Question: I think I can make a better Biblical calendar!
Reply: There are indeed problems with the Calendar - but I've yet to see a solution that does not have its own problems!

The following seem well documented:
(a) There is not enough information in the Bible to construct a calendar.  Perhaps this is a signal that Almighty God allows us a lot of discretion: "Man was not made for the Calendar, the Calendar was made for man."
(b) At the time of Christ, the Temple Calendar was essentially by intelligent observation. (Months not too long or too short, years not too long or too short)
(c) There were special adjustments: e.g., because there were not enough lambs for the Passover, to give time to prepare for Temple rituals, etc.
(d) The Calendar was self-correcting, so that adjustments and mistakes did not accumulate.
(e) Honest mistakes did happen, but the Jewish authorities came to the conclusion that, since God permitted the mistakes, God still honored their Holy Day observances, even if on the "wrong" day.
(f) There were calendar arguments at the time of Jesus.  (These may underlie the disagreement between John and the synoptics about the timing of the "Last Supper".)

What has happened among the Jews:
(a) The Pharisees switched Pentecost from Sunday to 6th Sivan after the destruction of the Temple (see discussion in shavuot.htm with reference to Megillath Ta'anith, "Scroll of Fasting" (ca. 150 A.D.) .
(b) Christian persecution of the Jews forced them to switch from observation to calculation.
(c) The calculation, including the postponements, were designed to imitate as closely as possible what actually happened at the Temple under observation.
(d) The "19 year time cycle" - invented in Babylon and refined by the Jews is good, but not perfect.  The Calendar is now running late, and needs an adjustment by one month.   The Jews cannot decide when to adjust it.  This is similar to our change from the Julian to Gregorian calendar.
(e) The last major Calendar argument among mainline Jews was in 921 A.D. (see abcog.org/saadia.htm). It did not lead to a change in the Calendar.

What is necessary to define a "new calendar".  Here are some considerations:
(a) when does the sun set?
(b) when is a "new moon"?
(c) when is "Green Ears" = "Abib"?
(d) is observation (by whom and from precisely where) or calculation (by whom and based on precisely where) to be trusted?
(e) if by calculation, in view of "wobbles" in the Earth's motion, how far in advance are calculations to be trusted?
(f) if by calculation, is the 19-year-cycle to be followed?
(g) if by observation, how far in advance must the observation be made? (Particularly important for the Feast of Trumpets) - but also important for booking Feast sites etc.
(h) if by observation, are climatic variations to be allowed? (Late Spring harvests? Late Fall harvests?)
(i) under what, if any, special circumstances would calendar adjustments be allowed?
(j) is there a minority sect of the Jews (e.g., Karaites) whose calendar we trust?

In summary, we are like the Jews in 1st Maccabees.  They didn't know what to do with the defiled altar.  So they did the intelligent thing until a prophet should tell them otherwise.  A prophet never did! 

What is the intelligent thing for us to do?  Trust a new "expert" or trust those who have managed to preserve the Sabbath cycle for thousands of years?

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