Mathematician: this is category theory. No, it didn’t have anything to do with categorization, it just helps us understand how spaces can map to each other. Yeah I guess it’s kinda like graph theory or algebra, but not really. We made a category of graphs, and you can use the category of graphs to represent endofunctors on the category of categories.
It’s a strange feeling to think you understand what you are reading until you get to the end, but you have given me that feeling. I was like “yeah category that’s a word I know. Let’s math the hell out of some categories.” Then I recognized other words you said, but by the time I was at the end of your post I wasn’t sure if I understood anything.
I don’t mind feeling dumb. Honestly it helps keep my narcissism in check. I like math because I don’t understand all of it even though it should be logical.
If it helps, category theory is affectionately referred to by mathematicians as “generalized abstract nonsense”.
It can be very confusing, but it’s sort of a field of math that helps to relate ideas on one area to similar ones in another domain.
Oh. Neat. Like a sort of language interpreter trying to explain an analogy from one language to another? The words might not mean the same when it comes down to the word for word interpretation, but the idea behind them is what matters.
Ok but can I use a graphing calculator to graph those graphs?
Also no! The “graphing calculator” is an abomination that should be more rightly called a plotting calculator. But that’s what happens when you let engineers in Texas name something.
I’ve read a fair few unintuitive mathematical things, but category theory has so far been the worst. Some things are just plain unintuitive and don’t catch your attention. Then there are things that are intuitive and really do reel you in. Finally there are things that seem intuitive but become so complex that your comprehension inverses: what you thought you knew feels wrong because of the new things you learned.
The latter has been my experience with category theory.
If only engineering documentation was as precise and comprehensive as this meme claims…
Yeah it’s a managerial function involving skill and time and therefore money, but if it doesn’t directly translate into profits for the corporation, then who has interest in that kind of investment these days?
Tbf advancement in math usually means “random shit we’re doing for the fun of it” and then 40 years later an actual application is discovered
It took centuries for people to realize number theory could be used for encryption
Someone just Veritasiumed.
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Oh man the university ptsd as an engineer. I once asked a physics prof at what width does the split slot experiment break down, she couldn’t understand the question. All the other engineering students were nodding their heads in agreement with the question and tried to explain the question in a different way, still no idea what we were asking.
My engineering friends and me propose that physicists should be referred to as theoretical engineers.
I propose engineers not be allowed to name things. Not everything needs to be an “engineer”
What are you, an engineer engineer?
Most mad scientists are actually mad engineers.
Topology: no, a set being open doesn’t imply that it is closed. What if it’s both? We call it clopen. Moving on.
As one in engineering, I think our work is less about precision and more about solving (challenging) problems with what is needed and nothing more.
Anybody can build a deck that stands up, an engineer can build one that’s just strong enough to stand up (for rated load haha)
Anybody can build a deck that stands up
Uhuh.
It doesn’t need to be true, just convey a point :p
I’ve taken multiple advanced trigonometry courses and still can’t really say what trigonometry is. Mathematics is just the fake thing that made puzzle kids feel smart before chess was invented. Oh wow you can make little symbols and they’re a special language only you can speak showing how clever you are. Neat they make a circle I thought I could draw one of those but I need a fucking PhD apparently.
I’ve ended up using calculus and trig for programming multiple times.
You may be able to draw a circle without math, but teaching a computer to draw a circle requires an understanding of math.
All of machine learning is rooted in linear algebra, rust is a very practical programming language that gains most of its power through category theory.
You don’t need to know high level math to be a successful developer, but it can really help in many areas. I can’t really think of how to categorize which areas high level math is more or less likely to show up in, which I guess itself kind of supports my point.
Just understanding what a derivative is and what an integral is can help you determine what problems are solvable and what aren’t, and let you think ahead about what information you might want to hold onto in your data structures. ( Think about what the +C in this integral represents in the real world, and what data you need to pin that down concretely ).
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Just for that, I’m defining the singleton set that contains only you.
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What about the set of all insects?
