stigmê [Greek, στιγμη]

Plural, stigmai (στιγμαι). In ancient Greece, a unit of angle. The sole evidence of this unit’s existence is a stela known as the “inscription of Keskinto,” on which the stigmê is defined. It appears to have been made in about 100 bce. Keskintos is a farm property on the island of Rhodes; the inscription was discovered there in 1893 and is now in the Pergamon Museum of the Staatliche Museen in Berlin.

Reading ancient inscriptions, battered and partial as they usually are, is a difficult business. Tannery read the inscription as saying the stigmê = ½ degree. He worked from a transcription, as did others over the century that followed, and during that time Tannery's value was generally accepted.

In the early 21st century Alexander Jones reexamined the stone itself and concluded it defines the stigmê as = ¹⁄₂₇ of a degree, which had also been the opinion of Hiller.

Was the stigmê used only for astronomical calculations, or could it also have been used to record observations? ¹⁄₂₇ degree is 2.2 arcminutes. One test of how small an angle can be resolved by the naked eye is whether it can distinguish (“split”) the components of a double star. The two stars forming the double star Epsilon Lyrae are separated by 3.5 arcminutes, and an experienced observer on a night with excellent viewing conditions can see two stars¹, but it is considered something of a feat. Analyses of the human eye on optical principles conclude its limit of resolution is about 2.5 arcminutes. The stigmê, at 2.2 arcminutes, thus lies just beyond the resolving power of the best naked eye under the best of conditions. An ancient Greek astronomer could not have meaningfully recorded his observations to the nearest stigmê.

Why ¹⁄₂₇th? It is the cube of one-third, but it is hard to see how that would figure in astronomical calculations. Jones has an ingenious and plausible speculation regarding its origin. Each line of the body of inscription refers to a planet and some sort of period of that planet, such as its period of revolution about the sun. Tannery realized that the periods are expressed as the number of times that period would occur in 291400 years. In other words, the author of the inscription believed in the existence of a Great Year, a period of time in which all heavenly bodies would return to their original positions. 291400 solar years are 291600 Egyptian calendar years (of 365 days), a unit often used in describing a Great Year. The 9720 stigmai in a circle × 30 is 291600.

1. See Robert Burnham's Celestial Handbook (NY: Dover, 1978).


Friederich Hiller von Gaertringen.
Inscriptiones Insularum Maris Aegaei praeter Delum,
fasc. 1, Inscriptiones Rhodi Chalces Carpathi cum Saro Casi.

Berlin: G. Reimer, 1895.

Hiller is the one who first published the inscription and who shipped the stela to Berlin.

Paul Tannery.
L'Inscription astronomique de Keskinto,
Revue des Études Grecques, vol. 8 (1895), pages 49-58.

Tannery, a prominent historian of mathematics, realized the inscription concerned astronomy and was the first to make sense of it.

Otto Neugebauer.
A History of Ancient Mathematical Astronomy.
Springer-Verlag, 1975.

See Part Two, page 698.

Alexander Jones.
The Astronomical Inscription from Keskintos, Rhodes.
Mediterranean Archaeology and Archaeometry, Special Issue, vol. 6, no 3, 2006.
Pages 215-222.


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