-- 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.

Ok but can I use a graphing calculator to graph those graphs?

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.

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.

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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?

I propose engineers not be allowed to name things. Not everything needs to be an "engineer"

Most mad scientists are actually mad engineers.

As someone with an engineering degree and a science degree, scientists are absolutely nothing like engineers.

I've heard applied mathematics used for us physicists but that one's new, nice

Someone just Veritasiumed.

I mean there’s not that much precision needed to pick out the toppings on a cheeseburger. You don’t need to specify the mass of the pickles man we do this all day.

I was gonna say...

I would say a important part of my job is to find the appropriate mathematical language to model computer programs. In my experience, using efficient language not only helps us discover more structures and connections between different kinds of program, but also leads to efficient and simplistic real-world implementations.

I would argue, from observing the development of this field, It seems like picking the right mathematical language is essential whether you are interested in theory or practicality.

I am not a mathematician, perhaps you can comment on this. From what I read, I feel like a good amount of the achievement for Grothendieck stems from finding the right language to describe the given problem. The result sometimes will follow like magic, once the correct language is discovered.

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.

Yeah, it's about applying physics to real world problems to come up with real world solutions.

Often in a more practical form because unlike in Physics, you can't start off with "assume zero gravity and a spherical cow shape"

I don't know what high school you went to, but we sure as shit didn't cover stuff like partial differential equations and functional analysis.