#manifolds

[len-yet-again]

I love the idea that all, if not most, of these are written by the same person

These are just a few examples, this phrase is freaking inescapable on Wikipedia (along with sister phrases such as "more generally,")

[doesitevenmatterlol]

WHY does the Einstein summation notation exist?

[fuckdumblr]

Why Light Speed Is The LIMIT?

Ever wonder why nothing can break the cosmic speed limit? 🚀

Most people think it's just "Einstein's rule" — but the real answer is WAY weirder. The speed of light isn't some arbitrary speed limit slapped onto the universe. It's literally built into the structure of space and time itself.

[isomorphismes]

“the Yang-Mills equations are nonlinear, therefore there is little hope of finding a closed-form solution.” Such a statement seems plausible. Linear differential equations with constant coefficients are the only differential equations for which a general solution is given in closed form. As often occurs in life, however, the exceptions to the rule are sometimes more interesting than the rules themselves. Let us digress from quantum physics to the motion of water, where British shipbuilder John Scott Russell noticed a solitary wave in a canal in August 1834. Neither Airy nor Stokes accepted this observation, yet in 1895 Korteweg and de Vries found an equation for a wave travelling in shallow water in one direction: u̇ + 6•u•uₓ + uₓₓₓ = 0. The KdV equation is easily solved by restricting from two independent space-time dimensions (x,t) to a single dimension x−λt — a frame matching the speed λ of a travelling wave.

Mikhail Ilʹich Monastyrskiĭ, Riemann, Topology, and Physics

[cosmictabulator]

People need to make more fantasy worlds based on weird manifolds, we have so many disk worlds and sphere worlds and torus worlds, I want an RP^2 world where you set out to find the edge and come back with the opposite orientation

[art-of-mathematics]

Some interesting edits of my triquetra-like manifold drawing:

[sevenfactorial]

Student: Are those our homeworks?

Professor: ....yes but they’re not all graded yet. But they are your homeworks

Student: oh

[anaxerneas]

Edith Stein, On The Problem of Empathy

https://www.youtube.com/watch?v=txHQUpn7pD0