27 Unhelpful Facts About Category Theory
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- Опубліковано 22 гру 2024
- Category theory is the heart of mathematical structure. In this video, I will drive a stake through that heart. I don't know why I made this.
Grothendieck Googling: / grothendieckg
Join my Discord server to discuss this video and more: / discord
MUSIC
Oregano
Vendla (Epidemic Sound)
Penumbra
Kevin MacLeod (incompetech.com)
I've kept my promise of making a serious follow-up which actually explains the details of category theory. You can find it here: ua-cam.com/video/yAi3XWCBkDo/v-deo.html
Disclaimer: Followup may not include breaks (like fact 16)
@@louiswong921 NOOO
Sometimes the Funnest part is the truth...
Yup. Thanks! 👋👍😀👍👍👍
And it was good indeed. I saw it first. Or at least watched it ig.
You've heard of "The mitochondria is the powerhouse of the cell", now get ready for "A monad is a monoid in the category of endofunctors"
Thats wild mate, like "a tensor is an object that transforms like a tensor"
@@VincentKun A vector is an element of a vector space
I'm pretty sure I've heard the latter way more often than the former. I never realized there's a natural transformation between them in the categories of jokes.
A monad is a category where objects are the image of some functor F and the arrows are of type A -> F(B). The requirement that a monad forms a category implied in particular that composition of those arrows (however it might work) ought to be associative and there ought to be an identity arrow, often called „pure“ (or „return“ if you look at it from the point of view of operational semantics).
@@markuspfeifer8473 You're referring to a Kleisli category of a monad.
“A coconut is just a nut” I absolutely lost it here, I don’t know why
it's the moment, when you realise that the "coco" in "coconut" is a double inversion, making it redundant and can therefore be safely removed... leaving you with just "nut"
@@mini_bomba but I’d like to remove excluded middle please, so coco doesn’t necessarily get you back to the same place
So a cocone is just a ne?
@@reo101 we are the coauthors who say ne! NE! NE! NE!
@@DiracComb.7585 Ah, a constructivist!
As a cocreator of this video, I very much like it.
As your coposter, I couldn't agree more.
I see no correlation in the replies to this comment and the original comment!
Uncreator, unpostor, unrrelation, unmment
If category theorists were in charge of naming things, children would be called "co-parents".
@@strangeWaters they did start as haploid cells cooperating via copulation
You made an entire video, just to explain to *270 000* people _juuust_ enough about category theory, so you could hit them with the worlds nerdiest your mum joke. Respect.
It was never told that it was a joke ;)
@@Sciencedoneright read fact 1 again (oh wait is it a liar paradox?)
@@KIT8882 oh 😂 I forgot, haha
Genius, isn‘t it
Read this comment right after that
A comathematician is a device that turns cotheorems into ffee.
Nah a comathematician turns theorems into coffee. Therefore, coffee is isomorphic to theorems, and so my proof for the Riemann hypothesis is... a half shot of Espresso
This is my favourite joke in mathematics, glad to see it here.
Wouldn’t it turn ffee into cotheorems?
@@jonasvanderschaaf no, arrows must be reversed! (the joke is on the common saying "a mathematician is a device that turns coffee into theorems"
@@c.a.7058 you're right of course, I must have been tired from trying to understand what the everliving **** the Yoneda lemma actually means
I feel like I now know less math than I did nine minutes and twenty-five seconds ago.
Every second that passes you know less math. We all do.
Well technically new math is developed at faster pace than you can consume, so every second you know less _part_ of totality of math whether you watch this video or not
There is no math. There is only maths
It's an example of coeducation.
Everyone knows you learn less in a coeducational dorm.
Don't worry. I spent 4½ years studying Category Theory in grad school. I 𝘥𝘦𝘧𝘪𝘯𝘪𝘵𝘦𝘭𝘺 know less math now than I did when I started that journey.
Thanks a bunch! If i’m ever at a party where someone asks me to prove my intelligence by naming 27 facts about Category Theory, i’m set! (No, wait, I’m Class!)
You're object of an elementary topos
@@Salmanul_ it's stalin
cool but having a picture of a genocidal dictator as your pfp is kinda cringe
just tell them that a monad is a monoid in the category of endofunctors
@@ilonachan so true
You say category theory's one application is functional programming, but among programmers, there is a joke about asking of the applications of functional programming
Apache Spark is written using functional programming in Scala. Spark is the most widely used computing infrastructure for big data machine learning. Functional programming is very suited to parallel computing.
@@jimbocho660 yeah but thats nerd shit
have you heard of... Rust? :D
@@koacado Rust is many things, most of which I like, but it is not a functional programming language.
Beautiful short code.
If you understand it...
*IF(!)* you understand it...
This was extremely unhelpful! Thank you!
*cohelpful
@Oliver Gottkehaskamp i'll have to disagree... This has been EXTREMELY helpful for my facial muscles; they did some work-out during this video like they haven't done in weeks (or maybe even months). xD
@@irrelevant_noob You missed the joke I'd say. Maybe check the video title again ;)
@@scialomy That fella just implied that the video is not doing its job correctly :^)
365th like
Finally, a video about math twitter.
The analogy of category theory being the "they are the same picture meme" is accurate. That is what makes category into a beautiful black whole where students fall and sometimes they never leave/recover
help
@@VerilyVeritasValio no
If there’s a black whole, is there a black separate?
@@eddie-roo that would just be a black cowhole
@@Dong_Harvey a co-whole is just a cow-hole
I hope you'll remain faithful and won't forget to make the serious follow up video
Only if I also remain full and essentially surjective on objects.
(Sorry, it’s another category theory joke, couldn’t resist.)
@@OliverLugg so if you transcend everything you just get insane? Nice Easter egg @god (just a joke this is a great video)
@@mrOverYeff this whole vid is a joke lol
and he did....
Just admit it: this whole video's point was to teach us category theory in simplest terms possible so that we all understand the joke about the terminal object in a set of people and sexual relations.
Or just the worlds most abstract and theoretical set up for a your mum joke.
Yeah I sensed that terminal object before I even finished laughing!
"Set theorists can construct the set of all things that cause you pain" im functing dead lmao, subbed
I spent 9 minutes 30 seconds watching a video learning about something I didn't know existed, and I'm pretty sure I know less now than when I started. I've since liked the video, subscribed, and hit the bell icon. Excellent stuff!
Achieving ignorance is the beginning of understanding.
@@walterbushell7029 achieving KNOWN ignorance, rather?
You co-learnt the material
You are obviously therefore in the category of people who are easily trapped by theories about nothing. Bon voyage to lala land.
Welcome to the study of Category Theory. It's like that all the way down.
I have been learning australian category theory for a while now, and only recently found out it is actually isomorphic to regular category theory. If you flip everything upside down, it is just category theory!
It's cocategory theory
"It's a good idea not to upset set theorists. They can construct the set of all things that cause you pain."
I'm invincible, though, because nothing causes me more pain than the set of all things that cause me pain. Well, unless they're using some model other than ZF. Then I'm screwed.
The main application of category theory is to make Haskell programmers look smarter than they are.
"I use Haskell, BTW"
Haskell and Arch Linux are isomorphic!
This is extremely true.
I don't know what's worse. The jokes in this video, the fact that I found them funny or the fact that I was genuinely disappointed that this was a joke video 😂
That coauthor joke worked on so many levels lol
He just followed up with a real one!
Category has so many funny, near incomprehensible sentences like "a monad is a monoid in the category of endofunctors". My absolute favorite has to be "A double category is a category in the category of categories".
Should I get a phd in category theory just so I can get paid to spout silly sentences like these?
"What do you call someone who reads a paper on category theory" is my new favorite math joke. Damn, dude. Damn.
I only just understood that it works on two levels: "co-author" as in the opposite of the author, and "coauthor" as in the field is so obscure that the only people who read papers are those who wrote them.
This was all well and good until mathematicians discovered another even more abstract field of maths where the basis of communication is flustered frustrated hand waving.
That's actually a proof technique in category theory called diagram chasing. You just ramble and point at parts of a diagram while pontificating about preimages and morphisms. For example that's how you prove the snake lemma and it's an incredibly annoying proof to do any other way. Like writing it down is incredibly tedious so most authors only do one part and leave the rest as an exercise.
@@abebuckingham8198 I remember the first time I saw diagram chasing. I's a frightened undergrad until that moment, when I realised I was allowed to do that sort of thing. Just draw the shapes that make sense in your mind, gesture vaguely at the blackboard, saying "See?"
I feel like the proper way to communicate a diagram chase is a flipbook. But the journals won't let me staple one to my paper :(
Economics?
230th like
As someone who didn't even know category theory was a thing, this was a somewhat good intro to category theory. It also explains those diagrams i keep seeing but had no idea what they were
A worthwhile video. By the way, Samuel Eilenberg was a world class collector of ancient South Asian bronzes. His collection was worth tens of millions. Alexander Grothendieck's radicalization is rather interesting historically. His Russian Jewish father had an arm amputated as a Czarist prisoner. His mother was a German socialist. Both patents were active in the failed Spanish Civil War while little Alexander was in the care of others. It's no wonder he had the political views he so strongly adhered to.
i have no idea if what you said is true but im liking this anyways for how absurd it sounds
Based Grothendieck
@@taggerung_ Truth is sometimes stranger than fiction and with mathematical geniuses, truth is sometimes far stranger than even Theater of the Absurd. To borrow from Hardy's comment on receiving Ramanujan's initial correspondence: I couldn't make-up such things; nobody would have the imagination to dream up such things. By the way, I have a great photo of Sammy Eilenberg reclining on his sofa, contemplating mathematics in his Greenwich Village apartment and using Chola bonzes as paperweights on his piles mathematics reprints. Those sort of Chola bronzes sell at $500,000 to $2,000,000 at auction these days, and he was well aware of their value. And Grothendieck was quite the eccentric sometimes self-publishing in mimeograph format. I have one of his rare mimeographed books (in French) and sadly, it's fading.
I like that in the question of one space or two between sentences that you went for the meme "why don't we have both?"
my favorite mathematician together with Conway
Functional programming is not really an application of category theory. It's at its core an implementation of lambda calculus. Since lambda calculus also has a natural representation in category theory, some (but far from all) functional languages use some terminology from category when describing higher order combinators.
Monads are very useful for encapsulating state and sequencing, and the monad operations form a category.
its also not really an application of category theory, as it is not useful itself :D
@@SteveBobbington i know there's a pun in there somewhere but:
Just beacuse B is not useful, that doesn't mean A→B isn't an application.
For example: suppose that the above statement is true. One application of math is to calculate demand for food (A→B), and one application of that calculation is to not waste food (B→C), and one application of not wasting food is increasing the amount of useable food (C→D), and one application of increasing the amount of useable food is increasing humans' lifespan (D→E), and one application of increasing humans' lifespan is making more jokes (E→F), and one application of jokes is... Well, jokes are useless things, and that makes E→F not an application, and that makes D→E not an application... and that makes A→B not an application.
So now, do you believe math doesn't have any applications?
I think I ran into two fallacies (if that is even the right word), 1- I conflated math having a use in calculating with math having only one use. But more importantly, 2- I measured "usefulness" of a given thing by the number of applications it has. which, you know, causes anything that is not evantually an application of itself to fail (teaching history helps students to become history teachers so that they teach students so that....) "=" useful, but things that evantually end aren't.
@@xXJ4FARGAMERXx *screams*
@@NXTangldoesn't everything form a category? Isn't that the entire point of category theory?
"A coconut is just a nut"
I lost it.
As a hobbyist Haskell programmer (as opposed to a competent other things programmer) - the video made quite a lot of sense.
Don't get me wrong, I did advanced maths in Uni, and had all that explained to me. And I flunked the same semester.
remind me to never touch Haskell
As a hobbyist Haskell programmer still in high school this video made some sense but I didn't understand the Yoneda Lemma stuff (heard of it but have never bothered to look into it)
@@trinity_null To be fair, you don't actually need to know any category theory to use Haskell. It got a lot of concept from category theory, but the theoretical background is meaningless as far as actual programming is concerned.
@@trinity_null NEVER touch Haskell !!!!
@@markhathaway9456 thx
I clicked the thumbnail, thinking this would be about how coconuts have hair & produce milk and are therefore mammals. So very different content than what I thought, but somehow exactly the same vibe. Also, I had no idea category theory was a field of math before this video... not sure I learned more than the fact that monads are monoids except they look like gonads now.
Thanks so much for this--very much appreciate the sarcastic and deadpan presentation of a really really confusing subject! Contrary to the title, this was actually very helpful as it reminded me of how much I love talking to and hearing from others about whatever math they've been up to. Hope you make some more math/CS related videos (parodies or non-parodies!) and keep up the great work : )
Years ago, I did a presentation about isomorphism showing how choosing the right representation can make a problem really hard to grasp to something really trivial. There were no big words, because I am not versed in really abstract mathematics. But the content was enough to get people in a WTF state ^^
One of the example was showing how to create a Gray code from a path on a cube or tesseract. Another was about how to easily win one game by playing another game which is isomorphic.
Then how to translate some programming constructs into other (akin to refactoring).
Too many programmers forget that computer sciences...is math. They simply make their live harder ^^
Do you still have it? Maybe the slides or something? This really interested me, I would so go to a talk about this topic
@@karen-7057 I can't find it. I did it about 10 years ago and it's not in my GDrive, MSDrive, slides, slideshare...neither on my website.
I still remember the content though. It showed the link between complex numbers, the plane and matrix.
It also showed the relation between a sum number game and 3 in a row (tic-tac-toe).
Also shown how to write for loops as while loops.
And how grey code can be found by navigating a n-dimentional square.
Also, SQL vs Set theory (But I learned that this one breaks quickly and relational algebra is a better fit).
Very simple stuff, but useful to understand for future analyst developers (that was the target audience).
Category Theory is the revenge of that one kid who was angry about having to show his working.
Fact 23 was a comprehension question. If you laughed, you passed. All tests should be structured like that.
the joke gets better the more you think about it
oh god
I didn't get it until I saw this comment...
that's hilarious
To be fair, you have to have a very high IQ to understand Fact 23. The humour is extremely subtle, and without a solid grasp of theoretical mathematics most of the jokes will go over a typical viewer's head. There's also Oliver Lugg's nihilistic outlook, which is deftly woven into his characterisation- his personal philosophy draws heavily from Alexander Groethendieck's literature, for instance. The fans understand this stuff; they have the intellectual capacity to truly appreciate the depths of these jokes, to realise that they're not just funny- they say something deep about LIFE. As a consequence people who dislike Fact 23 truly ARE idiots- of course they wouldn't appreciate, for instance, the humour in Oliver's existential catchphrase "What about maps between Functors ?," which itself is a cryptic reference to Samuels and Saunders paper What about maps between Natural Transformations?[Berlin 1969, Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques]. I'm smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as Lugg's genius wit unfolds itself on their television screens. What fools.. how I pity them. 😂
And yes, by the way, i DO have a Fact 23 tattoo. And no, you cannot see it. It's for the ladies' eyes only- and even then they have to demonstrate that they're within 5 IQ points of my own (preferably lower) beforehand. Nothin personnel kid 😎
@@misiraly this is some of the most adept mathematical shitposting I've ever witnessed
Fact 17 even more-so
"A monad is a monoid in the category of endofunctors"
Ahh, programming memes.
"What do you call someone who reads a category theory paper? A coauthor"
I died
I love that I was recommended this video and really enjoy it while understanding maybe ~30% of what is being said. You present the data in a very entertaining fashion!
I've tried reading a handful bunch of books on the subject, but could never understand beyond the third page. Your video was surprisingly very helpful indeed! I've learned a lot, thanks! Sorry if I was not supposed to.
As someone with a Master's in Algebraic Topology and Cohomology Theory, I very much enjoyed every joke in that video (especially the one with Russel) ! Great job
Autistic weeb has a useless masters in Algebraic Topology and Cohomology Theory?
Not surprising.
The period after WW2 has certainly been fruitful in the production of bullshit from pure mathematics and philosophy.
Although some of the crap from the likes of Gregory Cantor came way earlier.
Mathematics that doesn't describe numerical or value relationships in reality simply isn't mathematics.
@@BumboLooks Jesus christ, who hurt you? The first sentence of that reply was random baseless ad hominem attacks, and the rest just seems like pure speculation and one hell of an odd, bold take about what constitutes mathematics. Maths needn't inherently relate to reality. But almost any field of maths does somehow link in anyway, even if in a really obscure fashion. Maths isn't even easy to define - but I'd say "study of patterns", is good for a concise definition. Which essentially means anything goes, provided it's defined consistently. You can still look down on it, but it's mathematics nonetheless.
Honestly you sound like somebody who got salty about not being able to understand some math once upon a time, and took that to mean that whoever came up with it was confused, rather than perhaps the person looking into it, and then that spiralled into a hatred for any and all modern mathematics, which seems to even have extended to philosophy because why the hell not? The only thing missing is a "back in my day" quip.
Let people learn what they wanna learn - it's often not helping anyone, but it definitely ain't hurting anyone, either. Throwing insults at people can hurt, though - it's not a chore to just be nice, or at the least not be outright rude if unprompted?
Or, you're just trolling - but I know you aren't, I just like to leave that option open as a catch-all.
@@BumboLooksShouldn't you be pumping my septic tank right now? Maybe filling some potholes? 🤣
@@СемёнСемененко-ы6с What does that have to do with mathematics?
You’re right this was entirely unhelpful! Greatly appreciated.
As somebody who graduated with a pure (not applied) mathematics degree this made me giggle and have some serious flashbacks to abstract algebra. Thank you for the laugh
Only a pure math student would feel the need to put "(not applied)" lmao
1. To my surprise, the word "pentagonator" is officially recognized by UA-cam subtitle auto-generator. (Basically, in an ordinary monoidal category, associativity of a certain operation (formally called tensor product) is only satisfied up to isomorphism, so we get this thing called "associator" describing this mathematically. The associator itself satisfies the so-called pentagon axiom, which is a commutative diagram and hence an equality. A pentagonator is just weakening this equality in the same sense as before but in a higher categorical setting. Disclaimer: I know nothing about it, but it is a very educated guess if you know how category theory work.)
2. What are the morphisms in the category of edible food? and how composition work? or is it just a discrete category?
2. Joke 28: If you want to see real-world applications of category theory, just go to n-Category Cafe
the fact that you explained category Theory enough to deliever the final joke is just amazing
You found a practical application for category theory in Haskell, so now you just need to find a practical application for Haskell 😂
It is a well known result that the main practical application for Haskell is that it provides a practical application for category theory.
Now that I have actually learned a bit about category theory in my topology class, it's absurd how true this video is. Everything is either a joke or true, and it has both helped me understanding the topic a bit better and made me despair over why we had to learn this in topology, I don't ever want to see this shit in an exam
I'm seeing Tantacrul influences! A monad is a monoid in the category of endofunctors.
I'm summoning the tantacrul gang
This is so true #jank
Also my buddy MusicMelts wanted to say "Recalcitrant"
Categories are getting worse every year.
Good work, team!
I cracked so hard at the sudden "A coconut is just a nut"
3:03 "almost everyone"
programmers diminishingly rare as they are, yes
I put this video in my watch later list a few days ago because I also do category theory and today I saw a tumblr post about 5d chess with multiverse time travel so wanting to know more I searched it on UA-cam and stumbled on one of your videos. When I went to your channel to watch more I was so surprised to see this video at the top! Very cool selection of interest you have here.
my abstract algebra professor made us prove the yoneda lemma on a homework; the professor's solution said the proof was "extremely brutal yet entirely trivial". So he's in both camps.
1:29 actually, morphisms are also objects. Consider the set of all rational polynomials (a + bx + cx^2 ... / (n + mx + ...)), which are mappings (morphisms) from complex numbers to complex numbers. Those polynomials have morphisms as well: + - * /, which turn them into other mappings. So category theorists go super-extra meta with this, and consider all morphisms yet more objects.
Is this demonstrated in a 2-category? like how they have morphisms between morphisms?
@@mastershooter64 he made another video actually describing the various parts of category theory, but roughly: you can keep repeating this forever. every morphism is an object, so you can morph between those, and morph between those, and morph ...; idk the definition of a 2-category though
@@MrRyanroberson1 Guess you bailed out before fact 15 (6:22)? :-B
@@irrelevant_noob nah i just comment as i watch the video
@@MrRyanroberson1 still, did it take you 5 months to not advance past 7 minutes? :-s
This is the kind of content youtube was made for
Man that video is the funniest thing I've seen in a long time X) was literally laughing doing all my appartment cleaning and all X)
The co-author joke is too real...
6:00-6:30 "students flipflop between believing it's entirely trivial and the most complex thing they've ever seen" average philosopher
@1:56 wait, it wasn't invented by mathematicians Dr. Cat and Dr. Egory?
Gory is an adjective.
I finally learn how to express my functiful thoughts. I whished I learned about Category Theory earlier.
Belief it or not, my notes and diaries is written like these diagrams, and I'm struggling to explain any thoughts in my head.
Knowing such thing exist is going to make my life easier.
I did an internship on groupoids and this is quite useful to generalise what I learned.
Thank you for some great laughs...
You reminded me of a line in the Hitchhikers Guide to the Galaxy, about the funniest joke in the universe of all time was a mathematical joke...
"A coconut is just a nut"
I died
thank you, this is gonna help me relax a little if I ever follow lectures on the subject :)
"What'd you call someone who reads a paper on category theory? a co-author"
That was an aweseomely funny video, I don't know why I got recommended this several times but something in UA-cam's algorithm worked just right.
Fact 28: assuming you really have a defined categorical structure on the quiver (graph? hypergraph?) of all people and sexual relationships, you are cordially invited to take the identity morphism and go **** yourself.
(Sorry, I just could not resist after the last one. Nothing mean intended.)
If you wanna sound less friendly, you could say “rdially” instead of “cordially”
“As soon as Mathematicians start counting they can’t stop”
Why is this so true 😅
Yes, reminds me of cardinal numbers and dimensions.
A monad is a monoid in the category of endofunctors
I've never studied category theory and I've still found myself trying to read that somewhere
A monad is a monoid in the category of endofunctors.
it's a really good way of remembering it tho! You just write down the necessary commutative diagrams for a monoid in a strict monoidal category and then you instantiate it to End(C), and there you have it: the definition of a monad.
I thought setup&payoff didn't work in internet humor anymore, but the coauthor had me wheezing
I didn't understand any of this but I'm just assuming that category theory is the exact same thing as set theory except they replaced all the words people already know with different words that nobody knows
Not the "exact" same, remember FACT 8 (4:04). The ALMOST exact same. ;-)
that joke at 08:26 killed me
I’m in my last semester of a computer science degree. Glad to say I colearned because of this video
"A coconut is just a nut" is the best joke I've heard in a while
number 20 is the equivalent of "the mitochondria is the powerhouse of the cell"
As someone who likes Haskell and C++ the statement, “A monad is a monoid in the category of endofunctors” is a phrase to live and die by.
Aannddd I wrote this comment before u brought up Haskell lol
Why not a half group or group or sth?
This is the most accurate and funniest representation (pun intended) of category theory that I have ever seen. 😂🤣
Wait, what does the direction of the arrow mean in the last category mentioned?
And also the identity arrows?
Is this a category or (as another co-author of the video suggested) a quiver?
4:40 studying tensors without knowing what they are? so basically physics.
7:39 Dammit; I misremembered this line - and here I was about to make a joke about 'corona' is known in Australia as 'rona'
Category theory ➘
this exact video ➙ Terminal object ➙ *why*
Math in general ➚
Correction:
Category theory ➘
this exact video ➙ Terminal object ⇄ why
Math in general ➚
Both of your comments are difficult to parse (at least on mobile) because of it being unclear what parts of it is due to wordwrap and such
Pretty sure “why” is the initial object for all maths.
@@Axman6 The initial object for lots of modern maths is a disjunction.
PUBLISH v PERISH.
I sat throughout the entire video slightly confused only to be instantly one-hit-K.O.’ed by the ending. I’ve been laughing my ass off for 5 minutes!
i wanna see someone else who also studies category theory to watch this, i feel like im missing so many inside jokes
Anything outside applied mathematics is bedlam with research funding.
This dogma lets me sleep snuggly at night and also explains why category theorists decided that concepts are most easily explained by adorning a hypercube with arrows.
Now I'm proudly one step further away from understanding my math friends Twitter shitposts 😊
That coconut pun really paid off.
Australian category theorists can't be similar to marsupials because marsupials did not evolve independently in the old world and develop weirdly fascinating features which seem like wizardry to us placental muggles, but rather marsupials went extinct in most of the new world for as yet mysterious reasons leaving placentals like ourselves the only mammalian representatives in the northern hemisphere and, for reasons pertaining to swimming ability, placentals never found themselves on Australian shores. So unless Australian category theorists somehow disappeared elsewhere under mysterious circumstances and non-Australian category theorists have swimming disabilities, this would be a false equivalence...
I was just learning category theory! Thanks friend :)
I spent ages wondering weather or not I existed, weather my existence was true or false. Now though I see the light, the true answer is neither for I am a bottom.
I am coming to the conclusion that category theory is an elaborate prank being played on the general public by mathematicians who are fed up with "having to make sense"
Wouldn't an infinity category be a cyclic loop error?
a useful application of category theory is that NP functions (i.e. functions that can be checked in a polynomial [on the order of size^k with k a constant] time relative to the size [as opposed to exponential, i.e. k^size, or faster growing functions]) are equivalent, so that if one is found with a solution that can also be found (as opposed to verified) in polynomial time, it means that P=NP and we can find the best solution of a big NP problem fast. (e.g. minesweeper, travelling salesman problem, knapsack, and a bunch of other problems)
now that doesn't help us solve, but if we find any polynomial solution to a problem that can be equivalent to one of those, we know that it solves a lot of problems at once.
A real world application of category theory is teaching category theory to math students.
Maths is a Ponzie scheme.
I feel like I’m pretty good at understanding things, like I was able to conceptualize the rotation of a tesseract. But I feel like this is just a bunch of words that we’re saying relate to each other
actualy there are only 3 dimensions =
the overworld, the nether, and the end.
Sorry Shloomth tesseracts are amade up
@@ictogon you forgot the aether
I understand not even 3% of these jokes, yet I think this is the most hilarious vid on youtube, where do I map on the functors?
This feels like watching an alternate version of Tantacrul who studies math instead of music. Love it
true false or bottom describes twitter beautifully
The coconut joke was exquisite.
Trying to understand any of this drives me coconuts
All you need is the "they are the same picture" meme.
I'm almost angry about how good that explanation is (not in terms of accuracy neccessarily, but in terms of comprehensibility).
Loved it! The bit on co-author was really nice, thanks.
*trying to recover from the last 4 seconds of the video
I like these jokes. I think jokes are good way to help make something more accessible: you need context to laugh, and context necessitates explanations.
Actually I'd come across a real world application of Category Theory (maybe):
Proofing a set of operator replacement rules of a tensor algebra system is correct in all circumstances
A PhD student who was working on deeplearning computationial graph optimization