The earth could be both flat and spherical

The spherical shape of the earth

The earth is a sphere, no matter what else you should read on social networks for strange theories. Greek thinkers pondered why this is so already two thousand years ago. What else science, philosophy and astronomy have to do with each other, you can read in this article about the spherical shape of the earth as a philosophically safe contribution to astronomy and the history of science.

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The earth is a sphere, no matter what else you should read on social networks for strange theories. Greek thinkers pondered why this is so already two thousand years ago. What else science, philosophy and astronomy have to do with each other, you can read in this article about the spherical shape of the earth as a philosophically safe contribution to astronomy and the history of science.

Why it matters: In recent years, the flat earth theory has spread particularly in social media. However, the spherical shape of the earth has been known since ancient times. The development from the first idea to the justification of the spherical shape is closely related to the development of ancient Greek philosophy.

Situation before the emergence of philosophy

Before the first Greek philosophers appeared, the worldview was a mythical one. Around 600 BC The works of Homer and Hesiod were known throughout the Greek world. They combined gods and heroic legends; according to them, the cosmos was created by gods. Hesiod's best-known work Theogony (literally: origin of the gods) is at the same time a cosmogony, an origin of the cosmos. Gaia (earth) and Uranus (heaven) are thought of as deities. Despite its mythical form, it was probably the first Greek attempt to systematically describe the origin and structure of the world. Both Homer and Hesiod mention the same stars and constellations: Sirius, Pleiades, Hyades, Great Bears, and Orion (Homer, 2018, Iliad XVIII 483-489, Iliad XXII 24-31, Odyssey V 269-277; Hesiod, 2019, 383 -387, 609-611, 614-617). That speaks for a coherent worldview at the time before the first philosophers appeared.

The Milesian Philosophers

Miletus, a city on the Ionian coast in what is now Turkey, was the hometown of the first Greek philosophers Thales (born approx. 624 BC) as well as Anaximander (born approx. 610 BC) and Anaximenes (born approx. approx. 585 BC). They distanced themselves from mythical explanations and replaced them with explanations based on inner-worldly reasons.

Thales, probably influenced in his thinking by the discoveries of the Babylonians and Phoenicians (Kranz, 1986), was described by Aristotle as the forefather of philosophy and later assigned to the Seven Sages of Ancient Greece. Without exaggerating, he can also be described as one of the most important thought leaders in Greek mathematics and astronomy. He looked for reasons and explanations for the creation of the world. His methods were mostly speculative (sc. Theoretical-contemplative, not based on perception). He tried to explain the world without recourse to gods, but with the search for the arché, the principle, beginning or origin of the world. For Thales this was the water. He imagined the earth as a disk floating on water (Aristotle, 1983). For him, an earthquake was not caused by the will of the gods, but rather by the movement of the sea on which the earth was floating (Kranz, 1986). He secured his place in the history of astronomy primarily by predicting a solar eclipse for the spring of 585 BC. BC, which contributed decisively to the conclusion of peace in the war between Lydern and Medes, as both warring parties knew the Thales Vorhersage prediction and were accordingly impressed. The possibility of such a prediction indicates knowledge of the Babylonian star tables (van der Waerden, 1966).

For Anaximenes, another exponent of Milesian philosophy, air was the original principle. He taught that “the earth is flat and floats in the air” (Diels / Kranz, 1957, 13 A6), for him the sky was probably still a hemisphere resting on it. Of course, he still had to explain the movements of the sun and moon, which could not complete their daily rounds under the earth: "The stars did not move under the earth, but around the earth", or "The During the night, the sun would be covered by the higher regions of the earth ”(Diels / Kranz, 1957, 13 A7).

Anaximander brought a whole new abstraction into thinking about the world and its beginning. For him, the original principle was the apeiron, i.e. roughly the limitless or the infinite. The idea of ​​infinity can be found here for the first time in Greek thought (Kranz, 1986). Anaximander thought of the earth as a cylindrical column drum, the height of which is a third of its diameter, that hovers in the center of the world. For him, however, the sky was no longer a hemisphere, but already fully spherical - with that he could explain the movement of the sun and moon around the earth much better. What was completely new was that Anaximander drew a map of the world. Apparently he even made a kind of sky map, or at least a gnomon, with the help of which important astronomical data such as solstices, equinoxes and times could be determined.

From today's point of view, of course, some of the Milesians' explanations still seem quite simple. But one must not forget that these philosophers then had nothing more than their powers of observation and their rational thinking. They drew their conclusions solely from theoretical considerations.

Pythagoreans: inside - the earth as a sphere

The next step was made by Pythagoras (born 570 BC) and the Pythagorean School named after him, whose most important representatives in connection with astronomy are probably Philolaos (born around 470 BC) as well as Archytas, Hiketas and Ekphantos (all born late 5th century BC). It is not always clear to which Pythagoreans which idea goes back; Pythagoras himself probably did not write any of his own writings, i.e. his ideas have only been passed down through the pen of other Pythagoreans. It was now the Pythagoreans who consistently represented the spherical shape of the earth for the first time (Kranz, 1986). Around 500 BC The spherical shape was an established theory among the Pythagoreans. What process has led to this realization?

The basic scientific-philosophical principle for the Pythagoreans was: numbers or harmonies determined by numerical ratios. These harmonies formed the basis for a world law, the cosmos is ruled by them. Pythagoras ‘the philosophical-scientific structure of the world is described by Diogenes Laertius as follows:

The beginning of everything is the unity (monad); but from the unity originates the indefinite duality, which, as matter as it were, underlies the unity, its cause. Numbers come from the unity of distant and indefinite duality; from the numbers the points, from these the lines, from these the surface designs, from the surfaces the stereometric (mathematical) bodies, from which the sensually perceivable bodies, their elements, four in number, are the following: fire, water, earth, Air; they are subject to change and a constant changeability, and a soulful world is formed from them, rational, spherical, with the earth as its center, which in turn is spherical and inhabited. There are also antipodes for whom our below is above. (Diogenes Laertius, 2015, 8.25f)

This was a philosophical speculative train of thought; for the Pythagoreans, opening up was the adequate scientific procedure. The sphere was preferred as the shape of the earth for reasons of symmetry. Although the sources do not allow this to be proven with absolute certainty, it can be assumed that the Pythagoreans were inspired by some observations that Pythagoras himself may have learned about while traveling from Babylonians or Egyptians (van der Waerden, 1966).

Geocentrism vs. center fire

Historically, one can distinguish between two different worldviews with the Pythagoreans: inside: The first approach was geocentric, the sun, moon and planets moved on circular orbits around the earth, and it was later supplemented by Hiketas and Ekphantos by a rotation of the earth around its own axis .
In the second approach with Philolaos, the earth (and the other planets as well as the moon and sun) moved around a central fire located in the center of the cosmos. There were also counter images for all celestial bodies on the diametrically opposite side of the central fire, not visible from earth. The inhabited side of the earth was turned away from the central fire, so the central fire and counter-earth were not visible. The reason given was that fire was the most venerable of the four elements and therefore especially more important than the element earth (water and air are the other two), and this most venerable element was then reserved for the central place of space for reasons of symmetry. This is remarkable in that, for the first time, it is not a geocentric view of the world, but the earth becomes a planet (Heath, 1932). What we can say in common, however, is that in both Pythagorean worldviews the earth was spherical.

Plato and the Pythagorean School

Plato (428-348 BC) attended the Pythagorean School on a trip to southern Italy. He himself spoke of meeting the Pythagorean Archytas, whom he had apparently got to know personally (Plato, 2007, 7th letter 338c and 339d). There was also an exchange of letters between Plato and Archytas, in which the two philosophers exchanged views on different writings. Plato was strongly influenced by the Pythagoreans in his thoughts on mathematics and astronomy, and he repeatedly mentioned a geocentric view of the world with a spherical earth. For example, in Phaedo 108e-109a he wrote of the “shape of the earth”, which “stands as a round figure in the middle of the sky” (Plato, 2007). In Timaeus 40b Plato writes: "The earth, our nourisher, which is balled around the axis drawn through the universe" (Balss, 1949, p.59).

The moon, the sun and the five planets (Mercury, Venus, Mars, Jupiter, Saturn) moved in a circle around the earth. This picture was quoted again and again by Plato, for example in Nomoi 821b-822c, Politeia 616b-617d or Phaidon 108d-109a. This type of description is also found in Timaeus 38b-40d; In section 40b cited above, there are even some interpretations that consider a rotation of the earth itself to be possible. For example, Aristotle wrote about this passage in Timaeus that the earth “sways and moves around the pole stretched through space” (Aristotle, 1983, 293b30).
The passage by the Athenians in Nomoi 822a-b also has several possible interpretations: "Because this claim about the sun, the moon and the other stars that they wander around is incorrect [...], just the opposite of it takes place." , 2007)
Some commentators consider it quite possible that Plato rejects the daily rotation of the stars around the earth and describes the Pythagorean model with the central fire (cf. Heath, 1932).
So Plato was more of a dialectician than a systematic scientist. Instead of clearly derived results, there were several alternative options for him.

Mathematical advancement in the academy

Plato's school, the academy, had other essential connections to the Pythagoreans. Eudoxus (390-337 BC), born in Asia Minor, first traveled to Italy to study with the Pythagorean Archytas. Then he went to Athens, where he was active at the Academy and later also worked with Aristotle. He designed a purely mathematical model in which the orbits of the moon, sun and the five known planets can be described by superimposing different spheres. For example, he assumed “that the movement of the sun and the moon takes place in three spheres each [...]. Each of the planets move in four spheres ”(Aristoteles, 1994, 1073b17-23). For the fixed stars he assumed a further sphere, a total of 27.

His pupil Kalippos (370-300 BC), who also studied at the Academy, refined this model to better fit the observations and introduced seven more spheres (Aristotle, 1994, 1073b33-38). The essential point with both models is that they were not created speculatively (i.e. theoretically-contemplative), but represent a purely mathematical description without a speculative background.

Aristotle and the transition to science

All of these approaches were brought together by the great polymath Aristotle (384-322 BC). He was a student of Plato in the Academy and later worked with Eudoxus and Calippus. Aristotle defined a new type of science and also justified the spherical shape of the earth with it.

The most important requirements for a science at Aristotle consist of (Aristoteles, 1994, 980a-983a):
- Knowledge of the general (not an individual case)
- Knowledge of the causes and principles
- Necessity of the known
- Teachability through logical justification.

He writes: “Science is demonstrative behavior [...]. For where there is a certain conviction and one knows the principles, there is science ”(Aristoteles, 1991, 1139b31-33).
He then applied this basic principle to astronomy (Aristotle, 1983, 296a21-298a18). There were several reasons for the spherical shape. On the one hand, Aristotle formulated the claim that every part of the earth (especially water, of course) strives towards the center, thus creating a sphere through compression. As a second reason, he cited the observation that the earth's shadow on the moon is round during a lunar eclipse - which can only be explained with the spherical shape of the earth itself. Anaxagoras (born approx. 500 BC) had already discovered a hundred years earlier that the moon does not shine itself, but receives its light from the sun; and thus also brought a lunar eclipse into play as the interposition of the earth between the sun and the moon (Diels / Kranz, 1957, 59 A77; Platon 2007, Kratylos, 409a).
The third reason also comes from the area of ​​perceptible phenomena. If you travel south or north, the visible sky changes. This can only be explained in the case of a curved earth - which must also be small compared to the cosmos. He also concluded from the curvature of the earth that bodies falling to the earth do not move parallel. From this Aristotle inferred the shape of a sphere and not other curved surfaces, because objects fall vertically downwards everywhere on earth, and no place on earth is particularly distinguished. For reasons of symmetry, the spherical shape follows.

With Aristotle ‘, even in today's understanding of scientific justifications for the spherical shape of the earth, the paths of philosophy and astronomy as a science diverge. The path of the Greek philosophers from mythical-divine explanations in Homer and Hesiod through speculative models in the pre-Socratics to mathematical theories in the academy to the scientifically founded approach in Aristotle comes to a close here from a philosophical point of view. As a result, it is then specialized astronomers who make further progress. Aristarchus and Seleucus initially postulated a heliocentric worldview before Hipparchus and Ptolemy worked out in detail the geocentric and spherical worldview that prevailed throughout the Middle Ages and which then became the standard model of the church up to modern times.