Season 11 Episode 11

We've got another viewer request for the Maths Club, and this time for linear algebra and stochastic applications. We'll illustrate this with a very simple chat generation algorithm that might be useful for sheep.

Watch on YouTube

Further Reading

Archimedes’ method

For the puzzle at the start of the episode, we talked about  

Here’s the Google Doodle

Here's some background information from the mathematics consultant behind the scenes, Kit Yates.

Here's more information, on Wolfram MathWorld.

If you like Kit Yates’ writing, then you might like his popular maths books, The Maths of Life and Death and How to Expect the Unexpected.

Matrices and Markov chains

Here’s a simulator that lets you set up the “transition probabilities” and run a Markov chain, to explore what happens in the long run.

Here's a fun web app (you need a keyboard though, so find a computer if you’re reading this on a phone) called the Aaronson Oracle. You press the left and right arrow keys as fast as you can, attempting to act at random. The computer tries to guess what you’ll press next, based on (1) the last four keystrokes, and (2) what is has learned about you so far. For most people, the computer can predict their next keystroke about 70% of the time. Can you trick the computer by using your free will to act “truly at random”, making its guesses correct 50% of the time? Can you outwit the computer, so that its guesses are correct less than 50% of the time?