Position and shape of the earth

Anaximander stated that the earth is at rest because of it being perfectly balanced in the middle of the universe, ‘in equilibrium’; it is equally distant to all points in the surrounding environment. Thus it has no reason to move either this way or that. This is how Hippolytus and Aristotle represent Anaximander’s view:

“The earth remains aloft, unsupported by anything⁴⁸, because of its equidistance from everything”

(Hippolytus, Refutation 1.6.3 = DK12 A11 = KRS 124)

“There are some who say that the earth remains in place because of similarity⁴⁹, as did Anaximander among the ancients; for a thing established in the middle, with a similar relationship to the extremes, has no reason to move up or down or laterally; but since it cannot proceed in opposite directions at the same time, it will necessarily remain where it is.” (Aristotle, De Caelo B.13, 295b11-16 = DK12 A26

= KRS 123)

Aristotle shows how ingenious Anaximander was when he explained why the earth was at rest. There are several interesting points about this statement: First, as pointed out by Kahn (1994:77) the mathematical knowledge implied by it. This statement must presuppose that the standard definition of a circle is “that which is in every way equidistant from the middle to the extremes”⁵⁰. But this is only presupposed if, as Kahn believes, Anaximander envisioned the earth as surrounded by a sphere. This seems like a well-founded interpretation of ‘being in the middle, with a similar relationship to the extremes’. There is however the statement by

Anaximander that the earth is like a stone column; its shape is like a cylinder with a flat surface:

48 In other translations ‘not dominated by anything’ (Kahn); ‘held up by nothing’ (KRS); ‘overpowered by nothing’ (Barnes); originally κρατουμένην from κρᾶτέω; to be strong, to rule, become master of, ruler over, conquer, subdue, be superior over, hold fast, to order, command (LS)

49 Or ‘symmetry’; originally ὁμοιότητα, from ὁμοίως; in like manner, like, alike (LS). This term is also translated ‘equilibrium’ (KRS) and ‘indifference’ (Guthrie).

50 The interpretation of a mathematical argument to the cosmological question Algra (1999:55) does not agree with; the ‘equilibrium’ of the argument does not have to be an equilibrium conceived of in purely mathematical terms. Elsewhere in Anaximander ‘equilibrium’ implies balance between the opposites, Algra argues.

“Its form is cylindrical, with a depth one third of its width” (Pseudo-Plutarch, Stromatesis 2 = DK12 A10 = 122A).

“Its shape is curved, round, similar to a drum of a column; of its flat surfaces we walk on one, and the other is on the opposite side” (Hippolytus, Refutation 1.6.3 = DK12 A11 = KRS 122B).

Now, this is either a minor mistake by Anaximander, him failing to acknowledge that a cylinder could not be equidistant from all surrounding points if surrounded by a sphere, or he actually envisioned the surrounding elements as cylindrical, mirroring the shape of the earth.

It appears that the former explanation is preferred among the scholars on Anaximander⁵¹. There is also the fragment of Pseudo-Plutarch (Stromateis 2 = KRS 121 = DK12 A10) which states that at the creation of this world “a sphere (σφαῖραν) of flame (…) was formed round the air surrounding the earth” which shows that Anaximander in fact described the earth at one point, at least, as surrounded by a sphere. There is also the use of the word κύκλος, meaning circle, ring, to describe several other phenomena of the heavens, as the heavenly bodies in reality are circles of fire and air⁵². The picture of the earth as a sphere within a spherical surrounding universe emerges in Plato’s Phaedo, thus making the symmetry of the Earth and the universe more complete:

“I am therefore persuaded that, in the first place, since the earth is round and in the middle of the heaven, is has no need either of Air or of any other Necessity on order not to fall, but the similarity of the heaven to itself in every way and the equilibrium of the earth suffice to hold it still” (Plato, Phaedo 108e-109a).

If we allow Anaximander to construct an element surrounding the earth that is cylindrical, the symmetry that he aspires to almost every point of his cosmology is succeeded, at least more so than in the case of a cylinder inside a sphere. But this rings untrue to a universe ‘similar to itself’, all points of the earth’s surface could be equally distant to its surroundings but its centre would be highly off-balanced. The natural equality and balance of the circle seems the more likely explanatory model for a Presocratic cosmologist. Rather then making every point on the earth’s surface equidistant from its surroundings, then, Anaximander made the centre of the earth equidistant, i.e. equidistant from all surrounding points of the spherical inner

51 Kahn (1994:92) quotes Diels in ascribing to Anaximander “the first, if still imperfect, indication of the theory of geocentric spheres which dominated the astronomy of antiquity and of the middle ages.”

52 cf. KRS 126, 127,128

surface of the universe. This is the standard way of interpreting Anaximander’s thesis of the earth’s stability⁵³.

Secondly, Anaximander disqualifies the problem stated by Thales when he answered his own question ‘why does the earth not fall?’ by citing that the earth rested on water. Anaximander understood that there was no reason the earth should fall at all, if the universe was

symmetrical. The disqualification of the problem of earth’s stability and the solution offered are truly ingenious inventions by Anaximander. The disqualification of the common sense-supported idea that all bodies fall downwards, in the direction we know as ‘down’, that is, towards the centre of the earth, is unparalleled at least until fully developed atomism emerges.

Even the atomist Epicurus said that the natural behaviour of the atoms is to fall “downwards”.

The explanation of as to why the earth is at rest seems to be supported by a notion very similar to Leibniz’ Principle of Sufficient Reason: Everything which is true or real implies a reason why it is so and not otherwise, as this principle is formulated by Kahn (1997:77). If there is no sufficient reason for anything to happen, we need not explain why it did not.⁵⁴ The use of the Principle dictates that every event has an explanation and a reason, thus indicating that Anaximander has in fact discovered that all things have causes. It is tempting to conclude so, but it seems premature. For Anaximander does not say that all things must have causes, just the earth and its stability. Second, we do not know how much is Aristotle and how much is Anaximander in this explanation. I will return to these questions in part 3.5.1 The Principle of Sufficient Reason.

53 KRS gives a slightly diverging interpretation when they claim that the earth is in equidistance to the rings of the heavenly bodies (2004:134), and not equidistant to the inner ring of the surrounding universe, or to the Unlimited itself. This interpretation I cannot agree with; while Simplicius wants the earth to be equidistant to “all things”, thus supporting the interpretation of KRS’, Aristotle says that it is “equally related to the extremes” and these are not the heavenly rings, but rather the extremities of the surrounding circle, i.e. every point of the circle.

The idea that earth is balanced between heavenly bodies seems to me too closely related to ideas of ‘gravitational pull’ or some other notion of cosmic bodies having the power to draw other cosmic bodies to themselves. There is no reason to assume Anaximander held any such notions.

54 This principle is later used by the Atomists, using the explanatory rule of ou mallon, ‘no more’, as a means to claim sceptical indifference to an issue: some say p, some say not-p, hence there is ou mallon reason to chose p rather than not-p. Democritus used the slogan-like rule to express support for the Atomistic ban on certain perceptual properties in objects; as opinions on sense-perception differs, the object is neither this nor that, according to the rule of ou mallon (Hankinson 1998:209-211).