Yesterday’s Thoughts

September 8, 2006


Regular readers know have a handful of disparate phenomena that are interesting to me because they are mathematically similar. Each is a process that traverses a probability tree and becomes more or less probably as the number of branches in the tree increase. My posts on Wiio’s Laws, network effects in rural economies (Jane Jacob’s work, I’m working on a post for the future), probability and the justice system, take the first available turn, and analyzing an argument all bear on this subject.

The first phenomenon of this class that I ever thought deeply about was distillation. A distillation is a very well defined probabilistic tree that produces a defined result. At each step, one component, say alcohol, has a slightly higher probability of advancing to the next step than the other components. Chemists refer to these steps as theoretical plates and at each plate, the probability of a component moving to the next plate depends positively on its vapor pressure.

A distillation column has thousands, or hundreds of thousands, of theoretical plates and is very effective at separating components in a mixture based on vapor pressures. The analysis of distillation is nearly identical to the analysis of other chemical and physical processes for separation based on diffusion, size, charge, or other properties.

A distillation is an extremely powerful concept for analyzing the physical world and I am struggling toward a similarly powerful concept for analyzing ideas and concepts.

A significant difference is that distillations are linear in ways that analyzing an argument isn’t. The process involves molecules moving from A to B along a single path and at every theoretical plate in the distillation of most mixtures, the probability of a molecule advancing is that same as every other theoretical plate.

When you are analyzing an argument, it is unlikely for every step in the argument to have the same probability. More confoundingly the logic of the argument doesn’t necessarily follow directly from step to step: is possible for a speaker to make an assertion that has zero probability of being correct, and still ultimately arrive at a correct conclusion.

Still, I think the the logic of the distillation captures the interesting aspects of these ways of thinking.

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