The Poincare Sutra

The Poincaré Recurrence Theorem says that in certain physical systems, history repeats itself. More precisely, a closed frictionless dynamical system can change from one state to another, but sooner or later, any state repeats itself. Which means variety’s possible, but not novelty. But if novelty is ruled out, then it kinda rules out things like stories with love at first sight. What are some of the other stories that are ruled out? Friend, you already know the answer. This story helps you remember.

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One of the curious things about evolution is that there’s a lot of variety in lifeforms, but not much novelty. The same dozen or so body plans, the same few hundred critical gene sequences, and the same handful of reproductive strategies constitute most of life on Earth. Our genetic code is about 50% the same as that of the banana. That’s always staggered me when I think about it, which fortunately, I don’t do all that often.

The Poincaré Recurrence Theorem is perhaps best illustrated with the help of the banner image taken from a 1986 Scientific American article by Crutchfield et al. In their words:

The initial image (top left) was digitized so that a computer could perform the stretching operation. A simple mathematical transformation stretches the image diagonally as though it were painted on a sheet of rubber. Where the sheet leaves the box it is cut and reinserted on the other side, as is shown in panel 1. (The number above each panel indicates how many times the transformation has been made.) Applying the transformation repeatedly has the effect of scrambling the face (panels 2-4). The net effect is a random combination of colors, producing a homogeneous field of green (panels 10 and 18). Sometimes it happens that some of the points come back near their initial locations, causing a brief appearance of the original image (panels 47-48, 239-241). The transformation shown here is special in that the phenomenon of “Poincaré recurrence” (as it is called in statistical mechanics) happens much more often than usual; in a typical chaotic transformation recurrence is exceedingly rare, occurring perhaps only once in the lifetime of the universe. In the presence of any amount of background fluctuations the time between recurrences is usually so long that all information about the original image is lost.

I’d always wanted to write a story that made essential use of the theorem and a format that resembled the cutting, pasting and re-folding of the events of an unique story. I’d always found the story of Joseph in the Old Testament particularly poignant. His marriage to Asenath, daughter of Potipher, his former Egyptian slavemaster, and Asenath’s mother Zulaikha, the woman who caused him such grief, turned out to be just what I needed.

The story is based on the real-life persecution of the Copt Christians in Egypt. The “tidbits” mentioned in the story are all factual. Also, my thanks to Matthew Kressel, the editor of Sybil’s Garage, who had the patience to plow through a demanding story written in 55-word fragments.