Rabbi Gershon Tannenbaum, in his weekly My Machberes column in the Jewish Press talks about the Jewish calendar. As a part of this column, he makes the following observation:
In 4104 (344 CE), Hillel wrote his formulas predicting the Hebrew calendar until the Hebrew year 6000 (2240 CE). In 1949, the National Institute of Time and Technology established the Atomic Clock to standardize times throughout the world. Since its establishment, the Atomic Clock has been readjusted several times. Hillel's calendar has never been readjusted and remains supremely accurate. The precision of the Molad announced in every shul during Rosh Chodesh Bentching, indicating the exact time of the new moon in Jerusalem, continues to be breathtaking.
Now, as my mother told me when I was young, it's okay to toot your own horn, but don't do it by putting down others - and especially when don't toot your own horn and put others down when you're wrong.
The Hebrew calendar is pretty accurate, no question about it - but compared to the Atomic clock, it just falls flat.
First, a little background. The Jewish calendar, unlike most calendars, is a luni-solar calendar. While the months are reckoned according to the phases of the moon, it is occassionally reconciled to the solar calendar. Because the solar calendar is longer than the lunar calendar by 11 days (approximately), an extra month is inserted into the calendar 7 out of 19 years. As a result, there are 235 month (12 x 19 + 7 extra months) in the Jewish calendar every 19 years. These 235 lunar months come out to the same length as 228 solar months.
But not exactly.
As it turns out, 235 lunar months does not exactly equal 228 solar months. In fact, the 235 lunar months come out (on average) to about two hours longer than the 228 solar months. Now, two hours over a 19 year span may not sound like much, but over the course of the centuries, they add up. In about 216 years, you have a one-day difference. Since we're 1,665 years away from when the calendar was first set up by Hillel, the differences between the solar and lunar calendar have built up to about eight days. That means that we celebrate our holidays about eight days later in the year than Hillel did. Carried far enough (assuming Moshiach doesn't come by then), we could, in theory, begin celebrating Pesach in the summer! The Hebrew calendar may have been pretty accurate considering the technology of the time that it was established, but to say that it remains "supremely accurate" is just plain bunk.
As for the atomic clock, it's probably unfair to compare it to the Hebrew calendar. Part of the reason for that is that the atomic clock does not reckon time by the motions of heavenly bodies but by the occelations of a cesium atom. A second is no longer 1/31557600 of a year, but is now defined as follows:
The second is the duration of 9,192,631,770* periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
In other words, instead of reckoning time by the sun, they now use cesium atoms (hence the name "atomic clock"). As such, comparing it to the Hebrew calendar would be like comparing apples and oranges... they judge time by two completely different standards.
However, we can look at the Gregorian calendar, which has been in use for over four hundred years. The average Gregorian year differs from the astrnomical year by about 26 seconds per year. As a result, the Gregorian calendar gains a day every 3300 years. That being said, let's see which calendar is more accurate:
Gregorian: gains 1 day in 3300 years
Hebrew: gains about 15 days in 3300 years (1 day every 216 years or so).
Clear winner: Gregorian.
Of course, Pope Gregory had a twelve hundred year head start on Hillel, so it's understandable that his calendar might be more accurate. But to state that the Jewish calendar is "supremely accurate" while descibing the secular calendar as less accurate is just plain wrong.
While we're at it, we should also take a look at this statement of Rabbi Tannenbaum's:
The precision of the Molad announced in every shul during Rosh Chodesh Bentching, indicating the exact time of the new moon in Jerusalem, continues to be breathtaking.
It may be breathtaking, but it's also wrong.
The molad is based on an average period between new moons of 29 days, 12 hours, 44 minutes and 3 1/3 seconds. However, that period is actually wrong. The true period for the molad is about 3/5 of a second longer than that. Again, 3/5 of a second per month may not sound like a lot, but over the course of the centuries, they add up. Currently, the true molad is about two and a third hours later than the molad according to the Jewish calendar. Therefore, the molad that is announced in shul is no longer the exact time the new moon is visible over Jerusalem, but the time the new moon is visible over Afghanistan.
* I wonder if people in Chabad would find some significance in that number.