Units of Measure

Pesach-time it’s common for people to start discussing how much matzah and wine one is obligated to eat, so why should I be any different?

What are we trying to compute?

The definition of eating in numerous contexts requires a minimum quantity of a kezayis (like [the volume of] an olive [including the pit]). This measure, like most halachic measures (shiurim), is halakhah leMoshe miSinai. Usually, that’s literal — “a law [given] to Moshe from Sinai”. Sometimes it’s more idiomatic, meaning more like “[as certain as] a law…”

Rav Chaim Volozhiner famously holds that the term is prescriptive — a kezayis is defined by the size of an olive as they are in your place and time. Which implies that there is something particular about olives that define what it means to eat.  Well, it’s one thing to say G-d gave us, or Chazal decided, a shiur that happens to be the volume of a typical Second Temple era olive. But if it’s actually tied to the drift in olives sizes, so that the point is related to the olive… In a society where olives are a staple, I could see saying that whatever your local olive is, that’s what you general consider “akhilah“. But why would this still hold in RCV’s 18th (or early 19th) cent Volozhin? So I’m stymied by the idea.

But it would help explain what most people remember as common practice, of taking far less matzah than the range of theoretically derived kezeisim. Unfortunately, there is another explanation…. In the 18th century, matzos got thinner. This is around when the Ashkneazi cracker-style matzah began. We decided it wasn’t safe to exclude kneading time from the 18 minutes — what if the person gets tired and pauses? So, the whole process got rushed, and we moved to a thinner, more quickly baked matzah. Then the matzah machine was introduced, even more thinning the matzah. Some point along the way, all that was left was crust — a cracker. But in any case, the eye gets fooled by this. Two very thin matzos will register to your eye as as “thin sheets”, but one could be twice as thick as the other, and it would a sheet of only half the area to make of the volume of a kezayis. So, it could be the matzos got thinner faster than the estimate of the kezayis kept up with it.

Another reason why even the Chazon Ish’s large kezeisim could be possible is that Israeli fruit shrank in size (and declined in quality) drastically in the late tannaitic era. Y-mi Pei’ah 7:3 33a would place it around the time of the Hadrianic persecutions. (Note this is not about their mythic past, nor all that different than Palestinian experience trying to farm the same land as Gush Katif did. It may be exaggerated, but it’s unlikely to simply be medrashic metaphor.) The kezayis was decided before the Temple was destroyed, and well before Hadrian harasha. With that in mind, even the CI’s shiurim are possible. Olive pits found at Masada or Betar wouldn’t reflect the huge olives we had at the time we started talking about kezayis.

The positions cited at the two ends of the normally discussed range of values for shiurim are products of very different approaches. The Chazon Ish, following the Noda biYhudah’s general approach, deals with the question in purely theoretical terms. If they reach empirically unrealistic conclusions, they quickly invoke the notion that breeding or nutrition changed the size of the average forearm, or the egg, or the olive. R’ Chaim Naeh also invokes theory, but his shiurim are typical values used in practice in the communities of Jerusalem in his day. This is similar to a difference of approach often pointed out between the Mishnah Berurah and the Arukh haShulchan. The Mishnah Berurah more often ends up in more stringent rulings because he considers all positions equally. The Arukh haShulchan, however, reads more as an explanation of the theoretical underpinnings of the rulings accepted in Lithuania in his day (with a few exceptions where the Arukh haShulchan disagreed with accepted practice).

Personally, I do not see any reason why today’s kezayis must necessarily be the same as chazal’s was, even if kezayis was descriptive of a particular set volume (and unlike RCV). I presume halakhah is constitutional; ie what those with legal authority interpret it to be. It is a process, it is supposed to evolve. (In an extreme case: Ezra and his court required tubes running into the altar to receive libations, meaning that in their era, Shelomo’s altar woudn’t have been kosher!) So perhaps a kezayis is what the theoreticians and common practice say is a kezayis, regardless of whether the historical measure was recaptured.

A New Way to Compute a Historical KeZayis

All that aside, here’s my own suggestion for how to compute a historical kezayis.

On one of the sides of the presumed Even Shesiyah, the rock under the Dome of the Rock, there are two holes 43.7 cm apart, and there is a niche in it that is 131 cm = 3 x 43.7 cm long. Two slabs of rock used in the eastern wall are 2.6 m long, six times 43.3 cm. And these, I am told, are only a few of many many examples. The repeated use of multiples of a particular unit suggests that it’s a standard unit of measure. Or, that an ammah is 43.5 cm +/- 2 mm.

At the end of Hizqiyahu’s Water tunnel, dug during the first Beis haMiqdah, is a plaque by the diggers telling us of the moment diggers from both ends met, “and the water flowed from the source to the pool for 1,200 ammos“. The actual length of the tunnel was given various values by archeologists, but with more recent tools (Gitt 2001), it was measured as 525m. Which comes to 1,207 of our even-shesiyah-amos long. (Well within rounding and measuring error. An amazingly on-target number, actually. Even the longest estimate I found, 537.6 m length given in 1870, would be within rounding to the nearest hundred.)

But, for much of the construction of the Second Temple, the ammah was overestimated by 1/2 etzba (see Pesachim 86a), ie by 25/24, as the workmen wanted to err on the side that would avoid accidentally short-changing the sacred (me’ilah). And in a small underground room under the north east corner of the current platform, the recurring unit of measure is 42.8 cm. If it weren’t for the Water Tunnel, it might have implied that the 43.5 cm length was the overestimate, not the ammah. As it is, I have no explanation. (Perhaps it was from a different era, with a different halachic ammah? Perhaps it’s because the rationale about me’ilah only applies to measures of construction material, and not the foundation on the rock?) Despite this problem, the convergence of both archeological indications of the ammah seems compelling to me.

Well, there is a way to convert from an ammah to the volume measures used in the seder.

An etzba is 1/24 ammah, and a revi’is, the measure of wine one’s cup must hold (and one must drink most of the cup), is 2 x 2 x 2.7 etzba’os, or 10.8 cubic etzba’os. So, we get an etzba is 1.81 cm, and a revi’is would be 64.3 cc (= 2.17 floz).

A kebeitzah is 2/3 of a revi’is, and a kezayis is either 1/2 or 1/3 of a kebeizah. So, a kezayis would come to either 14.2cc or 21.4 cc (.483 fl oz or 0.725 fl oz), depending on that dispute. Since matzah is deOraisa, it is customary to use the larger measure. Which you use for maror, which is rabbinic if there is no Pesach offering, is a matter for discussion with your rabbi.

Above I argued that perhaps the commonly cited range of values should be more halachically binding than historically determined ones. To give you an idea of where the values I just suggest sit in comparison to that range:

ComputedRambamR Chaim NaehArokh haShulchan*R Moshe FeinsteinChazon Ish
Ammah43.5 cm45.6 cm48.0 cm53.3 cm54.0 cm57.6 cm
Revi’is64.3 cc75 cc86.4 cc118.6 cc130.6 cc149.3 cc
Kezayis21.4 cc< 15 cc25.6 cc26.3 cc43.5 ml49.8 cc

(* The AhS’s measures are computed based on OC 16:4, which says that 3/4 ammah = 9 ווייערסקעס  (singular: вершо́к = vershok], for which Wikipedia says 1 vershok = 4.445 mm, combined with the AhS’s position of 2 kezeisim per kebeitzah. And the “o” in “Arokh” is intentional.)

So, while the Temple Mount based numbers are slightly lower than accepted range, they are not unrealistically so.

R’ Mordechai Willig reports that matzah weighs half of water, so that 21.4cc would weight 10.7 gm. This is much like the Sepharadi practice of using weight as a more accurate proxy for kezayis than guessing at volume of a thin sheet, but Sepharadim take the very conservative estimate of assuming matzah weighs as much by volume as water (1 cc weighs 1gm), when experimentally we find it’s about half.

I do not feel comfortable recommending anyone follow these numbers, though. It needs far more review by people who understand the archeology and posqim who understand the halakhah better than I do.

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