Ignorance, as you said, not stupid (but we often conflate the two). But if he imposes his own opinion (business "intuition") in something he has no expertise in, what do we call it?

I hope that's not the obviously wrong reason you referred to.

He thinks it's a win. He thinks trade deficits between countries are just like losses for a company, and tariff is the only way to fix it (either directly as revenue, or making companies move back to US). Plus he thinks he knows better than everyone else, and kicks out anyone who tries to explain.

He isn't asking, he goes in and takes billions.

Star Wars也差不多，古罗马式的元老院就要被皇帝取代了。本来是想给孩子看些科幻的，凡尔纳的潜艇现代版就应该是宇宙飞船，结果还是肉搏（反正孩子看着开心）。这方面的确《三体》更好，虽然有很多其他问题。

One can probably allege the same towards photography vs oil painting. Will AI make oil painting great again (but cheap)?

Will? It’s already happening.

Are ambulances private? and ER visits come with big bills, but at least they can't refuse treatment.

God help us if insurance companies get involved in fire fighting.

还有这种情况？Good to know!

本身学术书很多是大学出版社出的，去大学书店可能更靠谱。

great to see that inclusion of the Chinese original has become the norm

I love that it's not just "turtles all the way down", but turtles all the way up, down, left and right, filling up the entire plane.

It was also soon discovered that you can decorate the tiles with stripes that line up. (The reflected turtles get three stripes, as they are where three lines meet.)

They noticed early on that they needed to use reflected hats, and they'd see a long stack of hats that go through those reflected ones.

If they had used turtles, the stacks would be more straight. With such clues, they found that the tiles do follow some pattern, not translational but hierarchical.

It has become known as the "ein stein" problem (German for "one stone").

In late 2022, David Smith, a "shape hobbyist" as he describes himself, first set his eyes on the hat. It's wonderful to read his own account, up to the release of the paper by the team of four in March 2023.

Moreover, the ONLY ways to tile the plane with the Penrose tiles — if we enforce some matching rules, or add jigsaw notches on the edges — are aperiodic. Check out this great video by @veritasium-science.bsky.social

The obvious question is: Can we do it with one shape?

For background, aperiodic tilings are tilings of the plane (no gaps, no overlaps) that do NOT follow a translational (i.e. periodic) pattern. The most famous are the Penrose tilings with a five-fold rotational symmetry, made up of two base tiles (either two "rhombs", or a kite and a dart).

As the hat was the first one discovered, the paper and the Internet are filled with hats; and when the special property of the spectre was revealed in a second paper, it too got a lot of publicity. However, I think the turtle deserves more love, so this thread is for the less-celebrated 🐢.

Seems more appropriate for the CDC. Let someone without a doctorate lead (i.e., destroy) the NIH!

If you are plotting the points like this, you may as well connect them (or perhaps only the ones from tangents, i.e., 1, 2, 4, 8... multiples of the generator).