David Peat

122 From Certainty to Uncertaintyond. In this way tiny effects accumulate until the entire system actswildly. Effects from one planet are feeding back into the orbit of theother. 4The same thing can happen with critical arrangements of the orbitsof two planets around the sun. The very tiny perturbing effect ofone on the other feeds back with each orbit of the planet, amplifyinguntil the whole system becomes unstable. In this way, Poincaré pointedout that within one of the most basic of all certainties—that the sunwill rise each morning—was hidden the potentiality for instability, surprise,uncertainty, and even chaos.Poincaré published his result in 1900. It was the same year asPlanck’s hypothesis about the quantum nature of energy. Five yearslater Einstein’s special theory of relativity appeared and then the flurryof contributions from Bohr, Sommerfeld, Heisenberg, Schrödinger,Pauli, Fermi, and Dirac that established modern quantum theory. Nowonder Poincaré’s remarkable result was marginalized and did not remainwithin the center of the scientific limelight. Physicists and mathematicianswere also discouraged by the difficulties they would have toface if progress were to be made beyond Poincaré’s initial result. Afterall, many scientists prefer to work on problems that will yield resultsfor publication, since publication often leads to promotion!It was not until halfway through the twentieth century that breakthroughsoccurred that gave birth to the present science of chaostheory. Three Russian mathematicians, A. K. Kolmogorov, VladimirArnold , and J. Moser, came up with general ways to picture the sort ofproblems on which Poincaré had been working. Another advance wasthe development of computers that could solve highly complicatedequations numerically and display the solutions on a screen. Todayscientists and mathematicians can visualize complicated systems and“see” what the solutions look like.4Feedback also occurs in a public address system. When the amplifier is turnedup too high or the microphone is too close to a speaker, a tiny noise in the hall ispicked up by the microphone, amplified, and emitted out of the loudspeakers. Inturn, the louder sound from the speaker is picked up by the microphone, amplifiedagain, and sent out into the hall. As an initially quiet sound circulates it feeds backfrom microphone to speaker until it grows to an ear-splitting screech.