Yamatarajabhanasalagam

Around 1960 the American mathematician Sherman K. Stein discovered a curious pattern in the Sanskrit nonsense word _yamátárájabhánasalagám_. The composer George Perle told Stein that the stressed (_á_) and unstressed (_a_) syllables form a mnemonic for rhythms, and correspond to long and short beats. Thus the first three syllables, _ya má tá_, have the rhythm short, long long. The second to fourth are _má tá rá_, long, long, long - and so on. There are eight possible triplets of long or short rhythms, and each occurs in the nonsense word exactly once. Stein rewrote the word using 0 for short and 1 for long, getting 0111010001. Then he noticed that the first two digits are the same as the last two, so the string of digits can be bent into a loop, swallowing its own tail. Now you can generate all possible sequences of three digits 0 and 1 by moving a long the loop one space at a time. I call such sequences _ourborean rings_, after the mythical serpent Ourboros, which eats its own tail. _ — Ian Stew

12 Jul 2014 by rm-hull