One of the problems in the presentation of cultural rank theory is that it is easy to think of it as a step function. When David Hays and I wrote the original papers, starting with “The Evolution of Cognition” (1990), it was all we could do to differentiate one rank from another. I would now like to take the Copernican Revolution in astronomy as an example of a more gradual transition.
For the Copernican moment is only the first of three moments in the transition from a Rank 2 account of the solar system to a Rank 3 account. The Ptolemaic model assumed without question that the earth was the center of the solar system. The geometry of the movements of the sun, the moon, and the other planets was then calculated accordingly. The movement to the Copernican model involved two conceptual changes. The first change, without which the second was impossible, was to give up the idea that the earth had to the center of the system. That was primarily a philosophical or metaphysical commitment, not a geometric one. Once that metaphysical commitment was dropped, astronomers were free to reorganize the geometry of the system with the sun at the center, the second change. Without this change the second and third changes would have been impossible.
The second change, then, was Kepler’s, dropping uniform circular motion in favor of elliptical motion. To be sure, uniform circular motion had a certainly philosophical attraction, but that was not so strong as that of geocentricism. Giving it up was accordingly easier. Once Kepler had done that it was easy to simplify the whole system by using elliptical orbits, thereby getting rid of the collection of equants and epicycles needed to make circular motion work.
The stage was now set for Newton’s contribution, which was to derive the elliptical orbits from his theory of gravity and the laws of motion. Now the geometry of the solar system was the outcome of physical laws, not merely a convenient description.
Now we need to work out how the conceptual ontology of the system changed from one version to the next. That’s tricky. And it’s something I’ve not thought about before. As a first guess, I’d saw that the planetary orbit is the object we should be thinking about. We can think of the orbit as an assignment between a set of observations and a geometry.
It’s not clear to me how we should characterize either the observations or the geometry. Each observation is a position in the sky and the time of day at which that position was recorded. Conceptually, is that assignment or componentiation? How do we characterize the geometry? How do we construct conic sections in classical compass-and-straight-edge geometry? We’ve got the focal point, or points, on the one hand and an eccentricity for the curve on other hand. Again, is that assignment or componentiation? I’m not sure, but I’m inclined to go with assignment in both cases.
However we handle that, there’s also the relationship between that complex and choice of center point, earth or sun. What’s that about? I’m thinking that’s about the relationship between our perceptual frame of reference and our analytical frame of reference, however we want to characterize that.
Finally, we have Newton’s gravity and laws of motion. That’s another conceptual complex to be added to the first two: frame of reference and geometry. The Newtonian component doesn’t even enter into the Ptolemaic, basic Copernican, and basic Keplerian schemes. Just how to handle this in terms of conceptual structure, that’s more than I can deal with in this casual note.
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