By James Bailey
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The Greeks had a much harder problem: determining the places of the sun and moon without first knowing the places of the stars. The Greeks believed in an orderly universe, a "cosmos," and used that belief as a central ingredient in their notion of place. When they looked up in the sky, they did not see a random scattering of stars all shining in parallel. In accordance with Aristotle, they saw "the ordered system of the heavens and the march of the stars and the sun and the moon .... "; The audacious Greek solution to their inability to understand the heavens by sight alone was to create a fictitious, well-behaved, computational sun and moon and use them, rather than the visible sun and moon, to determine the places of the stars.
27 In the abstract, nobody is likely to quarrel with Ulam. The reality, however, is new enough and different enough to be scary. Rene Descartes encountered the same kinds of entrenched resistance as he promoted the use of numbers and equations instead of the incumbent circles and lines of geometry. Not the least of the sins of a new equational view was that "it turns away the young from the study of the old and true Philosophy.. . An imprudent youth can deduce from it certain opinions which are opposed to the other disciplines and faculties and above all the orthodo~ Theology.
The epicyclic diagram, on the right, places the planets recursively on circles that themselves revolve on circles. Fifteen hundred years later, these two basic formulations retained all the expressive power needed to support Nicholas Copernicus's great work, de Revolutionibus. When it was published in 1543, however, printing was already well establisned. Diagrams like Copernicus's, so welcome in the scriptorium, were anathema to the composing room. Geometric maths were already being replaced by algebraic maths that could both express rates of change and be typeset.
After Thought by James Bailey