"philosophy is questions that may never be answered
religion is answers that may never be questioned"
- anonymous; some guy off a American football Buccaneers messageboard said this!
Many people recently have tried to call certainly string theory an epicycle theory. Some go so far as to call out Quantum Mechanics and Einstein's theories of relativity 'epicycle.' Maybe they are in some ways. Quantum Mechanics for one went through several stages of re-expression(equivalent expressions); pretty much, there was Bohr's combining of Planck's constant with Rutherford's experimental findings(and calculating the spectral formula experimentally determined decades earlier), then Heisenberg's Matrices, then Shroedinger's wave mechanics, and then more or less Paul Dirac's combining of special relativity with quantum mechanics(which predicted anti-matter). So, one could say that all the theories of quantum mechanics before Paul Dirac's were epicycle. One major difference between the quantum mechanics theories and Ptolemaic epicycles is that those quantum mechanics stages were confirmed by experiment. Ptolemy's epicycles were never really confirmed; they were always adding one device after another to fix this problem or that problem. It's a subtle difference.
I bring this up because Bertrand Russel points out that Einstein's General theory of Relativity essentially made Isaac Newton's F=ma a very terrestrial mathematical view. It's almost the mathematical equivalent of someone going out, looking around and concluding the Earth is flat. Someone that hasn't been on a boat long enough and travelled around enough to notice some odd occurences. So the thought came to me that F=ma is Ptolemaic like. Once again, the difference between F-ma and Ptolemy's epicycles is one has been confirmed scientifically. Another major difference is that Isaac Newton's F=ma wasn't necessarily disproven, it was put in its place and integrated in a more general theory - Einstein's General theory of Relativty.
I suppose I should finish there, but somewhat related is how John Stillwell in his "Mathematics and Its History" points out that Newton's mechanics is a very local theory. The inverse law works to describe each next point locally. As we know today starting from Henry Poincare, the three body problem leads to chaotic dynamics. Topology was established as a field by Henry Poincare to deal with this. If Newton couldn't do his differential calculus, the mechanics he created and led to the industrial revolution never would have happened. This reminds me of a point I made in the previous incarnation of this blog.
The problem Kepler had with his Platonic solids model of the solar system was Mars orbit was odd. Later after he tried the ellipse conic section, he saw that Mars orbit is eight degrees from perfect circularity. If Mars orbit had been imperceptively circular when Kepler came along, he never would have come up with his three laws. Newton never would of thought to derive them from any inverse square law. The industrial revolution never would have happened. Or it wouldn't have gotten far. It's just like the agricultural cultures for thousands of years before . . . where, when the crops didn't come, they'd resort to their nomad, hunter-gatherer skills for awhile, then try it again(see Silverman and Finkelstein's "The Bible Unearthed").
Well, Newton might have thought to figure out the motions of the planets; but, it might have taken far longer without Kepler already having found the three laws of planetary motion. Newton would need to do all the astronomical observations, struggle with what's the right model(ellipses). Still, Newton's inverse square law might not have been taken seriously. Before Newton does all the astronomy needed, or someone else, the cultures would have been destroying each other over all kinds of problems that can only be solved by a more scientific technology.