25: This chapter features the blueprint designs for the Ark of the
Covenant (Testimony). Some fun with numerology of the ark dimensions is
below, particularly with surface area to volume ratio and summation of
Verses 1 - 9: "And the Lord spoke unto Moses, saying: 'Speak unto the children of Israel, that they take for Me an offering; of every man whose heart maketh him willing ye shall take My offering. And this is the offering which ye shall take of them: gold, and silver, and brass; and blue, and purple, and scarlet, and fine linen, and goats' hair; and rams' skins dyed red, and sealskins, and acacia-wood; oil for the light, spices for the anointing oil, and for the sweet incense; onyx stones, and stones to be set, for the ephod, and for the breastplate. And let them make Me a sanctuary, that I may dwell among them. According to all that I show thee, the pattern of the tabernacle, and the pattern of all the furniture thereof, even so shall ye make it."
Now, is Moses still on Mount Sinai? Let's assume that he is unless proven otherwise.
The offerings that the children of Israel would voluntarily make unto the Lord were stupendous: precious metals, garments, animal products, spices, and precious stones. The surrendering of these possessions unto their God would have constituted a significant sacrifice.
Then God instructs Moses to build a sanctuary so He can "dwell among them". This passage laid the foundation the centrality of the synagogue or temple in contemporary Jewish life. God doesn't reveal himself directly to the ancient Israelis in the open air, or in their homes, or their places of work. He will be in their presence within the confines of the sanctuary. This is where the people would pray and worship their God.
Verses 10 - 12: "And they shall make an ark of acacia-wood: two cubits and a half shall be the length thereof, and a cubit and a half the breadth thereof, and a cubit and a half the height thereof. And thou shalt overlay it with pure gold, within and without shalt thou overlay it, and shalt make upon it a crown of gold round about. And thou shalt cast four rings of gold for it, and put them in the four feet thereof; and two rings shall be on the one side of it, and two rings on the other side of it.
The acacia wood must have been sufficiently sturdy enough to build the ark. Yet it's from the small acacia tree, which is often described as a shrub. One must wonder why God instructed the builders to use this particular wood. A clue might be from the above verses where acacia-wood is one of the offerings made unto God. It wouldn't have been requested as an offering if it wasn't valuable, and thus only high quality wood would be requested for the building of the holy ark.
Note: In both this chapter and Chapter 26, the computation of volume of objects or places (the ark, table, tabernacle) is a rough approximation since we don't know the thickness of the boards used for its construction. That thickness will add to the length of two sides of the object; the corner board of each side will add to the "thickness" of the adjacent perpendicular side.
Ark Part 1: Measurements in terms of Cubits
Let's see. The total volume of the ark = 2.5 x 1.5 x 1.5 = 5.625 cubits. The only interesting point here is that if all the digits in 5.625 are added together (5+6+2+5), it totals 18, which has great significance in Judaism. That is the number for "Chai", the Hebrew word for life. In Hebrew, Chai is a two letter word comprised of a Chet, whose numerical equivalent is 10, and a Yud, whose numerical equivalent is 8. The sum of the two letters is 18. The study of Gematria, the numerology of the Hebrew language, is fascinating.
Now, let us look at the total surface area of the ark. This equals 2*(length*width + length*height + width*height) = 2*(2.5*1.5 + 2.5*1.5 + 1.5*1.5) = 2*(3.75 + 3.75 * 2.25) = 2*(9.75) = 19.5 cubits. Thus, the surface area to volume (SAV) ratio in terms of cubits = (19.5)/5.625 = 3.4666666... . Here, we see the first of many examples to come of the infinitely repeating decimal (.66666... in this case). If we take the sum of the surface area digits divided by the sum of the volume digits (the SAV digit ratio), we get (1+9+5)/18 = 15/18 = .833333... (here, we get the infinitely repeating decimal of 333...). And the secondary surface area to volume digit ratio (the secondary SAV digit ratio) = (1+5)/(1+8) = 6/9 = .666... another repeating 666 case! Watch out!
Ark Part 2: Measurements in terms of Feet
In terms of feet, each cubit was believed to equal 1.5 feet. So, the dimensions of the ark in terms of feet are length = 2.5*1.5 (3.75 ft), breadth/width = 1.5*1.5 (2.25 ft), and height = 1.5*1.5 (2.25 ft). The volume = 3.75*2.25*2.25 = 18.984375. The sum of these digits is 45, which isn't anything special. To compute the surface area in terms of square footage, simply multiply the above square cubit surface area by 2.25 (1.5*1.5) = 2.25*(19.5) = 43.875. The sum of these digits is 27, which again is nothing special. But the SAV digit ratio = 45/27 = 1.66666... which features another repeating 666 decimal and is twice the amount of the cubit SAV digit ratio (1.666 ... = 2*.8333...). In terms of feet, the secondary SAV digit ratio = (4+5)/(2+7) = 9/9 = 1. This is 1.5 the amoung of the cubit secondary digit ratio.
Once built, this ark would look spectacular, lined with gold on its exterior and interior. The placement of four rings for its feet, one for each corner, and a golden crown upon it would give it a royal look-and-feel.
Verses 13 - 15: "And thou shalt make staves of acacia-wood, and overlay them with gold. And thou shalt put the staves into the rings on the sides of the ark, where-with to bear the ark. The staves shall be in the rings of the ark; they shall not be taken from it.
The four staves, placed in the rings, would be used to lift the ark.
Verses 16 - 17: "And thou shalt put into the ark the testimony which I shall give thee. And thou shalt make an ark-cover of pure gold: two cubits and a half shall be the length thereof, and a cubit and a half the breadth thereof.
Of course we're most curious about the content of the testimony that will be inside the ark. The ark cover, like the ark itself, will be beautiful and opulent.
Ark Cover, Part 1: Measurements in terms of Cubits
It's area is 2.5 x 1.5 = 3.75 cubits. Sorry, this time, there's no numerical significance of the sum of the digits (3+7+5 = 15). The only somewhat interesting fact is the ratio of the ark cover's area to the ark's volume: 3.75 / 5.625 = 2/3 = .6666....
The sum of the digits of the ark cover's area (3+7+5) = 15 while the sum of the digits of the ark's volume (5+6+2+5) = 18. 15/18 = .8333..., the same as the SAV digit ratio of the ark's surface area to volume. And, if we continue further with the summation of digits, the secondary SAV digit ratio = (1+5)/(1+8) = 6/9 = .6666
We're clearly developing a theme with the infinite repeating decimal in these formulations. Here we have seen .6666..., and we'll also see it below.
Ark Cover, Part 2: Measurements in terms of Feet
In terms of feet, the cover's area = (3.75 square cubits) * (2.25 square feet / square cubit) = 8.4375. The sum of its digits is 27, just like the digit sum of the cover's cubit area. The ratio of the cover's area to ark volume, in terms of feet, = 8.4375/18.984375 = .4444...!! The ratio of summation of digits in feet terms = 27/45 = .6
By the way, the surface area to volume (SAV) ratio is inversely proportional to the size of an object; the higher the ratio, the smaller the object. This is a very useful property in scientific applications, especially in cellular biology. Cells that are smaller (with higher SAV ratio) have a higher diffusion rate across their cellular membrances that permit more rapid deployment of nutrients and favorable growth substances within the cell's borders.
The summation of digits of a number is also useful in scientific applications, particularly in computer computations and network security. The summation of digits of a computed number, called the checksum, is used to validate or check the data integrity of calculations. In security applications, the checksum will be used to validate the encryption and decryption of a message to insure the authentication of the message's sender and receiver (i.e. to prevent theft of online information).
Verses 18 - 20: "And thou shalt make two cherubim of gold; of beaten work shalt thou make them, at the two ends of the ark cover. And make one cherub at the one end, and one cherub at the other end; of one piece with the ark-cover shall ye make the cherubim of the two ends thereof. And the cherubim shall spread out their wings on high, screening the ark-cover with their wings, with their faces one to another; toward the ark-cover shall the faces of the cherubim be.
The cherubim would be created from the golden ark cover. Their wings would cover the ark-cover, reminiscent of the protection administered at the Garden of Eden (there was one cherub guarding the garden's Eastern entrance with a flaming sword). Here, the cherubim would be facing each other looking downward at the ark-cover. They would have a watchful eye on each other and upon the ark that they are protecting.
Verses 21- 22: "And thou shalt put the ark-cover above upon the ark; and in the ark thou shalt put the testimony that I shall give thee. And there I will meet with thee, and I will speak with thee from above the ark-cover, from between the two cherubim which are upon the ark of the testimony, of all things which I will give thee in commandment unto the children of Israel."
We're even more curious about the testimony, and why God was determined to meet with his "children"! The presence of God between the cherubim now make it clear why they were aligned to face each other: they would be looking at God, demonstrating their loyalty to Him.
Verses 23- 25: "And thou shalt make a table of acacia-wood: two cubits shall be the length thereof, and a cubit the breadth thereof, and a cubit and a half the height thereof. And thou shalt overlay it with pure gold, and make thereto a crown of gold round about. And thou shalt make unto it a border of a handbreadth round about, and thou shalt make a golden crown to the border thereof round about
Table, Part 1: Measurements in terms of Cubits
Here, the volume of the table = 2 * 1 * 1.5 = 3 cubits. The surface area = 2*(2*1 + 2*1.5 * 1*1.5) = 2*(2+3+1.5) = 2*(6.5) = 13. The SAV ratio in cubit terms = 13/3 = 4.333... And again, the .333 infinite repeating decimal.
Table, Part 2: Measurements in terms of Cubits
In terms of feet, the surface area = 13*2.25 = 29.25 (with a digit sum of 18). And the volume = 3*(1.5^3) = 3*(3.375) = 10.125 (with a digit sum 9). So the SAV ratio in feet terms = 29.25/10.125 = 2.888... . And the SAV digit sum = 18/9 = 2.
Like the ark, the table was beautiful and opulent, overlayed with pure gold and topped off with a golden crown. The difference here is the presence of a border of a handbreadth's width (a handbreath was a Biblical measure of length, approximately the width of a palm of the hand).
Verses 26- 28: "And thou shalt make for it four rings of gold, and put the rings in the four corners that are on the four feet thereof. Close by the border shall the rings be, for places for the staves to bear the table. And thou shalt make the staves of acacia-wood, and overlay them with gold, that the table may be borne with them."
This was the same formula for the table's rings and staves; there was no difference between the ark's and table's rings and staves.
Verses 29- 30: "And thou shalt make the dishes thereof, and the pans thereof, and the jars thereof, and the bowls thereof, wherewith to pour out; of pure gold shalt thou make them. And thou shalt set upon the table showbread before Me alway."
Guess who's coming to dinner! And he wants the table set His Way!
Verses 31- 33: "And thou shalt make a candlestick of pure gold: of beaten work shall the candlestick be made, even its base, and its shaft; its cups, its knops, and its flowers, shall be of one piece with it. And there shall be six branches going out of the sides thereof: three branches of the candlestick out of the one side therof, and three branches of the candlestick out of the other side thereof; three cups made like almond-blossoms in one branch, a knop and a flower; and three cups made like almond-blossoms in the other branch, a knop and a flower; so for the six branches going out of the candlestick.
A six-branch menorah was to be hammered out of gold. The almond-blossoms shape undoubtedly added a nice aesthetic touch.
Verses 34- 36: "And in the candlestick four cups made like almond-blossoms, the knops thereof, and the flowers therof. And a knop under two branches of one piece with it, and a knop under two branches of one piece with it, and a knop under two branches of one piece with it, for the six branches going out of the candlestick. Their knops and their branches shall be of one piece with it; the whole of it one beaten work of pure gold."
This detailed description of the construction of the menorah is amazing, right up to the placement of the knops (knobs) between the branches.
Verses 37- 40: "And thou shalt make the lamps thereof, seven; and they shall light the lamps thereof, to give light over against it. And the tongs thereof, and the snuffdishes thereof, shall be of pure gold. Of a talent of pure gold shall it be made, with all these vesssels. And see that thou make them after their pattern, which is being shown thee in the mount."
Out of nowhere comes the 7th lamp! On what branch does it rest? In any case, this forms the basis of the seven-branch menorah. The "talent" in this passage referred to a monetary unit (equal to 3000 shekels).