As we try to make sense of the ancient model for the movements of the heavenly bodies, the most difficult conceptual leap (at least for this student of the mysteries) is the use of spheres-within-spheres to explain retrograde motion. It will be much easier to visual a planet moving backward against the star background when we turn to epicycles with Ptolemy. But we can'tjust dismiss the older model--it greatly influenced Copernicus. Let's see what it tells us about the culture that conceived it.

Plato and Eudoxus introduced concentric (or 'homocentric') spheres as a way of explaining such phenomena as retrograde motion.

I find it helpful to follow the genesis of this conception in Plato's work. The fundamental assumptions appear to be 'Pythagorean.'

In the 6th c. BC, Pythagoras organized a community of ascetics on Samos (just up the coast from Miletus) and later transferred his movement to S. Italy. The fundamental doctrine of Pythagoras and his followers was that Number organizes the world in harmonic ratios. All existence is driven by mathematical order, including the periods of purification beyond this life and rebirth into the next. The soul is a harmony and a piece of the World-Soul.

This Pythagorean numerology permeates Plato's work, most famously in the last book of the Republic where he imagines a hero returned from a near-death journey of the soul to tell of the elaborate geometry of the cosmos. It is here in the so-called Myth of Er that we get the picture of a vast beam of light forming the axis of the universe and around it the heavenly spheres are seated like nesting bowls, spinning at different speeds. Apparently each planet is carried around on the rim of its bowl.

Plato takes his metaphor from primitive textiles: the 'spindle of Necessity' is like the tool with which a weaver spins and gathers thread. This choice of metaphor is partly traditional: the Greeks spoke of the Fates--or better 'Portioners'--as old women spinning and measuring the span of a man's life. The nesting bowls of the planetary spheres takes the place of the 'whorl' or balancing top that stabilizes the spinning spindle.

That may not be particularly helpful for visualizing retrograde motion. So let's go one step further. Plato is pretty good at giving us mental exercises that lead us along to his concepts. And luckily we have one in the late cosmological essay Timaeus. Here he wants us to visualize not the whole sphere or bowl but just the band or hoop that carries the planet through its motions.

In Timaeus he describes the creation of the world as the work of a great creator god, the Craftsman--demiourgos. The Craftsman builds the cosmos in the form of an organism, a living creature (as mythic Prometheus made Man). He starts by framing the Soul with primordial material of Sameness and Otherness (or Difference) plus an amalgam of the two. He mixes these materials (as a smelter might make an alloy) and then hammers it into strips or bands, then measures to precise dimensions and links one end to the other to make circles. These circles of varying diameter are then joined, each to the next largest, at various axes.

Now what we have here is a set of concentric circles that spin at different angles. The planet rides on its spinning hoop. F ocus on just one pair of spheres. Try to follow the movement of the planet P as it would move on its own circle, while the outer circle of the stars turns in the opposite direction. You are at the center of the sphere.

The illustration is from M.R. Wright, Cosmology in Antiquity.


If you still can't visualize the planet moving backward as seen from the earth at the center, try to follow Plato's instructions: do as he describes the Craftsman doing. Use strips of poster board or whatever's handy (pure Sameness and Otherness being hard to come by). Make two hoops such that one fits closely inside the other; attach at an axis; mark any point on the inner hoop to represent the planet P; and turn the hoops in opposite directions (and at different speeds).

But the real puzzle is:

How did Plato & Co. even conceive of this mechanism? Where in the realm of human experience or imagination did they hit upon the notion of concentric bands or bowls? 

Basically try to reconstruct the assumptions that went into this paradigm.




[The following Questions 4-6 are for further study, with Kuhn's Copernican Revolution]

4) The theory that Ptolemy adopted in the 2nd c. AD was invented (more or less) when? Or by whom?

Try to explain in your own words the key terms:

deferent ....epicycle .... eccentric ....equant.


5) What was the function of 'minor epicycles' such as posited for the sun? (=What do they explain?)

What is the function of an 'equant' (=What does it explain?)


6) In the long paragraph p. 75, Kuhn gives an outline of 'the logical structure of a scientific revolution,' an influential model that he would develop in later work. In your own words, how does one theory overturn another.



Plato's Cosmology and the Problem of the Planets