Friday, December 31, 2010

Q&A - Can you comment on Exodus 30:36 Exodus 30:38 ?

Yes I can. In fact, I already have commented on these verses in this section.

Exodus 30:36 deals with the location of the Holy Incense. Namely, that it were to be placed upon the Golden Altar of Incense that stood inside the Holy Place of the Tent of the Tabernacle, like so:


Exodus 30:38 deals with the prohibition of making this incense for personal use and any other purpose than that of the priestly service. Luckily, most ingredients to make such incense cannot be identified today due to lack of research on the matter, so it is highly unlikely that it would be possible for most people to make one even if they would want to.

Perhaps the prohibition of making such incense for non-service use was due to the fact that this particular recipe had a very memorable scent qualities, and only very spiritually strong and disciplined person (such as the priest) could handle it, without getting too emotionally involved.

You can also check out this panoramic image that shows inside of the Holy Place of the Tent of the Tabernacle:

Q&A - How many pins were used in the Mishkan ?

I have covered this question in some detail in my previous posts, but I just wanted to summarize some information about these "Pins" (rather pegs or stakes) that were used to secure parts of the Tabernacle to the ground.

All Tabernacle Pins were made of Copper. Both Tent of the Tabernacle and the Courtyard parts were secured by using these copper pins. There were probably around 180 of these pins.

You can find reference to these pins in Exodus 27:19, Exodus 35:18, Exodus 38:20, Exodus 38:31, Exodus 39:40, Numbers 3:37 and Numbers 4:32.

Pins were basically Copper Stakes, just like any other stakes that are used in any old or modern tent, and looked like so:


There were probably around 60 such Copper Stakes for the Tent of the Tabernacle...

And probably 120 such Copper Stakes for the Pillars of the Courtyard...

This would make total number of Copper Stakes required for the Tabernacle - 180. This is my best approximation that is based on practical approach to the problem.

However, further research is needed to identify if there is indeed a way to exactly say how many of these Stakes are implied in the original text.

In my opinion, it is possible to do so, but this would be a very lengthy endeavor in itself.

Thursday, December 30, 2010

Q&A - Why there were 60 pillars in courtyard ?

As far as I can tell, the Tabernacle Courtyard among all other things functioned as a giant clock. By looking at the shadow cast by the Pillar of Smoke (Exodus 33:10) upon the Courtyard Hangings and Pillars, one could very easily tell time of the day.

And even though a very thorough research into this matter is needed, it is very easy to notice that 60 Pillars would signify 1/60 of a day, or 0.4 hour (24 minutes) of the day each. Just like any modern clock is divided into 60 sections, so was the Courtyard of the Tabernacle.

You can refer to this video to get basic idea of how it worked:



There are perhaps other, non astronomic reasons for such quantity of Pillars, but again, a thorough research is needed to identify what these reasons may be.

Q&A - How many pillars were in the courtyard?

According to Exodus 27:9-19 and Exodus 38:9-20, there were total of 60 Pillars that formed the Tabernacle Courtyard.

It is extremely important to note that the sum of the Pillars is NOT mentioned in the original text. This was done purposely, to prevent misunderstanding of the layout of the Pillars of the Courtyard, particularly those of the Eastern side (gate side).

Wednesday, December 29, 2010

Q&A - How many times do we see לַחְשֹׁ֖ב in the Chumash?

This expression, in this particular masoretic form, appears only once in Exodus 31:4 to describe great capabilities of Bezaleel to devise (design) cunning works.

Bezaleel was a chief engineer who was responsible for the construction of the Tabernacle, so he had to be very skillful and inventive in order to overcome any difficulties that arose during the construction.

The expression  חשב (khashav) itself means primarily "to devise" or "to design".

Here is a full description of this expression as according to the Strong's dictionary, which provides relatively comprehensive list of meanings:

  1.  to think, plan, esteem, calculate, invent, make a judgment, imagine, count
  2.  to think, account
  3.  to plan, devise, mean
  4.  to charge, impute, reckon
  5.  to esteem, value, regard
  6.  to invent
  7.  to be accounted, be thought, be esteemed
  8.  to be computed, be reckoned
  9.  to be imputed
  10.  to think upon, consider, be mindful of
  11.  to think to do, devise, plan
  12.  to count, reckon
  13.  to be considered




Q&A - What was the weight of beams in the Mishkan ?

According to the traditional opinions (Talmud Bavli), the weight of beams of the framework of the Mishkan was  ~25000 kg (according Rav. Jehuda opinion) or ~ 51000kg (according to Rav. Nehemiah opinion).

According to my opinion (and some other commentators), the proper weight of the beams (or rather - boards) of the Mishkan should have been around 1000kg if one would ever hope to transport them on 8 Bulls and 4 Carts (as per Numbers 7:8).

Diagram below shows all three opinions. You can also check these (or your own) values by using my Tabernacle Calculator here.




Monday, December 27, 2010

Tabernacle Questions and Answers

Ever since I have started this blog, I have been receiving many questions about different aspects of the Tabernacle. I was answering these questions as I have been going along, but I think it would be only beneficial to spend some time answering them publicly and in a separate section of this blog.

In my next posts I will be doing just that. The section (tag) will be called "Tabernacle Questions".

Wednesday, December 22, 2010

Exclusive Material: Exodus 26:23-24 - The Corner Boards of The Tabernacle Article

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.

For the most complete information on the Corner Boards, please visit this dedicated page and this section of my blog.

The Corner Boards of The Tabernacle

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.

Tuesday, December 14, 2010

Exodus 36:29 - Columnar Corner Elements in Architecture.

I found a pretty good example of what round corner elements could provide to any building from an aethetic point of view.

Here are the several images of the FLDS (Fundamentalist Church of Jesus Christ of Latter Day Saints) Temple. And even though this particular building has a very sad history, I think from an architectural point of view it can be considered very interesting. Check it out:




Monday, December 13, 2010

Exodus 28:15-21 - The Breastplate of Judgement

I found yet another web site (http://craigpages3.100megsfree5.com/Bible_Study/bib/Tabernacle.html) with a commentary on the Mishkan. It is not very interesting, except maybe for a couple of images related to the Breastplate of Judgement that a High Priest would wear.

Visit the original link for more images and description and check out these two images:


Sunday, December 12, 2010

Exodus 25:8 - Mystical opinion on the meaning and significance of the Tabernacle.

As much as hate to do it, I wanted to present a rather pseudo-scientific and somewhat mystical opinion on the significance and meaning of the Tabernacle. 

On the web site of Tony Badill, (http://www.templesecrets.info/) I found this image, which shows what Tabernacle (Mishkan), and later - the Solomon's Temple, represented as far as its spiritual and divine significance goes. Check it out:


To put this idea in words...
God created Man in His own image. Yet God commanded to build Mishkan so that His presence may dwell among the Children of Israel. Mishkan was a macrocosm and microcosm of the entire universe at the same time. This means that Mishkan was essentially reflecting an image of a man as well.

Thursday, December 9, 2010

Exodus 26:24 - Round Corner Boards design in other sources...

I was asked, if there are any other sources that directly mentions possibility of the round corner boards design. Well, the answer to this question is yes.

But unfortunately, I know of only one book. So here it is:

Commentary on the Pentateuch, Volume 2 of Ibn Ezra's Commentary on the Pentateuch, Abraham ben Meïr Ibn Ezra, H. Norman Strickman, Arthur M. Silver, Publisher Menorah Pub. Co., 1988, ISBN 0932232078, 9780932232076


And here is a quote (page 574):

"We do not know if the corner boards were square or round, for we have only one remaining cubit."

Tuesday, December 7, 2010

Exodus 26:33 - Panoramic Images of the Holy and the Holy of Hollies sections of the Mishkan.

I just wanted to add several remaining panoramic images of the Tabernacle that I have created, to give you an opportunity to see the Tabernacle from all possible angles.

Here is the view from an Entrance Curtain (Masach) of the Tent of the Tabernacle. You can see inside the Tent Holy (Kodesh) section and the Courtyard simultaneously.




And here is the view from inside the Tent, from the Holy section of the Tent.



Proceeding further inside the Tent of the Tabernacle, you can use this image to see both Holy and the Holy of Hollies (Kodesh ha-Kodashim) sections of the Tent. This view is at the Inner Curtain (The Vail) of the Tent.




And here is the view from the Holy of Hollies itself. On this image you can see the Ark of The Covenant.




And this final panoramic image brings you back outside, into the Courtyard. This view is 30 cubits above the center of the Courtyard, so that you can have an overview of the entire structure.

Wednesday, December 1, 2010

Exodus 40:17 - Panorama of the Tabernacle - Inside the Courtyard 2 & 3

Here are couple of other panoramic views from inside the Courtyard of the Mishkan.

On this one you can partially see inside the Tent and see the Table of Shewbread. This is a view from off the middle of the Southern side of the Courtyard.


And on this one, you can see the back side (west side) of the Mishkan. This is a view from North West corner of the Courtyard.

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