Sunday, August 10, 2008

Strange Loops

I recently picked back up the book "Godel, Escher, Bach" which is a look into how math, imagery, and music are all intertwined with each other in very strange ways. On the outset of this book, the author introduces the concept of "strange loops". It is most easily characterized by the very familiar works of M.C. Escher who elaborately depicts impossible loops such as the neverending waterfall, the neverending stairs, or the hands which draw each other.

But, this concept got me to thinking about an "audio illusion" that I once stumbled across called "Shepard's ascending tones". This recording is an audio representation of Shepard's paradox. Basically, the track has the auditory illusion of constantly rising tones. But, in reality, the tones are just repeating the same stair-stepped routine over and over again. Here is a visual representation of the paradox:

The audio representation of Shepard's paradox is available HERE for your enjoyment (and possibly your insanity). You can hear the "strange loop" (it's best to loop it when playing to get the full effect). The book is difficult to read sometimes for a "non-mathematician", but it is a very intriguing look into number theory, language theory, artificial intelligence, the turing machine, and much more fascinating nerd stuff.

Here's a link to the book on Amazon:

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