The Shepard Tone Scale is a famous auditory illusion. To hear it, press “Play” below. There is a tone in the background that appears to be constantly rising, but actually begins and ends on the same note, playing over and over again. Even listening carefully, it is difficult to tell when the loop starts and ends.
In Trillions, we talk about Shepard Tones as a particular example of what is known as a “strange loop.” In a strange loop, whether you move only down or only up in a hierarchical system, you always get back to where you started. A good example is Rock, Paper, Scissors. To illustrate why it’s a strange loop, let’s try moving only “down” in the hierarchy:
- Rock beats Scissors
- Scissors beats Paper
- Paper beats Rock
- Rock beats Scissors.
Interesting, right? We only went “down” the ladder, but somehow we ended up at the top again. We mention strange loops in Trillions because they are an example of a an underlying design pattern that can be found in music, games like Rock, Paper, Scissors, art, biology and mathematics. Finding hidden design patterns is one way we can understand and tame the complexity of a trillion-node world.
[from page 186 of Trillions, in the section “Rock, Paper, Scissors”]