August 04, 2016 at 05:07AM

Today I Learned: 1) Jeff Hasty's lab has engineered bacteria which can synchronously grow and die off together once they reach high density. This lets them maintain log-phase growth more or less indefinitely. The lab put some of these engineered bacteria into a mouse model for a human cancer, and the bacteria stayed more or less synchronous and pulsed together, maintaining a fairly steady population over a long period. 2) There is an algorithm, called the Bailey-Borwein-Plouffe (BBP) formula, for calculating any single binary digit of pi, directly, without calculating any of the intermediate digits. For some reason, it involves base 16 calculations. The BBP formula was a total surprise to mathematicians when it was introduced in 1995, and I imagine it still comes as a total surprise to math students today. More surprisingly, a bunch of other formulae for well-known irrational numbers have been discovered with the same form. There is no general technique for discovering those formulae. It's not clear whether or not all irrational numbers could be defined in terms of similar formulae. Here's the general idea of the algorithm. The BBP formula says that pi is an infinite sum over k from 0 to infinity of (1/16^k) * (p(k) / q(k)), where p and q are some (simple) polynomials in terms of k. Each term in the sum is a window of four binary digits (bits) of pi. If you want to know the 56th digit of pi, you figure out which window it's in by dividing the digit number by 4. That's k (in this case, 14). Now crunch out the values of p(k) and q(k) for your chosen k. Divide p(k) by q(k), and that gives you the k/4th digit of pi in base 16. Convert that digit to four binary digits, and you have your 56th binary digit. 3) Mantises can, to my surprise, rearrange their grip on their prey mid-meal. They're quite single-minded once they've caught prey, basically doing nothing but wolfing down the insect as quickly as possible, chitin and all (except for wings, often), backing away from overt threats lazily. So I was surprised to see a mantis *let go* briefly and rearrange its grip.