# Harmonograph

21 20 simPle unison 11 and the arrow of time The simplest harmonograph drawing is produced when both pendulums are the same length and the table is stationary. With the pen held off the paper both pendulums are pulled back to their highest points. One is released, followed by the other when the first is at its midpoint. The pen is then lowered on to the paper to produce a circle developing into a single spiral. If the two pendulums are released together then the result will be a straight diagonal line across the paper, the closed phase of the harmony, as opposed to the circular open phase. At intermediate phase points elliptical forms appear below. The runningdown of harmonograph pendulums is an exact parallel to the fading of musical notes produced by plucked strings, and can also be thought of as graphically representing the arrow of time see opposite, with the unchanging ratios of the frequencies representing the eternal character of natural law. The characteristics of the drawings result from the meeting of the runningdown process with the laws represented by the various frequencyratios. We see that music, like the world, is formed from unchanging mathematical principles deployed in time, creating complexity, variety and beauty. The inexorable direction of change, linked to the asymmetry of time beforenowafter, was vividly described by the scientist Arthur Eddington 18821944 on as the arrow of time. Throughout the process of continuing universal degradation, the dwindling stock of useful energy encounters a hierarchy of fixed physical laws conforming to mathematical formulae, and it is from the interaction of these unchanging laws with the arrow of time that comes a changing world of astonishing complexity, variety and beauty. The pendulum runs down from a state of disequilibrium to one of equilibrium, and the same is true, we are told, of the universe, the ultimate closed system. From a state of extreme disequilibrium it plunged via the Big Bang towards its future ultimate state of utterly dark, frozen equilibrium. Between the beginning and the end there is a continual, cumulative transformation of useful energy, capable of forming temporary structures and causing events, into useless energy forever lost.