Pythagorean astronomical system
An astronomical system positing that the Earth, Moon, Sun and planets revolve around an unseen "Central Fire" was developed in the 5th century BC and has been attributed to the Pythagorean philosopher Philolaus. The system has been called "the first coherent system in which celestial bodies move in circles", anticipating Copernicus in moving "the earth from the center of the cosmos [and] making it a planet". Although its concepts of a Central Fire distinct from the Sun, and a nonexistent "Counter-Earth" were erroneous, the system contained the insight that "the apparent motion of the heavenly bodies" was (in large part) due to "the real motion of the observer". How much of system was intended to explain observed phenomena and how much was based on myth and religion is disputed.
Philolaus (ca. 470 to ca. 385 BC) was a follower of the pre-Socratic Greek philosopher Pythagoras of Samos, who developed a school of philosophy that was both dominated by mathematics and "profoundly mystical" and is famous for developing the Pythagorean theorem. Philolaus himself has been called one of "the three most prominent figures in the Pythagorean tradition" and "the outstanding figure in the Pythagorean school", who may have been the first "to commit pythagorean doctrine to writing". Because of questions about the reliability of ancient non-primary documents, scholars are not absolutely certain that Philolous developed the astronomical system based on the Central Fire, but they do believe that either he, or someone else in the late 5th century BC, did create it.
While the earth and planets revolved around a central point in Philolaus's system, his could not be called a Heliocentric "solar system", because the central point the Earth and Planets revolved around was not the Sun, but the so-called Central Fire. This Fire was not visible from the surface of Earth—or at least not from the hemisphere Greece was located in.
Philolaus says that there is fire in the middle at the centre ... and again more fire at the highest point and surrounding everything. By nature the middle is first, and around it dance ten divine bodies - the sky, the planets, then the sun, next the moon, next the earth, next the counterearth, and after all of them the fire of the hearth which holds position at the centre. The highest part of the surrounding, where the elements are found in their purity, he calls Olympus; the regions beneath the orbit of Olympus, where are the five planets with the sun and the moon, he calls the world; the part under them, being beneath the moon and around the earth, in which are found generation and change, he calls the sky.
In this system the revolution of the earth around fire "at the centre" or "the fire of the hearth" (Central Fire) was not yearly but daily, while the moon's revolution was monthly, and the sun's yearly. It was the earth's speedy travel past the slower moving sun that resulted in the appearance on earth of the sun rising and setting. Further from the Central Fire, the planets' revolution was slower still and the outermost "sky" (i.e. stars) probably fixed.
The Central Fire (Dios phylakê) was also called "Watch-tower of Zeus" or "Hearth-altar of the universe". Rather than there being two separate fiery heavenly bodies in this system, Philolaus may have believed that the Sun was a mirror, reflecting the heat and light of the Central Fire. The 16th-17th century European thinker Johannes Kepler believed that Philolaus's Central Fire was the sun, but that the Pythagoreans felt the need to hide that teaching from non-believers.
In Philolaus's system, the earth did not rotate. This meant that neither the Counter-Earth or the Central Fire were visible from Earth's surface—or at least not from the hemisphere where Greece was located. There is "no explicit statement about the shape of the earth in Philolaus' system", so that he may have believed either that the earth was flat or that it was round and orbited the Central Fire as the Moon orbits Earth — always with one hemisphere facing the Fire and one facing away. A flat Earth facing away from the Central Fire would be consistent with the pre-gravity concept that if all things must fall towards the center of the universe, this force would allow the earth to revolve around the center without spilling everything on the surface into space. Others maintain that by 500 BC most contemporary Greek philosophers considered the Earth to be spherical.
The "mysterious" Counter-Earth (Antichthon) was the other celestial body not visible from earth. We know that Aristotle described it as "another Earth", from which Greek scholar George Burch infers that it must be similar in size, shape and constitution to Earth. According to Aristotle — a critic of the Pythagoreans — the function of the Counter-Earth was to explain "eclipses of the moon and their frequency", and/or "to raise the number of heavenly bodies around the Central Fire from nine to ten, which the Pythagoreans regarded as the perfect number". 
Some (astronomer John Louis Emil Dreyer) think the Counter-Earth followed an orbit so that it was always located between Earth and Central Fire, but Burch argues it must have been thought to orbit on the other side of the Fire from Earth. Since "counter" means "opposite", and opposite can only be in respect to the Central Fire, the Counter-Earth must be orbiting 180 degrees from Earth. Burch also argues that Aristotle was simply having a joke "at the expense of Pythagorean number theory" and that the true function of the Counter-Earth was to balance Earth. Balance was needed because without a counter there would be only one dense, massive object in the system — Earth. The universe would be "lopsided and asymmetric -- a notion repugnant to any Greek, and doubly so to a Pythagorean", because Ancient Greeks believed all other celestial objects were composed of a fiery or ethereal matter having little or no density.
In the 1st century A.D., after the idea of a spherical Earth gained more general acceptance, Pomponius Mela, a Latin cosmographer, developed an updated version of the idea, wherein a spherical Earth must have a more or less balanced distribution of land and water. Mela drew the first map on which the mysterious continent of Earth appears in the unknown half of Earth — our antipodes. This continent he inscribed with the name Antichthones.
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- Philolaus, Stanford Encyclopedia of Philosophy, Carl Huffman.
- Burch, George Bosworth. The Counter-Earth. Osirus, vol. 11. Saint Catherines Press, 1954. p. 267-294
- Source: Dante and the Early Astronomers by M. A. Orr, 1913.
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- "Philolaus". Sep 15, 2003. Stanford Encyclopedia or Philosophy. Retrieved 23 October 2013. "Philolaus appears to have believed that there was also fire at the periphery of the cosmic sphere and that the sun was a glass-like body which transmitted the light and heat of this fire to the earth, an account of the sun which shows connections to Empedocles"
- Johannes Kepler (1618–21), Epitome of Copernican Astronomy, Book IV, Part 1.2, "most sects purposely hid[e] their teachings"
- Burch 1954: 272–273, quoted in Philolaus, Stanford Encyclopedia of Philosophy.
- Harley, John Brian; Woodward, David (1987). The History of Cartography: Cartography in prehistoric, ancient, and medieval Europe and the Mediterranean 1. Humana Press. pp. 136–146.
- Burch, 1954, p.285
- Heath, Thomas (1981). A History of Greek Mathematics, Volume 1. Dover. p. 165.
- Arist., Metaph. 986a8–12. quoted in Philolaus, Stanford Encyclopedia of Philosophy, Carl Huffman.
- "Greek cosmology, The Pythagoreans". University of California, Riverside. "The importance of pure numbers is central to the Pythagorean view of the world. A point was associated with 1, a line with 2 a surface with 3 and a solid with 4. Their sum, 10, was sacred and omnipotent."
- Dreyer, John Louis Emil. History of the planetary systems from Thales to Kepler. p. 42. "To complete the number ten, Philolaus creatd the antichthon, or counter-earth. This tenth planet is always invisible to us, because it is between us and the central fire and always keeps pace with the earth."
- Burch, 1954, p.280
- Burch, 1954, p.286-7
- Pomponius Mela. de Chorographia.