cazlab.avaricestudios.com

I recently obtained and began reading Gödel, Escher, Bach.
One of its earlier thought experiments involves this MUI system devised by Hofstadter. The system itself is quite simple. There are a couple of rules to add characters to a string of Ms Us and Is and a couple string to remove them. The reader is encouraged to work through the system and try to reach the string MUU. The book walks through an orderly tree based approach and shows no such sequence of "moves" yields MUU in less than a dozen iterations.