In fact all of these points have valid reasons which simply reflect some form of cruft. For instance, until Caesar February was the last month of the year, so t

In fact all of these points have valid reasons which simply reflect some form of cruft. For instance, until Caesar February was the last month of the year, so there was an intercalation of a month of varying length every two years(which made more sense). Also, the months September, October, November, December actually were the 7th, 8th, 9th and 10th months of the year. And all the months were 30 days (actually alternatively 29 and 31 days), but the mensis intercalaris which was either 22 or 23 days. Julius Caesar changed this because during the Civil wars of the late Republic, many times there was no Great Pontiff to do the calculations, so the additional month were left out a few times and the calendar was really getting out of sync. He changed the beginning of the year from the Spring solstice to January 1st, because that was the day of the consular election (and the consuls were elected for one year, so that made more sense as the years were named from the consuls that were elected). As for the birth of Jesus, we now know that it must be off by a few years. But originally, it was just the best guess they could come with; once it was found that Jesus actually wasn't born when initially thought, well, tough luck, it simply stayed as it was because it was too difficult to change after centuries of counting this way already. Regarding the use of base 60 for time, it made sense because it allows matching the course of the Sun and the Moon across the year (about 360 days), across the month (lunar month is 29.5 days) and the day. That's also why we cut circles in 360°: to allow for easy astronomical calculation (by approximating the year to 360 days, the lunation to 30 days), and splitting the day and night into 12 hours. Notice that until the invention of mechanical clocks, there was 12 hours a day and 12 hours a night, therefore hours were of varying length depending upon seasons, but OTOH using a sundial was dead simple -- which made sense when you had sundials, but no clocks...