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Programme Note

ACHILLES AND THE TORTOISE (1983) for solo piano.
"Achilles and the Tortoise" refers with its title to the Greek philosopher Zeno´s famous paradox, in which he proves that Achilles will never catch up with a tortoise, if the tortoise i given just a small head start. The proof is constructed on the argument that when Achilles reaches the point where the tortoise started, the tortoise will have moved a little further ahead to a new point, and when Achilles reaches this new point, the tortoise will have moved slightly, further and so on.
Of course the music does not directly illustrate the race, but on one hand the fastest layer of the piece consists of two cyclic progressions or sequences of different durations, the one constantly passing up the other, As the two repeated lines are played at the same time, in a rhythmic “zipper”-technique (interlocking) the element of musical illusion and paradox is strengthened; on the other hand the most directly percerptible layers of the music are slow, large-scale projections of these quick movements. The piece can consequently be said to be a musical race between these elements, a race in which there is no winner.
“Achilles and the Tortoise” is dedicated to Yvar Mikhashoff, the Achilles of the piano (The fleetest of hands of all mortals).
Per Nørgård