Anonymous at Sat, 29 Mar 2025 00:04:59 UTC No. 16631402

faster computers
the cure for baldness
the cure for death
FTL travel
AGI

Anonymous at Sat, 29 Mar 2025 00:09:56 UTC No. 16631406

>>16631389
No shit, I recently looked into this stuff seriously. Been doing some crazy graph theory where edges are labelled by permutations. Orientation reversal occurs with some of the permutations and I wanted to represent the discrete reversal as a smooth motion.

Anonymous at Sat, 29 Mar 2025 00:21:54 UTC No. 16631414

it's used for counseling in Alabama

Anonymous at Sat, 29 Mar 2025 03:36:12 UTC No. 16631489

>>16631389
Step 11 does pinch, same color surface to same color is a pinch if you understood how topology works.

Anonymous at Sat, 29 Mar 2025 04:05:40 UTC No. 16631498

>muh applicationz

Anonymous at Sat, 29 Mar 2025 08:13:24 UTC No. 16631569

>>16631389
Is very useful to detect retards who were born to be beasts of burden and will never be able to appreciate the beauty of Math.

Anonymous at Sat, 29 Mar 2025 08:43:14 UTC No. 16631584

>>16631389
I guess if you need a stable oscillating circuit for stuff, this might be relevant

Anonymous at Sat, 29 Mar 2025 09:38:49 UTC No. 16631603

why do the rules allow for self-intersection? I feel like that breaks the alleged rules of topology of stretching and not cutting. If i had a rubber sphere i could not reverse it like that

Anonymous at Sat, 29 Mar 2025 09:50:24 UTC No. 16631609

they taught a woman math and this is the result

Anonymous at Sat, 29 Mar 2025 17:26:17 UTC No. 16631917

>>16631603
Because it's not just some autists playing with play doh like all these pop sci videos want you to think. Topology is about studying continuous maps between topological spaces. Topological space means there's a select subset of the power set of that space, whose elements are called open sets, that represents how points in the space are connected. Continuous means the pre-image of every open set is open. All of this produces the seemingly arbitrary rules you see in these pop-sci videos.

Anonymous at Sun, 30 Mar 2025 03:27:39 UTC No. 16632243

>>16631917
>Topology is about studying continuous maps between topological spaces.
Well i claim that these self intersections must violate some sort of mathematical smoothness or consistency situation. Like, you'd have multi-variate functions so not functions at all

Anonymous at Sun, 30 Mar 2025 04:33:25 UTC No. 16632265

>>16632243
>sort of mathematical smoothness or consistency situation.
To add up, these self intersections likely break common ideas of curves and surfaces being smooth, differentiable and infinite differentiable. Im sorry but once you start self intersecting you dont have concepts of continuity and tangents anymore. I dont have to explain this in great detal, it seems obvious already in simple curves in 2D

Anonymous at Sun, 30 Mar 2025 04:53:58 UTC No. 16632269

>>16631603
Yes, it's impossible to do it without self-intersections, so the lazy hack mathematicians decided to allow self-intersections and then advertised it as the real thing.

Anonymous at Sun, 30 Mar 2025 14:57:28 UTC No. 16632711

>>16632243
>must violate some sort of mathematical smoothness or consistency situation
No they don't. Learn basic definitions.
>>16632265
Differentiable, smooth, and infinitely-differentiable have nothing to do with continuity. Again, learn the basic fucking definitions.

Anonymous at Sun, 30 Mar 2025 14:59:22 UTC No. 16632713

Here's the most famous example of why muh differentiable isn't necessary for continuity.
https://en.wikipedia.org/wiki/Weierstrass_function

Anonymous at Sun, 30 Mar 2025 15:09:03 UTC No. 16632716

the problem is that you dont know math

Anonymous at Sun, 30 Mar 2025 20:17:02 UTC No. 16633100

>>16631389
It's one of the "simple" examples for Gromov's h-principle. I've yet to meet someone who has an actual understanding of it. There is a book by Gromov on partial differential relations, and a more introductory work by Eliashberg and Mishachev, but even the latter requires quite a broad mathematical horizon. The h-principle in the best case tells you something about the solvability of certain PDEs or PDRs depending on the space you consider them on. And there's your application. Solvability of fucky differential equations.
With enough obfuscating language, you can use the above to get a grant in string theory. So in more practical terms, the application is money lmao.

Anonymous at Mon, 31 Mar 2025 05:41:34 UTC No. 16633465

>>16633100
>Grant in string theory
Those don't exist.

Anonymous at Mon, 31 Mar 2025 05:45:16 UTC No. 16633468

>>16631402
This. OP doesn't "get it". Sad.

Anonymous at Mon, 31 Mar 2025 06:29:27 UTC No. 16633489

>>16632711
>Differentiable, smooth, and infinitely-differentiable have nothing to do with continuity. Again, learn the basic fucking definitions.
Irrelevant, why are you so defensive about this? I mentioned continuinty and differentiability, yet you get angry because of continuity?
>>16632713
>Here's the most famous example of why muh differentiable isn't necessary for continuity.
I knew thius 25 years ago and its irrelevant. You are saying this only because it a kwool fakt
Any curve or surface in any dimension that has self interesections isnt going to have a concept of tangents or differentiability, neither once nor infinitely. Yes this doesnt really means there wont be continuity, but the loss of a concept of tangents is bad enough

Anonymous at Mon, 31 Mar 2025 15:55:48 UTC No. 16633913

>>16631389

As with a lot of abstract math, the answer is "Does this particular thing help you build something cool? No. But it does help you understand the surrounding mathematical principles of an area of Math that COULD help you build something cool". Learning difficult math to find practical applications is a lot like diving for treasure in the ocean. You won't always find treasure in a dive. Maybe even seldom. But you won't know until you take the dive, and the deeper you can go, the more likely you'll find something no one else has

Anonymous at Mon, 31 Mar 2025 18:23:01 UTC No. 16634069

>>16633489
No, I'm angry because your entire complaint was "intersections may cause non-differentiability". So what? Topology is interested in studying CONTINUOUS maps regardless of whether they are differentiable or not.
>but the loss of a concept of tangents is bad enough
It's the exact opposite. It's great. Topology is not concerned with tangent lines and such, that's the subject of differential geometry. Relaxing this requirement of differentiability everywhere means you can study many more structures than differential geometry can. In category theory terms, the category of differentiable manifolds is a subcategory of topological spaces. So every single technique in topology applies to differential geometry, but not vice versa.

Anonymous at Mon, 31 Mar 2025 18:36:02 UTC No. 16634077

>>16634069
>intersections may cause non-differentiability". So what?
Nah nigger i dont believe you can sweep this one under the rug. You cant just lose the concept of differentials calculus and act like its no big deal.
By doing these intersections you are also breaking the topology you pretend to care about, you can create paths that would be impossible without the self-intersection and connect parts that should not be connected just with the magical touch of a self-intersection

Anonymous at Mon, 31 Mar 2025 18:39:52 UTC No. 16634083

Let’s take a down-to-earth example of why non-differentiability is a complete non-issue in topology and why it’s great. Everyone who studied complex analysis knows that the problem of integration reduces to a simple algebraic problem of enumerating pole residues. The contour shape does not matter in the slightest, what matters is what poles it encloses. That is a beautiful example of homotopy theory. The contours form homotopy classes and there is a one-to-one correspondence between these classes and all possible unique integrals of a given complex function. The contour can be whatever you want it to be, no need to be differentiable. The Cauchy principal value is two straight lines on the real line and a a circle centered at the pole, with two non-differentiable points at the intersections. Does it matter? No.

Anonymous at Mon, 31 Mar 2025 18:41:00 UTC No. 16634085

>>16634083
>>16634077
>You cant just lose the concept of differentials calculus and act like its no big deal.
So suddenly all of number theory is a fluke? Get the fuck outta here, you enginigger.

Anonymous at Mon, 31 Mar 2025 18:47:44 UTC No. 16634092

>>16634083
>>16634085
You are just creating situations that break the alleged topology
for instance a simple point in a circle is going to have two neighbor points...but with an intersection it can have 4, or 6, or 8, or any number and soon your 1D closed curve becomes a 2 dimensional object

Anonymous at Mon, 31 Mar 2025 18:52:43 UTC No. 16634094

>>16634092
You don’t understand what you’re talking about. “Breaking topology” by the very fucking definition is having non-continuous maps. You can’t break topology if your map is continuous. What I am explaining here is a tautology. Learn the fucking definitions.
>for instance a simple point in a circle is going to have two neighbor points..
That’s not how open sets are defined, you stupid fucking nigger. Go retake undergrad analysis. Every open interval is uncountably infinite, regardless of how small it is. So your “example” makes no sense. Construct an open interval with three points in it, I dare you. I can always find a number between the center point and one of the edges, so there you go, proof by contradiction.

Anonymous at Mon, 31 Mar 2025 18:59:18 UTC No. 16634102

>>16631389
What the fuck does unironic even mean?

Anonymous at Mon, 31 Mar 2025 19:32:39 UTC No. 16634129

you can impress girls with it

Anonymous at Mon, 31 Mar 2025 20:29:56 UTC No. 16634180

>>16634102
Nonsarcastic you dumbfuck

Anonymous at Mon, 31 Mar 2025 22:03:43 UTC No. 16634240

>>16631389
The guy who discovered this was blind. I think he won a Field's medal for it.

Anonymous at Tue, 1 Apr 2025 03:15:35 UTC No. 16634551

>>16634094
I dont care how pedantic you try to be with "delta epsilon" and $20 dollar buzzwords. You are not making any arguments while i already made mine. With these self interserctions you could transform a 1D curve into a 2D object. Say, you could transform a closed loop into the 2D cartesian plane

Anonymous at Wed, 2 Apr 2025 13:33:16 UTC No. 16635012

>>16634551
I just told you why your argument is nonsensical. It flew over your head because apparently it's all "buzzwords".
>Say, you could transform a closed loop into the 2D cartesian plane
How would you go about doing so? I'm genuinely curious. Please construct an explicit map from a unit circle to R^2. I'm waiting.

Anonymous at Fri, 4 Apr 2025 06:45:54 UTC No. 16637022

>>16631389
Oh, I remember this video...
>le can't have ring around the equator
>guy getting it, then not getting it, then getting it...
>le "you're pinching it infinitely tight"
>lady mogging the guy with topology, mathematica and 90's aesthetics at every turn
>*checks credits* wait...Karen!? That explains it...
>this parody exists: https://www.youtube.com/watch?v=Zv-XNlE1s8E

Great times, this...

Anonymous at Fri, 4 Apr 2025 06:58:14 UTC No. 16637031

Why is pinching not allowed?

Anonymous at Fri, 4 Apr 2025 07:04:18 UTC No. 16637033

>>16637031
Pinching should be allowed
Just pinch it ito a loop of radius A and take the limit to A->0
It would be continuous

Anonymous at Fri, 4 Apr 2025 07:07:23 UTC No. 16637034

>>16635012
>How would you go about doing so? I
You first turn the circle into a grid, which you can do because with a self intersection you can split a circle in 2, then 4 circles, and so on. You can make a grid of lines and if its dense enough you fill the 2D space with 1D lines like filling with a pencil

Anonymous at Sat, 5 Apr 2025 23:00:52 UTC No. 16638482

>>16637034
>You first turn the circle into a grid
Great, and how do you do that? I want an explicit map. A continuous map, mind you. How do you make all those connected pieces on the circle form disconnected lines on a grid? Go ahead, retard, elaborate.

Anonymous at Tue, 8 Apr 2025 13:20:36 UTC No. 16640464

>>16631569
true

Anonymous at Tue, 8 Apr 2025 17:10:51 UTC No. 16640571

>>16631389
Magneto hydrodynamics and contained plasma cavitation bubbles.

Model them without knowing this, and you are a near sighted person trying to see without glasses.
As in, the spheroidal inversion is a common waveform structure in these environments. If you can't model for it, you are left with approximations.

Anonymous at Tue, 8 Apr 2025 17:39:24 UTC No. 16640596

>>16638482
>Great, and how do you do that?
You self intersect a circle, say until it touches in only 1 point. Now you have two circles joined by one point. You can just go on and repeat and your circle becomes a grid
>Give me the map
I just did, i dont have to write some algebraic expression for it to tell you what the transformation is

Anonymous at Tue, 8 Apr 2025 18:50:14 UTC No. 16640647

>>16640596
You don’t know what an explicit map means, great. It means an equation, anon. Not wishy-washy explanations.
>You can just go on and repeat and your circle becomes a grid
Yes, a finite number of circles suddenly becomes an infinite grid. F-, anon.

Anonymous at Tue, 8 Apr 2025 19:08:37 UTC No. 16640657

>>16631389
easily cleanable bong, duh

Anonymous at Tue, 8 Apr 2025 19:52:04 UTC No. 16640689

>>16637031
if you could pinch it wouldn't be a sphere it would be a hypersphere

Anonymous at Fri, 11 Apr 2025 03:44:58 UTC No. 16642876

>>16637033
sounds legit

Anonymous at Fri, 11 Apr 2025 04:17:14 UTC No. 16642889

>>16637022
Kek, that video is hilarious

Anonymous at Fri, 11 Apr 2025 14:08:36 UTC No. 16643138

>>16631389
You don't know it yet but this is a vital data transformation function that will be the key to unlocking AGI