The ancient world's approach to time and calendrical reckoning is a fascinating window into different civilizations' cosmological assumptions. The basic problem — reconciling the solar year of approximately 365.25 days with the lunar month of approximately 29.5 days — was solved differently by different cultures.

The Babylonian lunisolar calendar inserted additional months periodically to realign lunar and solar years. The Metonic cycle (19 years = 235 lunar months to within about 2 hours) was discovered or rediscovered by Greek astronomers and encoded in the Antikythera mechanism. This calendar tradition, transmitted through Jewish religious practice, is still the basis of the Hebrew calendar.

The Egyptian civil calendar abandoned lunar reckoning entirely: 12 months of 30 days plus 5 epagomenal days. This produced a practical administrative calendar but slowly drifted out of alignment with the solar year at the rate of one day per four years. The Julian reform (45 BC) added the leap year correction to the Egyptian model, producing a calendar that was accurate to within 11 minutes per year and remained in use in the West until the Gregorian correction in 1582.

The Roman calendar before Julius Caesar had become so misaligned through neglect and manipulation (adding or omitting days for political purposes) that it was months out of alignment with the solar year. The 'Year of Confusion' (46 BC) required 445 days to bring the calendar back into alignment before the reformed system could begin. It's one of the more dramatic administrative interventions in ancient history.