The degrees of freedom: counting rule, year-beginning, epochs — what they do and who chooses which knob
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In-depth:
Josephus gives Herod two regnal figures: 37 years since the investiture, 34 since the capture of Jerusalem. Anyone who wants to extract a year of death from them sets four knobs: the year of the investiture, the year of the capture, the counting rule by which the years are added up, and the year-beginning at which a regnal year turns over. The Herod axis has no more degrees of freedom than that. The three chains set them thus:
investiture
capture
counting rule
year-beginning
year of death
C (Schürer/SVM; HV on these four)
40 BC
37 BC
inclusive
Nisan
4/3 BC
SY (Steinmann & Young)
39
36
non-inclusive, "except when an ordinal number is used"
Tishri
January of 1 BC
CA (Cameron 2018)
40/39
37
antedating
Nisan, varying
4/3, then winter 3/2
Three years of death, four years apart, from the same two figures. One knob makes that difference, and it is not the knob that stands out most.
2.1 The counting rule: what a year begun is worth
Inclusive reckoning counts every calendar year entered upon as a full regnal year; SVM gives the Mishnah form: "portions of a year as full years". Non-inclusive reckoning counts only completed years; the difference lies at the edges. The non-inclusive rule of Steinmann and Young carries an exception besides, "except when an ordinal number is used", and without that exception their own §3, Herod's "third year", falls. T is not a reproach, but a rule with an exception at its own awkward spot is no longer one rule.
Antedating, Cameron's rule, is not about the value of the partial year but about the question of to whom the transition year falls. Josephus counts, on Cameron's reading, regnal years as calendar years from a fixed year-beginning — year 1 is 37/36, year 34 is 4/3 — and the year in which the ruler dies falls to the successor, so that the death lies after the last counted year. Cameron demonstrates the rule on Josephus's own arithmetic before he uses it: AJ 15.260 counts 12 years from 37/36 and AJ 15.299 calls that same year Herod's thirteenth; recalculated on 25/24, that tallies. The rule is thus not ad hoc. But the last step — the transition year to the successor — is one branch of Schürer's rule, and Cameron calls the choice of that branch a "clarification". It is a choice, and it is the whole dispute.
2.2 The year-beginning: what it does not do
The year-beginning — Nisan for C and CA, Tishri for SY — looks like the second big knob and is the knob that does the least. All eight combinations of investiture year, counting rule and year-beginning have been computed. Exactly two reach January of 1 BC, both with investiture 39 and non-inclusive reckoning; whether the year turns over in Nisan or in Tishri is immaterial to that endpoint. Exactly one combination reaches the spring of 4 BC: investiture 40, inclusive, Nisan. One more, investiture 40, inclusive, Tishri, runs from Tishri 4 to Tishri 3 BC: the winter branch 4/3 (§6). The remaining four land in 3 or 2 BC, years without an umbral lunar eclipse.
The year-beginning thus bears the year of death on no chain. What it does decide is the seasonal boundary: whether "4/3 BC" runs from spring to spring or from autumn to autumn. Within the cell 4/3 BC, a Nisan year, two occupants are housed: Schürer's death at the beginning, between 1 and 14 Nisan, and Kushnir-Stein's death at the end, in the winter of 4/3. After the weighing of §6 HV arrives at: spring 4 BC; the winter of 4/3 remains possible but is less likely. The year-beginning cuts the cell; it does not choose between them. Whoever presents Nisan/Tishri as a load-bearing knob presents it wrongly.
The machine yields one more thing that runs against this work's own dossier: the consensus cell stands on one of the eight combinations, the SY cell on two. On robustness of the knob setting, that argues for SY and against C; the cost accounting (§2.5) weighs differently, but does not replace this measure.
2.3 The epochs: dated, not chosen
The two epochs are not free parameters: Josephus dates them. The investiture falls under the consuls of 40 BC; the capture under the consuls of 37 BC, in the 185th olympiad, "27 years after Pompey, on the same day". C reads the consuls and the olympiad of the capture plainly. The 184th olympiad given for the investiture had ended by the summer of 40; every chain, C included, sets it aside, so that it does not discriminate and stands outside the 20 primary data. SY shift both epochs by a year and, to do so, declare three data erroneous: of the consuls of 40, "the consensus date for this event must be in error"; the consuls of 37 and the olympiad are "contradicted". That is the whole hard cost of SY on those data: three V against zero for C.
The reason is the third dating in the same sentence. "27 years, on the same day" leaves no partial year to round off; the Mishnah form of inclusive reckoning finds no purchase here, and what remains is endpoint counting. For C this is the most expensive T on the ledger, and SVM itself sets the rejection beside it: "Josephus made a mistake in calculation [...] twenty-seven instead of twenty-six". But abandoning inclusive reckoning does not force one to 36 BC: Cameron keeps the consuls, the olympiad and the 27 years exact and pays on one other consular year. SY's three rejections are not the price of the constraint but of their way out of it.
The sabbatical year that Josephus places during the siege bears nothing under 37, in no direction. On Zuckermann's calendar 37 fits — but Zuckermann derived his calendar from the siege year 37 and himself calls his epoch "mit der Bescheidenheit einer Hypothese"; whoever adduces him as a leg under 37 adduces the outcome as ground for the input. On Wacholder's calendar the sabbatical year runs from Tishri 37 to Tishri 36; Sivan 36 falls within it, Sivan 37 does not, and AJ 14.475 then argues for a capture in 36. SVM sides with Wacholder and calls the passage "a considerable difficulty". For C an unresolved anomaly; for SY one of the three data that only they explain.
2.4 Who chooses which knob, and why
C chooses inclusive for the sake of the eclipse. SVM rejects, in the same edition, inclusive reckoning for the Hasmoneans and retains it for Herod. Cameron: SVM "acknowledges that the stated lengths for Herod's reign suggest that he died in 3 BCE, but he then falls back on [...] inclusive reckoning necessitated by the 4 BCE eclipse". The inclusive counting rule is thus not independently defended: it is applied to Herod, rejected elsewhere, and the eclipse is the license. This is the heaviest constraint against C's counting rule — and because HV reckons along with C on these four knobs, against HV too.
SY choose 39/36 and non-inclusive for the sake of AJ 14.487, and that brings them to January of 1 BC but no further. The regnal years of the three sons, counted back from their ends, come out before that year, and for that a fifth knob is needed: antedating of the sons. That knob was born on a single page to accommodate Julias/Paneas — "we may surmise that Philip, like his brothers, post-dated his reign from 4 BCE" — and in four published steps shifted from 4 BC to 6 BC (Tishri years). The epoch year is calculated from the three sons; the event it is supposed to mark is free, with as sole condition that it lies before the death. Neither of the two events they name holds up against the Greek text: BJ 1.461 concerns Antipater, Alexander and Aristobulus around 12 BC, dated by Steinmann and Young themselves "before the trials", which excludes their epoch year; BJ 1.573 and AJ 17.53 name not Philip but "Ἡρώδης ὁ ἐκ Μαριάμμης". The epoch has no attested event. One knob bears six rows on the ledger: they pay once, and that one postulate bears so much is the objection.
CA chooses antedating for the sake of a pattern, not of an outcome; that is his strength. His weakness is that the regnal figures do not bring him where he ends up. Year 34 from 37/36 is 4/3 BC, year 37 from 40/39 likewise; Cameron writes it himself and continues: "However, if Josephus was true to form, the year of Herod's death would not have been 4/3 BCE (Nisan), but rather the following year, 3/2". The step comes not from a figure but from the rule. And the "double confirmation" that 37 and 34 are supposed to give each other does not exist: the two anchors lie exactly three Nisan years apart and the two figures differ by exactly three, so every pair — n from Y, n−3 from Y+3 — coincides, whatever n; with Schürer just as neatly, a year earlier. The price of 3/2 lies with Philip. AJ 18.106 — Tiberius's 20th year, AD 33/34, Philip's 37th year from 4/3 — fits 4/3 untouched, Cameron's own note; for 3/2 the same verse requires two interventions: 20 to 22 on Latin editions without a Greek witness ("cannot be said to be compelling") and "37 years" read as "in the 38th". His only compelling datum for 3/2 is a city era — Caesarea Paneas, "year 220", era 3/2 or 2/1 — and that he himself makes dependent on his eclipse thesis.
2.5 The shared figure
The regnal figures 34 and 37 yield, counted plainly from the dated epochs, 4/3 BC — for C, and for CA before his last step. Only a counting-rule choice moves away from it: inclusive plus eclipse to the spring of 4 (C); antedating with the transition year to the successor to 3/2 (CA); investiture 39 plus non-inclusive to January of 1 BC (SY), where the epoch shift is not an independent knob but the consequence of their counting rule on AJ 14.487.
The cheapest surviving reading on this axis is thereby not a chain but a figure, 4/3 BC, with the prices of the rivals beside it. Within that year HV holds, after the weighing of §6: spring 4 BC; the winter of 4/3 remains possible but is less likely. SY buy January of 1 BC with three rejections and an antedating without an attested event. CA buys 3/2 with the transition-year choice, Philip as a loss entry and 19 corrections. C buys the spring of 4 with an inclusive counting rule that the same edition rejects for the Hasmoneans, licensed by the eclipse.
Within 4/3 BC the season remains open on this axis. The head cell hides Schürer's spring and Kushnir-Stein's winter, and no datum in the dossier decides between them. The only candidate — Gaius Caesar on the consilium against his consulship at Antioch on 1 January AD 1 — lies outside all counting conventions and has been measured on neither side.
2.6 HV's own knobs
HV shares with C the calculator, not the outcomes: the four knobs on the Herod axis are shared. Beyond them HV sets two knobs of its own, both on the baptism axis — in run B, that is, not in run A.
The first is an inclusive count of Tiberius's 15th year beginning in Tishri, which places the baptism after 20 October AD 27: late in the autumn of 27 or in the winter of 27/28. The scholarly literature knows it: Steinmann calculates the window himself — "For the inclusive method, the fifteenth year would have been one year earlier, AD 28 or autumn AD 27 to summer AD 28" — and Smallwood calls the count "presumably by Jewish reckoning". But the knob is not symmetrical with SY's Tishri knob. Against inclusive reckoning for Tiberius lie four positive measurements, not silence: RPC I 4270 (Antioch, double-dated on the Actian year), RPC I 4330 (Seleucia), the Alexandrian final-year test (year 23 present, 24 absent in the year in which Tiberius died) and Philo's twice-repeated 23. They measure the pagan provincial systems and show that those counted non-inclusively; the Jewish Tishri framework that Luke would be using they do not measure, and there is nothing there to measure either: the coins of the Judean prefects cannot separate the two counts. The cost is real and bounded: Luke must reckon in the Jewish manner, and within that framework a Nisan count is a live alternative alongside Tishri 27. Against HV's knob lies material, against SY's mainly the absence of it; whoever calls that equal is asymmetrical in their own favor.
The second knob is the shemitah chain. The siege year does not shift because of it (§2.3), the baptism anchor does: Tishri 27 on Zuckermann, Tishri 28 on Wacholder, and via Luke 3:23 the crucifixion axis and the birth window shift with it. Wacholder's entire deviation rests on Mur 18, and that reading is contested — Yaron reads line 7 as a prosbul clause, not as a date. Undecided between the calendars, and therefore absent in run A: what the window derives from this knob is measured by the difference between run A and run B, and that difference is an outcome, not an input.
Josephus gives Herod two regnal figures: 37 years since the investiture, 34 since the capture of Jerusalem. Anyone who wants to extract a year of death from them sets four knobs: the year of the investiture, the year of the capture, the counting rule by which the years are added up, and the year-beginning at which a regnal year turns over. The Herod axis has no more degrees of freedom than that. The three chains set them thus:
Three years of death, four years apart, from the same two figures. One knob makes that difference, and it is not the knob that stands out most.
2.1 The counting rule: what a year begun is worth
Inclusive reckoning counts every calendar year entered upon as a full regnal year; SVM gives the Mishnah form: "portions of a year as full years". Non-inclusive reckoning counts only completed years; the difference lies at the edges. The non-inclusive rule of Steinmann and Young carries an exception besides, "except when an ordinal number is used", and without that exception their own §3, Herod's "third year", falls. T is not a reproach, but a rule with an exception at its own awkward spot is no longer one rule.
Antedating, Cameron's rule, is not about the value of the partial year but about the question of to whom the transition year falls. Josephus counts, on Cameron's reading, regnal years as calendar years from a fixed year-beginning — year 1 is 37/36, year 34 is 4/3 — and the year in which the ruler dies falls to the successor, so that the death lies after the last counted year. Cameron demonstrates the rule on Josephus's own arithmetic before he uses it: AJ 15.260 counts 12 years from 37/36 and AJ 15.299 calls that same year Herod's thirteenth; recalculated on 25/24, that tallies. The rule is thus not ad hoc. But the last step — the transition year to the successor — is one branch of Schürer's rule, and Cameron calls the choice of that branch a "clarification". It is a choice, and it is the whole dispute.
2.2 The year-beginning: what it does not do
The year-beginning — Nisan for C and CA, Tishri for SY — looks like the second big knob and is the knob that does the least. All eight combinations of investiture year, counting rule and year-beginning have been computed. Exactly two reach January of 1 BC, both with investiture 39 and non-inclusive reckoning; whether the year turns over in Nisan or in Tishri is immaterial to that endpoint. Exactly one combination reaches the spring of 4 BC: investiture 40, inclusive, Nisan. One more, investiture 40, inclusive, Tishri, runs from Tishri 4 to Tishri 3 BC: the winter branch 4/3 (§6). The remaining four land in 3 or 2 BC, years without an umbral lunar eclipse.
The year-beginning thus bears the year of death on no chain. What it does decide is the seasonal boundary: whether "4/3 BC" runs from spring to spring or from autumn to autumn. Within the cell 4/3 BC, a Nisan year, two occupants are housed: Schürer's death at the beginning, between 1 and 14 Nisan, and Kushnir-Stein's death at the end, in the winter of 4/3. After the weighing of §6 HV arrives at: spring 4 BC; the winter of 4/3 remains possible but is less likely. The year-beginning cuts the cell; it does not choose between them. Whoever presents Nisan/Tishri as a load-bearing knob presents it wrongly.
The machine yields one more thing that runs against this work's own dossier: the consensus cell stands on one of the eight combinations, the SY cell on two. On robustness of the knob setting, that argues for SY and against C; the cost accounting (§2.5) weighs differently, but does not replace this measure.
2.3 The epochs: dated, not chosen
The two epochs are not free parameters: Josephus dates them. The investiture falls under the consuls of 40 BC; the capture under the consuls of 37 BC, in the 185th olympiad, "27 years after Pompey, on the same day". C reads the consuls and the olympiad of the capture plainly. The 184th olympiad given for the investiture had ended by the summer of 40; every chain, C included, sets it aside, so that it does not discriminate and stands outside the 20 primary data. SY shift both epochs by a year and, to do so, declare three data erroneous: of the consuls of 40, "the consensus date for this event must be in error"; the consuls of 37 and the olympiad are "contradicted". That is the whole hard cost of SY on those data: three V against zero for C.
The reason is the third dating in the same sentence. "27 years, on the same day" leaves no partial year to round off; the Mishnah form of inclusive reckoning finds no purchase here, and what remains is endpoint counting. For C this is the most expensive T on the ledger, and SVM itself sets the rejection beside it: "Josephus made a mistake in calculation [...] twenty-seven instead of twenty-six". But abandoning inclusive reckoning does not force one to 36 BC: Cameron keeps the consuls, the olympiad and the 27 years exact and pays on one other consular year. SY's three rejections are not the price of the constraint but of their way out of it.
The sabbatical year that Josephus places during the siege bears nothing under 37, in no direction. On Zuckermann's calendar 37 fits — but Zuckermann derived his calendar from the siege year 37 and himself calls his epoch "mit der Bescheidenheit einer Hypothese"; whoever adduces him as a leg under 37 adduces the outcome as ground for the input. On Wacholder's calendar the sabbatical year runs from Tishri 37 to Tishri 36; Sivan 36 falls within it, Sivan 37 does not, and AJ 14.475 then argues for a capture in 36. SVM sides with Wacholder and calls the passage "a considerable difficulty". For C an unresolved anomaly; for SY one of the three data that only they explain.
2.4 Who chooses which knob, and why
C chooses inclusive for the sake of the eclipse. SVM rejects, in the same edition, inclusive reckoning for the Hasmoneans and retains it for Herod. Cameron: SVM "acknowledges that the stated lengths for Herod's reign suggest that he died in 3 BCE, but he then falls back on [...] inclusive reckoning necessitated by the 4 BCE eclipse". The inclusive counting rule is thus not independently defended: it is applied to Herod, rejected elsewhere, and the eclipse is the license. This is the heaviest constraint against C's counting rule — and because HV reckons along with C on these four knobs, against HV too.
SY choose 39/36 and non-inclusive for the sake of AJ 14.487, and that brings them to January of 1 BC but no further. The regnal years of the three sons, counted back from their ends, come out before that year, and for that a fifth knob is needed: antedating of the sons. That knob was born on a single page to accommodate Julias/Paneas — "we may surmise that Philip, like his brothers, post-dated his reign from 4 BCE" — and in four published steps shifted from 4 BC to 6 BC (Tishri years). The epoch year is calculated from the three sons; the event it is supposed to mark is free, with as sole condition that it lies before the death. Neither of the two events they name holds up against the Greek text: BJ 1.461 concerns Antipater, Alexander and Aristobulus around 12 BC, dated by Steinmann and Young themselves "before the trials", which excludes their epoch year; BJ 1.573 and AJ 17.53 name not Philip but "Ἡρώδης ὁ ἐκ Μαριάμμης". The epoch has no attested event. One knob bears six rows on the ledger: they pay once, and that one postulate bears so much is the objection.
CA chooses antedating for the sake of a pattern, not of an outcome; that is his strength. His weakness is that the regnal figures do not bring him where he ends up. Year 34 from 37/36 is 4/3 BC, year 37 from 40/39 likewise; Cameron writes it himself and continues: "However, if Josephus was true to form, the year of Herod's death would not have been 4/3 BCE (Nisan), but rather the following year, 3/2". The step comes not from a figure but from the rule. And the "double confirmation" that 37 and 34 are supposed to give each other does not exist: the two anchors lie exactly three Nisan years apart and the two figures differ by exactly three, so every pair — n from Y, n−3 from Y+3 — coincides, whatever n; with Schürer just as neatly, a year earlier. The price of 3/2 lies with Philip. AJ 18.106 — Tiberius's 20th year, AD 33/34, Philip's 37th year from 4/3 — fits 4/3 untouched, Cameron's own note; for 3/2 the same verse requires two interventions: 20 to 22 on Latin editions without a Greek witness ("cannot be said to be compelling") and "37 years" read as "in the 38th". His only compelling datum for 3/2 is a city era — Caesarea Paneas, "year 220", era 3/2 or 2/1 — and that he himself makes dependent on his eclipse thesis.
2.5 The shared figure
The regnal figures 34 and 37 yield, counted plainly from the dated epochs, 4/3 BC — for C, and for CA before his last step. Only a counting-rule choice moves away from it: inclusive plus eclipse to the spring of 4 (C); antedating with the transition year to the successor to 3/2 (CA); investiture 39 plus non-inclusive to January of 1 BC (SY), where the epoch shift is not an independent knob but the consequence of their counting rule on AJ 14.487.
The cheapest surviving reading on this axis is thereby not a chain but a figure, 4/3 BC, with the prices of the rivals beside it. Within that year HV holds, after the weighing of §6: spring 4 BC; the winter of 4/3 remains possible but is less likely. SY buy January of 1 BC with three rejections and an antedating without an attested event. CA buys 3/2 with the transition-year choice, Philip as a loss entry and 19 corrections. C buys the spring of 4 with an inclusive counting rule that the same edition rejects for the Hasmoneans, licensed by the eclipse.
Within 4/3 BC the season remains open on this axis. The head cell hides Schürer's spring and Kushnir-Stein's winter, and no datum in the dossier decides between them. The only candidate — Gaius Caesar on the consilium against his consulship at Antioch on 1 January AD 1 — lies outside all counting conventions and has been measured on neither side.
2.6 HV's own knobs
HV shares with C the calculator, not the outcomes: the four knobs on the Herod axis are shared. Beyond them HV sets two knobs of its own, both on the baptism axis — in run B, that is, not in run A.
The first is an inclusive count of Tiberius's 15th year beginning in Tishri, which places the baptism after 20 October AD 27: late in the autumn of 27 or in the winter of 27/28. The scholarly literature knows it: Steinmann calculates the window himself — "For the inclusive method, the fifteenth year would have been one year earlier, AD 28 or autumn AD 27 to summer AD 28" — and Smallwood calls the count "presumably by Jewish reckoning". But the knob is not symmetrical with SY's Tishri knob. Against inclusive reckoning for Tiberius lie four positive measurements, not silence: RPC I 4270 (Antioch, double-dated on the Actian year), RPC I 4330 (Seleucia), the Alexandrian final-year test (year 23 present, 24 absent in the year in which Tiberius died) and Philo's twice-repeated 23. They measure the pagan provincial systems and show that those counted non-inclusively; the Jewish Tishri framework that Luke would be using they do not measure, and there is nothing there to measure either: the coins of the Judean prefects cannot separate the two counts. The cost is real and bounded: Luke must reckon in the Jewish manner, and within that framework a Nisan count is a live alternative alongside Tishri 27. Against HV's knob lies material, against SY's mainly the absence of it; whoever calls that equal is asymmetrical in their own favor.
The second knob is the shemitah chain. The siege year does not shift because of it (§2.3), the baptism anchor does: Tishri 27 on Zuckermann, Tishri 28 on Wacholder, and via Luke 3:23 the crucifixion axis and the birth window shift with it. Wacholder's entire deviation rests on Mur 18, and that reading is contested — Yaron reads line 7 as a prosbul clause, not as a date. Undecided between the calendars, and therefore absent in run A: what the window derives from this knob is measured by the difference between run A and run B, and that difference is an outcome, not an input.