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 about nothing.
– No sets?
– No, forget the sets.
– You’ve got to have sets.
– Who says you’ve got to have sets? Remember when we were talking about functions of functions? That could be a theory all by itself.
So they are metagaming mathematics?
I don’t know that much of history, but by my accounts category theory is metagaming the metagame of the original mathematics metagamers.
So we’re at least 4 metas deep at this point?
Just wait until the infinity mathematicians shows up and starts assigning cardinalities to the level of meta
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.
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.
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?
Oh but don’t worry, there’s plenty of money to do it twice!
That’s tomorrow’s money though.
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.
Dereked
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.
It’s a good question, but asking it shows that the experiment was explained poorly.
The slits aren’t the reason you see an interference pattern. The slits function as two lenses, similar to a pinhole camera. That’s something that usually doesn’t get explained very well, you can use all sorts of lenses for this, but slits are the most basic (and crucially, glass lenses would cause an interference pattern even if light weren’t a wave).
The double slit experiment is basically “if light is a wave, a slit would behave like a lens, similar to a pinhole camera. If light is a particle, it will simply be a hole without any lensing. Two slits show multiple bars, due to interference from the lenses, which means light is a wave”
Which means this works at any scale. All you need is some light in the same frequency, and something to bend it. That can be two slits, some glass, or an entire galaxy.
There are local limits of course, where the effect still applies, but things become too blurry and diffuse to make out. But that’s more of a limit to your sensor than the experiment.
That’s when considering the slits as a lens though, which they will act as at any diameter however there’s going to be a width at which the angle of approach and wavelength of the light are insignificant enough that you practically can’t tell that the slits were even there right?
What a great comment!
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?
Now hiring for an Engineer². Don’t apply if you dont have 20+ years experience with LLMs
We aren’t the ones who did that. You need to have taken statics and thermo otherwise you’re just a sparkling tradesperson
Most mad scientists are actually mad engineers.
As someone with an engineering degree and a science degree, scientists are absolutely nothing like engineers.
They’ve got some things in common.
Technical aptitude. Complete unawareness, or purposeful neglect, of social norms. Science related dad jokes.
True, but I mainly mean in terms of their attitude towards research and their level of skepticism and critical thinking when presented with new information.
Engineers are always thinking in terms of “how can I make this work?” and scientists are trained to think in terms of “where does this theory/method break?”
This means that in general, engineers are far more likely to assume one positive result is significant, whereas scientists are far more likely to be looking at and poking holes in experiment methodology. This is a generalization, but in my experience, engineers are far more likely to fall for pseudoscience BS. Granted, my experience is mostly in chemistry and chemical engineering, but this idea in general has been a topic of discussion and research in peer-reviewed literature for years.
Similarly, from an engineer’s perspective, scientists are a great addition to the working group when you need to find the flaws in the system, but awful when you actually just need something to go into the real world and work 80% of the time ;)
Especially when you’re time constrained.
Definitely. Lots of scientists fall into the trap of letting “perfect” be the enemy of “good”
Topology: no, a set being open doesn’t imply that it is closed. What if it’s both? We call it clopen. Moving on.
Interesting. That’s not how I was taught (different time, different language). A set that has some boundary points not being part of a set is open. Otherwise it is closed. It was binary definition. A 1D-sphere (a circle) was classified as a closed set. No boundary. But I looked in google and now it is different.
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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?
