[28] Did the Jews use Calculation for their Calendar in the First Century?

On page 302 of Neusner's translation of the Mishnah the section Rosh Hashannah 2:8 appears, which is subdivided into parts “A” through “I” as follows, and Neusner wrote what is in square brackets below. This is quoted word for word.

A. A picture of the shapes of the moon did Rabban Gamaliel have on a tablet and on the wall of his upper room, which he would show ordinary folk, saying, “Did you see it like this or like that?”
B. M'SH S: Two witnesses came and said, “We saw it at dawn [on the morning of the twenty-ninth] in the east and at eve in the west.”
C. Said R. Yohanan Nuri, “They are false witnesses.”
D. Now when they came to Yabneh, Rabban Gamaliel accepted their
testimony [assuming they erred at dawn].
E. And furthermore two came along and said, “We saw it at its proper time, but on the night of the added day it did not appear [to the court].”
F. Then Rabban Gamaliel accepted their testimony.
G. Said R. Dosa b. Harkinas, “They are false witnesses.”
H. “How can they testify that a woman has given birth, when, on the very next day, her stomach is still up there between her teeth [for there was no new moon!]”
I. Said to him R. Joshua, “I can see your position.”

Now I have some comments on the above.

(A) Due to the other names, this is considered to be the grandson of the Gamaliel in the NT, and this is considered by Orthodox Jews to be in the second century, perhaps about 110.
(B) The story may be invented to illustrate the stature and greatness of Gamaliel II. One cannot accept the historical truthfulness of everything in the Mishnah.
(C) Part A above is taken by Orthodox Jewish commentators including Maimonides to imply that Gamaliel II was able to calculate what the new moon should look like and whether it could be seen, and through his questioning of the witnesses and his calculations he could judge whether the witnesses were lying. But this is reading far too much into what is said. Assuming that this is historically true, Gamaliel may simply be trying to rattle the witnesses, so that they would not try to falsely testify. In other words, he wanted to see how confident they would be in their claim. Each year at about the same season, the angle of the new crescent would be generally the same, but not exactly the same. Thus an ignorant person would not know approximately what it ought to look like, but a knowledgeable person would know its approximate angle, although a knowledgeable person at that time in history would not know in advance whether it would be seen. On the other hand, in the majority of cases months did alternate with 29 and 30 days.
(D) This is the entire evidence that exists of the claim that in ancient times learned Jews could calculate whether the new crescent could be seen.
(E) The claim in B is false because it is not possible to see the old crescent and the new crescent so close together in time.
(F) The statement at the end of E indicates that on the next night the court was not able to see the new crescent, and this is the reason for the analogy given in part H.
(G) Parts G and I indicate that some people doubted that the alleged witnesses saw the new crescent, despite the fact that Gamaliel II accepted their testimony.
(H) The whole procedure and interest in obtaining witnesses for having seen the new moon should make it obvious that if its visibility was declared to have occurred at the end of the 29th day, then the ending month had only 29 days. Hence they were not using a calculation to determine the start of a month.

From the above, does it seem rational to accept the opinion and
interpretation that in the early second century Jewish leaders could calculate whether the new crescent could be seen? Certainly not.