The Ptoloemaic system can be made as accurate as the Copernican system , so long as you keep adding epicycles. One of the things that tells us is that is that there is more to truth than observational accuracy. They other is that simplicity is important, and probably important for determining which observationally accurate theory is the truest.
I’m sure they could if you’re willing to sum up an infinity of them. Epicycles are fundamentally equivalent to a Fourier series/transform. The only reason to drop them is that obviously they’re a very high complexity rule that can be much more efficiently compressed if you only look at the phenomenon in a different reference frame.
I think those are good lessons to learn from the episode, but it should be pointed out that Copernicus’ model also required epicycles in order to achieve approximately the same predictive accuracy as the most widely used Ptolemaic systems. Sometimes later, Kepler-inspired corrected versions of Copernicus’ model, are projected back into the past making the history both less accurate and interesting, but more able fit a simplistic morality tale.
The Ptoloemaic system can be made as accurate as the Copernican system , so long as you keep adding epicycles. One of the things that tells us is that is that there is more to truth than observational accuracy. They other is that simplicity is important, and probably important for determining which observationally accurate theory is the truest.
The Copernican system actually had more epicycles than the Ptolemaic one.
But yes, you could keep adding epicycles to the Ptolemaic system and change parameters to match the accuracy even of today’s planetary movements.
But epicycles couldn’t explain hyperbolic movements of objects that only fly into the solar system once.
I’m sure they could if you’re willing to sum up an infinity of them. Epicycles are fundamentally equivalent to a Fourier series/transform. The only reason to drop them is that obviously they’re a very high complexity rule that can be much more efficiently compressed if you only look at the phenomenon in a different reference frame.
I think those are good lessons to learn from the episode, but it should be pointed out that Copernicus’ model also required epicycles in order to achieve approximately the same predictive accuracy as the most widely used Ptolemaic systems. Sometimes later, Kepler-inspired corrected versions of Copernicus’ model, are projected back into the past making the history both less accurate and interesting, but more able fit a simplistic morality tale.