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@ai_art_bot one of the things I like about this bot is checking the alt text "...in the style of..." to broaden my art horizons.

A "hybrid" course at #CHI2022 in which the instructor and all registered (paying) attendees were remote. Someone was guarding the door to make sure nobody snuck in to watch the Zoom session being projected to the completely empty room.

Or maybe you're thinking "This is the kind of math I like!" Then take a look at her paper.

She defines derivations of operads, and shows entropy is a derivation of the operad whose space of n-ary operations is the (n-1)-simplex!

(4/n)

mdpi.com/1099-4300/23/9/1195

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Something I've wondered more than once on birdsite:

\( 1729 = 12^3 + 1^3\), so it's a multiple of 13.

\(1729 = 10^3 + 9^3 \), so it's a multiple of 19.

It's also a multiple of 7. Where does that come from? (i.e., is there a way to find *all* of the factors of a taxicab number given the cubes that sum to it, or similar?)

As it's #StarWarsDay, I thought I'd share a mini thread of a selection of Star Wars treasures from my childhood. All 1977-79, before there were 'episodes', before anyone had heard the word 'franchise' to describe a film series (photo of my 7th birthday) #MayThe4thBeWithYou 1/

The electric and magnetic fields are very different when viewed as fields on space.

But we can unify the electric and magnetic fields into a single field on space𝘵𝘪𝘮𝘦: the 𝗲𝗹𝗲𝗰𝘁𝗿𝗼𝗺𝗮𝗴𝗻𝗲𝘁𝗶𝗰 𝗳𝗶𝗲𝗹𝗱!

To do this, it helps to use 1-forms and 2-forms.

(1/n)

Quanta article about how a team of mathematicians recently managed to coax the Navier-Stokes equations into producing some non-unique solutions for certain initial conditions, exposing a weakness in the equations' modeling of physical reality

quantamagazine.org/mathematici

so um, I was going to spend tonight answering your questions about the updates from the conference I posted earlier...

but I'm more than a little distracted by the supreme court getting ready to overturn my rights as a uterus holder in this country.

I'm worth more than my uterus.

Taking a break from the afternoon break to bring you some of the most exciting new #science results from the #Exo4 #Exoplanets conference! I'll tell you why I'm excited about these in a thread!

⬇️⬇️⬇️⬇️⬇️

(1) A detection of a proto-planet in the TW Hya Disk. It's currently somewhere around the size of Neptune, but still growing!

(2) 30 new Hot Jupiters from TESS! (Transiting Exoplanet Survey Satellite)

(3) a sub-Earth planet around Proxima Centauri, our nearest neighbor! @asmasca

In quantum mechanics, the magnetic field says how much the phase of a charged particle rotates when you move that particle around a loop!

(Not counting other effects.)

This means that the magnetic field is fundamentally something you want to integrate over a surface.

(1/n)

Now that I know that
this discussion exists, I'd
like to contribute


Hi all! I'm Cody, a refugee from Twitter math.

Mostly interested in proof theory and logic, but interested in a lot of mathy things.

I haven't seen *nearly* enough here, and almost nothing from the !! So here are some of my most-visited pages, according to my browser history.

ncatlab.org/nlab/show/Thomason

(weak equivalences created by taking nerves)

ncatlab.org/nlab/show/multicat

(morphisms can have n-ary source for n > 1)

ncatlab.org/nlab/show/simplici

(combinatorial version of topological space)

ncatlab.org/nlab/show/Grothend

(convert a general functor into a fibration of slice categories)

Consider a ring $R$, and let $\mathcal{L}$ denote the language of rings over $R$ (e.g formulae composed of quantifiers and equalities of $R$-valued polynomials). It's possible to take a "Grothendieck group" of an $\mathcal{L}$-theory $F$.

First, define an equivalence relation $\sim$ on $\mathcal{L}$-formulae as $\varphi(x_1,..., x_n) \sim \psi(y_1,..., y_m) \iff$ there exists $\eta(x_1,...,x_n, y_1,..., y_m)$ s.t for every $R$-algebra $A$ where $A \models F$, the subset of $A^(m+n)$ ...

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