Question

I recently tried to find out from when the counting of the Sabbatical cycles began, the cycles because of which the Babylonian exile was decreed—but without success. While searching I came across an article (in the link below) about a proof that seems impressive but also thought-provoking, that the Exodus took place in 1446 BCE. Below is a summary of the argument for the benefit of Hebrew-speaking humanity.
 
The Babylonian Talmud mentions two events in the biblical period, and only two, in which the Jubilee applied. One is in Arakhin (12b) about Ezekiel, and the other in Megillah (14b) about Josiah. The Talmud in Arakhin deals with the fact that the New Year mentioned in Ezekiel 40 falls on the 10th of the month, and concludes from this that it was obviously a Jubilee year.
But it is written (Ezekiel 40:1) “In the twenty-fifth year of our exile, at the beginning of the year, on the tenth of the month, in the fourteenth year after the city was struck”— what year is it in which the beginning of the year is on the tenth of the month? You must say: this is the Jubilee.
Ezekiel dates the vision in this verse in two ways. First, the 25th year of his exile (the exile of Jehoiachin). According to the Babylonian chronicles, Jehoiachin was captured on the second of Adar, 597 BCE, meaning that the first year of that exile was the Judean regnal year that began in Tishrei of 598 BCE, and it follows that the 25th year began in Tishrei of 574 BCE (below we will denote the regnal year by the Gregorian BCE year in whose Tishrei it begins, with the suffix t, thus: 574t). The second dating Ezekiel provides is “fourteen years after the city was struck.” “After” tells us that 14 full years had passed since the fall of the city, similar to the style of the genealogies in Genesis 5 and elsewhere in the Bible. Jerusalem was captured in Tammuz, in the summer of 587 BCE, in the year that began in Tishrei of 588 BCE (588t). Fourteen years later again brings us to 574 BCE, which matches the first method of dating.
In the second case, the Talmud is bothered by the question of where the leading sage of the generation, Jeremiah, was when Josiah’s representatives went to consult Huldah.
Rabbi Yohanan said: Jeremiah was not there, because he had gone to bring back the Ten Tribes. And from where do we know that he brought them back? As it is written (Ezekiel 17:13) “For the seller shall not return to that which is sold.” Is it possible that the Jubilee had ceased and the prophet prophesies about it as though it would cease? Rather, this teaches that Jeremiah brought them back.
True, the idea that Jeremiah brought back the Ten Tribes is entirely imaginary, but its purpose is to explain how the Jubilee could have been observed in that year. Rabbi Yohanan’s reasoning is that for the Jubilee to apply, the Ten Tribes had to be in their place, and he tried to reconcile that with the fact that the Jubilee was observed in the year when Josiah’s representatives consulted Huldah—in the 18th year of Josiah (2 Kings 22:3). That whole chain of inference is of course mistaken, but it does not follow that the basic assumption from which the Talmud began, and which it is trying to explain, is also mistaken. What the Talmud sees as the authoritative sources, for which it offers its interpretations, are the biblical passages cited and the idea that the Jubilee was observed in Josiah’s 18th year, and the various opinions are stated around those sources. The assumption that the Jubilee was observed in the year of the meeting with Huldah arises because it is mentioned in Seder Olam, and in principle the Talmud regards Seder Olam as an authoritative source. Chapter 24 of Seder Olam cites what is said in 2 Kings (22:3) about the 18th year of Josiah, stating: “That year a Torah scroll was found in the House of the Lord, and that year was the beginning of the Jubilee, and that year Josiah inspected the Temple.” The passage in Arakhin also plainly shows that this is the source of these traditions, since the discussion there begins with three quotations from chapter 11 of Seder Olam.
When was that Jubilee observed? The scholar Edwin Thiele established the year of Josiah’s accession as 641t. His reign, 31 years in length, ended in 610t. His 18th regnal year was therefore
 641t – 18 = 623t
exactly 49 years before the second Jubilee mentioned in the Talmud, in 574t.
The author of the article expands on the claim that the early sources provide decisive evidence that the Jubilee cycle was 49 years, not 50. Although post-Talmudic sources like Rashi and Maimonides generally settled on 50, the pre-Talmudic sources put all the weight on the view that in practice these were 49-year cycles. These sources include the Book of Jubilees (2nd century BCE), Qumran fragments known as 11QMelchizedek or 11QMelch (early 1st century), and more. The Book of Jubilees could not have had credibility in the eyes of its target audience if people in the 2nd century BCE thought that a Jubilee might be 50 years. Daniel’s “seventy weeks” (9:24) are interpreted straightforwardly in the Qumran fragment as seventy Sabbatical cycles, and the 490 years as 10 Jubilee cycles. In Samaritan history, the Jubilee cycles were preserved as 49-year cycles. In addition, there is no biblical source that hints at two consecutive years in which the field is not sown. All these problems are solved at once once one assumes that the 49th Sabbatical year is identical with the Jubilee. The author of the article points to further evidence.
So on the one hand, we have the fact that the two Jubilees mentioned in the Talmud are located exactly 49 years apart, matching the varied evidence that establishes the Jubilee cycle as 49 years. On the other hand, it is clear that the authors of the Talmud could not themselves have arrived at the fact that Josiah’s 18th year was exactly 49 years before Ezekiel’s vision by means of the computational methods available to them. In the Talmudic method of calculation, the final year of one king was counted twice, once for him and once for his successor, so that when adding up reign lengths one must subtract one year from the years stated in the Bible in order to determine the total elapsed time. The source of the method is Seder Olam (as emerges from chapters 4 and 12), and only by means of it is it possible to treat the number of years that “Israel spent in the land from when they entered it until they left it” (Seder Olam 11) as 850. The Talmud accepts this figure (Gittin 88a, Sanhedrin 38a) without objection. And yet, it knows that Josiah’s 18th year was a Jubilee.
The author of the article calculates that according to the mode of calculation in the Talmud and Seder Olam, the interval between the two Jubilees comes out to 47 years (and not 49—the time established in modern scholarship, and as confirmed by the Babylonian chronicles). From this he derives a clear proof that the Talmud and Seder Olam did not base Josiah’s Jubilee on any calculation, and if anything, such a calculation should have prevented them from making that attribution. The only plausible alternative, which also explains why the gap between them is specifically 49 years, is that the date of both was fixed independently in tradition because of the historical memory of the events themselves. This was possible because the priests were still counting Sabbatical and Jubilee years in those times. Of course, that does not mean the people observed them, only that the priests—Ezekiel being one of them, as was Jeremiah—remained faithful to their obligation to preserve meticulous records of the Sabbatical and Jubilee cycles. As in other societies in the ancient Near East, things of this sort were part of the priest’s duty.
The author discusses the Jubilee as an exceptional instrument for measuring time over long periods. The mutual combination of the two cycles, seven sabbaths of years that together form a Jubilee cycle, was a mechanism for ensuring the accuracy of the count over the hundreds of years in which Israel lived on its land. Because of the short length of the Sabbatical cycle, the resulting method of counting years prevents errors of even a single year, while the longer Jubilee cycle adds to this the documentation of long spans of time. If the priest preserved dates in this way, then this is a system that surpasses even the Assyrian limmu records in precision, though those are usually considered the backbone of ancient Near Eastern chronologies. This is probably how Jephthah the judge knew that 300 years had passed from the conquest of Transjordan until his own time (Judges 11:26), and it also explains how the author of 1 Kings (6:1) knew that 479 years had passed from the Exodus until the laying of the foundations of Solomon’s Temple, so that he could state that it occurred in the 480th year after the Exodus. Evidence for this is also found in Sanhedrin 40a, where it says that in the time of the Judges the courts would examine in which Sabbatical cycle within the Jubilee it was, and which year within the Sabbatical cycle. To this may be added the Book of Jubilees from the 2nd century BCE, whose descriptions are analogous to what is described in the Talmud.
Additional confirmation that priests were still counting Sabbatical years toward the end of the Judean monarchy can be presented from the date of Zedekiah’s emancipation of the slaves (Jeremiah 34:8–22). According to the calculation presented above, the emancipation occurred exactly in a Sabbatical year (with the Jubilees in 574t and 623t, which means that 588t was a Sabbatical year), precisely the year that also comes out as the year of Zedekiah’s slave release according to other calculations based on references to the events described in the Bible (William Whiston, Cyrus Gordon, Nahum Sarna).
Another proof from Seder Olam. In chapter 11 it says there:
“And so it says (Ezekiel 40:1): ‘In the twenty-fifth year of our exile, at the beginning of the year, etc.’ When was this said to him? At the beginning of the Jubilee.”
Then Seder Olam mentions that that Jubilee completed 17 Jubilees, a number repeated by the Talmud in Arakhin (12b). Is it possible that here too we are dealing with a specific memory preserved by tradition, as with the Jubilees in the time of Josiah and Ezekiel, and not with a retrospective calculation?
One can simply do the calculation. If the 17th Jubilee occurred in 574t, then the first Jubilee, 16 cycles earlier, should have fallen in
574t +(49 x16) = 1358t 
The year that began in Nisan 1358 BCE was therefore the 49th year of the first Jubilee cycle, in accordance with Leviticus 25:8–10. That is, the first year of this cycle, 48 years earlier, was the year that began in Nisan 1406 BCE. The reference to the 17th Jubilee in Seder Olam and in the Talmud therefore allows us to place the entry into the land in Nisan 1406 BCE. And therefore the Exodus, 40 years earlier, occurred in Nisan 1446 BCE. All this fits exactly with the date that many scholars had already derived independently from the book of Exodus, based on the statement in 1 Kings (6:1) that the building of the Temple began in the 480th year after the Exodus, which was also the 4th year of Solomon’s reign, and also based on Edwin Thiele’s dating according to which 931n (Nisan-based BCE reckoning) was the year of Solomon’s death and the beginning of the divided monarchy. Thiele’s calculation, published more than 50 years ago, has stood the test of time and survived scholarly scrutiny. How can one explain the exact match unless we admit that 623t really was the 16th Jubilee and 574t really was the 17th Jubilee?
Without question, no author before Thiele’s time could seriously have established 1446 BCE as the date of the Exodus. The critical date for the beginning of the division of the kingdoms simply was not available to us before his work in the mid-20th century. And of course, the writers of Seder Olam and the Talmud, with their methods of calculation, could not have conceived that this was the date. It seems the only reasonable alternative here is that the counting of Sabbatical and Jubilee years began in 1406 BCE, and that there were priests in Israel who faithfully preserved over the generations the proclamation of the Sabbatical and Jubilee years, blowing the shofar every 49 years to a mostly indifferent public, until the tragic event 14 years after the destruction, when the time for the Jubilee arrived but it could no longer be observed on foreign soil even if they had wanted to.
To sum up
The Talmudic method of calculating chronology was not capable of correctly determining the two Jubilees in the time of Josiah and Ezekiel, so it must have been based on historical memory and not on calculation. The fact that a Jubilee occurred in 574 BCE can be derived just from looking at Ezekiel even without the Talmud, but the Talmudic consideration supports the insight that the Hebrew text draws our attention to the fact that this was a Jubilee. The other Jubilee in the Talmud, in Josiah’s 18th year, is dated 49 years earlier, matching the evidence and considerations that establish 49-year Jubilee cycles. The Talmud and Seder Olam describe Ezekiel’s Jubilee as the 17th Jubilee, which teaches that the counting began at the time of entry into the land in 1406 BCE, and from here 1446 BCE emerges as the year of the Exodus, in full agreement with Thiele’s dating for the start of the divided monarchy and the chronological notice in 1 Kings (6:1). It is hard to imagine how such an exceptional fit regarding the date of the Exodus, which emerges independently through two different methods of calculation, can be explained by theories that assume an entry into Canaan on a date other than 1406, or that deny that the legislation in the book of Leviticus dealing with Sabbatical and Jubilee years already stood before the people of Israel at the time in question. The Talmudic Jubilees fit Ezekiel (40:1), and the dates derived from them constitute confirmation that the 480 years that the Bible attributes to the Exodus, and the year of the Exodus that emerges from that number, reflect authentic historical reality. It is hard to believe that all these facts are aligned by chance: Zedekiah’s Sabbatical year matches Ezekiel’s Jubilee, the memory of an additional Jubilee (in the time of Josiah) comes out exactly 49 years before Ezekiel’s Jubilee, yet later writers were not capable of calculating this correctly, the fact that by coincidence the Jubilee dates in the time of Josiah and Ezekiel make 1406 BCE—the time of entry into Canaan according to 1 Kings (6:1)—the first year of the first Jubilee cycle, and the extreme coincidence that specifically 1406 BCE marks the beginning of the first cycle when one takes into account the tradition that Ezekiel’s Jubilee was the 17th Jubilee.
 
http://www.rcyoung.org/articles/jubilee.pdf