Elegance, illustrated: heliocentrism vs geocentrism


#1

[Read the post]


#2

Ok, fine, we revolve around the sun, but the earth is still flat, right?


#3

I’m convinced: Geocentrisms is the much more interesting and therefor true model!


#4

Unfortunately the example is very flawed. Heliocentrism is NOT simpler than geocentrism if you don’t know Kepler’s discovery of elliptical orbits. To explain heliocentrism with combinations of circular orbits requires just as many epicycles as geocentrism - in fact I remember our lecturer telling us that Copernicus needed more epicycles because he was using observations more accurate than those of Ptolemaeus.
Of course, once you introduce elliptical orbits and Kepler’s laws of motion, you are left with a choice between the heliocentric system and the Tychonic system in which the Sun and all the other planets rotate around the Earth as a helicentric system. The total number of ellipses is the same in both cases but you are left with the odd question of why do Mars-Saturn have orbits around the Sun that go outside the Sun’s orbit around the Earth. At that point it might occur to you that perhaps the Earth goes round the Sun. If your observations become accurate enough you might also notice the Sun’s apparent wobbling caused by Jupiter, but that’s beyond the astronomy of the period.

tl;dr The images in the post seem to be comparing epicycles to ellipses, which is significantly different from helio versus geo centricity.


#5

The circular orbits and the geocentric orbits also fail to explain why/how the orbiting planets speed up and slow down, based on the planets’ distances from the sun. I can’t imagine the complexity of the circular and geocentric equations that would have to account for/predict for that.


#6

Part of the problem with epicycles is that they have too many degrees of freedom i.e. they don’t constrain the system enough to be predictive. For example, with epicycles, you can draw Homer Simpson:


#7

[quote=“doctorow, post:1, topic:71892”]
when you assume that all the bodies in our solar system are in orbit around the sun, rather than the other way around
[/quote] The other way around? You mean the sun orbiting around all the planets? That’s not what the second picture shows, it shows all bodies orbiting around the Earth.


#8

You brought a tear to this lecturer’s eye with that. Thanks.

As you say, Ptolemaic geocentrism was an astonishingly brutal mishmash of weird-ass spherical trigonometry, ancient-even-for-Ptolemy data points, and quick-and-dirty approximations. And Copernican heliocentrism was much worse, from a calculation standpoint! If this .gif here were about Copernicus, it’d have all the same weird epicyclic loops that the geocentric model does. Actually, it’d have more.

And don’t even get me started on that nutbag Kepler. :wink: Oh, sure, elliptical orbits make sense (once you have Tycho’s freakishly accurate naked-eye observations in your saddlebag). But he’s also talking about invisible cosmic icosahedrons the size of Jupiter’s orbit! And so forth. Everything in the history of science looks weird if you don’t understand that people had, you know, reasons for taking the flying intuitive leaps they took.

I know Cory’s not trying to actually rewrite history here, but it’s always worth refuting the great myths of the history of science when the opportunity presents itself. People in olden times weren’t dumber than us, weren’t less inherently curious, weren’t oppressèd by the evil church/gummint/superstitious mobs nearly so much as conventional wisdom has it, and so forth. The fact that we reach astonishingly different answers nowadays is fully explained by the fact that we begin from an astonishingly different starting point, one that is every bit as culture-bound as Ptolemy’s and which will look every bit as dumb to the subpar students of history of the future.


#9

Actually, that was the simpler part of the deal. Ptolemy and almost everyone who followed in his footsteps just put the center of the circle around which planets moved at a different point than the earth. Effectively it just makes the imaginary circle into a kind of crappy makeshift ellipse, with the Earth at one “focus” and the point around which any given planet orbits another, but it does the trick.

It only gets insanely complicated when you have to deal with retrograde motion via epicycles.


#10

I’ve heard this example (heliocentrism vs geocentrism) given as an illustration of Occam’s razor. The context of the point being made was that Occam’s razor isn’t meant to differentiate between an actual right or wrong assertion (the interpretation of it that most people seem to intend), but a heuristic in the utility of choosing between a model of more or less complexity, other things being mostly equal.


#11

I wish I’d said as much and I am delighted to have been partly responsible for such an informative post.

But I take a very small issue with you over Kepler. (I made the pilgrimage to his house once, btw.) He was no more a nutbag than was Newton (unless your wink is to indicate that this is ironic). His problem was that along with the new explanatory powers of maths went a world picture riddled with Aristotelianism, Platonism and various other isms, so much so that from the mindset of an educated person of the period, trying to explain the distances of the orbits based on a nesting of the Platonic solids was quite rational, just as Newton’s bibliochronology was quite rational. When I encounter educated mathematicians and engineers today who believe in Biblical literalism, I am reminded of the short distance we have come in men’s minds from shamans mounting to the heavens on their drums. (Actually now I read it more carefully I realise that you are being ironic and I’m duplicating your points. I’ll let this comment stand as a warning of over hasty reading, and because I like any excuse to write about Kepler.)


#12

It seems Bill didn’t invent it anyway Myth of Ockham’s Razor

But it’s pretty dead in the water of modern theoretical physics anyway, since all of String Theory and its offshoots are currently entia which are being fit praeter necessitatem. Part of me, the nasty part, wants String Theory to turn out to be another Ptolemaic planetary theory, because it has the same ability to produce models to fit the observations but with no experimental backing to suggest that there is any benefit from the huge structure.


#13

Flat and rectangular- I’ve seen the maps!


#14

Actually, thinking about it, this is a lot less than the audience is expected to swallow in any Star Wars film.

[Utterly, completely OT - how much did the Death Star makers get fined for releasing a product with such a serious design fault? And how did they organise the product recall on any other Death Stars out there?]


#15

The Tychonic system was one where all the planets but the Earth rotated around the Sun, and the Sun rotated around the Earth. It’s the sort of uncomfortable compromise you’d expect when the Ptolemaic system is obviously not working. I shudder to think what the math was like calculating those orbits.


#16

Yes, I left that to be understood by the reader but I’ve now edited it for clarity.


#17

Don’t be too hard on Tycho. Putting everything BUT the Earth going around the Sun made the math much simpler than a purely geocentric or heliocentric system.

What looks like a godawful guilty compromise to us, looked to his peers like a sensible fusion of two promising but unwieldy approaches.

But more importantly, Tycho was not trying to come up with a physical system of the cosmos. He was an instrumentalist, not a realist: he was concerned with finding numerical tricks that would predict where the little dots in the sky would go. For most astronomers of his era (and the preceding millennium or so) the physics of the celestial realm were either covered separately by the Aristotelian corpus, or just something to shrug about.


#18

I’d slip in a bit of disagreement there. our current view of the universe is manifestly and testably less wrong than Ptolemy’s. We can accept that there are errors in both (in fact we implicitly do this whenever we try to improve upon any of our theories) but to write off anything that is inaccurate without seeing the progress towards a more accurate understanding of the universe is simply wrong.
This is like saying that Aristotelian gravity and Newtonian gravity are both “wrong”. Sure, subsequent theories have surpassed both of them, but the relative wrongness of both is very different, and Newtonian gravity is objectively better at describing the universe.


#19

I think @semiotix is not saying that our view is equivalent to that of Ptolemaeus. It models a lot more features of orbits, for one thing, and it is astonishingly precise for another - it gets satellites to match orbits with comets.
But although our physics gives very precise, accurate and testable results we have no idea of whether our understanding of, for instance, space-time is actually correct. The complexity of the Feynman diagram approach to QED, the enormous architecture of String Theory and the obvious question “Why?” for the group theory approach to particle physics - these all suggest that we are missing something big, just as Ptolemaeus was missing the central place of the Sun and Kepler was missing gravity - which was at the bottom of his idea of the nested solids.

That’s exactly our problem - what does “objective” mean? The equations of central force given an inverse square law and a posited gravitational field give accurate results. The question is whether this works because reality “is like that” or because we just happen to have chosen a model that fits. Does General Relativity imply that gravity is not “real”, just a convenient model of how mass warps spacetime?


#20

Yes, because the universe is a two-dimensional hologram!