This article is taken from the November 2022 issue of Fraternal Review titled, “Kabbalah 2”.
In my article, “From a Point to a Line,” from the April 2021 Fraternal Review on Kabbalah, I discussed how the early Babylonians and Assyrians, using Geometry, developed their calendar, astrology, and mathematics. As Masons, we are taught that Geometry is the greatest of the Seven Liberal Arts. Geometry gives man the powers of proportions and magnitude; without Geometry, man cannot conceive how to build, or to navigate, or when to plant and harvest.
Plato and Aristotle each described the ratios of nature—the circumference of a circle to its radius, the hypotenuse of a right triangle, among others. The most beautiful of these ratios is the Golden Ratio, represented by the Greek letter Phi (φ). Euclid defined the Golden Ratio in The Elements as: “If a straight-line is cut in extreme and mean ratio, then the square on the greater piece, added to half of the whole, is five times the square on the half.” Euclid’s proof forms rectangles into square triangles (), which gives us the irrational value of 1.618033… (Livio).
The Golden Ratio in the Bible
The Great Architect of the Universe created the “Divine Proportions” that appear throughout existence. These proportions are the guide of creation: the Golden Ratio; the Fibonacci sequence; Pi (π); pentacles; and the sexagesimal (base-60 numbering). From these we also derive the Golden Triangle, the Golden Ellipse, and the Platonic Solids. These are the building blocks of the Universe, from our DNA, to how the planets are arranged in the solar system.
The Golden Ratio has been suggested to be the “thumbprint” that God placed on his creation. The Biblical references to the Golden Ratio and the Fibonacci sequence are instructions from God on how to pray and to build Temples and other religious icons.
Noah’s Ark
In Genesis 6:15, God commands Noah to build an ark, saying, “And this is how thou shalt make it: the length of the ark three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits.” (Tanakh) The ratio of the length to the width is a Golden Ratio, as is the ratio of the width to the height of the Ark.
God then commands Noah how to taper the Ark, “to a cubit shalt thou finish it upward,” a truncated triangle. (The Jewish Publication Society of America) The angles of the triangle are also proportioned in the Golden Triangle ratio.
The Ark of the Covenant, the Tabernacle, and King Solomon’s Temple
Upon delivering the Ten Commandments on Mt. Sinai, God instructs Moses and Aaron to create a Sanctuary, so that God may dwell among the people. Exodus 25:8-9. In Exodus 25:10-23, God commands Moses and Aaron to build the Ark of the Covenant, with an Altar two and a half cubits long, a cubit and a half wide, and a cubit and a half high. The Ark, altar, and other items that God had commanded were placed in the inner and outer Sanctum of the Tabernacle, or mishkān (ןַכְשִמ .(Thus, the ratios of the Ark, the Altar, and the Inner and Outer Sanctums were all constructed by the Golden Ratio.
In his The Chronology of Ancient Kingdoms Amended, Sir Isaac Newton gave a detailed description and depicted floor plans of King Solomon’s Temple. The South, East, and North Gates form the entrances to the Outer Chamber and the Altar.
Of particular interest to Freemasons are the Middle Chamber and the Holy of Holies (Sanctum Sanctorum), which are also configured in the Golden Ratio (Newton). Our modern Lodge rooms being representations of King Solomon’s Temple, Masonic Ritual and mythology begin with this Temple—its ratios and proportions.
The Geometry of the Tree of Life
Geometry comprises the Tree of Life, with its various aspects interconnected by means of triangles, hexagons, and circles. The Tree of Life consists of ten spheres connected with 22 paths. These 22 paths correspond to the letters of the Hebrew alphabet, from which are derived the meanings of Gematria. These aspects, in proportion to the divine ratios, together bring out our experience of Kabbalistic Reality. The Sephirot (spheres) are divided into three Pillars. The three Sephirot on the right form the “Pillar of Severity” and those on left the “Pillar of Mercy”—together representing Jachin and Boaz—while the center is known as the “Pillar of Equilibrium.” Together, they allude to the ten qualities of God; with the benign of the left modifying the rigor of the right, so that Divine Justice is always tempered by Divine Mercy. This equilibrium is also seen throughout the symbolism of Freemasonry.
Our ritual states that Jachin (יןִכָיְו (translates to “he establishes” while Boaz (זַעֹב (translates to “in the strength of” or “in him is strength.” Thus, Jachin is the pillar of Mercy and Boaz is the pillar of Severity. Also, Jachin is the man, represented by the Celestial Sphere and Boaz is the woman, represented by the terrestrial sphere. The middle pillar, the Pillar of Equilibrium, represents The Divine. The Zohar begins with the universe being filled with God’s presence, and continues that God desired to emanate and create the world. God brought forth light into a point at the center of a circle. Writing in The Tree of Life, Isaac Luria Ashkenazi, aka Ari, comments thus on Beresheet: “Before the emanations were emanated and the creatures were created, the upper simple light had filled the whole reality.” Above Kether there was God and the Eternal Light.
When God said, “Let there be light” there was a flash—and a point of light was created; this was the topmost sphere Kether. That point of light split into 10 spheres, each carrying its part of the Divine Light. In the Tree of Souls,
Mythology of Judaism (p. 122), Schwartz states that the ten spheres, “like a fleet of ships, each carrying its cargo of light,” broke apart under the powerful divine light.” As a lightning bolt, from Kether, there emerged the succession of ten Sephirot. It was not until the lightning bolt had created the tenth sphere, Malkuth, that the physical world was created.
As Ari stated, the “the harsh spark came out, the force of Din that was disclosed in Malchut, emerging from Ein Sof, and carved a carving in the upper light… And in that empty space, all the worlds and all that is in them subsequently emerged.”
The World is Divine Geometry
Freemasonry calls God the Great Architect of the Universe. The geometric progression of creation, as shown in the Kabbalah’s Tree of Life, demonstrates how, in all of nature, the greatest of the Arts and Sciences truly is Geometry.
Works Cited
1. Ben, Jacob, et al. The Torah with the Baal HaTurim’s Classic Commentary. Mesorah Publications, 1999.
2. Euclid, and Thomas L. Heath. The Thirteen Books of Euclid’s Elements. Edited by Thomas L. Heath, Translated by Thomas Heath, Cambridge University Press, 2014.
3. www.zohar.com/zohar. Accessed 6 Aug. 2022.
4. Livio, Mario. The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. Broadway Books, 2003.
5. Newton, Isaac. The Chronology of Ancient Kingdoms Amended, Etc. F.P. Printed for J. Tonson, Etc.: London; Sold By Messieurs Smith & Bruce: Dublin, 1728.
6. “Parashat Beresheet יתִ אשֵׁ רְ בּ | Jewish Website.” Jewishwebsite.com, 3 Oct. 2018, jewishwebsite.com/featured/parashat-beresheet.
7. Rosenbaum, M., and A. M. Silberman, editors. Pentateuch with Targum Onkelos, Haphtaroth and Prayers for Sabbath and Rashi’s Commentary: [I-V] (2 Vol.). Shapiro, Vallentine and Co., 1946.
8. Schwartz, Howard, and Caren Loebel-Fried. Tree of Souls: The Mythology of Judaism. Oxford University Press, 2007.
9. Shyfrin, Eduard. “Torah and Mathematics: The Secret of Noah’s Ark.” Chabad.org, www.chabad.org/parshah/article_cdo/aid/3514607/jewish/Torah-andMathematics-The-Secret-of-Noahs-Ark.htm. Accessed 3 July 2022.
10. The Jewish Publication Society of America Holy Scriptures. The Lakeside Press, 1917.
Written by Mark Poliner