Thursday, February 4, 2010

Chaos at Toyota

The situation with Toyota is, of course, compounded by the arrogance of a large multinational corporation, but I believe a large part of it, especially with the Prius brakes, is a result of the inevitablity of chaos -- unpredictability in complex systems -- a basic theme in the book and movie Jurassic Park. As a mathematician I have seen the proofs of how large systems, obeying complex rules (non-linear differential equations), are very sensitive to "initial conditions", i.e. the "given" or "set-up" rules.

In simple terms, if you have a complex system you simply cannot be 100% certain it will behave as you predict, because you can't ever measure or set up things accurately enough so that 100% predictability is even theoretically possible. Only time and much tinkering can ameliorate the situation, and even then there are inherent, unavoidable possibilities for the unforeseen.

When Toyota decided to completely redesign its braking system and build it around regenerative braking -- the transfer of the energy of the moving vehicle into battery power -- it created a new and complicated system with all the inherent possibilities for chaos. Only time and lots of fixes and recalls will help tame this problem, and there will be others. The history of any innovation shows this phenomenon over and over. (A classic is the airplane-mounted machine gun, which in the early days would often shoot out the plane's prop. There was also the bridge that self-destructed when a simple weather system created resonant and destructive vibrations that had been unforesee by its engineers.)

I discussed chaos previously in a blog about economic theory.

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