It is a generally accepted rule in the world of “lomdos” (analytical learning)  that even where a dispute amongst Chazal appears to be about facts [can a child father a child or not ,is one example of many (Sanhedrin 69a) as is דם מפקיד פקיד או מחבר מחבר ( Kesubos 5b) ] , if it is something that can be readily checked, we attempt to show that the argument is really based on something other than just superficial facts ( is someone who has matured to the point that he can father a child still considered a child, or is דם perceived halachically as if it is מפקיד פקיד or מחובר מיחבר , for possible, if not problematic examples )

When the dispute is about facts that cannot be easily verified by observation , like some historic arguments ( like how old biblical figures were at certain times ) or unobservable phenomena , there is no need to do this, as the dispute can simply be explained as being based on different interpretations of the evidence or pessukim.

On this daf, we learn the chiddush of Rabbi Nosson that whilst the minimum quantity of wine required to transgress the melacha of carrying is a reviis, if the wine is conjealed to the point that it is more solid than liquid, the minimum measure of a kezayis  applies instead. 

The Gemora understands that this is because when a reviis of wine congeals, it shrinks to a kezayis.

Rav Yoseif then suggests that this view is the same as that expressed by Rabbi Yossi son of Rabbi Yehuda regarding the blood of an animal that dies without halachik slaughter (a neveila)

A kezayis of flesh from a neveila can make someone impure, but what about liquid blood?

Beis Shamai holds that blood of a neveila is considered like the flesh and does not cause impurity, whereas Beis Hillel holds that it does.

Rabbi Yossi holds that even Beit Hillel require at least a reviis of blood to make someone impure, because if a reviis of blood were to congeal, it would shrink to a kezayis.

Rav Yoseif understands from this that both Rabbi Nosson and Rabbi Yossi agree that a reviis of liquid is the equivalent of a kezayis of solids.

However- Abaya questions this assumption, and suggests that on the contrary, they may in fact totally disagree.

He points out something that students of physics should recognize, namely the fact that not ALL liquids are equal (nor are all solids.)

Blood as a liquid is much thicker than wine as a liquid, and therefore it does not have to congeal as much to become solid.

It therefore follows that if a reviis of wine is required to produce a kezayis of congealed wine, less than a reviis of blood is required to produce a kezayis of congealed blood.

and if a reviis of blood is indeed required to produce a kezayis of congealed blood, then MORE than a reviis of wine is required to produce a kezayis of congealed wine.

If so, it follows that the amount of liquid blood and wine respectively that are required to produce a kezayis of the congealed equivalent is actually a matter of dispute between Rabbi Nosson and Rabbi Yossi!

This appears to be a classic example of a machlokes metzius (factual dispute) that should be easily checked out by experimentation, rather than debated.

We also need to explain what Rav Yoseif himself was thinking- surely he was not unaware of the basic fact that blood is thicker than wine?

I think that one can perhaps explain Rav Yoseif’s view by way of the important principle that Halachic rules are very often NOT based on precise facts, measurements, or statistics, but rather on fixed approximations based on perceptions.

When it comes to working out the required dimensions of a round Sukkah (Sukkah  7b) or of a round beam on top of an eruv (Eiruvin 13b), the Mishna simply applies a round ratio of 3 to 1 between the circumference of a circle and its diameter, substantially less than even a reasonable estimation of pi, which at the time of Chazal was historically already known to about 2 decimal places. (see also Bava Basra 14b)

Whereas Tosfos in Eruvin are bothered by this discrepancy, and seem to understand that the Mishna and certainly the accompanying sugya are taking the ratio of 3 to be precise, the Tosfos haRosh there actually suggests that Chazal are intentionally imprecise, based on precedent from the passuk describing the pool that Shlomo built.

We see from there that in at least some areas of halacha, the Torah does not require precise measures that fit absolute scientific reality, but rather simply estimations that Chazal taught us, which are perceptibly close to the real measurement but simple enough to apply across the board.

This principle is actually applied  by the Chazon Ish in very novel ways to issues relating to the dateline (subject of 2 previous posts) , whereby he allows it to follow the coastline and deviate somewhat from the 90 degrees he claims is its absolute geographic position.

Perhaps, Rav Yoseif believes that the relationship between solid and liquid measurements is also an example of a case where the Torah allows for an estimation, and we are not required to make allowances for the precise density of the liquid or the solid.

Similarly, perhaps Abaya holds that either there is simply no justification for applying such estimations in this case, or that the variance in density and resulting solid size is too high to be comparable to the pi analogy.

Perhaps a similar idea can be used to explain the machlokes that Abaya sees in Rabbi Nathan and Rabbi Yossi’s rulings, in that they are not debating the facts- both agree that neither a reviis of wine or blood is the precise equivalent of a kezayis of their congealed version.

Or perhaps the reviis to kezayis ratio is only true of some hypothetical congealable liquid with a density somewhere between that of wine and blood, and the dispute is on which side of the line to estimate?

One thing we seem to see  for sure from this daf at least, is that there is a direct relationship between the side of a kezayis and  that of a reviis, and if one follows a certain view as to the size of the kezayis, one should certainly follow the same view in regards to the size of a reviis!

in this parsha, we are told that 20 is the determining age for maturity regarding being counted in a census, going to the army, etc.

We also know from numerous sources (among them a few daf ahead in our Masechta), that it is also the also the determining age for liability to punishment in the hands of heaven.

We know from the Torah sheBaal Peh that when it comes to many other matters, including the obligation to perform mitzvos and liability to punishment in Beis Din, the cut-off age is 13.

Although it is clear and obvious that there is a huge variation in maturity amongst different 20 year olds, and different 13 years olds, we see here clearly that at least to some extent, halacha is not determined by precise objective factors, but by fixed estimations- the same argument can be applied to most halachik measurements.

However, unlike what we saw regarding pi and perhaps the other examples we mentioned, the actual age or measurement provided by the Torah here appears to be absolute- a minor who is one minute younger than 13 will be exempt , and one 13 or older will be liable.

A young man 1 day younger than 20 will be exempt from the army, and one day later will be recruited.

I suggest that wherever it is simply and straightforward to make a fixed precise measure, this is indeed what the Torah does, but when it is impossible (like in the case of pi) or extremely difficult for people to use  a precise fixed measure, an estimated fixed measure is provided instead.

so much to say still, but shabbos beckons- please share your thoughts either way.

Shabbat Shalom and Yom Yerushalayim Sameach