The first is overlooking the issue of overfitting using hand calculation and imperfect observations. The calculated “best fit” for the data available did involved adding a bunch of epicycles and there was no theoretical reason to avoid doing so.
The second is playing fast and loose with a fat line drawn over a squiggly line based on a better model. It’s being mathematically rigorous but intentionally deceptive. You can fairly trivially construct a set of epicycles to fit some desired shape, but working backwards from observation there’s nothing guiding you to the most elegant possible solution for a given situation.
The first is overlooking the issue of overfitting using hand calculation and imperfect observations. The calculated “best fit” for the data available did involved adding a bunch of epicycles and there was no theoretical reason to avoid doing so.
The second is playing fast and loose with a fat line drawn over a squiggly line based on a better model. It’s being mathematically rigorous but intentionally deceptive. You can fairly trivially construct a set of epicycles to fit some desired shape, but working backwards from observation there’s nothing guiding you to the most elegant possible solution for a given situation.