Revising the eclipse prediction scheme in the Antikythera mechanism

Abstract

In 1901, an extraordinary ancient Greek artefact was discovered in a shipwreck just off the tiny island of Antikythera. It was later shown to be a complex astronomical calculating machine and is now known as the Antikythera Mechanism. In 2005, it was established that it predicted eclipses, using a 7th century BC Babylonian eclipse cycle of 223 lunar months, known as the Saros Cycle. Understanding the complex eclipse prediction scheme on the Antikythera Mechanism has resulted from a fascinating series of discoveries. The eclipse prediction scheme is implemented through descriptive glyphs, inscribed round a 223-month Saros Dial at the rear of the Mechanism: a glyph in a particular month indicates a predicted eclipse. A 2008 publication deciphered the meaning of the glyphs: they indicate whether the predicted eclipse is lunar or solar; the possible visibility of the eclipse; and its time of day. The glyphs also include an alphabetical Index Letter, referring to inscriptions round the Saros Dial, which describe eclipse characteristics. In that publication, the full eclipse prediction scheme was not understood but subsequent work in 2014 made substantial progress. The eclipse characteristics, such as the colour and magnitude of the eclipse, are listed together in the inscriptions, together with a group of Index Letters for the eclipses to which they apply. The deeply puzzling grouping and ordering of these Index Letter Groups was solved with a simple mathematical model, which both explained these groups and the distribution of the glyphs round the Saros Dial-revealing an eclipse prediction scheme of extraordinary sophistication and ambition. Later work in 2016 proposed a radical revision of this eclipse prediction scheme, though it did not challenge the mathematical basis of the scheme. The 2016 scheme implied a completely different picture of the whole of the back plate of the Antikythera Mechanism, destroying its essential mathematical symmetry. This revision is comprehensively refuted here, except for the identification of a new text character in one of the Index Letter Groups, which implies an interesting revision of the 2014 scheme but which preserves the elegant 2014 reconstruction of the back plate of the Antikythera Mechanism.

The Back Plate Inscription and eclipse scheme of the Antikythera Mechanism revisited

“…40 As at Freeth/Crowther 2014, S13, 125, against Anastasiou et al (2016, 159 and162) (dotted epsilon). 41 As at Anastasiou et al (2016, 159) against Freeth (2019). 37 As at Anastasiou et al (2016, 159 and 161).…”

“…Cell 67: Freeth et al 2008, Freeth/Crowther 2014and Freeth 2019; line 2 = ὥ̣ ρ̣ (ᾳ) η΄, Anastasiou et al 2016. In line 1, there is a faint but visible sigma, nu, and the lower vertical hasta of upsilon above it in ligature.…”

“…The crossbar of the final alpha is faint, but there.Line 37: μέλαν, Freeth/Crowther 2014/2019 andAnastasiou et al 2016. Line 38: vΤvΗ̅ vΘvΡ̅ vΨ̣̅ , Freeth/Crowther 2014/2019and Anastasiou et al 2016. The overlines over eta and rho are clear.…”

“…Cell 79: Σ(ελήνη), ἡμ(έρας) | ὥρ(ᾳ) κ΄ | Υ,Freeth et al 2006 (= cell 107); Σ(ελήνη), ἡμ(έρας) | ὥρ(ᾳ) ι΄ | Υ,Freeth et al 2008, Freeth/Crowther 2014, Freeth 2019, and Anastasiou et al 2016.Cell 114: Σ(ελήνη), ἡμ(έρας) | ὥρ(ᾳ) ι̣ β΄ | Γ̅ , Freeth et al 2006 (= cell 142), Freeth et al 2008, Freeth/Crowther 2014 and Freeth 2019; line 2 = ὥρ(ᾳ) ιβ΄ | Γ̅ , Anastasiou et al 2016. In line 2, the iota is clear, and in line 3 the gamma is clear.…”

“…].Λ | [-], Freeth et al 2006 (= cell 212); Σ(ελήνη), ἡμ(έρας) ὥρ(ᾳ) δ΄ | [Ἥ(λιος) ὥ̣ ρ̣ (ᾳ) α΄ | [Σ̅ ], Freeth et al 2008, Freeth/Crowther 2014 and Freeth 2019; lines 2-3 = Ἥ̣ (λιος) ὥρ(ᾳ) α΄ | Σ̅ ̣ , Anastasiou et al 2016. The letters are all clear in photographs, except for part of the lower left angle of the index letter sigma.Cell 190: Σ(ελήνη), ἡμ(έρας) | ὥρ(ᾳ) θ΄ | Τ̅ ,Freeth et al 2006 (= cell 218),Freeth et al 2008, Freeth/Crowther 2014, Anastasiou et al 2016and Freeth 2019…”