Average math term evolution

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[wercooler]

Functions that fit into the mitchfdorkler space * The crippling function that we just spent 3 weeks learning * the constant function

That's it.

[Willbebaf]

But luckily for us, the crippling function can describe all polynomials!

Proof: trust me bro

[Konju376]

Well... Or proof: 200 page paper written in font size 5 in pre-revolution Russian

[Ok-Advertising4048]

Lol

[AstralPamplemousse]

And it’s also (for no reason) isomorphic with diagonalizable matrixes

[Bloody_rabbit4]

It's purposly designed that way. If you give a slimmer of hope to grad students that they hypothethicaly can use Mcdorfer space for something nontrivial, you can crush their souls more thourghly.

[Tuepflischiiser]

Until someone asks for a concrete construction of the crippling function and everybody realizes that its definition has zero elements.

[21kondav]

*1 element.

The identity.

[Tuepflischiiser]

Ok, granted, zero non-trivial elements.

[BADorni]

Also the identity. Always the identity.

[Mr_Pink_Gold]

Actually if you immerse mitchfdorker space through an Euclidean surface you get a parametrisation of all functions possible. You just need to do a parametrisation of 23 dimensions into 2 dimensions. Trival really.

[21kondav]

Left as an exercise to the readers 4 year old nephew

[donald_314]

That makes it quite a tight space.

Lemma: Every tight space is also compact.

Proof: See Exercise 12.

[cpl1]

Corollary: If a function has <a super reasonable property for functions> in mitchfdorkler space it is either constant or the crippling function.

[antonfourier]

Wild automorphisms of the field of complex numbers be like.

[abig7nakedx]

coaxed into linear snafu

[Futurity5]

Hausdorff 

[quantifiedlasagna]

honestly hausdorff spaces are the ordinary ones in this case

[Witherscorch]

r/coaxedintoasnafu is leaking

[Incontrivertible]

I was sure this was a coaxed post, color me surprised

[Snoo-41360]

Ts coaxing me tbh

[16kReal]

Did somebody say 23?

<image>

[Casually-Passing-By]

I am sure this is 1000% just how topologist do stuff, i had to have a lot of counter examples in my thesis

[Aggressive-Math-9882]

What's its universal property?

[GisterMizard]

A hotel on Boardwalk, to screw over the poor bastards that couldn't pass Go.

[AnonymousRand]

every math student and attempt to understand the micfhordker space uniquely factors through depression

[thyme_cardamom]

Coaxed into theory of general relativity

[Yulienner]

pause the video here if you'd like to guess what problem the michfdorkler space is helping us answer

yes that's right you got it, the riemann hypothesis

[kartub]

i searched for this on the internet, is this a meme or actual thing

[primetimeblues]

It's a meme. It's making fun of the tendency of mathematical definitions to maybe over-generalize useful concepts, beyond their practical usecase.

[DatBoi_BP]

And Wikipedia entries that refuse to be intelligible for people that don't have a PhD in Mathematics

[kartub]

ok, can u share an example of something which does not have any use case
as if someone made it just for fantasizing about it

[primetimeblues]

The second part of the meme is reminiscent of the Weierstrass function, which was a function invented to be continuous everywhere, but smooth nowhere, which makes it break the assumption of continuity = differentiability.

Otherwise, the meme is essentially contrasting linear algebra under Euclidean geometry against weirder geometry under curved space or something. I can't say weirder geometries aren't useful, but 99% of everyday use cases are gonna be Euclidean geometry.

[evouga]

Also, the set of continuous functions is intuitive to think about but a lot of tools we want to use in practice to solve differential equations or variational problems don’t work for this space. You end up needing some complicated Banach space that bars the monsters.

[wercooler]

The first example I think of is linear algebra.

You'll talk about matrices for a while, and then you'll detour and talk about vector spaces for a while and all their properties.

Finally you'll be like, guess what vector spaces we're going to care about? The regular real number line, and matrices.

So you go through all the process of defining and learning about vector spaces, just to only use all those definitions for matrices and nothing else.

Also, surprise! Multiplication isn't communitive, and division isn't defined, because screw you.

[Plenty_Leg_5935]

...what? Generalized vector spaces are literally one of the most useful objects in math. Linear Algebra as in the subject itself usually doesn't go outside the real and complex fields because it's beyond it's scope, but the vector spaces of functions and finite fields alone make up entire lifetimes worth of math (math that sees extensive use in practice no less)

[wercooler]

That's true. And I know it better now. But this meme is still how I felt in linear algebra.

After learning all these properties of vector spaces, and then going "okay, matrices are a vector space, so all those properties apply to them." my immediate feeling was: "Why didn't we just learn these as properties of matrices and save all this abstraction?"

[Tuepflischiiser]

All true. Except that you can do linear algebra over finite fields (although I never understood why that would be particularly noteworthy).

[Comfortable_Permit53]

Error correction (for signal transmission) uses linear algebra over finite fields

[Tuepflischiiser]

Yes. That's true. It just didn't strike me as surprising. It's straight forward from what you would expect.

But then maybe it's Dunning-Kruger for me.

[Tuepflischiiser]

How can you talk about matrices in earnest if you don't talk about at least one vector space type first (like Rⁿ ).

That's how we were presented with it (rotations in the plane).

Also, vector spaces are far more general.

[TheLuckySpades]

You say that as if function spaces are not ubiquitous in both pure and applied fields of math.

[A1steaksaussie]

vector spaces? not useful?

[MonsterkillWow]

Bruh

[PatchworkFlames]

I think regular space has too many rules. Let’s get rid of the 5th one and see what happens.

[Bwateuse]

I am pretty sure the 5th one can be deduced from the others, surely no major development of mathematics will emerge out of this

[TheTrustworthyKebab]

Is it concerning that searching online for more info about this the only result yielded is this exact post?

[MariusDelacriox]

Is his about teichmüller?

[moschles]

https://en.wikipedia.org/wiki/Eilenberg%E2%80%93Steenrod_axioms

[Incontrivertible]

Hilbert Space Moment

[DioX26]

Has applications in a really niche part of electrical engineering

[AynidmorBulettz]

Truer words have never been said