The wheel in the sky keeps on turning.

Having recently mostly blogged about bad popular history of science and questions of historiography and methodology I thought it was time to return to writing about some real history of science. Back in 2010, I blogged about the fact that there were not just two cosmological-astronomical systems competing with each other at the beginning of the seventeenth century, as commonly believed and also falsely claimed by Galileo (Copernicus contra Ptolemaeus), but a whole menagerie of systems battling it out for ascendency till Kepler’s elliptical heliocentrism won out in about 1660. Another common misconception is that there was only one geocentric astronomical system inherited from antiquity. There were in fact several competing systems and I would now like to sketch the history of one of these systems that usually gets ignored in discussions on the subject but proved very resilient from its conception in the sixth century BCE up to the middle of the seventeenth century CE, the geocentric-geokinetic system.

In this system the earth is at the centre of the cosmos but it is not stationary; it rotates on its polar axis. To understand how this system came into being we have to take a look at the original Greek two spheres model of the cosmos, which originated in the sixth century BCE. In this model the earth is a sphere at the centre of the cosmos the outer limits of which are delineated by the sphere of the fixed stars. In the standard version of this model the earth is stationary but the sphere of the fixed stars rotates from east to west completing a complete rotation in twenty-four hours. In the geocentric-geokinetic model the sphere of the fixed stars is stationary whereas the earth rotates around its polar axis once a day. Both rotations are known technically as diurnal rotations but for simplicities sake we shall refer to the geocentric-geokinetic model as the diurnal rotation model.

The arguments proffered in defence of the diurnal rotation model are interesting because although they are based on a false premise, they are in fact strictly physical arguments. The false premise is that the sphere of the fixed stars really exists and is not just an optical illusion. Already in the third century the Greeks had a fairly accurate idea of the true size of the earth and although they had no idea how far away the stars really were they knew that the earth was incredibly small in comparison to the sphere of the fixed stars. In the second century CE Ptolemaeus writes in his Syntaxis Mathematiké:

Moreover, the earth has, to the senses, the ratio of a point to the distance of the sphere of the so-called fixed stars. [The so-called refers to the precession of the equinox meaning the sphere is not fixed but shifts if only very slightly]

He then brings a series of mathematical arguments based on optical perceptions that the earth has no perceptible size in relation to the distance of the heavens.

Both arguments in favour of earthly rotation are based on this immense difference in size of the two spheres. The first argument says that it is more probably that the comparatively small mass of the earth rotates rather than he immeasurably greater mass of the sphere of the fixed stars. The second argument is based on velocity. A point on the equator has a velocity of approximately 1600 kmph. If the sphere of the fixed stars only had a radius 1000 times greater than the earth then a point on its equator would have a velocity one million times greater and would simply fly apart. Both arguments are very convincing but are countered by the standard problems of the fact that we experience no sense of movement on the surface of the earth; no headwind etc. as I have previously discussed here. In general the latter facts dominated and earthly rotation was generally rejected. However it had its proponents and remained in the mainstream cosmological discussions until heliocentrism finally won out in the seventeenth century.

Although the theory was supposedly held and discussed earlier the earliest known major proponent of diurnal rotation was Heracleides a fourth century BCE pupil of Plato. In a work falsely attributed to Plutarch, The Opinions of the Philosophers it is written that:

Heraclides of Pontus…makes the earth move not in a progressive motion, but like a wheel in a rotation from west to east about its own centre.

With less detail the same view is attributed earlier to the Pythagoreans Hicetas and Ecphantos about whom almost nothing is known. Cicero attributes the theory to Hicetas and even to Plato in the Timaeus but says that the passage is obscure. He is indeed right in saying that Plato is here very obscure and it is in fact difficult to determine if he believed in earthly rotation or not; Copernicus, in the 16^th century, seemed to think that he did. Seneca thought the theory worthy of serious consideration

That this system was still being discussed in the second century CE can be seen in the Syntaxis Mathematiké where Ptolemaeus writes:

But certain people […] they supposed the heavens to remain motionless, and the earth to revolve from west to east about the same axis [as the heavens] making approximately one revolution each day; …

He then goes on to produce a series of arguments contradicting this possibility.

In the early middle ages the early Christian authors of course rejected the theory. However in the fifth century CE the widely read and highly influential Indian mathematician and astronomer Aryabhata was an enthusiastic supporter of the theory bringing a relativity theory to justify himself:

As a man in a boat going forward sees a stationary object moving backwards, just so at Lanka [the earth’s equator] a man sees the stationary asterisms [stars] moving backwards [westward] in a straight line.

It is often falsely claimed that Aryabhata propagated a heliocentric system but although he clearly supports diurnal rotation for the earth he never mentions annual rotation of the earth around the sun.

In the seventh century his landsman and fellow mathematician and astronomer Brahmagupta who was equally wide read and influential, especial amongst the mediaeval Islamic astronomers, described the theory but rejected it.

In the high middle ages the theory was discussed by several Islamic astronomers. In the fourteenth century two of the so-called Paris physicists Jean Buridan and Nicole Oresme both discussed the theory very favourable in their writings. Both of them acknowledged that following the principle of simplicity, now known as Occam’s razor, diurnal rotation of the earth was preferable to diurnal rotation of the sphere of the fixed stars. In fact in his philosophical discussion of the principle of simplicity Buridan uses exactly this theory as an example of the principle in operation. Both of them, like Aryabhata, also drew upon a relativity of motion argument using moving ships to explain the apparent motion of the sphere of the fixed stars. Having come this far, both of them then reject the theory on the grounds of tradition.

In the fifteenth century Pierre d’Ailly discusses the theory in order to reject it. Nicholas of Cusa subjects the theory to the same very favourable discussion as Buridan and Oresme like them however finally rejecting it on grounds of tradition.

In the sixteenth century Nicolaus Raimers Baer published, in 1588, the first so-called Tychonic, heliocentric-geocentric, model of the cosmos in which the planets orbit the sun but the moon and the sun both orbit the earth but in his system as opposed to Tycho’s own system the earth has diurnal rotation. In 1600 William Gilbert published his De Magnete a book that was highly influential on the development of science in the first half of the seventeenth century. In the final section of his book Gilbert posits a geocentric system with diurnal rotation. His justification for this model is his, mistaken, believe that a terrella, i.e. a spherical magnet, when suspended will continue to rotate. Having to his own satisfaction demonstrated that the earth is a large spherical magnet it too would rotate on its axis. The widespread popularity of Gilberts book was a major contributing factor to the fact that when a heliocentric-geocentric system became the primary accepted model of the cosmos between approximately 1620 and 1660 it was Raimers Baer’s system with diurnal rotation rather than Tycho’s static one.

I personally think that it is very interesting that throughout history people were more easily prepared to accept a moving earth rotating around its own axis than one hurtling through space around the sun.