We started our session going over Sequences and Series, both Arithmetic and Geometric.

We then dove into a deep discussion on the nature of math, how it relates to human endeavour, and the yin / yang approach of starting with “atomic” components and working your way up to modelling aspects of the universe, and looking at nature and working your way inwards to modelling it better and better. We compared this to on the one hand wooden puzzle boxes where you have to learn a complex series of manipulations, and origami, where you start with total simplicity and build complexity out of it.

We talked about the basic shape of what math is all about, compared how math is taught (ideally) to the “master strikes” of Liechtenauer’s 14th century Longsword school.

We explored (in his words) “the relation between linear order, structural order and functionality” – a delicious phrase which I’m going to hang on to. How you learn sequences of manipulations to do in certain mathematical sequences, but how in situ it’s like mountain climbing: you have to figure out how to apply those fairly linear manipulations properly in an extremely nonlinear, creative way to help you reach the specific goal you’ve set.

We talked about equations as compressed expression of patterns.