The calendar of the Roman Republic was based on lunar phases. Pagan Roman priests, called pontiffs, were responsible for regulating the calendar. Because the pontiffs could also hold political office, it provided opportunity for abuse. Intercalating1 an extra month could keep favored politicians in office longer, while not intercalating when necessary could shorten the terms of political opponents.
By the time of Julius Cæsar, months were completely out of alignment with the seasons. Julius Cæsar exercised his right2 as pontifex maximus3 (high priest) and reformed what had become a cumbersome and inaccurate calendar.4
In the mid-1st century B.C. Julius Cæsar invited Sosigenes, an Alexandrian astronomer, to advise him about the reform of the calendar, and Sosigenes decided that the only practical step was to abandon the lunar calendar altogether. Months must be arranged on a seasonal basis, and a tropical (solar) year was used, as in the Egyptian calendar....5
Notice that Sosigenes' big innovation was an abandonment of lunar calendation:
The great difficulty facing any [calendar] reformer was that there seemed to be no way of effecting a change that would still allow the months to remain in step with the phases of the Moon and the year with the seasons. It was necessary to make a fundamental break with traditional reckoning to devise an efficient seasonal calendar.6
To bring the new calendar into alignment with the seasons required adding an additional 90 days to the year. This was done in 45 B.C., creating a year of 445 days. "This year of 445 days is commonly called by chronologists the year of confusion; but by Macrobius, more fitly, the last year of confusion."7 The first puzzle piece in establishing the truth of the calendar, is to realize that the Julian week of 45 B.C., did not look like the Julian week when Pope Gregory XIII modified it, and thus did not look like the modern Gregorian week of today. This is the first assumption made by both Jews and Christians, regardless of the day on which they worship.8