By James Bailey
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As humans, we simply cannot maintain the levels of detachment demanded by Plato. If a formulation saves the appearances, we feel that there must be something more to it. The vocabulary 0/ the mathematical/iction inexorably becomes the vocabulary with which we describe the reality. This is the reason that a change from sequential equations to parallel matings and breedings is so seminal. It affects all of us, not just scientists. It will literally change heaven and earth because it will change the way we conceive of them.
The two competing concep- THE FIRST FICTION 47 tions of time, one geometric and the other numerical, manifested themselves explicitly in the forerunners to the mechanical clock. The most famous of these early devices, known as the di Dondi clock after its designer, was a miniature version of the heavens themselves. All the major motions of the planets were carried out in obsessive detail. The planets moved on physical epicycles, expressed as trains of gears. What makes this device so jarring to the modern sensibility is that such clocks were "only very incidentally time-telling devices ..
17 The time-telling devices that later came to be made in Niirnberg and Augsburg, and soon throughout Europe, were full-fledged versions with the focus increasingly on the hands and dials that "tell time" in the modern numerical sense. Using these new tools, scientists could access concepts like "velocity" for the first time. Mechanical suns and moons and planets, the tellers of geometric time in the original sense, gradually receded into a purely decorative role. Regiomontanus missed this emergence of a new form of clock and with it a new role and meaning for time in computation.