Fractals & Chaos Recap for 11/6

In class with Mr. Drix today you had your debrief of the Chaos Hits Wall Street article, pointing out some key phrases like state space, which is a broad term that describes the current status (state) of a dynamic, changing system (space). You drew some sketches of state space diagrams for a perfect frictionless pendulum, then a more realistic damped pendulum, closing out the lesson with a look at the random, chaotic behavior of a double pendulum. Through this you learned a new property of chaos (in addition to the constrained randomness from yesterday): sensitivity to initial conditions. Changing the starting state of the double pendulum even slightly resulted in a wildly different oscillation pattern

For a more modern take on Chaos Theory in the financial investment industry, check out this 2010 blog post from What We Can Learn from the Stock Market Genius That Wall Street Loves to Ignore.

Keep in mind, however, that this “technical analysis” approach of stock market forecasting (as opposed to the “fundamental analysis” approach of looking at the strength of a company) is not without its detractors. For a counterpoint, see this bluntly-titled post from The Motley Fool, also from 2010: Technical Analysis is Stupid

Fractals & Chaos Recap for 10/31

We spent most of today discussing the geometry of hypercubes, and how the patterns of numbers vertices, edges, and faces develop over increasing dimensions.

If you’re interested in reading more about the 4th dimension, check out the links below. I especially recommend the short story And He Built a Crooked House.

  • The Adventures of Fred, Bob, and Emily – a detailed look at how the lives of a 2D (Fred), 3D (Bob), and 4D (Emily) creature interact with each other. See especially the “World” section, where the author, Garrett Jones, imagines how wheels, water, and war would work in these universes.
  • And He Built a Crooked House – a short story by “Big Three” science fiction writer Robert A. Heinlein about an eccentric architect who designs a house in the shape of an unfolded hypercube. An earthquake hits, and the house folds back up on itself to concerning results (see also this student film version of the story)
  • Some Notes on the Fourth Dimension – some animations and movies showing the geometry of the fourth dimension, including some of those featured in the Flatland dvd bonus features.