Why printed tables disagree

Two sources, both consistent, both different

A reader with a printed table on paper and a converted date on screen finds that the two do not agree. The table gives one start date for a sign, the same date year after year. The conversion gives a date a day earlier or later for this particular year. Nothing looks broken. Each source is internally consistent, and neither explains the gap.

The question underneath is not which one is correct. It is what kind of object a fixed table is. A printed date answers the question of when a sign usually begins. A computed date answers when it begins in one named year. Those are different questions, and the useful thing to know is how far apart their answers can fall, and how often they do.

Two leap rules, one whole day to assign

Both calendars answer the same problem — the year is not a whole number of days — by different methods. The Gregorian calendar inserts its leap day on a fixed arithmetic schedule, settled in advance and indifferent to the sky. The Persian year begins on the day of the vernal equinox, so its leap years fall where the equinox falls. Two calendars correcting the same drift by unrelated methods do not stay in step, and the mismatch is what a printed table has to absorb.

The equinox does not return to the same civil day each year either. The tropical year runs a fraction of a day longer than a whole count of days, so the equinox comes slightly later each year and is pulled back when a leap day intervenes. A civil calendar has to assign it to one whole day, and which day that is changes. Each sign in these tables has 3 distinct start dates across the window, and the furthest a printed date sits from a real one is 1 day.

Across 12 signs and 101 years, a fixed table claims 1212 boundaries. Its date is right for 936 and wrong for 276 — 22.8 per cent, or 78 years right and 23 wrong per sign out of 101. The window is the Persian years 1329 to 1429, or 1950 to 2051 in the Gregorian calendar: a count over a documented span, not a property of printed tables everywhere. The comparison was also charitable. Each sign was given the date that occurs most often, the best any single fixed date can do; a real table may print a conventional date instead, and the second-best date for a sign is wrong in 81 of the 101 years. So 22.8 per cent is a floor, not a worst case.

Every sign is wrong in the same years. One equinox-anchored boundary shifts, and fixed month lengths carry that shift through all twelve signs: one error, seen twelve times.

What this means when a date matters

When the two sources disagree, the gap is 1 day, and it is never confined to a single sign. If a printed start date is off in one year, the printed dates for the other signs are off in that same year and in the same direction. The thing to check is the year, not the sign.

For a sense of season — which sign covers late spring, roughly when a month opens — a fixed table is a reasonable guide, and per sign it agrees with the calendar in 78 of the 101 years measured. For the boundary day itself, in a named year, only a date computed for that year gives the day the calendar actually assigns. The table is a summary of a century; a conversion is a statement about one year in it.