Fractran

The idea of encoding an arbitrary finite string of integers as a single fraction (by looking at a product of primes to appropriate powers) will probably not be new to any mathematician, and certainly not to any logician; but I think the idea that this encoding can be put to any practical use will probably be a surprising one. Of course one's value of 'practical' can differ, but John Conway has suggested a way to write a computer program as a string of fractions. The resulting language ('Fractran') is -- but of course! -- Turing complete.