We started by going over conversion of various SI measurements.

We then dove into an amazing conversation on the Mandelbrot Set, specifically around how the pretty picture that most people know is really just an answer to a simple question about the underlying math: does the infinite sequence of numbers represented at this point lead to infinite or not.

We then talked about the nature of those infinite sequences of numbers that lay embedded in each point of the Mandelbrot, about their shape, their nature, and the amazing and wacky symmetries and asymmetries they make. We talked about the three-way infinity involved (X, Y, “orbits”) and why unlike many situations each of those dimensions has its infinity express in interesting ways in the Mandelbrot. We even touched on the infinite set of Julia fractals embedded within.

We also talked about the dawn of the era of experimental mathematics, and the waste of potential our computers represent (the amazing areas of uncharted waters mathematically speaking that have yet to be traversed & discovered).

We also talked about math & programming and how they should be taught, and about programming as art, language, map and compass for exploring the world.

We made a brief foray into paradoxical shapes (Koch snowflakes with finite volume but infinite perimeter).

We talked about world travel and amazing goals for travelling to every continent, including the political and technical challenges that would be involved in boating from Australia to Papua New Guinea, the Bhutanese index of happiness (as opposed to GDP), the Tibetan Government in exile (and the excitement that was going on when Ken and I were there), and the perils and benefits of advertising and sponsorship. Also about what sort of life one would set themselves up for by spending a decade travelling the globe.

We finished off talking about educational methodologies, and decided that next class after the math is done, we’re going to talk about approaches to designing personal study / coursework and maybe apply it to an area of interest.