The main thrust of this chapter is Kepler exploring the ghosts in the shell. The topic is centered on these two diagrams:
The diagrams here are somewhat complicated, but are essentially two different ways of explaining the same thing: That objects in the sky move faster from night to night along some parts of their orbit than others. Ultimately, they’re functionally the same, but the argument that Kepler makes here is that they share certain metaphysical differences, all of which are untenable anyway.
The diagram on the left looks complicated, but only so because it is trying to display things at numerous times. Let’s start by breaking it down.
Since the diagram is the Ptolemaic model for the motion of the sun, that’s how I’ll present my diagrams.
First off a bit of terminology. The red path is known as the deferent. It’s the motion that carries the sun west to east along the background stars. In other words it’s the sphere that generates the “proper motion” we saw in Chapter 1. But because the Sun sometimes moves faster than other times, Ptolemy added an epicycle, a favorite tool of Greek astronomers. By varying the speed of the epicycles and the direction they rotated, all sorts of motion could be explained.
For the Sun, Ptolemy had the deferent rotating counter-clockwise and the epicycle rotating clockwise at an equal speed. In other words, the epicycle would rotate once for every rotation around the deferent.
Let’s look at what that would mean for when the sun made it 90º around:
Had the sun not been rotating on the epicycle, it would be to the left at this second position (just the same as how a clock hand would be pointed out). But since the deferent went 90º one way, the epicycle went 90º the other, restoring it to the “up” position on the epicycle from this view.
This pattern of the sun keeping its orientation on the epicycle carries through the entire path:
And if we connect the position of the sun at all points, we see it sketches out a new circle with a new center, shown in black. The Earth is now off center which forces the speed to change throughout the full cycle.
Here, I’ve stripped away the deferent and epicycles just leaving the actual path of the sun to illustrate why the sun appears to move faster. If you look at the angles coming out of the Earth, the ones in the lower half are > 90º. The ones above the Earth are < 90º. Since the motion around the center of that circle is uniform, this means that, from Earth, it has a longer arc length to traverse in the same amount of time. Therefore it appears faster.
So to summarize that first diagram, having a deferent with an epicycle rotating the other way at the same rate moves the Earth off center of the actual motion changing the perceived speed.
The second diagram somewhat says the same thing. But instead of worrying about epicycles, it simply moves the Earth off the center of the deferent. So the result of all the geometry is exactly the same. Kepler’s chosen a few different points around the edge for his second diagram, but the meaning is the same. But as I noted above, Kepler draws some metaphysical conclusions about each one.
The argument asks the question: What moves the object?
This begs another question on the nature of the spheres. For this, there were two main schools of thought. The first was that the spheres were solid and crystalline (transparent), but were definite physical objects. The second was that the spheres weren’t really objects, but more of zones where things happened and were immaterial.
As noted back in Chapter 1, Brahe had observed a comet that passed through the spheres which pretty much put the notion of physical spheres to bed. Kepler accepts this as authoritative but adds in an argument from Aristotle stating that the motion of the spheres was eternal and infinite and since no physical object could be eternal. So we clearly see that Kepler is in the camp of immaterial orbs meaning the celestial bodies could no longer be passively carried. Thus these bodies
complete their courses in the pure aether, just like birds in the air.
But how, since the physical sphere was abolished and could no longer guide them?
The only solution Kepler could see based on the arguments previously given by Ptolemy and others, was to assign an animate soul with just enough intelligence to carry out the task. This was briefly touched upon in the introduction. But Kepler is not a fan of this idea either.
The first argument against it is that perfect spherical motion is beyond the ability of such a soul, for even us advanced humans do not operate in circles. Rather all our muscles function only in straight lines, extending and contracting. Therefore Kepler concludes that a spirit carrying these bodies in perfect circles is impossible.
But even if Kepler was willing to grant some sort of animate intelligence that could determine a perfect circle, it would still need a central point by which to measure its difference and each model has the spirits moving around a point around which there is nothing. In the first model, the deferent circles the Earth, so at least there is a guidepost there that is always equidistant, but the spirit driving epicycle must then constantly know where the center of the epicycle is with nothing there to guide it.
Similarly, in the second model where epicycles are done away with, there is only one spirit guiding the planet. But this circle is no longer centered on the solid Earth which means the distance is constantly changing. So is the spirit not only capable of understanding a perfect circle, but also consistently calculating the distance to the only beacon by which it could measure?
For Kepler, this veers far too much into the realm of having an intelligent mind beyond just a simple soul to drive motion. Kepler dismisses the notion, stating
I am making these absurd assumptions in order to establish in the end the impossibility that every cause of a plaent’s motions inhere in its body or somewhere else in its orb, and to build a path for other less difficult forms of motions that are more readily persuasive.