The Maths of Complexity

In year eleven maths teacher gave me an ultimatum about doing more work or just giving up. I called her bluff and dropped the course that day. I have a funny relationship with maths, I almost really like it, however, high school maths and I never got along because I always ended up asking 'but why?' and the answer always was 'you don't need to know, just work out this bit'. I always found that deeply unsatisfying and so have really enjoyed this week as it brings together the complicated bit with numbers with the real world.

That being said, as much as I have enjoyed it, it is still something I have a hard time getting to the bottom of and so have probably arrived at a point of deep-seated admiration rather than a satisfied comprehension of. I had a lot of fun playing The Chaos Game and making pretty patterns out of formulas and watching people much more in touch with numbers explain them to me in the documentary The Colours of Infinity.

I think in terms of complexity there is something especially important about maths, which I see parallel to art, in that it is a universal language that has the potential to transcend culture.

I really enjoyed Michael Barnsley's lecture, I love seeing people with so much energy and passion who can communicate with people outside their discipline. The salient points from Barnsley's lecture which I think can be applied to other areas are
  • I: Simple feedback systems may exhibit complex behaviour.
  • II: Simple systems can be very sensitive to initial conditions.

The best description I came across in terms of applying the idea conceptually came from the tutorial reading The Nazis' March to Chaos: the Hitler era through the lenses of chaos by Roger Beaumont:

Question: How do we apply these ideas if we have no way of determining the initial conditions?

Oh well, if my comprehension of mathematical concepts fails entirely I will just satisfy myself with the wonder of fractal broccoli.

Fractal Broccoli