The calendar is such a basic thing that we take it for granted. It consists of 52 weeks of seven days, plus one extra day, for a total of 365 days. Leap year adds one day every four years, except in years that are divisible by 400, except the year 2000, which was a leap year anyway.

Beneath that relative simplicity underlies a numerical puzzle that required thousands of years to solve. Complications arose because the motions of the earth, sun and moon are not synchronized, and it is not easy even to determine the number of days in a year.

Finding the simplest way to keep the calendar in harmony with the cosmos took thousands of years. The ancient Egyptians almost had it thousands of years ago, but their calendar had no leap year.

The error caused the starting date of the year to drift slowly forward with respect to the seasons, and it took 1,460 years to return to where it started. All they had to do was add a day every four years — so near but yet so far.

A thousand years later Mesopotamians added seven extra months over 19 years. The extra month was added in years three, six, eight, 11, 14, 17 and 19. It was added in the 12th month in most of those years except in the 17th year, when it was added after the sixth month.

Just try to keep track of the date using that system!

Two thousand years later the Romans were not as good at astronomy as the Egyptians, but they were able to develop a calendar with leap years. The Roman calendar began when Rom- ulus, the founder and first king of Rome, divided a year of only 304 days into 10 months. Numa, his successor, added two extra months.

The 12 months consisted of alternating 29- and 30-day months to roughly correspond with the moon cycle. Originally, the year contained 354 days, but an extra day was added to make the number odd, which was astrologically more favorable.

To keep this calendar in sync with the seasons, an extra month was inserted every second year, consisting of 22 and 23 days alternately, so that four years constituted 1,465 days, and the average length of the year was 366-1/4 days.

This made the year too long by one day, which made another correction necessary.

Since the one extra day added 24 days in as many years, every third eight-year period had only three extra months instead of four, consisting of 22 days each. This finally brought the average length of the year to 365-1/4 days.

Later, priests were given the power to add days as needed if the calendar was found to differ from the celestial motions. Bribes quickly caused abuses of this power as days were added for political interests to prolong or shorten a political term or to hasten annual elections.

The beautifully designed Roman calendar was thrown into chaos. By the time of Julius Caesar, the calendar was off by more than two months.

To end the disorder, Caesar decreed in 45 B.C. that every fourth year should have 366 days and the other years have 365. In order to calibrate the calendar, he ordered a one-time insertion of two months between November and December. Caesar’s calendar with its leap year began on Jan. 1 and is known as the Julian calendar.

This should have solved the major part of the problem, but things are never that simple.

Due to a misunderstanding, every third year instead of every fourth was made a leap year for some years, and because leap years were considered unlucky, they were avoided in times of crisis.

The final solution was the Gregorian calendar, introduced in 1582 by Pope Gregory I as part of the sweeping changes to the Roman Catholic Church in the face of the Protestant Revolution.

By then the date of the vernal equinox had drifted backward, and it was felt that March 21 was the proper day for it as the Council of Nicaea in A.D. 325 had established. Then the Julian calendar had Easter sometimes falling before the equinox, which cannot happen.

To bring the calendar back into sync with the heavens, 10 days had to be deleted. Many people were offended, angered or downright scared, being convinced that the change would shorten their lives by 10 days.

Our current Gregorian calendar is based on a cycle of 400 years, which is 146,097 days. Dividing 146,097 by 400 yields an average length of 365.2425 days per calendar year, which is close but not exact. The difference amounts to one day in 2,500 years.

The first correction is due in the year 4082. Don’t hold your breath!

Richard Brill is a retired professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.