Thursday, August 22, 2013

thought for the day/Ptolemaic epicycle theories

"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.


  1. Historically this is utterly inaccurate, as any history of astronomy will show. (A good recent book is James Evans, The History and Practice of Ancient Astronomy, 1998.)

    (1) Ptolemaic astronomy matched observation rather well, given the observational instruments available at the time.

    (2) "they were always adding one device after another to fix this problem or that problem" --- nope, pure myth. The Alfonsine astronomical tables of the 13th century were based on the same models as Ptolemy's Almagest of the 2nd century. There is one minor exception, trepidation, which led to two extra cycles in the whole system, but that was it. Two extra cycles in over 1000 years.

    (3) "put in its place and integrated in a more general theory" --- you can say the same about Ptolemaic theory. The basic Ptolemaic mechanism, the eccentric deferent and epicycle with equant, all have corresponding elements in Kepler's theory (his first two laws of planetary motion). The epicycle and deferent are really just the planet's orbit and the earth's orbit shuffled around a bit. The eccentricity of the deferent captures the most significant aspect of Kepler's elliptical orbit (numerically), namely the fact that the sun is at one focus. The shape of the orbits are very nearly circular for all the planets. And the equant is a pretty good approximation for Kepler's speed law (equal areas in equal times).

    (4) The Copernican system (as opposed to the later Keplerian system) was no more accurate than the Ptolemaic system. Also, Copernicus had epicycles --- more than Ptolemy did!

    (5) I don't know what you mean by Mars' orbit having "eight degrees from perfect circularity"; the eccentricity of Mars' orbit is about one-tenth.

    Summing up, Ptolemaic astronomy was first-rate science, indeed the model and foundation for the science that succeeded it.

  2. Hello Michael Weiss,

    I remember thinking about how Ptolemy's epicycle theory had a certain mathematical value in the making of curves with interesting properties. I forget what they call it; but, imagine rolling a circle on a flat surface with a pencil at one point of the circle, the result is a special curve. Beyond that, Ptolemy's epicycle theory was never really confirmed observationaly. You put this condition and apparently take seriously that the theory predicted phenomenon within the ability of the instruments at the time(which would be pre-telescopic and certainly nowhere near as good as say Tycho Brahe, who's clearly under-rated from all the great science done since).

    You've brought up that the Copernicus theory was epicycle; I never suggested otherwise! I just didn't get that involved in this one short blog article. I think you're definitely jumping the gun a little bit.

  3. I feel you're reply has brought up something very interesting in terms of your idea that Kepler's laws were somehow based on the previous epicycle theory. I've never heard of that. I've read things like Koestler's "Sleepwalkers" and other books. Eight degree eccentricity has always been said. I just checked out wiki and find your bringing that up is good of you. That is very interesting indeed . . . I have Ptolemies Almagest; unfortunately, despite paying forty dollars for it, I got one that is in the worst shape I've seen a book. Paper has some gum in it; this book is gummed together. And so, I never got around to really looking through it. I need to buy another, but I just havn't got around to it. Your comments about Kepler and epicycles makes me really want to learn German because my copy of Kepler's Astronomy Nova is in German!

  4. Two extra cycles in a thousand years? That I feel is way off. I've heard like 36! And then you say, Copernicus had more epicycles than Ptolemy did; I can only suppose Copernicus had only two more . . .

    Ultimately, I'm thinking you're not getting a major point which maybe even I didn't quite make explicit(I may have assumed that those reading have read my entire blog; I for one get tired of restating points already made). In terms of the Ptolemaic theory, the reason why the Ptolemaic theory is the way it was is because people thought in terms of their current perspective. For instance, people have thought many times that the Earth is flat. Similarly, the Ptolemaic system comes from the human perception that the sun, moon and stars rotate around the Earth.