Catastrophe Theory for Dummies Part 1

An article in the Journal of the Naval Post Graduate School,  by Ted G. Lewis, “Cause-and-Effect or Fooled by Randomness?”, is a terrific short-form introduction to the problem, with no sacrifice in precision for the sake of brevity. If you can absorb the essence of it, you’ll have taken a leap way past faulty viewpoints based on “common sense” or claimed expertise, some of which appear as newly published books. I’ll supply some interpretation of the article in the next post.

In the Harpers article interview, “Six Questions for Ian Bremmer, Author of Fat Tail”, Ian Bremmer compares his book with the Black Swan Theory of Nassim Nicholas Taleb. Bremmer says, “Preston Keat and I believe that a good number of these risks can be measured and managed.”

Bremmer’s education is in geopolitics and political science. These days, such an education can involve a significant amount of applied statistics, but not at the level of mathematical theory. Taleb is a mathematician, with a focus on theory that impact’s Bremmer’s field. Bremmer relies on his “expertise” to posit a truth in contradiction to Taleb’s math.

So this is a situation of two fields of knowledge, each intruding on the domain of the other, resulting in conflicts of viewpoints and conclusions. Taleb’s Black Swan is a direct challenge to Bremmer’s expertise, because Bremmer has made his reputation in risk management for corporations and states, while Taleb asserts that, for very large events, it can’t be done. Taleb’s theory undermines Bremmer’s position.

Both Bremmer and Taleb have weapons at their disposal to convince you that their positions are the correct ones. For instance, to understand energy, Bremmer would lead you through an argument that you might feel gives you a new understanding of where the price of oil is going. To wit, Bremmer says,

“Fewer market players are keeping an eye on Iran, but the Iran risk hasn’t gone away. If anything, the risk of confrontation will be greater over the next 12 to 18 months as Iran moves closer to a technological point-of-no-return and increasingly anxious Israeli leaders weigh their options.”

The above might be a delectable read, but that doesn’t mean it’s nutritious. Taleb would claim that the understanding is  illusory, and inspires false confidence that the risk can be managed. The quote also has a Delphic openness, meaning that whatever the oracle says, always comes true, if only you can understand the wording. On the general subject of whether political expertise actually exists, Philip Tetlock’s book, “Expert Political Judgment: How Good Is It? How Can We Know?” is a general challenge to the predictive specialty of which Bremmer is a member.

With Bremmer’s specialty now sufficiently undermined, you have good reason to consider what Taleb has to say. The title of Taleb’s article, “UNDERSTANDING IS A POOR SUBSTITUTE FOR CONVEXITY” is by comparison a dose of cod liver oil. The challenge for you, the reader, is not to go to what might be your comfort zone, which could be reading about geopolitics, which always has the elements of an entertaining story, with good guys and bad guys. The challenge is to try to fit Taleb’s insights into the scheme of things, even if you are not a math thinker.

But I haven’t finished softening you up. I want to run by you an example of an experiment that is part of “undergraduate control lab” in electrical engineering curricula. If they don’t have the actual setup, they certainly discuss it at length. It’s a juggling stunt. A broomstick is balanced vertically at one end by some kind of mechanical hand. You could imagine one of those Japanese robots that looks so human. Instead of wheels, let’s give this robot a cushion of air. Here’s the scenario:

  • While balancing the broomstick, the robot navigates through a crowd, which subjects it to random jostles of varying strength.
  • Some are mere nudges; some push our little robot many feet.
  • The robot is never actually damaged or interrupted in its task.
  • At all times it is able to follow the computer program that moves the hand that balances the broomstick, trying to keep it vertical.
  • The robot has been programmed by the best programmers in the world. It has the best motors, huge batteries, and its hand is very powerful and fast. Everything “works right.”

The question for you is: Does the robot manage to keep the broomstick balanced forever? Or is this a catastrophe in the making? Is there some mathematical doom built into the situation?

The answer is coming. Check back for the next post.

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