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."

Thursday, November 18, 2010

Exodus 27:9-19 - The Courtyard of the Tabernacle as a Sundial (Exclusive Video)

One very interesting aspect of the Courtyard (Chatzer) of the Mishkan is the fact that it was, essentially, a giant sundial clock.

If you remember, the Courtyard of the Tabernacle was of a rectangular shape, with total of sixty (60) Pillars, and with the perimeter equal to 360 cubits.  And even though I do not want to engage into much speculation here, I must say that these numbers are very interesting at least.

To better illustrate the concept, I have created this video animation that simulates shadows cast by the partial framework of the Mishkan on a specific day.

Simulation specifications as follows:

Location: Shiloh, Israel
Coordinates: 32.05 N, 35.28 E
Date: September 18, 2010
Time: 6am - 6pm, UTC +2

Enjoy!



P.S. One interesting fact that can be assumed here, is that most likely the Northern, Southern, Eastern and Western direction that was specified for the Mishkan orientation, had to be a true one (defined by the Sun) as opposite to magnetic one (defined by the compas needle).

Monday, November 15, 2010

Exodus 26:15-16: What would it take to assemble the Tabernacle, if its boards were more than 0.5 cubits thick.

I have found a nice video that shows an assembly process of a purported life-size "replica" of the Tabernacle. 

Because this replica is using boards of approximately ~0.6 cubits, you will clearly see from the video how difficult and impractical such structure would become. Not only boards of this size would have to be hollow (and they are on the video) but they also would have to be supported  by additional crossbars (which are not part of the original description) at the top to give it necessary stability. Please also pay attention to the equipment involved in the process of assembly.

Also, this video very nicely shows what would happen if the middle Bar for the Boards would run through them, instead of outside of them. The assembly team in this video having very difficult time putting it through 30 cubits of length of the boards.


Wednesday, November 10, 2010

Exodus 25:17-22 - Torah and Science, or why it is good to know the proper density of gold.

I have found couple of interesting articles at Bar-Ilan University's Parashat Hashavua Study Center. But first of all, here are the direct links to the list of articles published by Bar-Ilan on weekly Torah portions: In English and In Hebrew.

Now, the article that I would like to cite here is not particularly interesting or revealing. What is most important about this article is that it is a very good example how scientific knowledge can be applied to understand the verses of Pentateuch. And at the same time, this article is a prime example of how an incorrect application of science can lead to the wrong conclusions and provoke and interesting responsa from more competent people, which will be presented right after the article.

You can find english translation of the main article right here, however the responsas are available only in hebrew, so I will present all of them in hebrew.



אוניברסיטת בר-אילן
הפקולטה למדעי היהדות
לשכת רב הקמפוס

ד ף ש ב ו ע י

מאת היחידה ללימודי יסוד ביהדות

מספר 642

פרשת תרומה, תשס"ו

"ועשית כפורת זהב טהור, אמתיים וחצי אורכה ואמה וחצי רוחבה"

פרופ' אברהם יהודה גרינפילד

פרופ' נתן אביעזר

המחלקה לפיסיקה



פרשת "תרומה" עוסקת בעיקר בבניית המשכן וכליו – נושא הנראה מרוחק משגרת החיים המעשית של היהודי בימינו. אולם, נראה שאין הדבר כך. מתיאור מידותיהם של הכלים המוזכרים בפרשתנו, אפשר ללמוד על שיעורי תורה, נושא בעל עניין רב בחיים היהודיים היום‑יומיים. ישנן מצוות "עשה" רבות שלקיומן יש צורך בחפץ מסוים, וכמעט כל "חפצא דמצוה" כזה מאופיין בין השאר גם בשיעורו, כמו כמות הפת שעלינו לאכול בליל הסדר ובליל ראשון של סוכות, כמות היין שיש לשתות בקידוש, כמות מי המקווה, ממדי הסוכה, ועוד. כמו כן מתלווים שיעורי התורה לרבות ממצוות "לא-תעשה", כמו שיעור המזון שאכילתו ביום כיפור עונשה כרת, או המרחק של טלטול ברשות הרבים בשבת שעונשו מיתה. שיעורי תורה הם גורם מרכזי שיש לו משקל רב בעולם ההלכה, ונראה שפרשתנו היא מקור חשוב לקביעתם.



אחת היחידות הבסיסיות של שיעורי תורה היא האמה, שמוזכרת שוב ושוב בקשר לבניית המשכן וכליו. במאתיים השנים האחרונות התעוררה מחלוקת על מידת אורכה של האמה. מקור המחלוקת הן המדידות של שיעור חלה שערך הרב יחזקאל בן יהודה לנדאו ("הנודע ביהודה", שחי במאה השמונה עשרה). שיעור הקמח המחייב הפרשת חלה הוא "עומר", ועל-פי "הלכה למשה מסיני", מסרו לנו חז"ל [1] שתי דרכים שקולות למדידת נפח העומר, האחת על-פי שיעור נפח ביצה והשנייה על-פי מידת "אגודל" מעוקב ("אגודל" הוא שיעור אורך). להפתעתו, מצא "הנודע ביהודה" במדידותיו סתירה בין שתי דרכי המדידה הנ"ל. מכיוון שלא מצא דרך ליישב את הסתירה, הורה "הנודע ביהודה" לנקוט על פי החומרה של שתי הדרכים.



לאור הסתירה הבולטת הזו בין השיעורים האמורים להיות זהים על-פי "הלכה למשה מסיני", התפתחו שתי אסכולות עיקריות: האמה (האמה שווה ל- 24 אגודלים) לפי שיטת ה"חזון איש" (הרב אברהם ישעיהו קרליץ) היא "אמה גדולה", ששיעורה 58 ס"מ; לעומת זאת, שיטתו של הרב חיים נאה גורסת "אמה קטנה", ששיעורה 48 ס"מ. בשנים האחרונות הוכנסה לזירה שיטה שלישית, שהציע אחד ממחברי מאמר זה (גרינפילד), הטוענת שאורך האמה הוא 44 ס"מ בלבד. כעת נראה מה ניתן ללמוד מהכתוב בפרשת "תרומה" אודות שלוש שיטות אלו לאורך האמה.



כלי המשכן עשויים מזהב, מכסף ומעץ. רוב הכסף נדרש כדי ליצור את האדנים המחוברים לתחתית הקרשים, ורוב הזהב נדרש כדי ליצור את הכפורת, שהיא לוח זהב המכסה את הארון. נתרכז בכלי הזהב - הארון, המנורה, השולחן, מזבח הזהב, הכרובים והכפורת. נראה, שיותר מ-80% מכלל הזהב במשכן נדרשו כדי ליצור את הכפורת.



השיעור של משקל בתורה הוא "שקל הקודש" והכיכר ששווה ל-3000 שקלים (לח:כה-כו). משקל השקל ידוע. ספרות תורנית ענֵפה [2] מראה שיש הסכמה בין הגאונים והראשונים שמשקל שקל הקודש הנזכר בתורה הוא 14 גרם. מאוחר יותר, הוסיפו חז"ל 20% למשקל השקל הנדרש בקיום מצוות מסוימות, כמו פדיון הבן, אבל תוספת זו אינה קשורה לשקל הקודש המוזכר בתורה. מכאן, שמשקל הכיכר (3000 שקל) הוא 42 ק"ג.



כמות הזהב שנדרשה כדי ליצור את כלי הזהב במשכן אינה כתובה בתורה, חוץ מהמנורה, שידוע לנו כי משקלה יחד עם כל אביזריה היה כיכר אחד (לז:כד). סביר להניח שליתר כלי הזהב במשכן (ללא הכפורת) היה משקל דומה לזה של המנורה. כמות דומה של זהב נדרשה לכסות את הקרשים. לפי הנחה זו, המשקל של כל כלי הזהב במשכן, ללא הכפורת הוא 5 – 10 כיכרות. במהלך הדיון נראה שהנחה זו מוצדקת.



כל הזהב במשכן היה 29 כיכרות ועוד 730 שקלים (לח:כד). לכן, אם מורידים 5 – 10 כיכר עבור כל כלי הזהב במשכן, נשארים יותר מ-20 כיכר זהב עבור הכפורת. עכשיו נאמת את הקביעה הזו.



מידות הכפורת כתובות במפורש בתורה ובגמרא: לוח זהב טהור שאורכו 2.5 אמות, רוחבו 1.5 אמות (כה:יז) ועוביו טפח (סוכה ה ע"א). לבד ממקרים מסוימים שאינם קשורים לכפורת, יש שישה טפחים לאמה (כלים יז:י). לכן, נפח הכפורת הוא 0.625 אמות מעוקבות.



כדי לחשב את משקל הכפורת, צריכים לקבוע מהו אורך האמה. מבין שלוש השיטות שהוזכרו לעיל, נתחיל את הדיון בהצעה הקצרה ביותר, דהיינו 44 ס"מ. לפי אורך זה של האמה, חישוב פשוט (44×44×44×0.625 סמ"ק) מראה ש-0.625 אמות מעוקבות של הכפורת שוות ל-53,000 סמ"ק. בהסתמך על המשקל הסגולי של זהב טהור (19.3 גרם לסמ"ק), יוצא שמשקל הכפורת (53,000×0.0193 ק"ג) הוא 1030 ק"ג (מעל טון זהב!), שהם 24.5 כיכר (לפי 42 ק"ג לכיכר). תוצאה זו סבירה בהחלט היות וכלל הזהב במשכן הוא 29.2 כיכר. דהיינו, נדרשה לכפורת קצת יותר מ- 80% מהכמות הכוללת של הזהב במשכן. תוצאה זו מצדיקה את ההנחה שלנו דלעיל, שרוב רובו של זהב המשכן נדרש לייצור הכפורת.



כעת נעבור לשיטות אחרות של אורך האמה. אם מניחים שאורך האמה הוא 48 ס"מ, יוצא שנפח הכפורת (0.625 אמות מעוקבות) הוא 69,000 סמ"ק, שמשקלם - 1330 ק"ג - שווה ל-31.7 כיכר זהב. היות שכמות זו של זהב עולה על כל הזהב במשכן כולו (29.2 כיכר), ברור שאורך האמה חייב להיות פחות מ-48 ס"מ. לפי מידת "האמה הגדולה", הסתירה בולטת עוד יותר. לפי אמה שאורכה 58 ס"מ, נפח הכפורת הוא 122,000 סמ"ק ומשקלה - 2250 ק"ג - שווה ל ‑ 56 כיכר, דהיינו, כמעט פי-שניים מכלל הזהב במשכן. המסקנה לגבי אורך האמה מתבקשת מאליה. [3]



לסיכום, אנו רואים מהניתוח דלעיל שעיון בפסוקי פרשת "תרומה" שופך אור חשוב על ענייני דיומא.

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[1] פרופ' א"י גרינפילד, "מידה כנגד מידה", מוריה, ז-ח (קכז-קכח), תמוז תשמ"ב, עמ' נט-פו.

[2] הרב ח"פ בניש, מדות ושיעורי תורה , בני-ברק, תשמ"ז (מהדורה שנייה), פרקים כא, כב, כז, ל. הרב י"ג וייס, מדות ומשקלות של תורה , ירושלים, תשמ"ד, פרקים כו-לב. הרב צ. וינברגר, רבע אצבע כשיעור עובי הדופן של אדני המשכן , בד"ד, כרך 2, חורף תשנ"ו, עמ' 19-11.


[3] הדרך היחידה ליישב את הסתירה הזו לגבי "האמה הגדולה" היא להניח שהכפורת הייתה חלולה, אז שמשקל הכפורת אינו קשור למידותיה החיצוניות. אולם, אין תימוכין בספרות התורנית להנחה זו.


Here is the first responsa to this article (here is the original link of the responsa)....


ד ף ש ב ו ע י

מאת היחידה ללימודי יסוד ביהדות
מספר 645

פרשת ויקהל-פקודי, תשס"ו

תגובה למאמר "ועשית כפורת זהב טהור, אמתיים וחצי אורכה ואמה וחצי רוחבה"

שמחה גוטגולד

רעננה



קראתי בעניין את המאמר, ולצערי נראה לי שהכותבים, כפי הנראה שלא לפי המתודה המדעית בתחום הפיזיקה, התייחסו לנתון אחד כעובדה מבלי לבדוק אותו. הכוונה שלי היא למשקל הסגולי של הזהב. אכן, כפי שכתבו, המשקל הסגולי של זהב טהור הוא 19.3, אלא שאי-אפשר להניח שהזהב שבני ישראל השתמשו בו במדבר היה זהב טהור (24 קראט). גם היום אין משתמשים בזהב ממש טהור לכל שימוש אפשרי, פרט אולי למחקרים במעבדות.



לפי האנציקלופדיה העברית, טוהר הזהב שנמצא מתקופת הפרעונים היה 15 קראט. אני חושב ש-15 קראט הוא רמת הזיכוך המקסימלית שניתן להניח שאליה יכלו בני ישראל במדבר להגיע. המשקל הסגולי של הזהב של בני ישראל במדבר תלוי, לכן, בחומרים השונים שהיו מעורבים בו, ובכל מקרה הוא נמוך מ-19.3.



לאור האמור ועל-פי החשבון שהוצג במאמר, ניתן אפוא להראות שלא רק 44 ס"מ אפשריים כאורך האמה, אלא גם 48 ס"מ. אכן, כדי שגם 48 ס"מ יהיו אפשריים, יש צורך להניח שבכפורת היו "כיסי אוויר" שנוצרו או בכוונה תחילה בגלל כמות בלתי-מספקת של זהב (הנחה שאינה סבירה, שכן כתוב : "מרבים העם להביא מדי העבודה למלאכה") או בגלל קשיי העיבוד של כמות זהב כה גדולה.



אגב, מכיוון שהכותבים שכחו להכניס לחשבון שלהם את כמות הזהב שהושמה בכרובים, הרי שגם לפי אמה של 44 ס"מ, אם נזכור את גודל הכרובים, יהיה צורך בהנחה זו של "כיסי אוויר" בכפורת, כדי שכמות הזהב של הכפורת והכרובים יחד תהיה קטנה מכמות הזהב הכוללת שנאספה לצורך המשכן. ההנחה על קיומם של כיסי אוויר, מונעת, כמובן, כל אפשרות להשתמש בשיטת החישוב הזו כדי לקבוע את אורך האמה.


And here is a responsa to responsa so to speak (original link is right here)

ד ף ש ב ו ע י

מאת היחידה ללימודי יסוד ביהדות

מספר 645

פרשת ויקהל-פקודי, תשס"ו

תגובת פרופ' אברהם יהודה גרינפילד ופרופ' נתן אביעזר

פרופ' אברהם יהודה גרינפילד ופרופ' נתן אביעזר

המחלקה לפיסיקה



הופתענו לקרוא בתגובה למאמרנו "ש-15 קראט [זהב] הוא רמת הזיכוך המקסימלית שניתן להניח שאליה יכלו בני ישראל במדבר להגיע".



כל מאמר על זהב יאשר שזה אינו נכון. לדוגמא: באנציקלופדיה בריטניקה, כרך 10 עמ' 534 (המאמר על "זהב") כתוב: "זהב נמצא במצבו הטבעי [24 קראט] או בסגסוגת של כ-20% כסף [כ-20 קראט]". וכל ספר בכימיה יאשר שקל מאד לטהר את הסגסוגת הזו ולקבל זהב טהור ותהליך הטיהור היה ידוע גם בעולם הקדמון.



לכן, כאשר כתוב בתורה: "ועשית כפורת זהב טהור", אין סיבה לסטות מפשטות המילים ולהניח שהזהב לא היה טהור.
So, as you can see from the discourse, even though the author of the main article makes a proper application of scientific approach to approximate the value of a Cubit, and somewhat - the weight of the Mercy Seat of the Ark of The Covenant, his limited knowledge of properties of metals (gold, in this case) had led him to the incorrect conclusions that the first responsa tried to address. However only the third responsa on the main article was able to provide more or less clear picture of what values of density of gold can be used to approximate the value of a Cubit.

Therefore - there you have it! Even though the description of the Mishkan may seem to be very simple and may look like that it would only require a very limited scientific knowledge to understand its design, it is only an illusion. In fact, to understand the structure of the Mishkan would require very deep and thorough knowledge in many scientific disciplines, if one to hope to properly comprehend its beauty and hidden mysteries.

Sunday, November 7, 2010

Exodus 26:15-25 - The Thickness of the Boards of the Mishkan

I wanted to post another short excerpt from the book called "פירוש אליהו על ספר שמות" by "אליהו שץ".

In this section of his commentary, Dr. Shatz discusses the thickness of the Boards (kerashim) of the Mishkan. He uses backward approach in calculating the thickness of the boards, simply by approximating the reasonable weight of the materials involved. And even though such approach is rather questionable, it is still very worthy to check it out, especially the part, where Dr. Schatz talks about reasonable thickness of gold overlay of the boards, as well as its weight.



Here is a very "lazy" OCR hebrew transcript of the text (sorry!):

( כו 30-15 : הקרשים. בריחיו. טבעותיו ואדניו (ציור 6) (השוה לו 34-20

כו 15 ) ועשית את הקרשים למשכן עצי שטים עומדים ־ תשתמש בעצי שטים מן

הסוג שמגיע לגובה של כעשרה מטר (עץ השיטה המלבינה; ראה כה 5), כדי

לעשות מהם את קרשי המשכן (הקרשים: לוחות עץ ארוכים ודקים. עצי שטים

עומדים: כנראה, עץ השיטה המלבינה).

כו 16 ) עשר אמות אורן הקרש ואמה וחצי האמה רוחב הקרש האחד - אורך

הקרש 10 אמות ורחבו 1.5 אמה. לא צויין עובי הקרשים כי הם היו דקיםי

בעלי עובי של כסנטימטר אחד. לפי אמה השווה ל 43.2- ס״מ, מידות הקרשים

ס"מ. המשקל של קרש כזה, בהנחה שצפיפות x 1.0 ס"מ x 64.8 היו 432 ס"מ

העץ שווה ל־ 0.5 גרם/סמ"ק, הוא בערך 14.0 ק״ג. אם עובי הקרשים היה

אמה אחת (כפי השיטה של רש״י) אזי משקל כל קרש היה בסביבות 605 ק״ג.

בלתי אפשרי שב״י היו יכולים להוביל משקלים כאלו בנסיעתם במדבר.

במיוחד, ארבע עגלות לא היו מספיקות להסיע 46 קרשים כאלו (ראה במדי ד

,( 33-29 ; ז 8). בנוסף, משקל האדנים היה רק 34.2 ק״ג כל אחד (לח 27

והאדנים לא היו מסוגלים להחזיק באופן יציב קרשים ששקלו 605 ק״ג.

כו 17 ) שתי ידות לקרש האחד - שתי בליטות (ידיות) בתחתיתו של כל קרש,

העשויות להיכנס לחלל בתוך האדנים, כדי להחזיק את הקרשים במצב עומד.

משולבות אשה אל אחותה - מקבילות זו לזו כמו שלבי הסולם. כן תעשה ל כ ל

קרשי המשכן - שהידות יהיו משולבות. המונח "כל קרשי המשכן" כולל: 20

20 הקרש לפאת צפון (פסוק 20 ), ששת הקרשים ,( הקרש לפאת נגב (פסוק 18

לפאת ימה (פסוק 22 ), ושני הקרשים למקוצעות המשכן (פסוק 23 ). אפשרות

הגיונית אחת לצורות הקרשים מוצגת בציור 6, בהנחה: 1) שהאמה שווה

x 2.0 ל־ 43.2 ס"מ; 2) שמידות הידות הן 20.0 ס"מ גובה \ 1.0 ס"מ עובי

ס"מ רוחב; 3) שהאדנים הם בצורת תיבה והיו בערך 20 ס״מ גובה \ 20 ס"מ

.( ס״מ רוחב (פסוק 19 x 9.5 עומק

כו 18 ) ועשית את הקרשים למשכן עשרים קרש לפאת נגבה תימנה - בצד דרוס

עומדים 20 קרשים, וכל אחד מהם ברוחב של 1.5 אמה (נגבה תימנה:

אמה. לפי אמה השווה x 1.5 = 30 20 דרומה). לכן אורך צד דרום הוא

ל־ 43.2 ס״מ, מקבלים שאורך המשכן הוא 12.96 מטר.

כו 19 ) וארבעים אדני כסף תעשה תחת עשרים הקרש, שגי אדנים תחת הקרש

האחד לשתי ידותיו, ושני אדגים תחת הקרש האחד לשתי ידותיו - האדנים
 
היו בסיסים עשויים מכסף, עם חור באמצע האדן המתאים בדיוק לגודל יד

, הקרש. כל יד משתי הידות של הקרש תהיה תקועה באדן אחד. לפי לח 27

המשקל של כל אדן היה ככר ( 3000 שקל) דהיינו 34.2 ק״ג היות שהשקל

שווה ל 11.4- גרם. הצפיפות של כסף טהור היא 10.5 גרם/סמ״קי אבל נניח

כאן שלא השתמשו בכסף לגמרי טהור אלא במסגי כסף שהכילו מספר אחוזים

של נחושת ומתכות אחרות (ראה כה 3), ולכן צפיפות הכסף היה קרוב יותר

ל־ 9.0 גרם/סמ"ק. לפי זה, נפח ככר של כסף הוא 34200/9.0 = ש 38 סמ״ק.

אם האדן היה בצורת קובייה, אזי כל צד של האדן היה 15.6 ס"מ. אבל אז

האדן לא היה מתאים לקרשים שבמקוצועות (פסוק 23 ). טוב יותר להניח

ס״מ רוחב; x 9.5 שמידות האדן היו בערך 20 ס״מ גובה צ 20 ס"מ עומק

ואז האדנים היו מתאימים לכל הקרשים.

כו 20 ) ולצלע המשכן השנית לפאת צפון עשרים קרש ־ בצד צפון עומדים 20

.( קרשים, כמו בצד דרום (פסוק 18

כו 21 ) וארבעים אדניהם כסף, שגי אדגים תחת הקרש האחד, ושני אדגים

.( תחת הקרש האחד ־ בדיוק כמו בצד דרום (פסוק 19

כו 22 ) ולירכתי המשכן ימה תעשה ששה קרשים ־ בקצה המשכן בצד מערב

ולירכתי: החלק האחורי. ימה: ) . ( x 1.5 6) תעשה ששה קרשים, שהם 9 אמות

. מערב). ועושים בצד מערב עוד שני קרשים הנזכרים בפסוק 23

כו 23 ) ושני קרשים תעשה למקוצעות המשכן בירכתים - בנוסף לששת הקרשים

הרגילים תעשה עוד שני קרשים מיוחדים בפינות המשכן בצד מערב

(מקוצעות: פינות). רוחב שני הקרשים בפינות היה רק חצי אמה כל אחד,

. ( x 2 + 1.5 x 0.5 6) וסך הכל אורך צד מערב הוא 10 אמות

כו 24 ) ויהיו תואמים מלמטה ־ שני הקרשים במקוצעות יהיו מתאימים

מלמטה עם שאר הקרשים; כלומר, יהיו להם שתי ידות הנכנסות לתוך שני

אדנים. ויחדיו יהיו תמים על ראשו אל הטבעת האחת ־ הקרש בפינה ייגמר

בקצהו העליון כך שטבעת אחת תחזיק את הקרש למעלה ביחד עם הקרש בסוף

הצד הצפוני או הדרומי. כן יהיה לשניהם, לשני המקוצעות יהיו - שני

הקרשים במקוצעות יהיו מסודרים באופן מיוחד גם למטה וגם למעלה.

כו 25 ) והיו שמונה קרשים - יהיו בצד מערב ששה קרשים רגילים ועוד שני

קרשים מיוחדים במקוצעות, סך הכל 8 קרשים. ואדניהם כסף, ששה עשר

אדנים, שני אדנים תחת הקרש האחד ושני אדנים תחת הקרש האחד ־ לכל

שמונת הקרשים, אפילו לקרשים בפינות, יהיו שני אדני כסף מלמטה.

כו 26 ) ועשית בריחים עצי שטים, חמישה לקרשי צלע המשכן האחד - תעשה

בצד דרום 5 בריחים כדי לוזבר את 20 הקרשים ביחד (בריחים: מוטות עץ).

כו 27 ) וחמישה בריחים לקרשי צלע המשכן השנית ־ תעשה 5 בריחים בצד

צפון, שגם שם יש 20 קרשים (השנית: לצד צפון. ראה פסוק 20 , "ולצלע

המשכן השנית לפאת צפון״). וחמישה בריחים לקרשי צלע המשכן לירכתים

ימה - תעשה 5 בריחים בצד מערב ששם יש שמונה קרשים.

כו 28 ) והבריח התיכון בתוך הקרשים ־ הבריח האמצעי, שהוא אחד מחמשת
 
הבריחים, עובר באמצע גובה הקרשים, דהיינו בגובה של כחמש אמות. מבריח

מן הקצה אל הקצה ־ כל אחד מן הבריחים עובר מן הקצה האחד של הדופן אל

הקצה השני של הדופן. בכל דופן היו שמים שני בריחים בצד הפנימי, אחד

למעלה ואחד למטה; ושני בריחים בצד החיצוני, אחד למעלה ואחד למטה;

ועוד בריח בצד החיצוני באמצע גובה הקרשים. הבריחים היו מונעים

מהקרשים להתנדנד עם הרוח. נניח שהבריחים היו בצורת גליל, בקוטר של 4

קוטר x ס"מ. לפי זה, מידות הבריחים בצד דרום ובצד צפון היו: 30 אמות

של 4 ס״מ. לפי אמה השווה ל־ 43.2 ס״מ, וצפיפות העץ של 0.5 גרם/סמ"ק,

0.5 ק״ג. x7^x2x2x43.2x30 =8.1 מקבלים שמשקל כל אחד מהבריחים האלו היה

0.5x7^x2x2x43.2x10 =2.7 כמו כן, משקל כל אחד מהבריחים בצד מערב היה

ק״ג.

Monday, October 25, 2010

Exodus 25:10-22 - The Weight of the Ark of the Covenant

While I'm contemplating on the details of the design of the framework of the Mishkan, I wanted to go back a little bit and provide you with the original source (in hebrew) for this article by Elihu Shatz on the weight of the Ark of the Covenant. So here it is (click to enlarge):


From the book called "פירוש אליהו על ספר שמות" by "אליהו שץ"





I will add the hebrew transcript of the text later.

Wednesday, October 20, 2010

Tabernacle Layout: The Key Questions Checklist

While studying the Layout of the Tabernacle, it is very important to take in the account all of the details of the description simultaneously. But because it may be difficult for some people to do that, I have decided to write up a short checklist of the Key Questions, that would allow anyone to examine validity of any proposed layout of the Tabernacle.

As you know, there are many different opinions as to what the Tabernacle might have looked liked. Here are some of the most widely accepted versions:

Here is a version according to Mizrachi (taken from this web site):


Here is the version according to the Levush HaOrah (taken from this website)


And here is the Ma'ase Choshev version (from here)


Here is a Baraita De-Melekhet Ha-Mishkan version (from this book - תבנית המשכן וכליו)


And here is a version that is based on a mix of opinions of Rashi, and Rab. Nechemiah (mishna)

And here is again Maase Hoshev version, but with tall courtyard pillars (10 and 15 cubits high).

And here is Chabad's version of Mishna opinion again, with modifications.

Therefore, the only way to analyze which version is correct, one must remember to check proposed layout for the following:
  1. Correct uutilization of meaning of the words "Mishkan" and "Tent" for the First and Second Coverings in Exodus 26:9, Exodus 26:12-13. Word "Tent" must refer only to Goat's Hair Covering, and word "Mishkan" must refer only to wooden Framework and Coverings with Cherubims. 
  2. Differences between the location of the Clasps and Loops of the First and Second Coverings  (Exodus Exodus 26:5 vs 26:10). Loops "on the edge" vs Loops "at the edge"
  3. Ability of the layout to provide an explanation of how the Width and Length of the Holly of Hollies (Kodesh ha-Kodashim) was calculated. Both Internal and External. (Exodus 26:13 - expression "to cover it")
  4. How the Thickness of the Boards of the Mishkan was calculated (Exodus 26:16)
  5. How layout explains the placement of the Inner Curtain (Parochet) "under the Clasps"? Which Clasps? (Exodus 26:33)
  6. How location of each set of Clasps was calculated? What was the purpose of the location of each set of Clasps? (Exodus 26:6, Exodus 26:11 and Exodus 26:33)
  7. How the shape, location and dimensions of the Inner and Outer Pillars were identified and calculated (Exodus 26:32 and Exodus 26:37)
  8. How the dimensions of the Courtyard Pillars were calculated? (Exodus 27:17)
  9. How the shape and location of the Courtyard Pillars was identified and calculated? (Exodus 27:17)
  10. How dimensions of the Courtyard Curtains were identified and calculated. (Exodus 27:18)
  11. What about quantity of Courtyard Curtains (i.e Exodus 27:9 - usage of the expression "hangings" in the plural form)
  12. How an Overall dimensions of the Courtyard were calculated?
  13. How an Overall dimensions of the Courtyard Perimeter identified by the Pillars were calculated?
Of'course, these are just general and most important questions that have to be answered in order for the proposed Tabernacle Layout to be valid.

In order to illustrate the importance of these questions, I'm going to show you what happens when you apply these questions to one of the traditional layouts. Let's take the last layout from the ones above as an example:


The answers to my checklist for this layout will be as follows:

  1. This version uses incorrect assumption, that the "folding of the extra sheet to the forefront of the tent" means having half of the remaining sheet (2 cubits) of the Goat's Hair covering to hang off the front side (east side) of the wooden framework. This is because the author did not notice that the word "Tent" in this chapter NEVER refers to the wooden framework. This already invalidates the proposed layout.
  2. In this layout, the Loops located in the edges of the halves of each of the two Coverings. No differentiation is made, even though the description is pretty clear. This also invalidates the layout.
  3. The Width of the Holy of Hollies in this layout is specified as 10 cubits (inner) and 12 cubits (outer). Since the widest Covering (Goat's Hair covering) is only 30 cubits, it leaves 1 cubit of the framework on North and South sides uncovered (due to the thickness of the Boards being 1 cubit). This invalidates the layout because of Checklist Question #4
  4. No explanation is given as to how the thickness of the Boards of the framework was calculated. Moreover, the thickness of the Boards may wary between 1 cubit and 0 cubits, without any implications upon the proposed interpretation of the text that this layout is based on. The only thing that would change, is the amount of Coverings hanging in the front of the framework. But since it does not have to be 2 cubits (see #1), this means that any thickness of the Boards between 0 and 1 cubits is acceptable, and thus invalidating this layout again due to this mathematical inconsistency.
  5. This layout puts both set of Clasps one under another and exactly 10 cubits from the inner side of the western wall of the framework. However, since the Clasps located exactly one under another (see #2), this leaves a see-through gap in the Coverings, that would not be acceptable.
  6. Calculation of the location of the Clasps is explained. But because it is based on the invalid #1-5 assumptions above, it also cannot be considered valid.
  7. No explanation is given whatsoever.
  8. No explanation is given whatsoever.
  9. No explanation is given.
  10. No explanation is given. Plural form is ignored.
  11. No explanation is given. Plural form is ignored.
  12. Based on the length of the Curtains. Listed as 100x50 cubits.
  13. No explanation and dimensions are provided. Perimeter identified by the pillars in this layout is 2 cubits larger, than that of a Curtains, or 102x52 cubits (because Courtyard Pillars here located on the outside)
Therefore, and as you can see by using provided checklist, it is now very easy to see huge inconsistencies in the proposed layouts, as well as to see if the proposed layouts hold any water so to speak.

Thursday, September 30, 2010

Exodus 26:17 - A closer look at the Tenons ("Hands") of the Boards of the Tent of the Mishkan

I wanted to add more information about the most likely design of the Boards of the Tent of the Tabernacle. As you remember, each Board of the Tent had special Tenons (ידות, meaning lit. - "hands") that helped to connect them together. Let's take a look at Exodus 26:17:

17 Two tenons shall there be in one board, set in order one against another: thus shalt thou make for all the boards of the tabernacle.

‎17 ‏שְׁתֵּ֣י יָד֗וֹת לַקֶּ֙רֶשׁ֙ הָאֶחָ֔ד מְשֻׁלָּבֹ֔ת אִשָּׁ֖ה אֶל־אֲחֹתָ֑הּ כֵּ֣ן תַּעֲשֶׂ֔ה לְכֹ֖ל קַרְשֵׁ֥י הַמִּשְׁכָּֽן׃
The traditional interpretations of the word  ידות , understands that it refers to the bottom side of the Boards, and therefore to this design (image is courtesy of Kollel Iyun Hadaf of Har Nof Rosh Kollel: Rabbi Mordecai Kornfeld (daf@shemayisrael.co.il @ http://www.dafyomi.co.il/shabbos/)


However, this design has a flaw. This design does not address the problem of creating tight connection between the adjacent boards, in order to make the structure more rigid, as well as to prevent light and other elements from getting through into the Sanctuary.

If you remember, I have been following more contemporary approach (which is also supported even by some of the traditional commentators) in dealing with these "Tenons", which you can find in my previous posts.
The only thing I did not cover properly, is the actual interlocking mechanism for the Boards and its possible design. Therefore, I would like to concentrate on this and show you a couple of examples of what the "Tenons" might have been really referring to.

Here is an image of the so-called "Tongue and Groove" interlocking system for the hardwood flooring. This is basically a more modern and modified system of "tenon and mortise" and as you can see from this image, such mechanism would have been almost ideal for our purpose:

However, as you also see from this image, this particular design of the interlock lacks one major feature that we need. More specifically, it has "Tenon" only on one side of the Board, whereas our verse states that there had to be two "Tenons", one on each of the sides of the boards.

Therefore, I would like to show you the most advanced and modern system of interlock mechanism, that fits this description perfectly.

Here are couple of images that I found on this website, that shows a system of interlocking hardwood flooring using the so-called "unilin" and "valinge" locking mechanisms:

Here is a classic Unilin locking system:
 And here is the latest "Valinge" locking system:

Since the images are very self-explanatory, I would like to leave it up to you to make necessary conclusions of applicability of these designs to the "Tenons" of the Boards of the Mishkan.

Friday, September 24, 2010

Exodus 26:32 & 26:37 - Playing with Pillars and the Schematic Layout of the Tent of the Tabernacle

I wanted to show you the schematic layout of the Tent of the Tabernacle. I figured that a gray scale rendering of only major parts of the Tent would allow you to better understand the design.

On this image, you can see the major parts of the Tent of the Mishkan:

And on this image, you can see the corner boards of the Tent of the Mishkan. As you can see, these two-parts corner boards were cylindrical in shape and hollow.

While I was making this rendering, I also had a chance to check out my theory about a slightly different layout of the Pillars of the Tent of the Mishkan. If you recall from Exodus 26:32 and Exodus 26:37, there were two sets of Pillars, that served as a mounting points for the respective curtains of the Tent.
32 And thou shalt hang it upon four pillars of shittim wood overlaid with gold: their hooks shall be of gold, upon the four sockets of silver.

32 ‏וְנָתַתָּ֣ה אֹתָ֗הּ עַל־אַרְבָּעָה֙ עַמּוּדֵ֣י שִׁטִּ֔ים מְצֻפִּ֣ים זָהָ֔ב וָוֵיהֶ֖ם זָהָ֑ב עַל־אַרְבָּעָ֖ה אַדְנֵי־כָֽסֶף׃
37 And thou shalt make for the hanging five pillars of shittim wood, and overlay them with gold, and their hooks shall be of gold: and thou shalt cast five sockets of brass for them.



‎37 ‏וְעָשִׂ֣יתָ לַמָּסָ֗ךְ חֲמִשָּׁה֙ עַמּוּדֵ֣י שִׁטִּ֔ים וְצִפִּיתָ֤ אֹתָם֙ זָהָ֔ב וָוֵיהֶ֖ם זָהָ֑ב וְיָצַקְתָּ֣ לָהֶ֔ם חֲמִשָּׁ֖ה אַדְנֵ֥י נְחֹֽשֶׁת׃ ס




I have made a similar gray scale rendering of this modified design of the Tent, so that you can compare it to my current design. As you can see from the image below, in this improved design, I have increased the diameter of pillars from 0.5 cubits to 1 cubits (just like the corner boards), and also moved three middle Pillars out of five Outer Pillars 0.5 cubits inward from the center line of the Outer Pillars. (NOTE: even  though it may not be seen clearly from this rendering, even with pillars being 1 cubits in diameter, there seem to be still plenty of space left between the pillars for the priests to pass through - about 1.5 cubits)


And here you can compare a footprint of the Tent of the Mishkan of my reviewed design...
 ....with the footprint of the Tent of the Mishkan in my current design.

I'm not going to discuss in detail as to why I wanted to change the diameter of the Pillars. However, all I can say for now, it seems to me that this new design may help to resolve some of the problems with the arrangement of the elements of the Tent, improving an overall compliance to the original description. Once I will get a chance to examine this design thoroughly, I will try to discuss it in much more details.

Thursday, September 23, 2010

Numbers 4:5-6 - Transportation of the Ark of the Covenant - Location of the Staves

For quite some time I wanted to post one very good image of the Ark of the Covenant during its transportation, as well as to comment on a certain details of that image. So here it is:

Israel Enters the Promised Land, as in Joshua 3:5-17, illustration from a Bible Card published between 1896 and 1913 by the Providence Lithograph Company (circa 1896-1913). 

Now, if you recall, Numbers 4:5-6 states:
5 And when the camp setteth forward, Aaron shall come, and his sons, and they shall take down the covering vail, and cover the ark of testimony with it:

6 And shall put thereon the covering of badgers' skins, and shall spread over it a cloth wholly of blue, and shall put in the staves thereof.
‎5 ‏וּבָ֨א אַהֲרֹ֤ן וּבָנָיו֙ בִּנְסֹ֣עַ הַֽמַּחֲנֶ֔ה וְהוֹרִ֕דוּ אֵ֖ת פָּרֹ֣כֶת הַמָּסָ֑ךְ וְכִ֨סּוּ־בָ֔הּ אֵ֖ת אֲרֹ֥ן הָעֵדֻֽת׃

‎6 ‏וְנָתְנ֣וּ עָלָ֗יו כְּסוּי֙ ע֣וֹר תַּ֔חַשׁ וּפָרְשׂ֧וּ בֶֽגֶד־כְּלִ֛יל תְּכֵ֖לֶת מִלְמָ֑עְלָה וְשָׂמ֖וּ בַּדָּֽיו׃
As you can read, even though the illustration above is very well done, it lacks the detail mentioned in the Verse 6 of this chapter. Namely, in the image above, the Staves of the Ark appear to be covered with the coverings of the Ark, instead of being on the outside, helping to support coverings of the Ark from falling off.

Same also had to be true for all other artefacts of the Mishkan, that had been carried by the means of Staves. You can read about it in the following verses: Numbers 4:8(table), Numbers 4:11(golden altar), Numbers 4:14 (altar of burnt offering).

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