Some time ago we set out on two diverging roads. One road sent us exploring the infinite, while the other started out looking at discrete patterns, and how they may be abstracted. As we moved along the roads, however, we found the first hints of cross fertilization: our results about the infinite allowed us to propose pattern algebras for infinite patterns — the result being that the algebra was precisely that of numbers. From here on in the two separate paths begin to align, running quite separate but parallel courses. The cross fertilization of ideas will continue, and we will begin to see increasing similarities between these two very separate worlds of abstraction. The paths ahead will soon become interesting indeed.

## Archive for September, 2007

### Parallel Paths

September 11, 2007
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