Interlocking tessellations

Last evening I watched the documentary M. C. Escher, Journey into infinity. The film is a recounting of his life and the art he created. The narrator read words from his letters and other writings. Two of his sons and one of their wives also added what life with him was like. Escher was born in 1898 into a wealthy and well educated family in the Netherlands. We don’t learn until the end of the film that for much of his life he lived off the family wealth. He attended the Haarlem School for Architecture and Decorative Arts, focusing on drawing and making wood prints. He moved to Italy and strengthened his craft by sketching and creating prints of the villages around where he lived. The film cut between a scene and his prints of the scene. Mussolini came along and his elder son wanted to be a little fascist just like his schoolmates. It was time to leave. So on to Spain for a visit. Escher wanted a way of eliminating boring backgrounds so tried to have background of one figure actually be another figure. He wasn’t satisfied with his solutions to this idea. Then he came to the Alhambra and its elaborate tile patterns. Ah, this showed the solutions he was looking for. But the tiles showed only geometric shapes. Escher studied them but wanted figures from nature rather than geometry. And that was the start of the style, the interlocking tessellations, we know him for. He lived for a while in Switzerland, but decided that was too much snow. So to a suburb of Brussels, then to Baarn, Netherlands where he waited out the war and lived for the rest of his life. After a while he began to wonder if the mathematics crowded out the art. He didn’t have mathematical training but seemed to understand how the mathematics of a drawing had to work, such as when a pattern reached towards infinity at the center or edge of a circle. Another voice in the film was Graham Nash, of Crosby, Stills, and Nash. He contacted Escher to complement him on his art. Escher responded I’m not an artist, I’m a mathematician. Even though my area of expertise is music and not art, I would insist Escher is very much a good artist as his early work shows. His later work also has an underlying mathematical structure. Escher’s fame took off in the 1960s as it began to be associated with psychedelic culture. That link became stronger when his black and white or subdued colored images were reprinted in fluorescent colors. Escher was appalled. Especially since no one asked his permission or paid royalties. He died in 1972. I watched the film through the Detroit Film Theater at the Detroit Institute of Arts. It is available through the end of the month and is about 80 minutes. More on Escher at his Wikipedia page. Nina Turner tweeted:

I find it obscene that a Congress full of millionaires (funded by billionaires) is trying to means test the difference between $50,000 and $75,000 for a life-saving survival check during a pandemic. We need more working people in our government.

Bree Newsome tweeted something similar:

Again— anyone who says they want to “means test” the distribution of a $2k relief check but won’t support a 2% wealth tax on billionaires is not seriously concerned about $$$ going to people who don’t need it.

New York Times Opinion tweeted a video that mapped smartphone location data of those involved in the nasty guy rally the morning of the Capitol attack. Once the rally was over those cell phones moved to the Capitol. The video is only 13 seconds, so the shift happens quickly. However, it shows most of those at the rally moved on to and into the Capitol. That’s more proof that the nasty guy’s words that morning were a reason why the Capitol was attacked. I shoveled three inches of snow off my driveway a few days ago. The temperature now is 18F and predicted to go to -2F by the end of the week. So I appreciate a bit of snow humor here and here.