4 ms·

> The perturbative expansion is created by adding successive corrections to the simplified problem. Wait, so the Theory of Epicycles is morally a Perturbation

by platz 4y ago

> The perturbative expansion is created by adding successive corrections to the simplified problem. Wait, so the Theory of Epicycles is morally a Perturbation Theory? (disregarding matching evidence from relativistic effects yadda yadda). In that sense —morally speaking— Epicycles at the time doesn't sound that like it was that crazy to do scientifically. Generally speaking, Epicycles would be on the same level as how perturbation theory is used in quantum mechanics.

Sniffnoy 4y ago
The thing to note here is that the theory of epicycles was never actually a thing; contrary to popular belief, geocentric astronomy did not fix its problems by adding additional layers of epicycles. It had one layer of epicycles, that was it; it did have additional complications, in the form of the eccentric and the equant, but these additional complications were not additional layers of epicycles that could be stacked arbitrarily. (Copernicus may have used a second layer of epicycles in his heliocentric system, which eliminated the equant (but not, I believe, the eccentric)? Admittedly two does suggest the possibility of generalizing in a way that one doesn't, but I don't think that generalization was ever performed at the time before Kepler made the whole thing irrelevant.) Had it been used, it basically would have been Fourier series, yeah! I don't know whether that counts as "perturbation theory" proper. But it's worth noting that the real development didn't happen that way, and the further corrections that were actually used were the eccentric and the equant, not further epicycles!
- platz 4y ago
  interesting history, thanks! I was mainly noting the "recursion"/series similarities, yes. but didn't know the complications from epicycles were more varied in nature.
6gvONxR4sf7o 4y ago
Not exactly. The interesting thing with perturbation theory as I remember it is that you have a series of infinitesimal perturbations, not just any old perturbations.
hpcjoe 4y ago
Basically ... yes. This is one of my arguments about the scientific method in general. You start with something you can't really explain, that seems to match data a bit better than the previous theory. You keep refining it, and eventually someone (often someone else) derives an insight from this work. I note this, as most of the popularizations of solar system astronomical history I'd seen, generally derided epicycles as a bad thing. They weren't. They were a sort of perturbation theory. One that generated other problems. But still did a somewhat better job than the (at the time) accepted theory.

by platz 4y ago

Sniffnoy 4y ago

The thing to note here is that the theory of epicycles was never actually a thing; contrary to popular belief, geocentric astronomy did not fix its problems by adding additional layers of epicycles. It had one layer of epicycles, that was it; it did have additional complications, in the form of the eccentric and the equant, but these additional complications were not additional layers of epicycles that could be stacked arbitrarily. (Copernicus may have used a second layer of epicycles in his heliocentric system, which eliminated the equant (but not, I believe, the eccentric)? Admittedly two does suggest the possibility of generalizing in a way that one doesn't, but I don't think that generalization was ever performed at the time before Kepler made the whole thing irrelevant.) Had it been used, it basically would have been Fourier series, yeah! I don't know whether that counts as "perturbation theory" proper. But it's worth noting that the real development didn't happen that way, and the further corrections that were actually used were the eccentric and the equant, not further epicycles!

platz 4y ago
interesting history, thanks! I was mainly noting the "recursion"/series similarities, yes. but didn't know the complications from epicycles were more varied in nature.

6gvONxR4sf7o 4y ago

Not exactly. The interesting thing with perturbation theory as I remember it is that you have a series of infinitesimal perturbations, not just any old perturbations.

hpcjoe 4y ago

Basically ... yes. This is one of my arguments about the scientific method in general. You start with something you can't really explain, that seems to match data a bit better than the previous theory. You keep refining it, and eventually someone (often someone else) derives an insight from this work. I note this, as most of the popularizations of solar system astronomical history I'd seen, generally derided epicycles as a bad thing. They weren't. They were a sort of perturbation theory. One that generated other problems. But still did a somewhat better job than the (at the time) accepted theory.