Recent content by Hornbein

The elements of N are numbers while the elements of P(N) are sets. None of the elements of P(N) are elements of N. The intersection of N and P(N) is the empty set.

Knot theory grew more popular in 1890 when Lord Kelvin used it to explain atoms.

Beryl is almost always colored so they were looking at the world through aquamarine glasses. That was better than the bubbles in glass.

When the first eyeglasses were constructed in 13th-century Italy, the lenses were made of beryl Be3Al2(SiO3)6 (or of rock crystal) as glass could not be made clear enough. Consequently, glasses were named Brille in German[10] (bril in Dutch and briller in Danish).

Transporting a huge sack of empty water bottles on a motorbike.

Family life is important. I bet all the girls were in love with his baby butt.

The panic completes day three. Lines up to two miles long reported. That could be as many as two thousand motorbikes. It would take all day to get through a line like that. You gotta do what you gotta do. The news features a video of a gas station employee screaming at the governor of...

A couple of years ago I used the free version of ChatGPT to create a small program in a programming language I didn't much know. It did a great job. The code was error free and well organized. It made a number of helpful suggestions about things to try that I never would have thought of. It...

From a punk concept album. Shades of Avril Lavigne. Whoops! It's AI. They failed to label it. I'm gonna report them. This person has taken it to another level by putting fake publicity photos and biography onto the Internet. It had to happen. Clearly though it is just a hobby. Not...

Daria Zaritskaya sings Michael Jackson's Beat It.

A tanker delivering fuel to Bali fouled its anchor, blocking offloading for 15 hours. Bali has a second such offloading port but it is further from the gas stations so there were delays in getting the fuel distributed. Some stations ran out. The news spread quickly. Fossil fuel consumers...

That was in the Institute for Advanced Studies in Princeton NJ. This was fictionalized in episode six of Mission : Impossible! I thought the theme song was the coolest thing in the world.

From AI. I'm too lazy to check it. Publication: On July 25, 2026, Ramana Kumar published an AI-assisted Lean repository containing a sorry-free formal proof purporting to show that the Collatz conjecture was false by exhibiting an orbit that does not return to 1. [1, 2] The Kernel Bug (Issue...

Does anyone have a sweeter voice than AJ Lee?