Saturday, October 14, 2017

Wall Thickness Between the Tauim Part 2

SUMMARY After seeing a first printing of Tiferes Yisrael's commentary to the Mishnah, it was necessary to come up with a new, reduced wall thickness for the tauim.

In the previous post I set out to find an early printing of Tiferes Yisrael's commentary to the Mishnah in order to resolve a question about the wall thickness between the tauim. Unfortunately, first printings of Tiferes Yisrael's commentary are not all that common and sell at auction for a small fortune.
Here's one that was listing for over $4000! (Enter 76 in the page field to see the specific page)

Fortunately, many of these first printings are held in libraries. Even so, finding them is not always as easy as typing a few words into a search field because academic spellings can be a little unusual and not all of the holdings are always searchable online.

On the advice of my Rosh Kollel I started with the Hebrew Union College in Cincinnati. I contacted them via email and they very helpfully replied right away that after scouring their shelves they could not find what I was looking for. They recommended that I try the Jewish Theological Seminary in New York. The nice people over there also told me that they do not have the book I am looking for, but they did find a copy in, of all places, the New York Public Library!

After an extended email conversation with NYPL they confirmed that they do, in fact, have a TY first printing (Koenigsburg 1850). To make my life even easier, they offer a document copying service that will provide me a PDF of any book for less than the cost of a bus ticket to Manhattan.

It took another few emails with their resident Hebrew scholar to describe to her the exact pages I was interested in. After that the book had to be evaluated by the scanning department to see if it was even going to be possible to scan it because the library binding was very tight. Happily, after all was said and done, a PDF was on its way to my inbox.

Ancient Wall Thicknesses

In the meantime a different discussion brought me to I Kings 7:9 where the verse states that the stones used for the construction of the First Temple were כמידות גזית, lit. of the size of hewn stone. Radak explains that "gazis" here refers to some sort of standard size of hewn stone known to the people of the First Temple era, just as this same term was later used in Talmudic times to refer to a wall of hewn stone that was five handbreadths thick (see Bava Basra 1:1).

Now I was actually expecting Radak to go in a completely different direction. After all, if we find a term that appears both in Tanach literature as well as in Mishnaic literature, why not assume them to mean the same thing? Why not apply our known definition of "gazis" from Bava Basra to the First Temple construction and conclude that the Temple walls were five handbreadths thick?

Apparently Radak does not find my logic compelling [so much for Occam's Razor]. Radak was willing to allow for the fact that in the First Temple era the term "gazis" referred to a wall of a different thickness and that the building codes listed in Bava Basra are not a universal standard but rather the products of their specific time and place.

On that note, while waiting for my PDF to arrive, I began to consider a Plan B with regard to the walls between the tauim. Turns out that was a good idea.

Tiferes Yisrael's First Edition

When I thought about what the TY first edition print would look like I envisioned a book with hard-to-read print, irregular letters, and poor contrast. Actually, that is what I was hoping for, because the more illegible the type, the more I could argue my case that subsequent copyists simply misread the original.

Well, I was begrudgingly disappointed in every regard. The type was crisp, the contrast excellent, and overall the book was remarkably easy to read. Here is the relevant part of Diagram Key §63:

Material courtesy of the New York Public Library's Dorot Jewish Division

There was no doubt that the phrase I was looking for (second line from the bottom in the image above) read ז אמות בקרוב, approximately 7 amos.

A New Approach

New math would be needed. In fact, had I started with math in the first place it would have shortened the process of discovery a bit. I went back to the same formula I used before and plugged in all of the known values except for wall thickness:

(S - n × t) ÷ N = L

S = total available space
n = number of dividing walls
t = wall thickness
N = number of tauim
L = tau length

For the northern and southern tauim, some trial and error for the value of t (wall thickness) showed that it would have to be between 0.2 and 1.3 amos thick to produce a value for L of "approximately 14."

In the west for the two tauim on the top level, trial and error showed that the wall between them could be anywhere from 0 to 1 amos thick.

In the west on the first two levels trial and error showed that the walls would have to be between 0 and 0.25 amos thick.

The range of wall thicknesses that works in all three calculations is 0.2 to 0.25 amos.

A New Wall Thickness

If you follow the rule of "tafasta merubah lo tafasta" you would conclude that the walls between the tauim were 0.2 amos thick. If you want stronger walls you would conclude that they were 0.25 amos thick.

What would TY conclude? When he performed his calculation he obviously started with a fixed wall thickness. What value in the seemingly arbitrary range of 0.2 to 0.25 would make the most sense to pick as the "standard" thickness for these walls?

Looking back at the first Mishnah in Bava Basra once again we find that the smallest stone used in Talmudic times was the "half-brick" which measures 1.5 handbreadths (0.25 amos) wide. [There are 6 handbreadths in one amah.] Now, standard practice in those days was to build two stacks of these bricks spaced one handbreadth apart to leave room for the mortar, thus, a proper wall made of half-bricks was 4 handbreadths wide (two-thirds of an amah).

In theory, you could also use just a single stack of these bricks (and put the mortar in between the layers of the stack, as we do in our modern brick walls). Being that TY was familiar with the half-brick as the smallest size of hewn stone, he may have decided that 0.25 amos would be an acceptable thickness for the dividing walls of the tauim.

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