## 5. Homer the Mathematician

A major advance in our study of Homer’s Odyssey as a source of astronomical learning was analysis of the considerable numerical data embedded throughout the epic.

This data is directly related not only to the construction of a luni-solar calendar system and sophisticated cycles of the sun, moon and planet Venus, but also to an exposition on pi, the ratio of the diameter of a circle to its circumference (a concept also known in contemporary Egypt and Babylon).

An introduction to Homer the Mathematician begins in Homer’s Secret Odyssey, Chapter Four, Homer’s Wizardry with numbers, and continues throughout the book.

‘Sailing days’ and the moon

Such was Homer’s astronomical ability that some of the numbers embedded in the Odyssey  are significant in terms of phases of the moon in a luni-solar calendar system.

These numbers are used in various contexts, including the days and nights that Odysseus sails on the ‘wine-dark skies’.

Translations  include the following examples:

Odysseus sailed for 17 days and on the 18th…’ ( E.V. Rieu (Od.5.277)

Odysseus sailed For six days and six nights and on the seventh…’  (Rieu Od.10.80)

Odysseus is adrift for nine days and on the ‘tenth night’ washed ashore.  (Rieu Od.7.250)

Odysseus is at sea for a whole month. (Rieu Od. 12.326)

The significance of these numbers is that they record the number of days between phases of the moon during a lunar month.  For instance:

18 Days (Od.5.277) the period from the first quarter of the lunar month to the third quarter.

7 Days (Od.10.80) the period from the third quarter of the lunar month to dark moon.

10 Days (Od10.28) – third quarter to new crescent.

‘… for a month’ (Od.24.115)a lunar month.

Phrases such as those above divide the monthly cycle of the moon into useful units of time and may  have served a similar purpose to ‘weeks’ and ‘fortnights’ in more modern times.

Seven days as a unit of time is found in other ancient cultures in astronomical terms and has been associated with seven heavenly bodies; the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn.

3 days – Periods of the lunar month are not confined to ‘sailing days’ and at Od 17.515 (Rieu)  Odysseus is hidden in the hut of Eumaeus  for three days and nights which marks the dark period between the last sighting of the waning moon and the appearance of a new crescent moon at the climax of the Odyssey. See Homer’s Secret Odyssey p168 ff.

The dark period of the moon varies between 1.5 days and 3.5 days.