Chaos and instability, concepts only beginning to acquire formal definitions, were not the same at all. A chaotic system could be stable if its particular brand of irregularity persisted in the face of small disturbances. [Edward] Lorenz’s system was an example… The chaos Lorenz discovered, with all its unpredictability, was as stable as a marble in a bowl. You could add noise to this system, jiggle it, stir it up, interfere with its motion, and then when everything settled down, the transients dying away like echoes in a canyon, the system would return to the same peculiar pattern of irregularity as before. It was locally unpredictable, globally stable. Real dynamical systems played by a more complicated set of rules than anyone had imagined. The example described in the letter from Smale’s colleague was another simple system, discovered more than a generation earlier and all but forgotten. As it happened, it was a pendulum in disguise: an oscillating electronic circuit. It was nonlinear and it was periodically forced, just like a child on a swing.
It was just a vacuum tube, really, investigated in the twenties by a Dutch electrical engineer named Balthasar van der Pol. A modern physics student would explore the behavior of such an oscillator by looking at the line traced on the screen of an oscilloscope. Van der Pol did not have an oscilloscope, so he had to monitor his circuit by listening to changing tones in a telephone handset. He was pleased to discover regularities in the behavior as he changed the current that fed it. The tone would leap from frequency to frequency as if climbing a staircase, leaving one frequency and then locking solidly onto the next. Yet once in a while van der Pol noted something strange. The behavior sounded irregular, in a way that he could not explain. Under the circumstances he was not worried. “Often an irregular noise is heard in the telephone receivers before the frequency jumps to the next lower value,” he wrote in a letter to Nature. “However, this is a subsidiary phenomenon.” He was one of many scientists who got a glimpse of chaos but had no language to understand it. For people trying to build vacuum tubes, the frequency-locking was important. But for people trying to understand the nature of complexity, the truly interesting behavior would turn out to be the “irregular noise” created by the conflicting pulls of a higher and lower frequency.
~Gleick – Chaos: Making A New Science, pp. 48-9
My question: what if van der Pol could not have noticed the patterns he did if he had simply used a graph? What if the structures of music (e.g. chord progressions, key, octaves) can allow insight into patterns that cannot be fully conveyed via visual media, i.e. graphs?
There’s a flash game related to this topic here. Though I normally avoid such frivolous things, this one is quite simple, yet allows for a great amount of creativity. If Noam Chomsky could develop syntax out of a little grammar game he would play between sessions of ‘serious’ linguistic work, so, perhaps, one might be able to eventually come up with some practical application for playthings like this…
People’s seemingly inherent attraction to games is something that I still don’t understand, but it is nonetheless quite fascinating, not to mention (potentially) useful, as in this case.