|
The Pi Ratio in the Bible
Historians have been aware for some time of the basic knowledge that the pi ratio was utilized in ancient Egypt, Babylon and the far east. There has also been much written on the pi ratio used specifically in the dimensions of the Great Pyramid, along with other applications in ancient Egypt. This subject will be handled in more detail in the coming section of this web-site, related to the Biblical Astronomy of the Great Pyramid. For our purposes in this short study, we will focus more on how the Biblical usage of pi surpasses its mathematical use in ancient Babylon, and and resembles more closely it's use in the Great Pyramid. A Biblical perspective on this subject has for the most part been sorely lacking, and even ridiculed as we will see. Thus one goal of this study is to present a truer Biblical perspective of this problem than perhaps has been available up to now. As always, when we allow proper space for the perspective of God's Word on a subject, we will always benefit from the new light the Scriptures will shed. The divine view of a thing is always superior to man's view.
From a historical perspective, the Egyptians, compared to the Babylonians were limited geometers, where their use of pi is concerned, applied to ancient geometry. Early on, their valuation of pi was on par with the surface value of pi in the Bible; [3] which we will detail in this article. Later, their valuation of pi improved to 3.125. The ancient Egyptian priests used a formula to accurately determine the volume of a cylinder, that includes the recognition of pi. There are those like Petr Beckmann,1 who are aware of the basic reference to the pi ratio in the Bible in I Kings 7, but they don't put much stock in it.
I Kings 7:23-30 23And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about. 24And under the brim of it round about there were knops compassing it, ten in a cubit, compassing the sea round about: the knops were cast in two rows, when it was cast. 25 It stood upon twelve oxen, three looking toward the north, and three looking toward the west, and three looking toward the south, and three looking toward the east: and the sea was set above upon them, and all their hinder parts were inward. 26And it was an hand breadth thick, and the brim thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths. 27And he made ten bases of brass; four cubits was the length of one base, and four cubits the breadth thereof, and three cubits the height of it. 28And the work of the bases was on this manner: they had borders, and the borders were between the ledges: 29And on the borders that were between the ledges were lions, oxen, and cherubims: and upon the ledges there was a base above: and beneath the lions and oxen were certain additions made of thin work. 30And every base had four brazen wheels, and plates of brass: and the four corners thereof had undersetters: under the laver were undersetters molten, at the side of every addition.
What follows will provide ample reason why this or any other Scriptural references should not be glossed over, as Beckmann does, or rejected out of hand, by evaluating the surface value of pi in I Kings 7:23 as an "amusing curiosity."2 As we consider the Biblical usage of words related to how the pi ratio is revealed in Scripture, we will gain insight into the divine perspective of how the Creator thinks about this subject. This will speak volumes to those who have eyes to see and ears to hear the God's truths.
The Hebrew word for "line" of thirty cubits, in verse 23 is "qav" [*H6957]. The word carries the primary meaning of a measuring cord, a ruler, or standard of measure. We are also familiar with this concept by another term known as a "canon." On the surface the Bible gives the basic mathematical value of pi as 3, but the surface is for the neophytes. The deeper truths of God's Word lie below the surface, for those who have the heart and will to look for them. Before we take a peek under the covers, lets take a look at some other places where this Hebrew word "qav" occurs.
In the 38th chapter of Job, God is discussing the foundations of the Earth. Verse 5 asks: "Who hath laid the measures thereof, if you know? Or who hath stretched the line upon it?" The obvious Biblical answer to these questions is the Creator. In light of the usage of "qav" in I Kings 7:23, God's exercise of Pi as a standard ruler or measure in laying and measuring the spherical dimensions and foundations of our planet, recorded in the book of Job, the oldest book of the Biblical Canon is enlightening. This is especially the case when we consider the context of Job 38, which deals with a series of questions about various elements of Creation, that only God Almighty could be the answer to. We need also remember that the furnishings of both the Hebrew Temple & Tabernacle, [ohel] which are the subject of I Kings 7, along with the structure of each edifice, represent certain heavenly things, [Heb. 8:5]. The Intelligent Design specifications of the planet Earth would easily fall into this category, as to how the Earth's spherical dimensions and temporal order fit into the celestial context of Creation. We can see the sense of this clarified even more in our next reference to the Hebrew word "qav."
In Psalm 19, The heavens declare the glory of God... Verse 4 says,
"Their line is gone out through all the earth, and their words to the end of the world. In them He hath set a tabernacle for the sun."
Once again the Hebrew word for "line" here is qav. Let me ask you, what is the heavenly or celestial line that is a tabernacle, or provides the houses of the sun? The only sensible answer is the ecliptic! This is quite logical when we consider that the Israelites, during their 40-year sojourn in the Sinai wilderness were led by God, seen as a pillar of cloud during the day, and one of fire by night. The pillars dwelt over the Holy of the Holies of their Tabernacle, signifying the Creator's personal presence among His people. When they camped during the evenings, Numbers 2 tells us they camped in the order of the tribes as it matched the order of the course of the sun on the ecliptic, (east, south, west, north). Israel's twelve tribes, as we are aware by now, also matched up with the twelve signs of the zodiac in their God-ordained significance, before they were corrupted in heathen Astrology and mythology. This tribal order is also found in the twelve jewels of the High Priest's breastplate, [Ex. 28:15-21]. Thus the celestial gospel originally related the story of the coming redeemer of mankind, which God wrote in the stars before He ever committed it to His Written Word. These are the words of Ps. 19:4 that have gone out through all the earth, unto the end of the world. This application of the Pi ratio (the mathematical relation of the diameter of a circle to its circumference) by God, in reference to the ecliptic is certainly intriguing in light of the Sun's apparent 360-degree path through its 12 houses of the zodiac, as viewed from Earth. In this light we should also be aware of the earlier context of I Kings 7.
1 Ki 7:13 And king Solomon sent and fetched Hiram out of Tyre. [14] He was a widow's son of the tribe of Naphtali, and his father was a man of Tyre, a worker in brass: and he was filled with wisdom, and understanding, and cunning to work all works in brass. And he came to king Solomon, and wrought all his work. [15] For he cast two pillars of brass, of eighteen cubits high apiece: and a line of twelve cubits did compass either of them about.
The word for "line" in verse 15 above is not qav, as it is in verse 23, but it still indicates a line for measuring, so let's take a closer look at these brass pillars anyway. As we know, Pi has long been considered a transcendental number, or constant of mathematics (3.14159....), linking a straight diameter to a curved circumference. The French archeologist and mathematician Charles Funk-Hellet points out that:
"Solomon had Hiram contribute to building a temple whose brass columns were 18 cubits high, and 12 cubits around. In other words, one cubit equaled the twelfth part of the circumference of the arc of 30 degrees, or pi/6. By subtracting the circumference from the height, they obtained 6 cubits in a straight line, which was equal to 1/2 circumference, or the exact value of pi; so that a thousand years before Christ the Hebrews knew that a cubit was a mathematical entity dependent on the circumference, and were able to resolve pi to four points of decimal." 3 (emphasis mine)
Funk-Hellet's observation that: "By subtracting the circumference from the height, they obtained 6 cubits in a straight line, which was equal to 1/2 circumference, or the exact value of pi/6...."4 is worth remembering when we come to the subject of the celestial symbolism of the Menorah, and its application of the pi ratio, which builds on what we have found here.
Funk-Hellet goes on to say that: "the Biblical cubit is equal to the Egyptian Royal cubit, which was incorporated into the Temple at Jerusalem as pi/6, or 523.6 millimeters. Using one unit of measure as the radius of a circle, the ancients found the trigonometric value of 30 degrees to be pi/6, (which divided the full circumference of the circle into 12 equal parts) and was the value of the royal cubit, or .5236 of the unit used: 3.1416/6 = .5236"5 (parenthesis & emphasis mine)
In effect, we have an architectural representation of the twelve-fold division of the heavens preserved in the dimensions of the Temple's Brass columns, all based on the mathematical standard Pi, long before most modern scientists imagined the ancients knew anything about Pi at this level of accuracy. This provides more evidence showing the perfect wisdom of the Creator and Nature's Great Geometer, at work in the dimensions of His Temple, as an illustration of heavenly realities [Heb. 8:5], which He gave to King David by revelation. Also symbolically contained in the dimensions of the Temple's brass columns, is a figure of the 12 calendar months of 30 days, totaling the 360 days of their year, a calendar also used going all the way back to Noah's time, in the context of the 360-degrees of the ecliptic. This reveals the true origin of the 12 - 30° segments of the ecliptic, as a standard celestial measure. And since Noah was already 600 years old when the Bible records the details of this luni-solar calendar in Genesis 7, it also implies that it was used by the earlier Biblical Patriarchs prior to the flood, and centuries before history and human science thought this level of astronomical sophistication was known. For more information on Noah's Calendar, please go to the article under the same title on this website.
Since the pattern shown to Moses for the Tabernacle was by divine revelation, just as the pattern of the Temple was shown to King David, these men of God did not receive the blueprints for these sacred edifices, or their related measurements, by scientific trial and error. Thus they didn't need to wait on the Greeks, like Archimedes, generally considered the greatest of ancient scientists, to rediscover them or to apply them in divine architecture. Although Archimedes is to be commended for his application of the pi proportion, it pales in comparison to what we find in the Biblical uses of "qav" as it relates to pi.
As we can see in the above Biblical usage of the Hebrew word "qav," God's exercise of the concept of Pi far exceeds any previous application of it by mankind. It is amazing what God's Word can teach us when we only give the Creator the proper credit for Who He really is! At times it seems men of scientific Materialism will go to any length to prevent naming God as the Creator, or even acknowledging His presence. They would rather credit the non-entity of chance, than to give credit to the only One Who could ever truly claim the authority to speak things into being from nothing, our Mighty and Omnipotent Heavenly Father. Only from the Creator's viewpoint in His Word, do these applications of the pi ratio make sense. Only He could apply the pi ratio with the ecliptic and the dimensions of our planet, a concept which is borne out in much greater detail, in how the pi ratio is symbolically and architecturally applied in the Great Pyramid.
The pi ratio in I Kings 7, should also be considered with any close approximation of pi in King Solomon's day. On this subject there is information concerning a practical approximation of pi in the ancient world, based on septenary units of measure. In some ancient traditions, the relation of the Diameter to the Circumference, embodied in the pi ratio, symbolized the names of God; Elohim and Jehovah. With Elohim, the Creator representing the Circumference, of the curved line of the totality of His Creation, and Jehovah as the straight line Diameter, or God in relationship to His Creation, the geometrical expressions of these relations were realized in the pi ratio. We find the basic elements of the Circle's diameter inscribed the circumference of a surrounding Sphere inside a Cube, in II Kings 7:30 above, contained in the square base that carried the circular brasen sea. This principle has survived through the centuries in the domed sacred architecture of many temples & churches, where the circular dome is surrounded by a square building. We should take note that the Holy of the holies, which contained the Ark of the Covenant, was a perfect cube, contained within a double-square ground-plan of the Hebrew Tabernacle. This provided the divine foundation of many practices in the "sacred geometry" of the secular world. The practical approximation of pi in the ancient world of sacred architecture, has preserved this concept of God the Creator in relation to His Creation, in a systematic application of principles of sacred geometry, based on septenary units of measure. According to Stechini, in this system the "circumference was considered 22/7 of the diameter; this approximation of pi rendered (3 1/7, or 3.142857) is still in use today as an adequate approximation in many problems of engineering." 6
As Beckmann points out, "Archimedes started with a hexagon and progressively doubling the number of sides he arrived at a polygon of 96 sides, which yielded pi as 3 1/7, or 3.142857." 7 The importance of relating pi to septenary units is obvious in a Biblical light when we consider God's abundant use of the number seven in His ordering of Creation. Some of this evidence is covered in our website essay on the Calendar of the Israel. This ratio of 22/7 is also intriguing because it expresses the ratio between the 22 letters of the Hebrew alphabet, in relation to its seven vowels. This is a supporting factor in the idea that the roots of writing & the first alphabet originate in the celestial gospel. As the first "written" revelation to mankind, the stars in this gospel were named and numbered by God [Ps. 147:4]. The divine message of the coming redeemer and the means God chose to deliver it, thus provide the sacred foundation of all language and mathematics. As the divine original source of this wisdom, the witness of the stars was above reproach. The pi ratio expressed as 22/7, reflects this perfection of the celestial gospel, in at least the mathematical, geometrical and linguistic contexts.
This trend continued when God's media of revelation transitioned to the written word, when God first wrote the 10 Commandments in precious stone, which Moses the Lawgiver delivered to the people of the Nation Israel. This marked the start of the Mosaic Law Administration. The Canon of truth for the Patriarchal Administration was the celestial gospel, given directly by God, but is was up to men to apply these truths according to the principles of this system God put into place. Even so the Law began with writings from "the finger of God," but transitioned to the written Scriptures given by revelation from God, to "holy men of God, who spake as they were moved by the holy spirit" [II Pet. 1:21]. During this transition from the Patriarchal to the Law Administrations, men became the carriers of the divine message, and the potential for corruption was introduced into the equation. The Human Will must be freely subject to the Will of God to keep the corruption out in both divine systems of revelation. This brings us to the answer that lies beneath the surface of I Kings 7 as it relates to the ancient Gematria of the Hebrew language. Men like Dr. E.W. Bullinger in his book; Number in Scripture, reveal the details of this subject. We will only scratch the surface here. but before we do let's consider one final point connected with septenary measuring units.
The following note from Keil and Delitzsch' Commentary on I Kings 7:23 below, adds support to the application of pi relating to septenary units as seen in the brazen sea above, [3.142857]
and the knowledge of its application by the ancient Hebrews, via revelation from God, in the dimensions of the Temple and its sacred furniture and accessories.
"The brazen sea (cf. 2Ch. 4:2-5). - “He made the molten sea - a water-basin called יָם (mare) on account of its size - ten cubits from the one upper rim to the other,” i.e., in diameter measured from the upper rim to the one opposite to it, “rounded all round, and five cubits its (external) height, and a line of thirty cubits encircled it round about,” i.e., it was thirty cubits in circumference. The Chethib קוה is to be read קָוֶה here and in Zech. 1:16 and Jer. 31:39, for which the Keri has קָו in all these passages. קָוֶה or קָו means a line for measuring, which is expressed in 1Ki. 7:15 by חוּט. The relation of the diameter to the circumference is expressed in whole numbers which come very near to the mathematical proportions. The more exact proportions would be as 7 to 22, or 113 to 355.”8 [emphasis mine]
The septenary relation to pi uncovers the link between the pi and phi ratio, through the popular Fibonacci Series. This link makes it possible to obtain pi without the need for measuring! This is illustrated in the following quote from Livio Stechini:
"It is possible to use the Fibonacci Series to obtain an accurate relation for the diameter of the circle to its circumference, without recourse to pi. In the Fibonnacci series of 21, 34, 55, if 21 is taken as the diameter of a circle, its circumference will be 55 x 6/5 = 66, accurate to the one thousandth part, giving the Great Pyramid value of pi as 22/7 = 3.142857. Higher numbers in the fibonacci series provide increasingly finer values in whole numbers accurate to one ten-thousandth part. Prolonging the series to 80, 144, 233, 377, 610... a diameter of 144 (4 x 576) gives a circumference of 377 x 6/5 or a pi value of 3.1415. A diameter of 233= a circumference of 610 x 6/5 or a pi value of 3.1416..."9
Plate 1. The Pi and Phi Ratios in the Great Pyramid
This mathematical affinity between pi and phi (pi= ز x 6/5, equivalent to 2.618 x 6/5 = 3.1416) will be further expounded in our essay on the Great Pyramid, especially in the relation between its base and height as seen in Plate 1 above. Now lets look beneath the surface of I Kings 7. The Hebrew word for "line" in verse 23 is normally spelled with two Hebrew letters, but as Jochen Katz points out; this word is written with an extra letter.10 A subject that has gotten much attention of late is "Bible codes." These codes are revealed with the use of the numerical values of the letters of the Hebrew and Greek languages, used in the Bible. E.W. Bullinger captured the essence of this referring to "the supernatural design in the use of number both in the Works of God and in the Word of God." He delineates four topics below in his book Number in Scripture:
1. Numbers of things mentioned.
2. Numbers of words and things.
3. Numbers of words used for a thing.
4. Numbers formed by the letters of the words themselves.
The last category above, the ancients called Gematria.11 Since the letters of the Hebrew alphabet are used instead of numbers, each letter has a numerical value. As Jochen Katz points out: "we can take the ratio of (the gematriacal value of "qav") in its unusual word form (having three letters), to the regular word form with two letters which is 111/106."12 The value of this ratio (1.047198) when multiplied by the Bible's basic value of pi; (3) gives the result of 3.1415, or pi accurate to five digits! This formula is revealing because it employs the computation of a ratio hidden in the number values of the Hebrew language, to yield a higher degree of mathematical accuracy for the pi ratio, than its surface value of 3. This information is useful when we consider the application of pi in the Great Pyramid, and in light of the other Biblical uses of this word "qav," that we have just touched upon.
This sub-surface enlightening of how pi is used in the Bible again stretches the envelope of the historical awareness of the scientific sophistication in the ancient world. Since this expertise is revealed as an aspect of the dimensions of the sacred furniture of the Temple and Tabernacle, it makes sense that God's knowledge of these matters would far exceed human knowledge. This is exactly what Isaiah tells us:
Isa. 55:8-9
For My thoughts are not your thoughts, neither are your My ways, saith the Lord. For as the heavens are higher than the Earth, so are My ways higher than your ways, and My thoughts higher than your thoughts.
Only when we allow the Word of God to have its rightful say, are we allowed glimpses of His glory! We have seen that God's use of Pi relating to the measures of our planet, the ecliptic, the "pattern of the tabernacle" [Heb. 8:5, Exod 25:9, 40] and the temple of Israel, and the sacred geometry of the Menorah, reveal the Creator's Omniscient wisdom in His Intelligent Design of Creation, far above any historical application of pi by man. Those who play with the surface values and external truths of the Scriptures will never see beyond the level of God's Word as an "amusing curiosity." Only those who recognize God for Who He is, and give His Word the proper respect due it's unique position in the history of literature, will even begin to see the wonders of His glory.
In conclusion, as we turn our attention to more current events relating to pi, some of the most interesting "pi news" pertains to its recent computation by a team of Japanese scientists who were using a Hitachi supercomputer in an attempt to break their own record for calculating digits of pi. To their surprise and utter amazement, their Hitachi supercomputer solved pi at 1.3511 trillionth digit! This is not a misprint! That's right, they successfully completed this exercise three times for verification, with the same result! This stunning evidence, that pi is questioned as transcendental number, forced some to re-think their theorems, where pi was assumed as an infinite constant of mathematics. As we can see from the following report however, Colin Percival is not one of them:
In 1998, 17-year-old Colin Percival, calculated the five trillionth binary digit of pi. In 1998, researchers computed the first 51.5 billion decimal digits of pi. Percival discovered that pi's five trillionth bit, or binary digit, is a "0." His accomplishment is significant not only because it was a record-breaker, but because, for the first time ever, the calculations were distributed among 25 computers around the world. In all, the project, dubbed PiHex, took five months of real time to complete and one-and-a-half years of computer time. Percival, who graduated from high school in June, 1998 had been attending Simon Fraser University in Canada concurrently since he was 13.
Footnotes
1. A History of Pi, Petr Beckmann.
2. IBID p. 16.
3. Secrets of the Great Pyramid, Peter Thompkins, p. 263
4. IBID
5. IBID
6. IBID
7. A History of Pi, Petr Beckmann. p. 64
8. KEIL & DELITSCH Commentary on I Kings 7:23.
9. Secrets of the Great Pyramid, Peter Thompkins, p. 97 fn
10. "Value of Pi in I Kings 7:23," Jochen Katz @ "y" files .com
11. Number in Scripture, E.W. Bullinger. p. 48.
12. "Value of Pi in I Kings 7:23," Jochen Katz @ "y" files .com
13. *Numbers from Strong's Concordance are the source for word definitions.
|
