Clifford goes so far as to say

"...variation of curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or ethereal..."

But Clifford got things backwards, imagining a role for deviations from Euclidean geometry on small scales.

It was Einstein who finally got it right. Today we use Riemann's geometry as a tool for understanding gravitational phenomena that are most easily observed on very large scales.

Riemann also asked whether or not his approach to geometry, based as it was on mathematically local statements about space, could be a valid description of physical reality if matter is discrete.

He suggested that this was a question for physicists, not mathematicians.

Others would try to shape Riemann's ideas into a theory relating the motion of matter and the curvature of space. Clifford's "Space Theory of Matter" is a notable example.
https://mastodon.social/@mcnees/110311261444209164

Riemann's geometry is broader than the familiar Euclidean sort, and was based on two axioms that generalize the (infinitesimal) version of the Pythagorean theorem describing the distance between two points.

He introduced a number of now familar concepts in his lecture: the metric tensor as the quadratic form governing infinitesimal distances, curved spaces of arbitrary dimension, geodesics and normal coordinates, the Riemann curvature tensor.

Mathematician Bernhard Riemann gave his famous lecture "On the Hypotheses Which Lie at the Foundations of Geometry" #OTD in 1854.

Riemann expanded on ideas introduced by his mentor Gauss and introduced what we now call Riemannian geometry.

Image: Familienarchiv Thomas Schilling

@jeffzugale It’s tardi-great

William Anders, astronaut on the Apollo 8 mission, passed away earlier today.

Anders took the iconic Earthrise photo while orbiting the Moon with Borman and Lovell. No human had ever seen an Earthrise before.

On the transmission he says "Oh my God, look at that picture over there! It's the Earth coming up. Wow, is that pretty!"

🧪 🌕

Image: NASA

Most new technologies come with dangers, usually in proportion to how much we’re willing to let them take over our lives. But I honestly think the drumbeat of these headlines is as much a PR campaign as anything. If I were OpenAI, I would nurture (or plant) as many of these stories as possible. Just relentless messaging about the potency and inevitability of their product. No ad they buy could do this.

@jscalzi The guy is an absolute vampire. Artists exist to feed him.

@HoustonDog She definitely said it with a “J”

She named it “Jerry.”

The kid’s first tardigrade!

@HoustonDog I guess not! We’ve only had a few days over 80. Mostly it’s been in the 60s, some in the low 70s. So I can imagine the ground temp still being below 64 over here.

No cicadas here yet, so we drove out to the suburbs where they have taken over.

They were everywhere. The trees in the park were covered in cicadas.

Standing under a big tree full of them, my sound meter peaked at 93 dB — as loud as a lawn mower!

@thisismyglasgow Right down the street from my old flat on Kelvinhaugh St

Good evening. #Chicago

@stevenaleach Right. And how much of an expansive civilizations broadcast lifetime is tied to a planet?

@dcnorris @michael_w_busch How do you do, fellow intelligent civilizations?

Dr. Drake was also responsible (along with Richard Isaacman, Linda May, James C.G. Walker, Carl Sagan, and others) for the Arecibo Message, which I wrote about in the thread linked below.

It can be squeezed into just four posts, with room to spare, on my mastodon instance with its 500 character limit.

https://mastodon.social/@mcnees/111421557767168824

Dr. Drake was also responsible (along with Richard Isaacman, Linda May, James C.G. Walker, Carl Sagan, and others) for the Arecibo Message, which I wrote about in the thread linked below.

It can be squeezed into just four posts, with room to spare, on my mastodon instance with its 500 character limit.

https://mastodon.social/@mcnees/111421557767168824

Astronomer Frank Drake was born #OTD in 1930.

Can we productively talk about how many alien civilizations throughout the Milky Way might be actively broadcasting or receiving messages? How would we estimate that?

N ≈ R×fp×ne×fl×fi×fc×L

R = ⭐️ formation rate
fp = fraction of ⭐️ with 🌎
ne = 🌎 per ⭐️ on avg that could support life
fl = fraction with life
fi = fraction of life becoming intelligent
fc = fraction that 📡 into 🌌
L = how long they broadcast