As astronomical observations became more comprehensive, and as sea-faring became more widespread, the need for better star-charts in order to have more accurate time-keeping and navigation became imperative. In order to meet this demand for increased accuracy, the method of epicycles outlined by Ptolemy became more and more complicated, and was extended in different ways by different mathematical astronomers until it became hard to say what the Ptolemaic system was. Instead there were a whole set of different calculations all based on the Ptolemaic system, all getting increasingly complicated. And none of them quite agreed with the full range of good naked-eye observations. (p. 139. Most of the material in this post is from Thomas Kuhn’s book The Copernican Revolution and page numbers are from that book.) [Read more…]