add a pair of eyes and a mouth. Maybe even a little triangle nose! Or half circles for ears. We can now draw a face, which provides a basis for all sorts of expressions.
These simple additions can allow us to explore the wide range of human emotion and individuality.
This may seem like the basics of the basics. But that is what we want! In order to get to the point where we are able to draw complex, elaborate representations of humans and objects, we will need to start with simple shapes like lines and circles and build our understanding from there.
For instance, lets give our stick person some cool new features, such as hands and feet. I chose little squiggly circles to represent hands, and triangles to represent feet.
We can go a step further and modify the body of the stick person to include shoulders, hips, elbows and knees. These parts of the human body are quite complex in real life But here, all we need to do is add a few simple lines and dots to our stick person.
The lines provide some additional structural elements to our stick person's body, which are the shoulders and the hips. The dots indicate the points of articulation - elbows and knees, the places where the arms and legs bend!
Now we can use our stick person to show us an even wider range of human movement, action, and expression.
Our little drawing of a human being is evolving! All it took was adding a few more lines and shapes here and there.
By elongating some of the existing lines and making the head an oval instead of a circle, we can give our stick person proportions that resemble that of a real life human.
By this point, we have managed to add more complexity to our stick person simply by using our ability to draw lines, circles, and other basic shapes!
These basic ideas are the building blocks that will enable us to create more complex shapes.
The next part may be a considerable step up if you are absolutely new to drawing, but I have decided to include it in order to show you how complex objects like the human body can be built from shapes that are a bit more complex than circles and lines.
For example. Two ovals and a rectangle can be combined to create a cylinder.
Six squares can be combined to create a cube, or a box. Here, each square is distorted slightly depending on which way the cube is facing.
Note that the back faces of the cube and the bottom of the cylinder are hidden. These shapes allow us to visualize that which should not normally visible.
A sphere from all perspectives can be represented by a circle. But we can make it more like a sphere by adding lighting and shadow if we so desire.
Cubes, cylinders, and spheres are examples of 'solid shapes' because they consist of 3 dimensions.
Lets see how these solid shapes can be used to compose the human body.
By stacking three cylindrical objects, we can create a torso. Two spheres have been added to form shoulders, while a smaller cylinder forms the neck.
An arm is an alternating sequence of spheres and cylinders connected together. Note that the hand has been simplified for this example.
We can apply these solid shapes to the rest of the body to give us a more recognizable representation of the human form. It doesn't even have to be perfect. And just like that, our stick figure now has a silhouette that is unmistakably a person!
In the above examples, notice that we kept the stick person at the beginning while building up the shapes and solids around it. This is because the stick person serves as a guide for positioning the body and its various parts -> also known as posing.
You can do the same thing to everyday objects! Here, I drew a wine glass by stacking these three dimensional solid shapes.
The cup and its contents are two ovoid shapes that were cut in half. The stem is a very thin cylinder shape. The base is a cylinder with a slightly wider bottom.
Solid shapes help inform us how objects and parts of the human body may appear from different perspectives.
For example, a sphere can be used to demonstrate how the human head appears when looking up or down, turned to the side, or tilted at an angle.
With these examples, I hope I have managed to convinced you that if you can draw a circle and a couple of lines, you can draw a person! You just have to train your eye to recognize the simple shapes within complex objects. Try it with everyday objects as well! Or even your favourite media! A drawing subject can be as simple or as complex as you envision it to be.
Once you have mastered that, there are many aspects of drawing you can explore from here that may require you to seek additional resources or a fellow artist's advice.
Last of all, remember that drawing is an iterative process. Even if you draw something correct the first time, you will need to draw it again and again to get it right all times! And by making small changes like the ones we explored in this tutorial, your drawings will gradually transform!
I hope what I've demonstrated here are enough to provide the basics of how to get started with drawing objects and people, and also to help refresh more experienced artists. :) Hopefully I didn't go too off topic with what was requested, and let me know if there are any more questions I can answer.
Cheers :3
omg that's the most beautiful thing I've seen today
Chapter 2 of commutative algebra!
thinking about the time a prof told us that in real research mathematics it's fine to be slow, speed itself is not essential, as long as you can find it within yourself to make consistent unyielding inexorable forward progress, like the time some guy stole an M60A3 tank and terrorized a suburban neighborhood with it, said guy wasn't going that fast but plowed through cars and telephone poles and shit no problem. i'm not kidding that's what he said, that's the metaphor he used, he told us that the act of mathematics is like the 1995 san diego tank rampage
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
omg that sounds so cool
one of my friends found radiooooo which is a site that streams music from any country from any decade (well, most countries/decade combos work) and we’ve been digging going on a quest to find what is rad
so far the following is good
50s/60s/70s/80s russia
70s cambodia
20s japan
80s ethiopia
80s india
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.
this is a strawman. the distinction into the inattentive presentation and the hyperactive presentation is useful, because stimulant-based medication usually helps with the first kind of symptoms and the medication like atomoxetine will help mostly with the hyperactive symptoms such as emotional dysregulation or restlessness
the picture that made OP so angry was probably made by someone who has nothing to do with being trained in psychology, because there is something called combined presentation, which is what it sounds like: symptoms that are both from the inattentive and the hyperactive presentation
the term inattentive adhd makes sense because the deficits in the brain that cause the inattentive symptoms are similar to those with the hyperactive presentation, that's why they changed the name. it is literally the same disorder, just different presentations. besides, "inattentive" is just a name, every psychologist or psychiatrist who specializes in adhd knows that the problems come from regulating and directing attention
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I started replying before finishing reading the post and oh my god it gets even better? this is a joke right? please tell me that I started replying in a serious manner to a post that is supposed to be a joke because the other option is that someone seriously wrote something so stupid and believes it, and I don't want this to be true
okay. this fucking picture made me so mad i went on a 15 minute rant to my sister while she was trying to read her book.
so ive been looking at a lot of pictures of posts on pinterest because thats just where i spend most of my time. most of these posts are on the topic of adhd. ive never been properly diagnosed, but reading through these posts has made me feel so welcomed and understood (more than my parents have made me feel, pretending that this is "all just a phase that ill get over soon because pretending to have adhd is just the thing right now") that i realized ON MY OWN that "hey maybe i do have adhd." well.
i found this post while scrolling through pinterest, and it really sparked my anger.
i have a friend who was diagnosed with add before it was considered an "outdated" term and scrapped because apparently ALL FUCKING FORMS OF NEURODIVERGENCY THAT ARENT AUTISM ARE JUST "ADHD".
i read this post and it was what sparked my anger and my 15 minute rant to my sister. people who get degrees in this stuff, or counselors at schools, never really know what youre going through. all they know is that youre having some problems and they need to be solved.
which brings me back to this picture. if you look up "is add still a thing" on google, this is the first picture to pop up. and just seeing the visual aids they put with it makes me furious enough to throw something or someone out a fifth story window. the little girl is fucking SMILING while thinking about the most common shit people think us neurodivergent folks think when distracted. first off, no. false. we dont just think of video games and candy. we think of the randomest shit possible, like how long can i sit here without blinking or what kind of funny shit can i draw on this one sheet of paper.
and ALSO.
you cant just categorize adhd as TWO SEPARATE THINGS and call it good. we dont fit under two umbrellas. theres too many of us. we each have our own figurative umbrellas that only we ourselves can fit under, no one else. thats the problem with neurotypicals. they fit the typical stereotype for humans: we try to understand everything by putting it in a box. those lists of "symptoms"? i match every single one. on both sides. so ha. take that SCIENTISTS. what am i? some kind of freak of nature because i dont fit under just ONE of your precious categories?
i also looked up what "inattentive" means and it made me angrier. according to oxford languages, "inattentive" means "not paying attention to something", which doesnt seem too bad, right? it fits some people perfectly with their symptoms, right? but its not the definition that bugs me. its the example sentence thats used. "a particularly dull and inattentive student". basically saying that if you dont pay attention well to something, youre dull and boring.
im sorry, what? sometimes i have trouble paying attention, sure, but you ask any of my friends and they can agree i am NOT boring in any way, shape, or form. non of them would describe me as "dull". inattentive? sure, but not dull. so to call it "inattentive" adhd, instead of just add, is stupid! my friend with ADD (not fucking adhd, stupid scientists) is one of the funniest, most entertaining people ive ever met. shes an incredible artist, super smart, and knows how to make anyone laugh. does that sound dull to you? does she have problems focusing sometimes? yes. does she struggle with doing something sometimes? yes. but dont the rest of us?
my point is, when i see things like this, it pisses me off. like, unless all of the scientists who agreed "add" is an outdated term have it themselves, i refuse to believe its outdated and i will continue to say that my friend has it. she was literally diagnosed by the doctor telling her "you have attention deficit and hyperactivity disorder without the hyperactivity." THATS JUST FUCKING ATTENTION DEFICIT DISORDER YOU DUMBASS!!!
anyway, i hope im not the only one who feels this way. i just felt it necessary to get this out there. maybe someday, people wont be so dumb and single minded. in my opinion, neurodivergent people are superior in intellect and creativity, but i guess until someone like that takes over the world and dropkicks neurotypicals into the stratosphere, we'll never know.
at some point I was wondering what about the researcher publishing their paper in an expensive journal and it turns out that the author does not make a lot of money from that, so it really is about fucking this exploitative system and not doing any substantial harm to the researcher, if anyone was worrying like I was
This is about Sci-Hub. yeah we get it.. gatekeep knowledge and protect the interests of capital…
refseek.com
www.worldcat.org/
link.springer.com
http://bioline.org.br/
repec.org
science.gov
pdfdrive.com
studying for an exam but the course is super boring and you don't care about it at all, you just want to pass
start by making a list of topics that were covered in lectures and classes. you can try to sort them by priority, maybe the professor said things like "this won't be on the exam" or "this is super important, you all must learn it", but that's not always possible, especially if you never showed up in class. instead, you can make a list of skills that you should acquire, based on what you did in classes and by looking at the past papers. for example, when I was studying for the statistics exam, my list of skills included things such as calculating the maximum likelihood estimators, confidence intervals, p-values, etc.
normally it is recommended to take studying the theory seriously, read the proofs, come up with examples, you name it, but we don't care about this course so obviously we are not going to do that. after familiarizing yourself with the definitions, skim through the lecture notes/slides/your friend's notes and try to classify the theorems into actionable vs non-actionable ones. the actionable ones tell you directly how to calculate something or at least that you can do it. the stokes theorem or the pappus centroid theorem – thore are really good examples of that. they are the most important, because chances are you used them a lot in class and they easily create exam problems. the non-actionable theorems tell you about properties of objects, but they don't really do anything if you don't care about the subject. you should know them of course, sometimes it is expected to say something like "we know that [...] because the assumptions of the theorem [...] are satisfied". but the general rule of thumb is that you should focus on the actionable theorems first.
now the problem practice. if you did a lot of problems in class and you have access to past papers, then it is pretty easy to determine how similar those two are. if the exercises covered in class are similar to those from past exam papers, then the next step is obvious: solve the exercises first, then work on the past papers, and you should be fine. but this is not always the case, sometimes the classes do not sufficiently prepare you for the exam and then what you do is google "[subject] exercises/problems with solutions pdf". there is a lof of stuff like this online, especially if the course is on something that everybody has to go through, for instance linear algebra, real and complex analysis, group theory, or general topology. if your university offers free access to textbooks (mine does, we have online access to some books from springer for example) then you can search again "[subject] exercises/problems with solutions". of course there is the unethical option, but I do not recommend stealing books from libgen by searching the same phrase there. once you got your pdfs and books, solve the problems that kinda look like those from the past papers.
if there is a topic that you just don't get and it would take you hours to go through it, skip it. learn the basics, study the solutions of some exercises related to it, but if it doesn't go well, you can go back to it after you finish the easy stuff. it is more efficient to learn five topics during that time than to get stuck on one. the same goes for topics that were covered in lectures but do not show up on the past papers. if you don't have access to the past papers you gotta trust your intuition on whether the topic looks examable or not. sometimes it can go wrong, in particular when you completely ignored the course's existence, but if you cannot find any exercises that would match that topic, then you can skip it and possibly come back later. always start with what comes up the most frequently on exams and go towards what seems the most obscure. if your professor is a nice person, you can ask them what you should focus on and what to do to prepare, that can save a lot of time and stress.
talk to the people who already took the course. ask them what to expect – does the professor expect your solutions to be super precise and cuts your points in half for computation errors or maybe saying that the answer follows from the theorem X gets the job done? normally this wouldn't be necessary (although it is always useful to know these things) because when you care about the course you are probably able to give very nice solutions to everything or at least that's your goal. but this time, if many people tell you that the professor accepts hand-wavey answers, during the exam your tactic is to write something for every question and maybe you'll score some extra points from the topics you didn't have time to study in depth.
alright, that should do it, this is the strategy that worked for me. of course some of those work also in courses that one does care about, but the key here is to reduce effort and time put into studying while still maximizing the chances of success. this is how I passed statistics and differential equations after studying for maybe two days before each exam and not attending any lectures before. hope this helps and of course, feel free to add yours!
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
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
I know your thesis was about something to do with algebraic topology, may I ask what exactly it was about?
(and congrats to you getting your bachelors degree and into a masters program)
(thank you!)
my thesis was about an open question regarding a certain skein module of tangles on 2n nodes. the conjecture is that the module is free and in my thesis I constructed a generating set that is free for n=2,3 (direct calculation) but I have yet to prove that for a general n. if you are interested I can send you the paper in which the question was posed, all the details are explained there and would be hard to write down here without tex lol
21 VII 2023
oh god I haven't posted anything personal in a very long time
I've been super busy with exams, essays and then my thesis, all I did was sleeping and studying
I defended my thesis 40 minutes ago! it's done! in two months I am starting the master's degree program
this was probably the most brutal exam session I ever had lol it started a month ago and I had no day off since. after finishing my normal exams I've been working 12 hours per day to complete my thesis and thanks to my advisor who was working just as hard as me, we did it
I was so close to failing differential geometry. the exam was really bad, probably my worst ever. the questions were mostly about this one topic covered during the last class – we discussed maybe 3 problems and the professor decided that this is good enough lol basically we were supposed to read his mind and guess what else there is to learn. I scored 35% and apparently that's more than enough to pass – the grades go from 3 to 5 and I got 3.5, so that's literally "more than enough to pass". there were only 3 people who scored 50% or more, so yeah, that seems fair
that week of studying differential geometry was the most stressful week in the last 3 years, I fucking hate it when it's unclear what I'm supposed to learn and I have no idea how to do it. thank god I passed, I don't know how I would do it again before taking the september exam
anyway, I passed algebraic topology, number theory and algebra 2 with flying colors and the reviewers really loved my thesis! they strongly suggest publishing it, but I think I will try to finish the second part of the proof before I do that
I already found the advisor for my master's thesis, of course I don't know what it's gonna be about, but since I had some algebraic topology this year, I am thinking it's time to learn algebraic geometry now
sweet jesus it's finally over, I can't believe it. and something new is starting
Please fund my research in finding fewer applications of mathematics. I'm going to start my project with trying to find fewer uses of trigonometry, so that ideally we can eliminate the need for remembering trigonometric identities. Then I'm going to move on to researching fewer uses for integration by parts, because that tends to get real tedious real fast. With your unending financial support, I believe I can return mathematics to the purity and simplicity it has always yearned for.
5x5 Diamond rule, iterates 1-32
Iterates 40, 48, 56
Iterate 64
Iterate 128
This is a 2D cellular automaton generating a 3D fractal layer by layer. I coded it in Microsoft Excel - each pixel is 1 cell.
See more MSExcel fractals