If the Y-axis is reliability (correctness) and the X-axis is distance from the source, then after calibration one can in principle determine the location, though I admit it is hard to quantify.

The numbers on the Y-axis are the ratio of correct to incorrect, where “correct” is defined as: no dispute within the same group that has a similar distance from the source. It is not certain that when there is no dispute the ruling is correct, but when there is a dispute, the ruling will certainly be defined as mistaken, since the two opinions (equal in weight because of their similar closeness to the source) cancel each other out. On the plateau this ratio would be constant.

That is, the graph at X=0 reaches infinity (Moses our Teacher. There were places that were not explained to him, but he had no dispute with himself), and on the plateau it reaches some constant value that I do not know. Something like Y=1/X.

I do not know how to define “correctness” well, because one has to exclude trivialities such as things the Sadducees also agreed with. There, the truth is not a result of closeness to the source. But the enormous number of disputes indicates a great distance from the source. It should be noted that the Sadducees were at the same distance from the source, and that further increases the number of disputes relative to agreements. (And we have not even gotten to the Dead Sea Scrolls yet.)

By way of general impression, this ratio is the same among the Tannaim, the Amoraim, etc. That indicates that they are all on the plateau.

I admit I am speaking on the basis of impression and not on the basis of a precise count, and you will certainly find quite a few inaccuracies in the definitions. I did not bother with that for obvious reasons, but the general impression is nicely reflected in the crushing answer (with a smile) and the one that is almost always correct to the question “What is the Jewish law?” — “A dispute!”

In any case, I agree with your claim that closeness to the source could be a very major factor, except that based on our sources and on general history it seems that the decay constant is very large. It is not known that a student of Stradivarius produced a violin of the same quality.

Therefore, I am not even sure that the Amoraim understood the Tannaim better than we do (not to mention the medieval authorities).

In any case, it seems to me that the burden of proof is on the one who claims that over such generational spans, closeness is a factor even of the third order.

I really do not know how you arrived at that conclusion. The fact that there is a dispute does not in itself say anything. The question is how many disputes there are and how large the gap is between the opinions. After all, it is clear that there are many more disputes among the Amoraim than among the Tannaim, and even more among the medieval authorities (for every Amoraic opinion there are several opinions among the medieval and later authorities). The fact is that every generation acknowledges that the previous generation understood better, and therefore that is my starting point.
Beyond that, as I explained in the lesson, the later authorities in their interpretation and rulings use more detailed analysis than the medieval authorities, who simply state the Jewish law without many reasons. The feeling is that the later authorities understand less intuitively and therefore need more logical, scholarly analysis. And likewise with the medieval authorities and the Amoraim.
And regarding understanding the words of the Tannaim (not the Torah itself), I find it very hard to accept your claim that we are in the same position as the Amoraim, who lived almost immediately after them. That seems implausible to me. At least from one generation to the one before it, this reasoning seems simple and clear to me.
The Sadducees operated with different assumptions, so it is hard to compare them to the Pharisees.

The question is not “how many disputes there are.” What determines it is not the number of disputes but the ratio between them and the agreements. That normalizes the growth and branching of the tree of halakhic rulings.

“The fact is that every generation acknowledges that the previous generation understood better, and therefore that is my starting point.” That is indeed a fact. It does not mean it is also true. Many reasons can be found for this acknowledgment. The Hasidim, regarding the rebbe (especially if he is dead), continue this to this day. If I bad-mouth previous generations, I undermine the justification for the tradition I believe in.

“The feeling is that the later authorities understand less intuitively and therefore need logical, scholarly analysis.” Agreed, that is a feeling. The ancients intuitively assumed that the world is made of four elements. We do not have their powerful intuition, so we added gluons and all the rest. (Sorry for the sarcasm.)

“The Sadducees operated with different assumptions, so it is hard to compare them to the Pharisees.” In Kishon-style — you’ve now played the Ben-Gurion card (know the sketch?). The assumptions of the Sadducees do not derive from closeness to the source!? (With a slightly different political game in those times, we all would have been good Sadducees.)

1. I do not agree with the dependence you presented on the ratio of disputes to agreements, because the agreements are sometimes not presented and the disputes usually are. There are topics that did not come up for discussion at all in earlier generations. So in my view, the number of disputes does matter. I already wrote that in fact, regarding quite a few Tannaim, there are several Amoraic opinions for each Tanna, and even more so regarding each Amora there are several opinions among the medieval and later authorities. The spread definitely increases in a clear way, and agreement steadily decreases.
2. True, there may be other reasons for deference to earlier generations, but it is also possible that they are right, no? For some reason you assume that the very existence of other reasons means they are necessarily not right. That is why I wrote that this is my starting point, not that it is the truth.
3. The comparison to the discussion about the four elements is unfounded. I am talking about a process of transmission, not scientific research. In scientific research, the next generation necessarily knows more than its predecessor (even if only as a dwarf standing on the shoulders of a giant). But in transmission, the logic says there is a reduction in understanding.
4. I do not know whether my being a continuer of the Pharisees is only a political matter, and I am not at all sure of that. Be that as it may, if I am discussing matters within the Pharisaic-halakhic framework, then according to its assumptions the Sadducees were mistaken in their assumptions and were not transmitting a different tradition. By the same token, you could argue that under different politics I could have been a Christian or an atheist. In my opinion that is not relevant to the discussion, because it is taking place within the framework we have accepted (or that I have accepted), and I am discussing it from within that framework and according to its method.