Quaternions were a new kind of numbers, invented in the 19th century by W. R. Hamilton. The interesting thing about them is that they don’t commute – x.y is not usually the same as y.x. They are rather special because they’re the unique non-commutative field finite-dimensional over the complex numbers.
If you have a tablet or large-screen mobile phone you can place that device on the music stand of your piano as you you follow the lesson. Stop and rewind as often as needed. Play the movie in full-screen for the best experience.