@paul Still trying to figure out a good non-bench use for these, c. 2009 and 2010.

Happy #Titanniversary!

Huygens discovered Saturn’s moon Titan #OTD in 1655, using a telescope he built with his brother.

This mosaic of near-infrared images was captured by the Cassini spacecraft in August 2014.

Credit: NASA/JPL/Univ. Arizona/U. Idaho

@Jordanhillphoto Stunning shot.

Recent jumps in the capabilities of LLMs remind me of domestication selecting for mimetic muscles that allow dogs to make facial expressions wolves aren’t capable of, like puppy eyes.

It doesn’t really change what they are, but it dramatically changes how we respond to them.

When you look at some of the smaller accounts associated with rightwing extremist disinfo on Twitter, you pretty quickly notice that many of them A) have a blue checkmark, B) aren't using real names, and C) have what appear to be fake profile photos. They really have the run of that place.

Astronomer who hypothesized the existence of neutron stars, or insouciant MI6 spymaster from a Graham Greene novel? Maybe he's about to coin the term supernova, or maybe his contacts in Marrakesh are about to smuggle you to safety. Hard to say.

Astronomer Walter Baade was born #OTD in 1893. With Fritz Zwicky he introduced the term "supernova" and hypothesized the existence of neutron stars.

Image: George Stranahan / Caltech

@dgoldsmith Thanks!

If you liked the graphic I posted a bit further up in the thread, and want a vector version or a desktop-sized copy at retina resolution, I put those up on GitHub!

https://github.com/mcnees/Everything

Don't skip this one: Jim Kakalios invokes Noether to explain the physics of the Infinity Stones!

http://kakalios.com/the-physics-of-the-infinity-stones/

And a piece by Dr. Matthew R. Francis for Symmetry Magazine:
https://www.symmetrymagazine.org/article/june-2015/mathematician-to-know-emmy-noether

An Emmy Noether piece in Science News, by Emily Conover:
https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math

My friend and collaborator @AstroKatie , talking about Noether for The Laborastory:
http://thelaborastory.com/stories/emmynoether/

A lecture at the Institute for Advanced Study by Abel prize-winning mathematician Karen Uhlenbeck, explaining Noether's contribution to our understanding of symmetries and conservation laws.

https://www.youtube.com/watch?v=Ca7c5B7Js18&embeds_euri=https%3A%2F%2Ftwitter.com%2F&feature=emb_logo

Now, let me share a few links to some of the many great resources for learning more about Emmy Noether and her work.

First, a 2019 “In Our Time” podcast on Noether.
https://www.bbc.co.uk/programmes/m00025bw

And here is Dr. Ruth Gregory, a physicist at the University of Durham, giving a lecture on Noether at the Perimeter Institute. (I was at this wonderful talk.)
https://www.youtube.com/watch?v=O7BBL5LF3qM

As a physicist, I am most interested in Noether's work on symmetries and conservation laws. But she is best known to mathematicians for her contributions to abstract algebra.

In 1932, she delivered the plenary address at the International Congress of Mathematicians. Just a year later, the Nazis purged Jews from German universities and Noether was forced to flee to the US.

Noether took a position at Bryn Mawr, and remained there until she passed away in 1935.

Physicists like Einstein and Hilbert quickly understood the importance of Noether's work, but many prominent scientists of that generation and the next were unsure of the primacy of variational principles. So for many years Noether's work wasn’t fully appreciated.

By the second half of the 20th century, variational principles had reemerged as the language in which most theories were formulated. Noether’s work was rightly recognized as one of the foundational insights of modern physics.

In all these cases, Noether’s Theorem relies on what is called a “variational formulation” of the physics. Another common name for this is an “action principle.”

Almost every modern physical theory is (or can be) formulated in this way. So Noether’s Theorem really is central to understanding a lot of modern physics.

There is a local (varying from place-to-place) redundancy in our description of gravity via general relativity: the choice of coordinates cannot matter.

The thorny problem of figuring out how conservation of energy works in this context prompted Noether’s work on her theorem!

Here is a thread from earlier this year about Noether's work on conservation of energy in GR. Klein got lots of credit, but he and Hilbert both acknowledged that the result belonged to Noether.

https://mastodon.social/@mcnees/109734841593777790

Let me quickly illustrate the difference between a symmetry and a gauge symmetry.

[You actually, physically rotate an object and it looks the same. That's a symmetry.]
◾ → ◆ → ◾

[You write down a model, recognize a redundancy in the description, and say “ta-da!” That's a gauge symmetry.]
◾ → ◾

Gauge symmetries are fundamental ingredients of the quantum mechanical theories used to describe particle physics (we even call them "gauge theories"). So Noether’s Theorem has been essential for developing the Standard Model of Particle Physics and understanding its predictions!