Sunday, February 19, 2012

How to properly understand Exodus 25:8

This time of year, according to the Jewish tradition, is the time to read about the Tabernacle (parashat Terumah). This is why I would like to dedicate this post to the review of the key verse of the Chapter 25 of the Book of Exodus and the subject of the importance of the Tabernacle. And even though I have outlined the most important concepts on this blog page, I believe a repetition is in order:

So, let's take a look at Exodus 25:8:

Masoretic Text
ועשו
לי
מקדש
ושכנתי
בתוכם
Transliteration
wĕʻá֥ş̂ẇ
li֖y
miqĕḋá֑ş̌
wĕş̌ákanĕţ̇i֖y
ḃĕţwòkáֽm
Strong's Concordance
6213
--
4720
7931
8432
Literal Translation
and_they-make
for_me
sanctuary
and_i-tabernacle
in_midst-of_them

As you can see from this nice table above, God commands the Children of Israel to make Him a Sanctuary so that He could tabernacle in their midst. 

At this point, many people make an incorrect assumption that God wants to dwell in the midst of the Children of Israel and thus commanding them to make Him a Sanctuary. This is incorrect! 

What this verse really states is that God gives Children of Israel a choice to make Him a Sanctuary so He could dwell in their midst. And precisely because of this the Tabernacle is so important!

Only by willingly and wholeheartedly (without any reservation or back-thought) creating a proper Sanctuary to God, the Children of Israel would be worthy of having His Presence to dwell in their midst. 

In other words this verse describes a possibility that needs to be earned, instead of an unearned privilege.  

And this is why it is very important to understand the text properly so as not to draw any mistaken conclusions. This is why the description of The Tabernacle takes so much space in the original text and this is why it is so important to study and try to understand it.

Sunday, February 12, 2012

Volume of the Corner Boards of The Tabernacle

It has occurred to me that I have never tried to calculate the volume of the round Corner Boards of the Tent's Frame. If you have not yet familiarized yourself with my article on the Corner Boards, please do so before reading this post any further.

As you know, the Corner Boards of the Tabernacle were essentially hollow tubes, 10 cubits tall, 0.5 cubit in outer radius and 1.5/pi of inner radius each.

The best and the most practical way to calculate the Volume of the Corner Board is to subtract the volume of its outer cylinder from the volume of its inner cylinder. This way its not only easier to calculate, but it is also consistent with the description provided by the original text.

Here is the table summarizing the diagram above:


Outer Cylinder (#1, Blue) Inner Cylinder (#2, Yellow) Resulting Tube (#3, Blue-Yellow)
The Corner Board
Height 10 Cubits 10 Cubits 10 Cubits
Inner Radius -- (1.5 / pi )Cubits (1.5 / pi) Cubits
Outer Radius 0.5 Cubits -- 0.5 Cubits
Thickness -- -- (0.5 - [1.5 / pi]) Cubits

The standard formula for the volume of a cylinder is V = pi * r ^ 2 * h. By applying this formula to our table above, we would get the following results:


Outer Cylinder (Blue) Inner Cylinder (Yellow) Resulting Tube (Blue-Yellow)
The Corner Board
Height 10 Cubits 10 Cubits 10 Cubits
Inner Radius -- (1.5 / pi )Cubits (1.5 / pi) Cubits
Outer Radius 0.5 Cubits -- 0.5 Cubits
Thickness -- -- (0.5 - [1.5 / pi]) Cubits
Volume 2.5 * pi (22.5 / pi) Cubit^3 (2.5 * pi - [22.5 / pi]) Cubit^3

To even better see all characteristics of the Corner Boards let's also include the Area and the Circumference of the cross-section of each cylinder:


Outer Cylinder (Blue) Inner Cylinder (Yellow) Resulting Tube (Blue-Yellow)
The Corner Board
Height 10 Cubits 10 Cubits 10 Cubits
Inner Radius -- (1.5 / pi )Cubits (1.5 / pi) Cubits
Outer Radius 0.5 Cubits -- 0.5 Cubits
Thickness -- -- (0.5 - [1.5 / pi]) Cubits
Volume (2.5 * pi) Cubit^3 (22.5 / pi) Cubit^3 (2.5 * pi - [22.5 / pi]) Cubit^3
Cross-Section
Circumference
pi Cubits 3 Cubits (pi - 3) Cubit
Cross-Section Area (0.25 * pi) Cubits^2 (2.25 / pi) Cubit^2 (0.25 * pi - [2.25 / pi]) Cubit^2

Or, with rounded numerical values (to the 4th decimal) as such:


Outer Cylinder (Blue) Inner Cylinder (Yellow) Resulting Tube (Blue-Yellow)
The Corner Board
Height 10 Cubits 10 Cubits 10 Cubits
Inner Radius -- ~0.4774 Cubits ~0.4774 Cubits
Outer Radius 0.5 Cubits -- 0.5 Cubits
Thickness -- -- ~0.0225 Cubits
Volume ~7.8539 Cubit^3 ~7.1619 Cubit^3 ~0.6920 Cubit^3
Cross-Section
Circumference
~3.1415 Cubits 3 Cubits ~0.1415 Cubit
Cross-Section Area ~0.7853 Cubits^2 ~0.7161 Cubit^2 ~0.0692 Cubit^2

As you can see, all of the resulting numbers are very interesting. However, the most apparent is the ratio of the volume of an outer cylinder (2.5 * pi) to the Circumference of the inner cylinder (3 cubits or 1.5*2). Because if you remember, the Ark of The Covenant was 1.5 cubits * 1.5 cubits * 2.5 cubits in dimensions, as well as the each corner board was formed from two regular boards width of each was 1.5 cubit. 

This clearly implies that there is a direct connection between the values of the dimensions of each part of the Tabernacle, as well as a certain connection between integrated values of each dimension of each part.

Again, at this point I would rather not draw any definitive conclusions, as this topic requires much more through investigation. However, I hope this post provides you with at least very basic information on the details and values relationship of this crucial part of the Tabernacle - The Corner Boards.

P.S. The volume of the actual tubular Corner Board is very close to quarter pi, which is also very interesting. But just like I pointed out above, more thorough investigation is needed.

Sunday, February 5, 2012

Petach vs Masach vs Parochet

One very important aspect of the terminology used in the description of the Tabernacle is the difference between three Hebrew terms: Petach (Door; Opening or Portal in some translations), Masach (Portiere; or Hanging in some translations) and the Parochet (Partitions; Curtains or Veils in some translations). 

And even though I have covered details of the Parochet in this and this posts of mine, I think it would be beneficial to review this subject again and in more details (to include the Petach and the Masach) all at once.

To do this, I will begin by using the Parochet (Inner Curtain of the Tent of the Tabernacle) as an example, which as you know looked somewhat like this:

Now, take a look at this diagram:

As you can see, there were 5 Parochet (Veils) that constituted 1 so-called Masach (Portiere), which is essentially an Inner Curtain, less the Columns and other hardware.

On the other hand, the so-called Petach (Door) of the Holy of Holies room refers to the actual physical boundary where the Parochet(5 Partitions which constituted 1 Masach) were located (shown in green on the image below). 

So that you do not get confused, here are a few extra diagrams that should clarify the matter:

This first one shows that there were total of 3 Doors in the Tabernacle. One inside the Tent, one on the eastern part of the Tent and one on the eastern part of the Courtyard. 

These three Doors were comprised of 1 Masach (Curtain) each; total of 3 Masach.

And each Masach was comprised of several Parochet (Veils), namely 5 Partitions for the Inner Masach,  4 Partitions for the Outer Masach and 4 Partitions for the Court Gate Masach. Total of 13 Parochet (Veils).

So, as you can clearly see, the Parochet(Veils) was not a singular piece of fabric, but rather several pieces of fabric, and there were total of 3 sets of Parochet (Veils) in the Tabernacle. 

This fact is not only very important to properly understand the original description(i.e Exodus 26:31, Exodus 26:36, Numbers 3:26),  but it is also crucial to understanding the traditional Jewish and Christian interpretations of the Veil. 

In both traditional interpretations the Veil is represented by a singular piece of fabric due to its origin from the Second Temple, which has nothing to do with the Tabernacle and possibly even with the First Temple.

In other words, traditional interpretations must be dismissed when studying the description of the Tabernacle, as they are not rooted in the original text, but rather in latter (and vastly different/modified) descriptions. 

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