There are a "few" steps to it. In my own case they went something like: 1. buy some permutation puzzles. 2. read about some ways to solve (hard) and scramble (easy) the Rubik's group, start with the smaller ones that stay "closer to the identity". 3. also use computer algorithms to investigate the dynamics of the numbers of symmetries 4. read up some more about algebra and group theory, since the puzzles are all obvious groups of "elements in sets". 5. try out some optimization techniques to find the logarithmic orders and general groups in the structures 6. develop computational model that can map Galois to a triangulated 'signal space' = a category-parser that sorts the symmetry groups. of course, I did all of that the first time I solved the cube - in principle - so it was only a matter of delving into "the math" by following a certain path, certain people's names were dropped in the article apart from Mr Hofstader's. Also there are possible uses for such a model as in 6 - if I can design a real one. Step 1 there is then design it. Basically the whole problem is about division algorithms. Here Bob Doran came in handy because he knows a bit about parallel design and such. Is anyone up on the design of a logarithmic-order category parsing machine?