The cycle problem

Which Hebrew calendar are we even reconstructing?

The eclipse debate is about choosing between AD 30 and AD 33. This page is about something more awkward: whether the machinery that produced those two candidates in the first place describes what anyone in first-century Judea was actually doing. The honest answer is that it probably doesn't, quite.

What the dial is actually animating

The volvelle on the front page inserts a thirteenth month on years 3, 6, 8, 11, 14, 17 and 19 of a nineteen-year cycle. That is the modern rule — the fixed, calculated, arithmetic calendar. It is traditionally traced to Hillel II around 358–359 CE, three centuries after the events this site is used to examine.

Before that, months were not calculated. They were declared. The Sanhedrin decided, and the Talmud preserves the kinds of consideration that went into deciding: whether the barley was ripe (aviv), where the spring equinox fell, whether the roads and bridges would carry pilgrims, whether the lambs were grown. This is agricultural and political judgement, not arithmetic — and judgement is not reproducible from an ephemeris two thousand years later.

Talmud, Sanhedrin 11a–b, on the criteria for declaring a leap year.

The sequences don't agree with each other

Even within the calculated tradition, the pattern this site draws is not the only one that has been used. The Encyclopaedia Judaica records rival intercalation sequences circulating as late as the tenth century:

  • (1, 4, 6, 9, 12, 15, 17)
  • (3, 5, 8, 11, 14, 16, 19)
  • (2, 5, 7, 10, 13, 16, 18)
  • (3, 6, 8, 11, 14, 17, 19) — the one that eventually won, and the one you are watching

These are not trivial variations. Shifting which years take a thirteenth month moves Passover by a whole lunar month in the years where they disagree.

The finding that cuts deepest

The most serious problem for any backwards projection comes from Sacha Stern's Calendar and Community, the standard scholarly history of the Jewish calendar. Three of its conclusions matter here, and each one weakens this site's own engine.

There was no single calendar

Stern's overall picture is of a period moving from diversity to unity — a variety of solar and lunar calendars in use, converging only much later. Speaking of "the Hebrew calendar" in the first century is already a simplification. Some Jewish groups, notably at Qumran, reckoned by a 364-day schematic year that has nothing to do with the moon at all.

Intercalation stayed unsystematic for centuries

On Stern's account there was still no uniform system of intercalation as late as the sixth century. The fixed calculated calendar evolved gradually from the third century onward, largely under pressure from the Babylonian rabbinic community, and only became dominant across the Jewish world by the tenth.

Early practice ran late

This is the one that bites. Stern finds that until the first century CE, Jewish lunar calendars tended to run late relative to the solar year — Passover would always fall after the spring equinox. By the fourth century the adjustment had shifted the other way, and Passover frequently fell earlier.

What that does to this engine

The code here picks Nisan as the first lunar month whose full moon falls on or after the equinox. That is a reasonable modern reconstruction. But if actual first-century practice systematically ran later than the rule assumes, then in some years the real Nisan was the following month — and every date computed for that year is wrong by roughly twenty-nine days.

Stern, S., Calendar and Community: A History of the Jewish Calendar, 2nd Century BCE – 10th Century CE (Oxford University Press, 2001).

So why does the engine still produce the right answer?

A fair question, and worth being precise about. The reconstruction on this site reproduces the two candidate Fridays that the scholarly literature also arrives at. That is a real result and it is not an accident — the astronomy underneath it is sound, and the tests pin it.

But agreement with other reconstructions is not the same as agreement with history. Humphreys and Waddington projected essentially the same kind of rule backwards. When two models share an assumption, their agreeing tells you the arithmetic is consistent; it does not tell you the assumption is right. The AD 30 and AD 33 candidates are stable across reconstructions because those reconstructions are close cousins, not because a first-century record confirms them.

The load-bearing caveat. This site can tell you, accurately, which Fridays a particular set of rules produces. It cannot tell you that the Sanhedrin followed those rules in any given spring. A body of men looking at barley and weather could have declared a leap month in a year the arithmetic says they shouldn't have — and nothing in the astronomy would ever reveal it.

Next: exactly what the engine computes, and where it stops →