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Corner Boards

Here is a little formal article that I wrote about the Corner Boards of the Mishkan. I hope that it will be a nice addition to the rest of the material presented on this blog, as well as I hope it will help to clarify certain points about the importance of the Corner Boards.

This article was published in a slightly edited and abridged form in the Jewish Bible Quarterly Journal Vol. 40:4 (160). Here is the link (it is filed under my name).



by Aleksandr Sigalov

After the Children of Israel left Egypt and received the Law of The Covenant at the Mount Sinai, they were commanded by God to build Him a portable temple - the Tabernacle [mišəkan]. It consisted of a Tent of Appointment [ōhel mwō‘ēḏ], several furnishings (Ark, Altars, Menorah e.t.c) and a courtyard [ḥăṣar].

The Tent of Appointment of the Tabernacle was essentially a set of several special coverings which were spread upon a gold plated wooden framework.

Up to this day, exact design of some elements of this framework remains a subject of debate between religious and secular Biblical commentators, both Jewish and non-Jewish alike. One of such elements, the corner boards, is especially problematic due to a very obscure description provided in the original text, and due to its key importance to the entire structure from an architectural point of view.

Since it would be impossible to discuss every proposed solution to the problem within the scope of this article, I will concentrate only on the widely accepted opinion of Rabbi Nehemiah from Babylonian Talmud[1], while comparing it to my own. I will also omit all irrelevant details of the description in lieu of making the discussion easier to understand even for an unprepared reader.

According to the chapter 26 of the Book of Exodus, the Tent of Appointment consisted of a wooden framework and several coverings.

One of these coverings, the only one that is relevant to our problem, was made out of goat's hair, and was 30 cubits wide by 44 cubits long[2].

The wooden framework of the Tent of Appointment, if looking from above, was essentially a Π shaped structure, with its open side oriented toward the east. It was constructed by putting together identical wooden boards [qərāšîm], each of which was 10 cubits tall, 1.5 cubits wide and of an unspecified thickness[3]. Each board stood upon two silver sockets[aḏənê-ḵesef] of an unknown shape and dimensions, but of exact same weight[4]

On the south side of the framework there were 20 boards, making southern wall of the framework 20x1.5cubits=30cubits long, and the number of its silver sockets 20x2=40 pieces[5].

On the north side of the framework there were also 20 boards, making northern wall of the framework 20x1.5cubits=30cubits long, and the number of silver sockets 20x2=40 pieces[6].

On the west side of the framework there were 6 boards[7], totaling at 6x1.5cubits=9cubits long, and the corner boards of which we read the following:

"And two boards shalt thou make for the corners of the tabernacle in the hinder part.

And they shall be double beneath, and in like manner they shall be complete unto the top thereof unto the first ring; thus shall it be for them both; they shall be for the two corners."   (Exod 26.23-24, JPS 1917)



The description of the western part of the framework concludes with the following statement:

"Thus there shall be eight boards, and their sockets of silver, sixteen sockets: two sockets under one board, and two sockets under another board." (Exod 26.25, JPS 1917)
According to Exod 26.13, the 30 cubit wide goat's hair covering would have to fully cover the resulting framework along its width. Namely, 10 cubits of height and thickness of its northern and southern walls and the entire length of the western wall. This, in turn, would leave us with at least 30 – 10 – 10 - 9 = 1 cubit of empty space to fit both corner boards, or 1 / 2 = 0.5 cubits for each.

To sum things up, we have ended up with the goat's hair covering, 30 cubits wide by 44 cubits long. And with a Π shaped wooden framework, which was 10 cubits tall, 30 cubits long and at least 9 cubits wide, leaving at least 0.5 cubits of space on each side of its western wall to fit the corner boards.

So what was the shape and dimensions of these corner boards?

According to Talmud[8], because there was only 0.5 cubits of space left for the corner boards on each side of the western wall, and because Exodus 26:23 and Exod 26.25 appear to imply that only 2 boards were dedicated for the corners of the framework, it must be that these 2 corner boards were just like the rest of the boards (10x1.5cubits), and 1 cubit thick.

Talmud[9] calculates the value for thickness of the boards by subtracting 0.5 cubits needed to be filled by the corner board from its 1.5 cubits length. This makes the inner width of the framework 9+0.5+0.5=10 cubits and its outer width 9+1.5+1.5=12 cubits, with all 20+20+8=48 boards being identical in shape and 1 cubit thick.

However, such solution has two major flaws:

First of all, a wooden board 10 cubits tall, 1.5 cubits long, and 1 cubit thick would weigh about ~683 kg[10]. This would put the total weight of wood required for all 48 boards at ~34 metric ton. Such weight of the boards alone would be far above carrying capabilities of 8 bulls[11] that were dedicated to this task, as mentioned in Numb 7:8.

Secondly, it is not clear why value of 1 cubit was chosen for the thickness of the boards if, in proper mathematical terms, it could vary from 0.5 to 1 cubit under the conditions specified by Talmud[12]. Partly, due to the fact that the original text does not explicitly specifies an inner width of the framework.

Some may argue, that Talmud uses the dimensions and description of the goat's hair covering (Exod 26.12-13) to calculate the inner width of the framework, and thus the thickness of the boards. However, this assumption would be completely incorrect, because Talmud states[13] that the goat's hair covering did not cover the entire height of the northern and southern walls of the framework.

Instead, Talmud simply assumes[14] that the goat's hair covering would cover only 9 out of 10 cubits of these walls, while the remaining uncovered cubit would have been hidden by the silver sockets of the boards, which baselessly assumed to be 1 cubit tall for the sake of making measurements to fit.

As an example, it is possible to make the thickness of all boards 0.9 cubits without violating any conditions specified by Talmud. This would only affect the inner width of the framework, which will now be 10.2 cubits instead of 10, while still allowing the goat's hair covering to cover only 9 out of 10 cubits of the sides of the framework and preserving 1 cubit for the sockets.

Similarly, all other solutions that try to explain how the framework of the Tabernacle was put together suffer either from one (or both) of these flaws.

Therefore, I would like to present my own solution that is free from aforementioned shortcomings.

First of all, let's go back to the length of the main portion of the western side of the framework, which according to Exod 26.22 covered only 9 out of 10 cubits of its internal width, leaving us with at least 0.5 cubits of space on each side that was necessary to reach its southern and northern walls.

Secondly, we know from Exod 26.23 that there were to be 2 boards for the corners of the framework. I propose to understand this verse as implying that we need to use 2 boards for EACH of the corners, instead of 2 boards total for both of the corners.

In support of this interpretation we can use the description provided in Exod 26.24, that requires “twinning” [ṯammîm] of these 2 boards to make each corner board for each of the corners. But since this verse also tells us that these boards were to be twinned “to one ring”[el-haṭṭaba‘aṯ hā’eḥāṯ], I propose that the proper interpretation must imply that we need to “twin” these boards together so that they form a single corner board of a round[15] (“ring” like) shape.

In order to do it, each of the corners of the framework would have to be composed of two regular boards, that would be bended into a semi-cylindrical shape, and would be put together (“twinned”) to form a singular hollow column with a circular cross-section (“ring”).

If you would carefully consider such arrangement, you would notice that an internal circumference of the resulting tubular corner board would be twice the length of a regular board, or 1.5+1.5=3 cubits, and its inner radius would be calculated by the standard circumference formula C=pi x 2 x r and equal to r = 3 / (2 x pi) = 1.5 / pi = ~0.477 cubits.

However, we must be able to somehow find board's outer radius in order for this solution to work. Luckily, we can easily do this by recalling how much space we needed to fill between the main portion of the western wall and the northern and southern walls of the framework; it was 0.5 cubits, and now it had become our outer radius for our tubular corner board.

Now that we have both internal and external radiuses, we can easily find the thickness of the corner board. It would be equal to the difference between the radiuses of the corner board, or [0.5] – [1.5/pi] = ~0.0225 cubits (about 1.01cm based on 45cm cubit; or about a fingerbreadth).



But because our tubular corner board was essentially made out of two boards that were identical to the rest of the boards, we can now rightfully say that we have found the thickness for all the boards of the framework. Thus making each and every board of the framework 10 cubits tall, 1.5 cubits long and [0.5-(1.5/pi)] cubits thick.

Summarily, the framework of the Tabernacle consisted of 48 boards. The Northern and Southern walls had 20 boards each, and the Western wall had 8 boards. Both corner boards were 1 cubit wide tubular-shaped columns made out of 4 regular boards. Silver sockets for the corner boards would be of a matching round shape[16]. The thickness of all boards of the framework was about 1cm.



The advantages of my approach can be seen right away:

1.The thickness of the boards is now clearly defined by one specific value of ~1cm, as opposed to an interval of values (i.e 0.5 < = > 1 cubit) as in most traditional opinions.

2.Now, the weight of each board would be approximately 14kg[17], as opposed to 683kg as in most traditional opinions. This would make it possible to easily transport all parts of the framework upon 8 provided bulls.

3.Tubular-shaped corner boards would provide very good structural stability and a certain degree of aesthetic and symbolic beauty to the framework of the Tabernacle. Technology[18] and skills[19] required to make such round-shaped boards would have been easily available to wandering Israelites due to its simplicity[20], and considering Israelites background as Egyptian slaves and laborers[21].

4.Knowing correct shape of the corner boards of the Tabernacle, would help to identify correct shape for the corner elements mentioned in other books of Tanakh. For example, it may very well mean that in the future Temple the corners [miqəṣō‘wōṯ] of the outer court mentioned in Ezek 46.22 will be of a round shape, as opposed to a square shape that is usually assumed in the proposed reconstructions based on this prophecy. Such interpretation can also be supported by the fact that the rectangular 40x30 cubits “perfume courts” [ḥăṣērwōṯ qəṭurwōṯ] described in the same verse can be perfectly inscribed into a round-shaped corners 50 cubits in diameter[22].


5.My solution may also help to explain the source of a relatively strange approach to measuring round objects in Tanakh. For example, the Molten Sea of Solomon mentioned in 1 Kgs 7.23-26, was measured by its internal circumference and outer radius[23], similar[24] to how my solution proposes to measure the round corner boards of the framework of the Tabernacle.

From all the arguments presented it is clear, that a proper scientific and architectural approach must be followed when attempting to solve this problem.

And even though I'm fairly certain that the corner boards were of a pillar like shape, 1 cubit in diameter and ~1cm thick, a much more thorough collaborative inquiry had been long overdue to truly unravel the hidden mysteries and divine beauty of the Tabernacle.

As I see it, without the proper understanding of these two corner pillars that united and strengthened all parts of the framework, it would have been impossible to construct the Tabernacle.

So neither can we, the devout believers, hope to become united and strong in our faith, without properly understanding and embracing our two eternal corner pillars: The One God and His divine Law!

[NOTES]

1. Babylonian Talmud, Seder Mo'ed, Sabbath 98b.

2. Exod 26.7-11, JPS 1917

3. Exod 26.16, JPS 1917

4. Exod 38.27, JPS 1917

5. Exod 26.18-19, JPS 1917

6. Exod 26.20-21, JPS 1917

7. Exod 26.22, JPS 1917

8. Babylonian Talmud, Seder Mo'ed, Sabbath 98b.

9. Ibid

10. This calculation does not include the weight of gold overlay or the rings of the boards. It is based on 45cm cubit, and a very conservative estimate of the density of Shittim wood at 500 kg/m^3.

11. Tim Harrigan, Richard Roosenberg, Dulcy Perkins, John Sarge, Estimating Ox-Drawn Implement Draft Technical Guide (Kalamazoo MI, Tillers International, 2009).

12. Babylonian Talmud, Seder Mo'ed, Sabbath 98b.

13. Ibid.

14. Ibid.

15. Abraham ben Meïr Ibn Ezra, H. Norman Strickman, Arthur M. Silver, Commentary on the Pentateuch, Volume 2 of Ibn Ezra's Commentary on the Pentateuch (New York, N.Y: Menorah Pub. Co., 1988), 574.

16. According to Exod 38.27, silver sockets for boards and pillars of the Tent of Appointment had only one common characteristic: the same weight (1 talent of silver). From this we can deduce that the shape and dimensions of the silver sockets were different and defined only by the relevant parts of the framework.

17. Same as the values used in 10.

18. Richard S. Barnett, All kinds of scented wood: wood & woodworking in the Bible, (Fairfax, VA: Xulon Press, 2002), 30.

19. Frederick M. Hocker, The philosophy of shipbuilding: conceptual approaches to the study of wooden ships, (College Station, TX: Texas A&M University Press, 2004), 14.

20. In order to bend wood one can use variety of simple techniques. For example, steam bending and planking of wood requires only basic tools and steam. This technology was very well known and widely utilized in ancient Egypt to build ships, furniture e.t.c, so by the time of Exodus Israelites were almost certainly familiar with it as well.

21. According to Exod 5.14-19, not all Israelites were doing menial slave work. Some were appointed to be foremen of the Egyptian taskmasters. Therefore, some Israelites had to have at least some kind of formal education and skills to perform supervision tasks on various building projects.

22. According to Pythagorean theorem, a rectangle 40 cubits long and 30 cubits wide has a diagonal of 50 cubits (sqrt [30^2+40^2] = 50). And since geometry dictates that diagonal of the rectangle inscribed in a circle will be circle's diameter, we can confirm plausibility of our theory that the corners of the outer courtyard of the Temple were most likely intended to be round; and that the expression “cut-out” [miqəṣō‘wōṯ] most likely implies a round shape.

23. According to 1 Kgs 7.23 and 2 Chr 4.2, Molten Sea had 10 cubits outer diameter and 30 cubits inner circumference.

24. According to my solution, thickness of the corner boards of the Tabernacle (and thus, the rest of the boards) was calculated from its 1 cubit outer diameter and 1.5+1.5 = 3 cubits of its inner circumference.

4 comments:

Anonymous said...

When the bible says the corners were squared I'm pretty sure it means what it says... not that we should assume that it really means they were round because the diagonal of a square within a circle equals the diameter of the circle. To employ such an idea doesn't even make sense!

Aleksandr Sigalov said...

Please tell me exactly where "the bible says the corners were squared". Thank you ;)

Esteban said...

Hi. First, sorry for my English. Based only in the text of Exodus 26 and Exodus 36 "... and they were coupled beneath, and coupled together at the head thereof, to one ring: thus he did to both of them in both the corners.", In hebrew the word translated to "coupled" means "twins", in other versions was translated as "double", like that board was double beneath up to the first ring. I draw that in my mind, that the corner board is not 1.5 cubit wide, but 0.75 cubit wide, because is double, but it is double up to the first ring because it needs be able to left room to insert the bars (sticks) by the rings.

Aleksandr Sigalov said...

Hi, Esteban,

Sorry for the delayed response. I did not exactly understand what you were saying. But if you would take a 1.5 cubits wide board and put it together with another such board in a circle, you gonna get boards that a round and 1 cubit wide.
I would need you to clarify what you've meant if you want me to answer your question.

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