Notes on “the difference between Pre-Copernican and Copernican heliocentrism”

A new paper in the Archive for History of Exact Sciences by Christián Carman argues that we have greatly overestimated classical Greek understanding of heliocentrism. According to Carman, “pre-Copernican heliocentrisms (that of Aristarchus, for example) have all the disadvantages and none of the advantages of Copernican heliocentrism,” because they postulated only that the earth revolves around the sun, not, as has commonly been assumed, that all the other planets do so as well. This supposedly “explain[s] why Copernicus’s heliocentrism was accepted …, while pre-Copernican heliocentrism” was not.

I think Carman is wrong. I think his argument is very implausible for an obvious reason that he does not acknowledge. Namely: Why would Aristarchus have affirmed and written a treatise on heliocentrism if it had nothing but disadvantages? What possible reason could he have had done for doing so? None, in fact. Yet this is exactly what Carman proposes.

Let’s go though it from the beginning. The basic facts are as follows. Copernicus’s heliocentric system has a number of advantages, including the determination of planetary distances. It also has a number of disadvantages, notably the absence of annual parallax, which means that the stars must be very far away to explain why they don’t look sometimes close and sometimes more distant as the earth changes position in the course of a year. In other words, there is a lot of “wasted space” in the universe. This was commonly considered implausible, and hence an argument against heliocentrism.

Aristarchus wrote a treatise arguing that the earth revolves around the sun. Archimedes mentions it when discussing the size of the universe, in a way that shows that Aristarchus was well aware of the parallax issue.

The great bulk of first-rate Greek astronomical works are no longer extant, including Aristarchus’s treatise on heliocentrism and virtually everything from the very active century following it (which could very well have included a dozen skilled heliocentrists for all we know).

According to Carman, Aristarchus’s treatise most likely concerned only the sun and the earth and said nothing about the planets. Or, if it did consider the planets, it most likely made the planets go around the earth rather than around the sun. Either way, the treatise would amount to nothing but a trivial point about relativity of motion, namely that A moving in a circle about B is equivalent in terms of relative positions to B moving in a circle about A. Thus either hypothesis could account for the same phenomena.

I say: there is no reason for Aristarchus to write such a treatise, and plenty of reasons for him not to. For one thing, the result in question is rather trivial and has nothing to do with the sun and the earth specifically—it’s a result about circular motion generally. Indeed, as Carman himself notes, it is found as such in Euclid’s Optics. Carman somehow tries to construe this as support for his reading: “Aristarchus’s treatise on Heliocentrism could be understood as an application of these propositions of Euclid’s.” This does not make sense to me. Of course one possibility in Euclid’s theorem is to take A=sun and B=earth. How could you possibly fill an entire treatise making this elementary point that I just expressed in a single sentence? Furthermore, why apply it to the sun and the earth, rather than, say, the earth and the moon?

Which brings us to the core problem of Carman’s account. Let’s say for the sake of argument that, as Carman supposes, Aristarchus’s treatise only talked about the earth-sun system and proved that either orbiting the other would give rise to the same phenomena as far as their relative positions are concerned. He would then have faced the inevitable and obvious follow-up question: Which of the two hypotheses is the right one?

How would Aristarchus have answered this question? As far as one can tell from Carman’s account, only one relevant consideration was known to Aristarchus: the parallax problem, which he explicitly recognised, as Carman himself admits. This strongly suggests that it is the earth that is stationary. Thus Aristarchus should clearly have concluded against heliocentrism.

Yet we know for a fact that Aristarchus not only discussed the hypothesis of the earth’s motion about the sun, but also asserted it as physical reality, as Carman also admits. Why? Why would Aristarchus write a treatise proposing this bold hypothesis, discuss a major argument against it (the parallax argument) and no arguments for it, and then conclude that the hypothesis is true? And why, furthermore, would Archimedes, who was perhaps the greatest mathematician of all time, cite this treatise with tacit approval as a viable description of physical reality? It makes no sense.

The only reasonable explanation is that Aristarchus recognised an advantage of placing the sun in center. And the obvious guess for what this was is that he saw the same advantages as Copernicus did, including the argument from planetary distances. Indeed, we even have Aristarchus’s only surviving treatise on the relative distances of the sun, earth, and moon, which proves that he was a highly competent mathematician very much concerned with celestial distances. What are the odds that, despite this, he somehow failed to put two and two together and make the straightforward connection between his heliocentrism in one treatise and his preoccupation with celestial distances in the other? It seems to me extremely unlikely that this connection could somehow have escaped the attention of Aristarchus, not to mention the century of highly competent mathematical astronomers who followed him.

Furthermore, note that Aristarchus’s surviving treatise also treats the sizes of the sun, earth, and moon. Combined with his heliocentric hypothesis, this means that smaller bodies orbit bigger ones, rather than conversely as in the geocentric system. This is arguably a physical plausibility argument in favour of the heliocentric theory. Again it is very difficult to imagine that this could somehow have escaped Aristarchus’s attention even though it was right under his nose. Much more likely is that Aristarchus explicitly made this connection too, which would immediately have suggested to him that the planets revolve around the sun as well.