Dirk Couprie

In Book 6 of his Christian Topography, Cosmas Indicopleustes, the famous defender of the flatness of the earth who lived in the sixth century A.D., intended to prove that the sun is much smaller than the earth. Cosmas applied to his flat earth the ancient Greek geographical idea of κλίματα (climates) on a spherical earth. This is not the place to elaborate on this concept, so I quote the most essential characteristics from a recent article: “The term κλίμα originates from the verb κλίνω and thus was intended to note the angle of inclination of the celestial sphere and the terrestrial latitude characterized by this angle (…) and in most cases, it can be safely be translated as ‘latitude.’” “There were “two ways two express the latitude numerically: (1) by the ratio of the gnomon to the shadow of its equinox, and (2) by the length of the longest or shortest day (or night) at the solstice, or by their ratio.” Sometimes, the term is used as a synonym for ‘zone,’ to divide the spherical earth from north to south into parallel zones of equal width. In this sense, it was used in Chap. 10.1007/978-3-319-97052-3_8, Fig. 8.2c.

The flat earth cosmology of the Presocratics is not always easy to understand. The interpretation of Xenophanes’ ideas on cosmology in particular is notoriously difficult. This has led to the suggestion that Xenophanes allowed himself a certain degree of fantasy and possibly humor and irony. Moreover, his bizarre original statements would have led to misunderstandings on the part of the doxographers. One might add: as well as confusion among modern scholars. Most of Xenophanes’ cosmological teachings have come to us through the reports of later authors. Only one of them is documented by a quotation from his poem:Γαίης μὲν τόδε πεῖρας ἄνω παρὰ ποσσὶν ὁρᾶταιἠέρι προσπλάζον‚ τὸ κάτω δ᾽ ἐς ἄπειρον ἱκνεῖται.

One of the strangest theories, combined with one of the most enigmatic images in Presocratic cosmology, which have puzzled many scholars, is ascribed to Anaximenes. According to him, says Hippolytus, the sun and the other celestial bodies do not go underneath the earth, but move around it like a felt hat (or a turban, or a ribbon) around our head:(Anaximenes) denies that the heavenly bodies move under (ὑπὸ) the earth, as others suppose, but he says they turn around (περὶ) the earth, like a felt cap (πιλίον) turns around our head (περὶ τὴν ἡμετέραν κεφαλὴν στρέφεται). The sun is hidden not by going under the earth, but by being covered by the higher parts of the earth (ὑπὸ τῶν τῆς γῆς ὑψηλοτέρων μερῶν) and by being a greater distance away from us (διὰ τὴν πλείονα ἡμῶν αὐτοῦ γενομένων ἀπόστασιν).

Anaximander’s cosmology is often described as a bizarre concoction of strange images that has nothing to do with observational data. One example out of many is Dicks, who writes: “The tertiary sources (…) attribute to him a fantastic theory (…). The unsatisfactory nature of the evidence, which is garbled and contradictory (…) makes it highly doubtful whether it has any historical worth.” Another example is Daniel Graham, who writes: “Anaximander’s imaginative model accounts for the apparently circular orbits of the heavenly bodies at the cost of making them radically different from their manifestations.” In Chapter 10.1007/978-3-319-97052-3_4, on the contrary, I will show that the images in Anaximander’s cosmology are not the result of a bizarre fantasy and that they are never chosen arbitrarily. They refer to things and events from everyday life, but at the same time they reflect deep-rooted archetypes. In Chapter 10.1007/978-3-319-97052-3_5, I will show that Anaximander’s account of the astronomical phenomena remains as close as possible to what we can observe directly in the heavens. Therefore, I would call it a phenomenological astronomy. More specifically, I will show that his explanation of the phases of the moon and solar and lunar eclipses is not weird but purely rational and describes precisely what we see happening in the heavens. In Chapter 10.1007/978-3-319-97052-3_6, the problem of Anaximander’s numbers for the heavenly bodies, which has intrigued me since I began studying his cosmology, is dealt with again. Referring to a recently published paper, I argue that a new interpretive approach is needed.

In 1995, when I discussed several visualizations of Anaximander’s world picture and added my own attempt, I took the interpretation of Anaximander’s numbers by Tannery and Diels for granted. Later, I got my doubts about the right understanding of the doxography on the distances of the heavenly bodies. In 2001, I wrote about my own interpretation: “Even if some parts of this reconstruction might be wrong. I think the conclusion still stands that Anaximander is the originator of the Western world picture or, in other words, the discoverer of space.” In 2003 I wrote: “Any interpretation entailing unacceptable observational consequences that were easy for Anaximander himself to observe must be wrong. In other words, Anaximander’s numbers cannot be in flagrant discrepancy with observational data, for otherwise he would have noticed it.” In 2009, in an article, entitled Problems with Anaximander’s Numbers, I discussed a number of interpretive problems and proposed solutions for understanding them. I concluded that even a symbolical interpretation of the numbers such as “far,” “farther,” “farthest” would not help, because on a flat earth the heavenly bodies are not far away. I tried to save the standard interpretation of the numbers by suggesting that Anaximander did not make a three-dimensional model of his conception of the cosmos. In 2011, this conclusion was repeated, although in Chap. 10.1007/978-3-319-97052-3_10 of Heaven and Earth, although I felt increasingly uneasy about it. Since then, my doubts as to whether Anaximander’s numbers as transmitted in the sources are in any of their current interpretations consistent with the conception of the celestial bodies being close by have only become more serious. In this chapter, several interpretations will be discussed and especially one that no longer takes the numbers as indications of distances in the universe but as a kind of calculator for a lunar-solar calendar. At the end of this chapter, I will make up my mind and outline my current position.

In the two parts of this book, I discussed two concepts of flat earth cosmology which tried in different ways to solve the problems that arise from the premise that the earth is flat. There is little point in trying to decide which system succeeded best, but it is worthwhile to recapitulate the differences. The main difference is that the ancient Greeks, with the possible exception of Anaximander, conceived of the heavens as a hemispherical dome over or as a full sphere around the earth, while the Chinese gai tian imagined a flat circular heaven parallel to a flat square earth. Another important difference, which was immediately related to the difference in conception of the shape of the heaven, was that the Greeks considered Delphi as the center of the earth and thus the celestial axis, around which the heavenly bodies orbit, as tilted, while the Chinese thought that the celestial axis was perpendicular between heaven and earth and their land at a certain distance from the center of the earth. A major drawback of the Greek conception was that they were unable to solve the problem of time differences on a flat earth. As far as we know, they even seem to have almost completely ignored it. The great achievement of the Chinese gai tian system was that it made time differences on a flat earth understandable. Their flat heaven and perpendicular celestial axis made it possible to accomplish this, even though they needed a set of auxiliary constructions, the most important of which were the limitation of the area of sunlight and the limitation of the range of visibility. However, these were notions of common sense. The example of the receding torch that becomes invisible after a while, illustrated both concepts at the same time. The horizon was considered as the visual the boundary beyond which nothing can be seen.

In this chapter, I will explore the interrelations between three astronomical theories that are attributed to Anaxagoras. The first theory is the explanation of the Milky Way as effectuated by the shadow of the earth. The second is the explanation of eclipses of the moon as caused by the earth’s shadow. The third is the explanation of eclipses of the moon as due to invisible heavenly bodies below the moon. I will examine how well these theories are attested, to what extent they are mutually compatible, and whether or not they harmonize with Anaxagoras’ other astronomical conceptions, particularly that of a flat earth. In Chap. 10.1007/978-3-319-97052-3_10, some consequences will be drawn regarding the light and phases of the moon. Chap. 10.1007/978-3-319-97052-3_11 will address the question of how Anaxagoras could have measured the distance of the sun.

The ancient Chinese model of the cosmos called gai tian (“canopy heaven”) that is explained in the Zhou bi (“gnomon at Zhou”) in the first century BC (but containing much older material) and in additional sources, differs fundamentally from the usual archaic conception of a flat earth with a hemispherical celestial vault, like that of the Presocratic Greeks and the Chinese rivaling system called hun tian. In the gai tian model, the heaven is thought to be flat and parallel to the flat earth. For us, since we are used to think in terms of a spherical earth, it is not so easy to comprehend the implications of an earth conceived of as flat. The conceptual transition to understand the gai tian is, as we will see, even “much more difficult to make than the switch from a spherical to a flat earth,” as Cullen rightly notes.

According to Aëtius, Thales stated that the earth is shaped like a ball. Diogenes Laërtius reports that Hesiod, Anaximander and Pythagoras taught that the earth was spherical. These testimonies are usually considered false. Several scholars have argued that Parmenides was the first to accept the earth’s sphericity. In the Phaedo, Plato tells us that someone has convinced Socrates that the earth is a sphere, without indicating who this “someone” was or what his arguments were. He then compares the earth with a dodecahedron. There must have been a heated debate among ancient Greek cosmologists about the shape of the earth, some of which can still be followed in the reports of the doxographers. For example, a curious argument, attributed to Anaxagoras, that is intended to prove that the earth is flat. Aristotle, who was familiar with the ins and outs of the debate, sought to terminate it by putting forward arguments for the sphericity of the earth and arguing against alleged evidence that the earth is flat. Since then, hardly any serious philosopher or astronomer has doubted that the earth is a sphere. Aristotle’s arguments can be divided into two groups: theoretical and empirical.

Students of Presocratic philosophy have an abundance of textbooks available. Next to Diels’ Doxographi Graeci and Diels/Kranz’s Fragmente der Vorsokratiker, I frequently used Graham’s The Texts of Early Greek Philosophy, Laks and Most’s Early Greek Philosophy, and incidentally Dumont’s Les Présocratiques, Reale’s I Presocratici, Mansfeld’s Die Vorsokratiker, and Gemelli Marciano’s Die Vorsokratiker. Additionally, for Thales, Anaximander, and Anaximenes I used the two volumes of Wöhrle’s Traditio Praesocratica published so far, for Xenophanes Lesher’s Xenophanes of Colophon and Untersteiner’s Senofane, Testimonianze e frammenti, for Anaxagoras Gershenson and Greenberg’s Anaxagoras and the Birth of Physics and Curd’s Anaxagoras of Clazomenae. For the most relevant chapter of Aëtius’ Placita we have now at our disposal Mansfeld and Runia’s Aëtiana II.2, and for the confrontation of pseudo-Plutarch’s and Stobaeus’ versions of Aëtius in general Bottler’s pseudo-Plutarch und Stobaeus. We must be very grateful to the scholars who have provided us with this essential material.

Except for members of The Flat Earth Society, some orthodox religious and a few Indians in the Amazon forests, we all know or should know for sure that the earth is a sphere. Yet, in daily life we act as if the earth is flat. When we travel from one city to another, or from one country to another, we do not use a globe to find our way, but look on a two-dimensional map as if the earth were flat. The idea of a spherical earth is as counter-intuitive as the idea of the earth orbiting around the sun. Perhaps this is why we tend to think there cannot be a problem in understanding the world-picture of ancient people who did not know better than that they lived on a flat earth. However, when I ask people who consider themselves as educated, to place themselves in the position of cosmologists living in the time of Aristotle and to mention arguments for the sphericity of the earth without taking refuge to modern knowledge such as the circumnavigation of the earth and photographs of the earth in space taken by astronauts, they are most of the time unable to deliver more than just the argument of an approaching ship at sea, of which we first see the mast and only later the hull. When asked if they have seen this themselves, they often must confess that they have it from hearsay. Perhaps such experiences can make us somewhat more modest towards the ancients who thought that the earth was flat.

In Chap. 10.1007/978-3-319-97052-3_9, I stated that two different theories about the shadow of the earth have been attributed to Anaxagoras. According to the first theory, the shadow of the earth was responsible for the phenomenon of the Milky Way, while according to the second, the shadow of the earth caused eclipses of the moon. I argued that these two theories are incompatible. I also argued that Anaxagoras’ explanation of the Milky Way, which was underpinned by the notion that lights shine brighter in the dark, is better attested than his alleged adoption of the correct explanation of lunar eclipses. Finally, I argued that Anaxagoras’ alleged adoption of the correct explanation of lunar eclipses does not harmonize with the rest of his astronomical ideas, especially that of a flat earth. My first conclusion was that Anaxagoras could not have discovered or embraced the theory that lunar eclipses were caused by the shadow of the earth. My second conclusion was that the idea of one or more invisible bodies between the moon and the earth, which according to the doxography was merely additional to the true explanation, in fact constituted Anaxagoras’ one and only explanation of lunar eclipses. I suggested that the source of the misunderstanding was a text in Aristotle that mentions some Pythagoreans and the notion of invisible bodies causing lunar eclipses. My interpretation did not, however, address one serious remaining problem, which did not concern eclipses but the light and phases of the moon. During the month, the moon exhibits phases, from new moon to waxing crescent, first quarter, waxing gibbous, full moon, and then back to waning gibbous, last quarter, waning crescent, and new moon. In Chap. 10.1007/978-3-319-97052-3_10, I will investigate how Anaxagoras could have explained these phenomena.

Anaximander’s model of the heavens stays as close as possible to what we actually see when we look at the sky. When we look at the stars with an unbiased eye, they give the impression of some kind of fire contained within the surrounding air, which fixes their positions relative to each other and makes them move in circles around the polar axis. Anaximander’s picture of the heavens is, so to speak, the direct translation of this experience: the heavenly bodies are regularly circling wheels of air with fire hidden inside that we see through openings. The star wheels circle always in the same orbit, but the wheels of the sun and moon have a second movement up and down the celestial axis to cause the seasons. At first sight, the weirdest part of Anaximander’s conception of the heavenly bodies is his explanation of the phases of the moon and lunar and solar eclipses. They are said to result from the partially or totally closing of the apertures in their wheels:There are some airy breathing places (ἐκπνοὰς τόπους τινὰς ἀερώδεις), through which the heavenly bodies appear. Accordingly, when the holes are blocked there are eclipses. The moon appears to be waxing or waning by turns according to whether the passages are blocked or opened.Anaximander says an eclipse of the sun occurs when the mouth of the fire-hole is closed off.Anaximander says an eclipse of the moon occurs when the opening on the wheel is blocked.

In this paper, three problems that have hardly been noticed or even gone unnoticed in the available literature in the cosmology of Philolaus are addressed. They have to do with the interrelationships of the orbits of the Earth, the Sun, and the Moon around the Central Fire and all three of them constitute potentially insurmountable obstacles within the context of the Philolaic system. The first difficulty is Werner Ekschmitt’s claim that the Philolaic system cannot account for the length of the day (νυχϑήμερον). It is shown that this problem can be solved with the help of the distinction between the synodic day and the sidereal day. The other two problems discussed in this paper are concerned with two hitherto unnoticed deficiencies in the explanation of lunar eclipses in the Philolaic system. The Philolaic system cannot account for long-lasting lunar eclipses and according to the internal logic of the system, during lunar eclipses the Moon enters the shadow of the Earth from the wrong side. It is almost unbelievable that nobody, from the Pythagoreans themselves up to recent authors, has noticed these two serious deficiencies, and especially the latter, in the cosmology of Philolaus the Pythagorean.

This book is a sequel to Heaven and Earth in Ancient Greek Cosmology. With the help of many pictures, the reader is introduced into the way of thinking of ancient believers in a flat earth. The first part offers new interpretations of several Presocratic cosmologists and a critical discussion of Aristotle’s proofs that the earth is spherical. The second part explains and discusses the ancient Chinese system called gai tian. The last chapter shows that, inadvertently, ancient arguments and ideas return in the curious modern flat earth cosmologies.

The usual interpretation has it that Anaximander made ‘the Boundless’ the source and principle of everything. However, in the works of Aristotle, the nearest witness, no direct connection can be found between Anaximander and ‘the Boundless’. On the contrary, Aristotle says that all the physicists made something else the subject of which ἄπειρος is a predicate. When we take this remark seriously, it must include Anaximander as well. This means that Anaximander did not make τὸ ἄπειρον the source or principle of everything, but rather called something else ἄπειρος. The question is, then, what was the subject that he adorned with this predicate. The hypothesis defended in this article is that it must have been ϕύσις, not in its Aristotelian technical sense, but in the pregnant sense of natura creatrix: the power that brings everything into existence and makes it grow and move. This ‘nature’ is boundless. It rules everything and in this sense it can be called ‘divine’. Being boundless, the mechanisms of nature, in which the opposites play an important role, are multifarious. The things created by boundless nature are not boundless, but finite, as they are destined to the destruction they impose onto each other, as Anaximander’s fragment says.

This book offers an innovative analysis of the Greek philosopher Anaximander’s work. In particular, it presents a completely new interpretation of the key word Apeiron, or boundless, offering readers a deeper understanding of his seminal cosmology and, with it, his unique conception of the origin of the universe. Anaximander traditionally applied Apeiron to designate the origin of everything. The authors’ investigation of the extant sources shows, however, that this common view misses the mark. They argue that instead of reading Apeiron as a noun, it should be considered an adjective, with reference to the term phusis, and that the phrase phusis apeiros may express the boundless power of nature, responsible for all creation and growth. The authors also offer an interpretation of Anaximander's cosmogony from a biological perspective: each further step in the differentiation of the phenomenal world is a continuation of the original separation of a fertile seed. This new reading of the first written account of cosmology stresses the central role of the boundless power of nature. It provides philosophers, researchers, and students with a thought-provoking explanation of this early thinker's conception of generation and destruction in the universe.

Based on secondary reports, one can assume that the works of the Presocratics dealt with the origin of the world, its appearance and transformations. These issues were expressed, as we will demonstrate, in words that describe the features of life. Living beings can move by themselves and we are used to thinking that this is what distinguishes them from ‘inanimate’ nature. The Milesians, however, understood life in a broader sense than is immediately apparent. Their theories of nature are known as hylozoism, which means that they understood matter to have the property of life and growth.

Generally speaking, the sources of the so-called doxographers were Aristotle and Theophrastus. As we have seen in the previous chapter, the little we know from Aristotle about Anaximander is embedded in his own philosophical theories, which were not particularly suitable for articulating Anaximander’s thoughts. Theophrastus and the doxographers, too, tried to grasp Anaximander’s ‘principle’ within the framework of Aristotle’s theory of the elements, as illustrated through the context of the only substantial fragment of Anaximander’s book.

One of the few occasions Aristotle mentions Anaximander by name appears in a passage from Physics. Here he contrasts Anaximander’s rendition of the process of generation with that of those who explain generation by condensation and rarefaction of the one underlying body. Anaximander, on the contrary, is grouped together with Empedocles and Anaxagoras, because they “separate out (ἐκκρίνεσϑαι) the contrarieties (τὰς ἐναντιότας) from the one in which they are present (ἐκ τοῦ ἑνὸς ἐνούσας)”. Simplicius also explicitly mentions Anaximander’s explanation of generation through the separation of opposites at the end of his report and, as we have seen, it features in other quoted texts as well.