The calendar was never the disagreement.

The robustness sweep ends with two years, and no better ephemeris will improve on that, because both AD 30 and AD 33 genuinely put 14 Nisan on a Friday. The ambiguity is not in the sky. Every narrowing to a single year is done with non-calendrical evidence — Luke's synchronism, the length of the ministry, the chain back from an inscription at Delphi. Those arguments are normally made one at a time, in prose, with each author holding fixed the assumptions that suit the conclusion. So this page does to them what the robustness page did to the astronomy: makes every assumption a parameter, runs all 20,736 combinations, and counts.

The constraints

Each is a falsifiable predicate: give it a candidate year and a setting of the parameters it depends on, and it admits the year, excludes it, or says nothing. A constraint that cannot return "excluded" is decoration rather than evidence, and the build fails if one slips in.

What the textual arguments say on their own

All 20,736 combinations of the undisputed constraints, counting how many admit each year:

The peak is AD 30 — a year that is not a candidate at all, because 14 Nisan does not fall on a Friday in it. Neither half of the evidence produces the received answer by itself. The textual arguments, enumerated without cherry-picking, centre on a year the calendar forbids; the calendar admits years the texts barely support. That is worth stating plainly, because every published treatment of this question presents one half as confirming the other.

The reading that actually decides it

This is the section the rest of the page exists for. The robustness sweep once reported AD 27 as the most robust year, and it was an artifact: one parameter dominated the space and the average concealed it. So rather than trust an average again, hold each parameter at each of its values and look at what changes.

Parameters are ranked by swing: how far the lead AD 30 holds over AD 33 travels as that one parameter is moved and everything else is left free. A parameter whose swing spans zero flips the ranking on its own — set it one way and AD 30 leads, set it the other and AD 33 does.

2 of the 11 parameters flip the ranking single-handed, and the largest is When the Nabataeans held Damascus at 16.2 points, ahead of Which epoch for Tiberius at 15.0. AD 30 leads across the space as a whole, but "leads" is doing very little work: set either of those two parameters the other way and AD 33 is ahead.

How stable is that, measured

An earlier version of this page asserted, in prose, that the ranking had "flipped three times". That claim was written by hand and nothing recomputed it — the exact failure this project has now caught itself in five times. So it is computed instead, by rebuilding each earlier state of the model as a restriction of the current one and re-running it.

As the model stands, AD 30 leads by 8.2 points, and 2 of the 11 parameters can overturn that on their own — when the nabataeans held damascus and which epoch for tiberius. That is a stability of 0.82, where 1 would mean nothing could overturn the result and 0 that everything could.

The trajectory in the table is the part worth reading. The model became less settled as it became more correct: the revision where nothing at all could overturn the ranking was the one with a constraint modelled lazily and a contested identification held as an unstated premise. Every change since came from adding a parameter rather than removing one, and every one of them came from reading a source rather than improving the astronomy. A result this sensitive to which questions somebody thought to ask is not a result to report as an answer — and the superseded versions are left standing on this page for the same reason the number above is computed.

The Galatians question is still the clearest to state, and it is now two questions rather than one. Galatians 2:1 says Paul went up to Jerusalem "after fourteen years" — and does not say fourteen years after what. If they run from the first visit of 1:18, they add to its three; if from the conversion, the two intervals overlap. That is worth three years. But the sharper question is which visit 2:1 describes at all: the Jerusalem council of Acts 15, or the famine visit of Acts 11:27–30 about three years earlier, which is how F. F. Bruce and Longenecker read it. This site assumed the council for a long time — not as a swept option but as an unstated premise, which is the worst way to hold a contested position.

On the reading itself the Greek is not quite neutral, though it is short of decisive. Galatians 1:18, 1:21 and 2:1 all open with ἔπειτα — "thereupon, thereafter" — a sequential adverb, with the time phrases attached to it epexegetically (Thayer). Paul is narrating stages, and a sequence marker most naturally measures from the stage just narrated. Against that, διὰ with the genitive of time does not by itself fix a terminus, and plenty of scholars still count both intervals from the call of 1:15–16. Both readings stay in the space, each with its reason.

One parameter is worth noting for doing nothing: when Pilate arrived. Schwartz's AD 19 against the standard AD 26 changes the answer by 0.0 points — the two rows are identical. A dispute can be perfectly real, well argued on both sides, and still have no bearing whatever on the question you are asking.

What reading one paper did to all of this

Everything above weights the four readings of Tiberius's reign equally, because this page had no reason to prefer any of them. That was an admission of ignorance, and it turned out to be a remediable one.

Andrew Steinmann, in Tyndale Bulletin 73 (2022), 91–118, surveys the first- and second-century literary, numismatic and inscriptional evidence for when Tiberius's reign was reckoned to begin. He finds Tacitus, Suetonius, Cassius Dio, Philo, Josephus, Clement of Alexandria and Tertullian — Roman, Jewish and Christian, east and west — “all unanimous in reckoning Tiberius's reign after Augustus's death”, and concludes there is “no support for an earlier dating of Tiberius's reign”. The co-regency reckoning rests on the grant of joint provincial authority in AD 12–13; no ancient writer is shown counting regnal years from it.

The 3 co-regency options are kept in the space, not deleted — a sweep that quietly drops the positions its author finds unpersuasive is not a sweep. But they are now flagged, and the page reports both answers:

That reversal was then withdrawn, and has since come back. It first depended on an assumption this page was making silently — that the Jerusalem visit of Galatians 2:1 is the council of Acts 15. Offering the Acts 11 famine visit alongside it, as F. F. Bruce and Longenecker read it, removed the reversal entirely: AD 30 led under every setting.

Then the Aretas constraint was modelled properly. It had been reduced here to "Aretas was alive", an upper bound at his death in AD 40, which made it nearly inert. But when the Nabataeans held Damascus is itself disputed, and on one reading they held it only after Tiberius died in March AD 37 — which turns the constraint from a ceiling into a four-year window and excludes AD 30 outright. With that in the space, the sole-reign restriction reverses the ranking again, narrowly. Hold the Galatians visit to Acts 15 as well and the AD 33 lead widens sharply — which is how the original reversal was manufactured.

Three things worth taking from the episode. First, both corrections came from reading rather than from computing — one peer-reviewed article and one identification this project had never offered as a choice. No improvement to the astronomy would have produced either. Second, the fix was to add an option, not to remove one. Widening the space made the answer more robust rather than less, which is the opposite of what one expects and is worth remembering the next time a parameter looks like an inconvenience. Third, this page has now stated three different things about the AD 30 / AD 33 ranking, and each superseded version is left visible above its replacement. A site that silently updates its answers is indistinguishable from one that never had a method.

Also worth noting: the same paper explains the Tertullian anomaly better than this site's own guess did, and corrects an error here about how Hoehner reaches a four-Passover ministry. One article, three corrections.

Where the two independent lines meet

The astronomical half knows nothing about Tiberius; the textual half knows nothing about the moon. Their errors are therefore independent, which is the only reason intersecting them means anything. Astronomically admissible years are those any best-evidenced configuration allows under any Nisan rule and either gospel chronology.

Four years survive both lines: AD 27, AD 30, AD 33, AD 34. Ranked by textual support, AD 30 carries roughly twice the configurations of AD 33, and AD 27 and AD 34 are all but dead — each admitted by well under one per cent of the textual space while remaining astronomically possible. That is a real narrowing, honestly earned, and it is a great deal less than a date. It does not tell you the year. It tells you that two of the four candidates are barely defensible and that the remaining choice is the Galatians one.

What the disputed arguments do

Two familiar arguments are excluded from everything above, for the same reason the eclipse is quarantined on its own page: they are contested, and folding a contested argument into a default would settle the question by assumption rather than by evidence.

What this does and does not establish

The astronomical half of the argument → · Every source behind both →