The Counter-Earth

The Counter-Earth

ἀντίχθων, antichthon

The system, with the Italian labels of the diagram's maker: Hestia the Central Fire, Terra and Anti-Terra on the innermost orbit and always opposite one another, each going round in twenty-four hours; then the Moon at twenty-nine days and the Sun at a year.

Proposed by	Philolaus of Croton
When	Fifth century BC
Orbits	A Central Fire, not the Sun
Position	Always opposite the Earth
The count
Bodies visible	Nine
Bodies required	Ten[1]
Reason	Ten is the perfect number
Shortfall made up by	This
Evidence
Observed	Never
Claimed observed	Never
Chief source	A hostile one

The Counter-Earth (Greek ἀντίχθων, antichthon) is a planet proposed in the fifth century BC by Philolaus of Croton, a Pythagorean, as the tenth body of a cosmos in which the Earth was one of the nine others and none of them stood still.^[1]

It is the first known cosmology to take the Earth off the centre, and it took it off for reasons that have nothing to do with observation. The centre was occupied instead by an invisible Central Fire, called Hestia after the hearth; the Earth ran round it once a day, keeping its inhabited face permanently turned outward, so that nobody ever saw the fire they were circling. The Counter-Earth kept station on the opposite side, and was invisible for the same reason twice over.

The count

Aristotle gives the argument, and gives it flatly:

"Since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nine that are visible, they make the antichthon the tenth."
– Aristotle, Metaphysics 986a

The tetractys: one, two, three and four, which come to ten and make a triangle. The Pythagoreans swore their oaths on it.

The nine are the sphere of the fixed stars, the five planets then known, the Sun, the Moon, and the Earth. Ten was not a round number to a Pythagorean but a sacred one: the tetractys, 1 + 2 + 3 + 4, the figure their oaths were sworn on. A universe of nine moving bodies was therefore not merely untidy. It was wrong in the way a false note is wrong.

So a tenth was supplied, and placed where the shortfall in the evidence could not be raised as an objection.

Number as physics

Pythagoras and Philolaus, from Gaffurio's Theorica musicae of 1492. The numbers on the pipes – 16, 12, 9, 8, 6 – are the harmonic ratios, and they are the reason the sky had to come to ten.

The move is easier to understand with the music in front of it. The Pythagoreans had found that the concords are ratios of small whole numbers: halve a string and it sounds the octave, take two thirds and it sounds the fifth, three quarters and it sounds the fourth. This is true, it is checkable in an afternoon, and it is one of the most consequential discoveries anybody has ever made.

What they drew from it is that number is not a description of the world but its constitution. If the audible order is arithmetical, the visible order is arithmetical, and an arrangement of the heavens that fails to come out to a significant number is evidence that something has been missed rather than that the number was the wrong thing to look at.

Read that way the Counter-Earth is not a lie or a lazy patch. It is a prediction, made on a principle its authors had excellent reason to trust, in a case where the principle happened to be false.

What the eclipses were doing there

Aristotle offers a second motive in the same breath, and it is the one recent scholarship has taken up: that the Counter-Earth was there to account for eclipses of the Moon.^[2]

The specific case is sharper than the general one. On Philolaus's arrangement, lunar eclipses seen at dawn and at dusk are difficult to produce at all with a single body available to cast a shadow; a second dark body, permanently on the far side, supplies them. That is an ordinary piece of saving the phenomena, of exactly the sort the numerological story denies the Pythagoreans.

Neither account has won. The Stanford Encyclopedia, having set out the eclipse argument as the more convincing, still allows that Aristotle's explanation "retains considerable plausibility", which is where the matter rests.^[2] Almost nothing Philolaus wrote survives, so the version everyone repeats is the unflattering one, from an author arguing against it – and that is the position from which most ancient doctrines reach us.

Not one of the phantoms

It is tempting to file the Counter-Earth with Vulcan, the planet inside Mercury's orbit that was announced, named and assigned an orbit by people who believed they had seen it. The two are not the same kind of thing.

Vulcan was reported. So were the canals of Mars, and Bathybius, and the N-rays: somebody looked, and said what they had seen, and was wrong. The Counter-Earth was never reported by anybody. It was placed, deliberately, in the one location in the system from which no report could come, and its invisibility was offered as part of the account rather than apologised for.

That makes it unfalsifiable, which is a serious charge in a modern argument and an anachronistic one here: the demand that a claim expose itself to refutation is younger than this idea by two and a half thousand years. What it also makes it is honest. Nobody pretended to have seen anything.

What it got right

The system is wrong in nearly every particular and is nonetheless a landmark, because of one thing it does that no earlier cosmology does: it moves the Earth.

Every scheme before it, and most for two thousand years afterwards, had the Earth at rest at the centre because that is what standing on it feels like: see geocentrism. Anaximander had already taken away its supports and left it hanging unheld in the middle of things, which is a considerable step and stops short of this one. Philolaus gave the Earth an orbit and a period, and explained the alternation of day and night by its own motion rather than by the sky's.

Whatever his reasons were – and the section above declines to settle them – he did it first, and by two centuries.

Copernicus knew, and said so. In the preface to De revolutionibus he lists the ancients who had already dared to set the Earth going, and Philolaus the Pythagorean is among them: the authority heliocentrism reached for, when it needed to show that a moving Earth was not an impertinence, was a man who had put the world in orbit round a fire nobody could see.^[3]

See also

• Vulcan – the planet that was reported, repeatedly, and was not there
• Geocentrism – the arrangement this one abandoned two thousand years early
• Heliocentrism – which cited Philolaus as precedent for moving the Earth
• Anaximander – who had already unsupported the Earth, without moving it
• Ptolemy – whose system won, and kept the Earth still for fourteen centuries

References

1. ^ Philolaus of Croton, c. 470 – c. 385 BC. The system is known chiefly from Aristotle, Metaphysics A5, 986a, and from De caelo; the quotation is from the Metaphysics. The nine visible moving bodies are the sphere of the fixed stars, Saturn, Jupiter, Mars, Venus and Mercury, the Sun, the Moon and the Earth. The Central Fire is the centre they revolve about and is not one of the ten.
2. ^ Aristotle reports the eclipse motive alongside the numerological one. D. W. Graham's version of the argument, summarised in the Stanford Encyclopedia's entry on Philolaus, is that the Counter-Earth accounts for lunar eclipses seen at dawn and dusk, which are otherwise hard to obtain on this model. The same entry judges Aristotle's numerological explanation to retain considerable plausibility, so the two motives are not settled against one another and this article does not settle them.
3. ^ Copernicus names Philolaus among the ancients who held the Earth to move. The citation is doing work: a proposal that offends common sense is easier to advance if somebody respectable has advanced it before, and for this purpose it does not matter that Philolaus reached it by counting.

External links

• Aristotle, Metaphysics 986a – the passage quoted above, in the Perseus Digital Library
• Philolaus – Stanford Encyclopedia of Philosophy – what can and cannot be attributed to him, at length