Numbers and the sky

We describe a year when the rules don’t work.

Not long ago we pointed out the danger we may face in the year 2048, when all our digital devices will need another register to keep count of the year in binary.  Thinking of that, our astronomer vaguely remembered something happening a decade sooner, and after some research found an anomaly in the computation of Easter.  That will probably require some explanation.

The early Christian Church decided that Easter should be the first Sunday after the first Full Moon after the spring equinox.  The lunar cycle was included because the Jewish calendar keeps months in step with the actual Moon, and the original Easter occurred after the Jewish spring feast of the Passover.  But notice that the Church required some kind of reconciliation of three distinct and non-commensurable cycles: the year, of 365.25 days (approximately); the synodical period of the Moon, about 29.5 days but somewhat variable; and the seven days in a week.  Dealing with some or all of them is the task of the calendar-maker, and is either fascinating or deadly dull depending on one’s attitude.  It put the Church in the position of sponsoring astronomical research.

But there were immediate practical problems.  Easter had to be predicted in advance, especially since other “movable feasts” depend on it.  One couldn’t use, say, national observatories to work out the date of the equinox, or the phase of the Moon; there weren’t any.  And the expertise to use what predictive power there was in Ptolemy’s Almagest was very thin on the ground.  Of course sending out yearly printed calendars to all the parishes of Medieval Europe was impossible.

So the Church calendar-people produced a set of tables and rules by which everyone could work out when the great feast would happen.  The equinox was fixed to be on March 21st, though it could actually vary back and forth over several days.  The 19-year saros cycle, which predicts lunar phases fairly accurately, was turned into a table.  You can still go through the procedure (it’s in the back of the Anglican Prayer Book, for instance), though nowadays it’s done for you and published well in advance.

It only breaks down under special conditions.  If the equinox is actually on the 19th or 20th (which can happen), it doesn’t actually matter as long as the next Full Moon is on the 21st or later.  You need, say, an equinox and a Full Moon on the 20th.  In that case, the formal rule has Easter on the following Sunday, while the tables place it a whole month later.  That’s what happens in 2038.

Does it matter?  To almost everyone nowadays, no.  In fact the Eastern Orthodox Church has been celebrating its feasts out of step with the western churches (or vice versa) for several centuries now, without much friction (on that matter, at any rate).  But in the past it was overwhelmingly important to many people that they perform their worship in the proper way, down to the last detail.  Celebrating Easter a month early or late was a grave, and obvious, error.

We wonder whether people might feel at least a niggling doubt about following the tables instead of the sky, fifteen years from now.