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geometry and the sacred symbol


part II - Symbolism and the Teachings of Freemasonry

W. M. Don Falconer PM, PDGDC

Geometry and freemasonry are synonymous and the sacred symbol is an emblem of the Deity whom freemasonry serves.

The traditional relationship

The blazing star is a symbol of the greatest antiquity, which was used in the ancient mysteries and probably before them. In freemasonry the sacred symbol has always been closely associated with geometry and also the blazing star, which is also called the glory in the centre. Down through the centuries many different symbolisms have been assigned to the blazing star, most frequently relating to attributes of the deity. It is not known when the blazing star was first used as a masonic symbol, but in speculative freemasonry in England its use was firmly established when it appeared on a primitive tracing board prepared for the instruction of Entered Apprentices very early in the 1700s. The blazing star was included in the furniture of the lodge in the Grand Lodge Instructions of 1735. Nowadays it is usually called an ornament of the lodge and is said to represent the sun, which illumines the earth and thus dispenses its blessings to mankind. The Reverend Dr. George Oliver (1782-1867) wrote a monumental work entitled Historical Landmarks and other Evidences of Freemasonry Explained. As a renowned antiquary and masonic writer, Dr Oliver said that the blazing star represents beauty and he called it “the glory in the centre”. From the earliest days of speculative freemasonry it has been customary, though not universally so, to include a pentacle or pentagram within the blazing star. Originally the pentagram included the letter G at its centre as a symbol of God.

In the Old Constitutions, under which the operative freemasons worked in medieval England, geometry held the pre-eminent position among the arts and sciences and was considered to be synonymous with freemasonry. The Halliwell or Regius MS is the oldest known copy of the Old Constitutions, but it is believed to be a copy of a much earlier document. When the Regius MS was found it was thought that it had been transcribed in about 1390, but it is now regarded as dating from the first quarter of the fifteenth century, preceding the Cooke MS by about fifty years. The Cooke MS was the oldest document available for reference by the Reverend Dr. James Anderson when he compiled the first and second editions of the Constitutions for the first Grand Lodge of England in 1723 and 1738. The older and more comprehensive Regius MS comprises some sixty-four pages of verse written on a finer kind of parchment called vellum. An eminent masonic historian, Robert Freke Gould, suggested the document should be named the Regius MS because of its historical importance, also having regard to the fact that it was in the Royal Library commenced by Henry VII and presented to the British Museum by George II. The Regius MS sets out “the Constitutions of the art of geometry according to Euclid”, using geometry and masonry interchangeably throughout.

In speculative craft freemasonry under the English jurisdiction, the earliest known version of the Fellow Craft’s Degree is a copy printed in 1730. In this version the catechisms include a question to the candidate asking why he was made a Fellow Craft, to which he replied: “For the sake of the letter G, which means geometry or the fifth science”. Then, with respect to receiving his wages in the middle chamber, the candidate was told that he would see “a resemblance of the letter G, which denotes the Grand Architect and Contriver of the Universe”. This theme is continued in a later catechism printed in 1766 in which the candidate, when asked why he was made a Fellow Craft, replied: “For the sake of the letter G, which is enclosed in a Great Light (the Blazing Star)”. When asked to explain this, the candidate replied: “Glory for God, Grandeur for the Master of the Lodge and Geometry for the Brothers”. In Hebrew the letter G is called Gheé-mel meaning a camel. It is interesting to note that Gheé-mel is considered to be a corruption of the letter Yod, which is the initial letter of Jehovah, represented by the Tetragrammaton, which to the Hebrews is the most sacred name of God. The Yod is also the symbol by which the Tetragrammaton is represented in the Cabala, the mystical philosophy of the Jews.

The Tetragrammaton

In most modern rituals of the English speaking fraternity, the second tracing board informs us that when the craftsman entered the middle chamber to receive his wages, his attention was especially arrested by certain Hebrew characters now depicted in a Fellowcraft lodge by the letter G, which denotes God the Grand Geometrician of the Universe. The characters referred to are the four that comprise the Tetragrammaton, a name derived from the Greek words tetra, meaning four and gramma, meaning letter. The equivalent Hebrew name is the Shem Hamphorasch, meaning the Separated Name. Reading from right to left in Hebrew the four characters of the Shem Hamphorasch are Yod He Waw He, which is also known as the Ineffable or Unpronounceable Name. It is called the Ineffable Name because it represents God who cannot be described in human terms and therefore is beyond human expression. It was the name of God that the Israelites in ancient times were forbidden to utter, for which traditionally they always substituted another word, such as Adonai meaning Lord. An eminent Jewish rabbi, philosopher and commentator and the foremost figure of medieval Judaism was Moses ben Maimon (1135-1204), who is usually referred to as Maimonides. In the Guide to the Perplexed, which probably was his greatest work, Maimonides said that all the names of God are derived from God’s works except the Shem Hamphorasch, which alone indicates the substance that is the self-existent essence of God, thereby expressing that which is altogether within Himself and completely separate from His works and His other attributes.

In the Ineffable Name the character Waw, which is also called Vau, may be pronounced either as a W or as a V according to the structure of the word. The four Hebrew characters of the Ineffable Name are variously transcribed as YHWH or JHVH in English. The original pronunciation is uncertain because the ancient Hebrew text was not vocalised, but modern research of inscriptions dating from the second and first millennia BCE indicate that it should be pronounced as Yahweh, which is supported by the early Christian literature. The Greek theologian, Clement of Alexandria (150-c.215), transliterated the word into Greek as iaoue. However, by the fourth century CE the Greek beta was pronounced as a V and the Ineffable Name was transliterated as iabe. In fact, Yahweh is the only real name of God that appears in the Hebrew Scriptures. The name Yahweh is derived from the Hebrew verb havah meaning to be, which is spelt He Yod He. It also is closely associated with the Hebrew verb chavah meaning to live, which is spelt Heth Yod He. The innermost substance of the Shem Hamphorasch was revealed at the burning bush when Moses asked God what he should say to the children of Israel when they asked who sent him to lead them out of Egypt. When God told Moses to say that “the God of their forefathers had sent him” he asked God, in Exodus 3:13-14, what he should reply when the Israelites ask him who is God. God tells Moses that he should say “‘ehyey ‘asher ‘ehyeh”, meaning “I AM; that is who I am”, which may also be translated as “I will be what I will be”. In this sentence I AM is expressed by the Hebrew word ‘ehyeh spelt Aleph He Yod He, another important four letter Hebrew name of God transliterated as AHIH in English.

The Tetragrammaton is commonly represented by the letters JHVH in English, which is spelt Jehovah and is usually transcribed as Lord in the Bible. In the Cabala, the characters of the Tetragrammaton are transposed and subdivided into two component pronouns. The first pronoun comprises the characters He Vau, the Hebrew word Ho meaning “He” in English. The second pronoun comprises the characters He Yod, the Hebrew word Hi meaning “She” in English. Thus, according to the Cabala, the Tetragrammaton mystically represents the twofold sex of the Creator, which is expressed in the passage in Genesis 1:27 which says:

“So God created man in his own image; in the image of God he created him; male and female he created them”.

Albert Gallatin Mackey (1807-1881) was one of the most erudite of the masonic historians. He drew attention to a remarkable coincidence with respect to the initial consonants of the three Hebrew words that mean Wisdom, Strength and Beauty, the three great pillars of freemasonry. Taken in their reverse order the first pillar is Gomer meaning Beauty, which is spelt Gheé-mel Mem Resh in Hebrew. The second pillar is Oz meaning Strength, which is spelt Ayin Zayin and the third pillar is Dabar meaning Wisdom, which is spelt Daleth Beth Resh. Thus Gomer, Oz and Dabar, the initial consonants of the Hebrew words for Beauty, Strength and Wisdom, transliterate as GOD in English.

Substitutes for the Tetragrammaton

The importance of the Yod, the initial letter of the Tetragrammaton, has already been noted in relation to the Cabala, the mystical philosophy of the Jews. It was of equal importance in the Talmud, the fundamental codes of the Jewish civil and canon law, respectively the Mishna and the Gemara. The Yod was peculiarly sacred among the Talmudists, who saw in it the inaccessible light of the deity that they considered to be of boundless efficacy. The Yod, inscribed within an equilateral triangle, has been the symbol of the deity from time immemorial. If a circle of rays surrounds an equilateral triangle with a Yod at its centre, it is called a Glory and is emblematic of God’s eternal glory. When the rays of the Glory emanate from the Yod at the centre of the triangle, thus enshrouding the Yod in their brilliancy, it is a symbol of the Divine Light. The Yod and the gallows square are very similar in shape. The gallows square was one of the original forms of the Hebrew character Gheé-mel and also of the Greek letter Gamma, both of which correspond to the letter G in the Roman and English alphabets.  

Gheé-mel has the numerical value of three, which alludes to the triune essence of the deity. Gheé-mel is also associated with the third sacred name of God in Hebrew, which is Ghadol and means “the Mighty”. In the ecclesiastical script used in medieval Europe, the capital letter G was represented by an upright gallows square having arms in the ratio of three to four. The gallows square is also shown embroidered on the vestments of the disciples as they are depicted in medieval paintings. Some eminent masonic researchers believe that the medieval operative lodges probably emulated the Jewish custom of using a character, such as the Yod, to represent the Tetragrammaton and to express the presence of God. In this context researchers have suggested that the gallows square would have been used instead of the Yod within an equilateral triangle, firstly to represent God, but also to express that pre-eminent characteristic of masonry, which is geometry, thereby concealing the symbolism in greater mystery. Moreover, as this would have kept the square in constant view of all the brethren and fellows, it also would have been a forcible reminder to them that the square is one of the most important of the moral emblems of the craft.  

A close study of most tracing boards of the Fellowcraft or second degree will reveal that four Hebrew characters, usually surrounded by a Glory, are depicted in the dormer above the screened entrance to the Holy of Holies, representing the Tetragrammaton. Thus, although the letter G nowadays is usually used to represent the Tetragrammaton in a lodge room, the Tetragrammaton is still depicted on the tracing board of a Fellowcraft. In Scottish lodges, the tracing board of a Fellowcraft usually incorporates another composite symbol, which complements the Tetragrammaton above the entrance to the Holy of Holies. It comprises two interlaced equilateral triangles, called the Seal of Solomon or the Shield of David, in the centre of which is a letter G. This composite symbol is usually surrounded by a “Glory” and is depicted near the upper edge of the tracing board. It is equivalent to the blazing star, or glory in the centre, which was suspended from the ceiling in early English speculative lodges, but later was replaced by the letter G alone. The composite symbol highlights the operative origins of speculative craft freemasonry in Scotland.

The original form of the blazing star, including the letter G, was discontinued in England after the Antient and Modern Grand Lodges united in 1813. Since the amalgamation the blazing star, or glory in the centre, is no longer referred to in English freemasonry as a symbol of the deity, but is said to represent the sun. Nevertheless, even nowadays when it is suspended from the ceiling over the centre of the mosaic pavement, the letter G is called the Sacred Symbol and is described as representing God, the Grand Geometrician of the Universe. The centre of the mosaic pavement is where the blazing star should be depicted, when it usually includes a pentacle or pentagram. In Scottish lodges the pedestal, with the three great lights placed thereon, are located in the centre of the mosaic pavement immediately under the letter G. This symbolises that all knowledge, goodness and light that is contained in the Volume of the Sacred Law and comprehended by the square and compasses, is derived directly from God.

The pentagram

The pentagram is an open five-pointed star formed by drawing a continuous series of interlaced straight lines, commencing from any one of five equally spaced points on a circle, then proceeding in a clockwise direction to every second point until returning to the original point. These five straight lines thus form an endless knot in the shape of a five-pointed star that includes a pentagon in the centre. Pentagram is derived from the Greek words pente or penta and gramma, which mean five and letter respectively. Because the star looks like a Greek alpha or capital letter A that has been interlaced cyclically five times, with one leg from each of the two As with their apexes at adjacent points on one side of the circle meeting and forming the apex of another A on the opposite side of the circle, it is also known as a pentalpha. The pentagram is also called a pentacle, from the Latin word pentaculum meaning five angles, which is analogous to the Old French word pentacol from pendre meaning to hang and col meaning the neck. The pentagon is a plane rectilinear figure having five equal sides and five equal included angles, from the Greek word pentagonon in which gonon is a derivative of gonia meaning an angle. In ancient times the pentacle, the pentagon and other similar figures were all worn as amulets.

The pentacle is said to have been the star of the Magians and five was a sacred number among the early Hebrews. The doctrine of numbers as symbols was fundamental to the philosophy of the Pythagoreans, who regarded five as a mystical number. Pythagoras (c.580-500 BCE) was a Greek mathematician and philosopher, who believed in immortality and the transmigration of the soul. He adopted the pentagram as the symbol of the school he established at Crotona, in southern Italy. The pentagram is an ancient symbol of the embodiment of the five sacred elements of earth, water, fire, air and ether or light; and also of the five senses of sight, sound, touch, taste and smell. Because of the many virtues attributed to the pentagram down through the ages, it has been given many titles including the “Sacred Pentagram”, the “Pentacle of Solomon” and the “Pentalpha of Pythagoras”. Medieval operative free masons regarded the pentagram as a symbol of deep wisdom, in deference to Pythagoras whom they called their “ancient friend and brother”. The pentagram was used as an architectural ornament in most of the ecclesiastical buildings constructed by the operative free masons during the Middle Ages. When first used in speculative craft lodges, the pentagram was adopted as a talisman and also to represent the morning star. Originally the pentagram had a gallows square in the centre, later replaced by the letter G. The “Antients” adopted the pentagram as their emblem of the Royal Arch, which is preserved in the jewel of an Excellent Master. In European lodges the pentagram is commonly used as the Master Mason’s jewel, confirming the close link between the degrees of Royal Arch and Master Mason.

From the dawn of history the pentagram has been a mystical symbol credited with magical virtues. The pentagram was used throughout the East as a defence against evil spirits and the Druids wore it on their sandals as a symbol of the deity. During the Middle Ages, in Europe and also in Britain, the pentagram was worn as an amulet or charm hung around the neck or attached to the clothing to ward off evil. It was also used as a door mark to keep out witches. The symbolic use of letters in the scriptures is typified in Isaiah 44:6, in which the Lord states that “I am the first and I am the last”. The symbolism is amplified and extended in Revelation 22:13, when the Lord God also states that “I am Alpha and Omega, the beginning and the end, the first and the last”. The description of the pentagram as a pentalpha, which is a series of five As interlaced, is of special significance. Most modern alphabets are descended either directly or indirectly from the pictographs that were used in Palestine at four thousand years ago or earlier. The Phoenicians were the first to formalise those pictographs as an alphabetical script, which were adapted by the Greeks and modified by the Romans, from which the modern English alphabet was derived directly.  
In most languages A is the first letter of the alphabet. In the English, Roman and Greek alphabets the capital letter A is almost identical with the first character of the Canaanite pseudo-hieroglyphic script, which was in use by about 2000 BCE. The first character in the Canaanite script represented an ox”, like the Egyptian hieroglyph that preceded it, although the two characters were quite different. The first character in the Hebrew alphabet is Aleph, which also represents an “ox”, but its resemblance to “the head of an ox” is much cruder than its Egyptian predecessor. When used as a word in Hebrew, the letter A originally meant with or together and also signified “the beginning”, from which was derived its associated connotation of “unity” or “one”. Because the Hebrew characters do not include numerals, numbers are represented by characters, in which respect Aleph signifies one. The Hebrew character Aleph is comprised of a Waw or Vau that is inclined from the upper left to the lower right, together with two Yods, one at the upper right corner of the character and the other is at the lower left corner. This combination of the Hebrew characters used to form Aleph is said to typify the “Trinity in Unity”, the “hook” of the Vau uniting the Yods of the deity, on which account the Aleph is regarded as one of the sacred Hebrew characters.

Geometry, Pythagoras, Euclid and Plutarch

The traditional history of the craft of freemasonry, set out in the Old Charges of the medieval operative free masons, says that Nimrod the King of Babylon was a Master Mason who loved the craft well and that masons were first made much of at the building of the Tower of Babel, called a ziggurat. A ziggurat typically comprised a series of platforms of diminishing area, commonly five in number, each of which was from about 5 metres to 20 metres in height. Babel was one of the chief cities built by Nimrod in the land of Shinar, or Sumer, in Babylonia. Nimrod was a son of Cush, referred to in Genesis 10:8-13. Archaeological investigations reveal that in fact the tower was built of burnt bricks jointed with bitumen, as recorded in Genesis 11:2-9. It is not known when the tower was first constructed, but it had been restored at the behest of Marduk in ancient times, many centuries before Sargon destroyed it by about 2350 BCE. Tradition also says that Nimrod sent sixty lodges of freemasons to build Nineveh on a site that has been occupied since about 4500 BCE.
When Imhotep, the royal architect of Egypt, designed the Step Pyramid he built at Saqqara for the Pharaoh Zoser in about 2650 BCE, he was the forerunner of a new era of geometry. The Step Pyramid is reputed to be the first great stone edifice built by man, so that Imhotep is usually credited with the invention of stone masonry, which thereafter replaced the mud bricks previously used to construct important buildings. Zoser’s pyramid was erected in six unequal stages over a traditional mastaba tomb constructed of mud brick. The Step Pyramid reached a height of 62 metres and was completely encased in dressed limestone. The Egyptians also credit Imhotep with establishing the science of medicine, even though his official title was Chief of the Observers, suggesting that astronomy must also have been one of Imhotep’s many capabilities. The famous Bent Pyramid of Dashour, built by Sneferu in about 2550 BCE, is about eight kilometres south of Saqqara. The northern or Red Pyramid at Dashour, which is also reputed to have been built by Sneferu, is considered to be the earliest known tomb that was designed as a true pyramid with uniformly sloping sides.
Abraham is known as the ancestor of the Hebrew people. He was born in about 2160 BCE in a city called Ur of the Chaldees, on the Euphrates River in Sumeria. When Abraham was about 75 years old he travelled to Haran, about 900 kilometres to the north on the Balih River, from whence he journeyed south into Canaan and thence westwards into Egypt. Abraham is reputed to have communicated to the Egyptians some knowledge of the more advanced Babylonian geometry. From about that time, the Egyptians were using a triangle with sides three, four and five units long as a square to set out a right angle. Pythagoras was born on the Greek island of Samos and travelled widely through Egypt, Chaldea and Asia Minor, where he solved many mathematical problems. Pythagoras is famous for the resolution of a right-angled triangle, known as Pythagoras’ Theorem, which is the foundation of the forty-seventh proposition of Euclid (c330-260 BCE), the distinguished Greek mathematician who was born in Alexandria. Euclid is best known for his systematic arrangement of previous discoveries, which he set out in the thirteen books that comprised his Stoicheia or Elements, nine of which dealt with plane and solid geometry using definitions, axioms and theorems.

In Egypt and India the number five was revered as a reminder of the five human senses and also of the five elements or manifested planes of nature, which were considered to be sacred. The five human senses are hearing, seeing, feeling, tasting and smelling. The five sacred elements are earth, water, air, fire and ether or light, which respectively represent the physical, astral, mental, buddhic and atmic planes of nature. The ancient beliefs concerning the five sacred elements are summarised by the renowned Greek biographer, Plutarch (c.46-120), in the following passage from his work entitled Morals:

 “The world may in a certain sense be considered as composed and compacted out of five other worlds; for example, the one is of earth, the other of water, the third of fire, the fourth of air and the fifth element some call heaven, some light and others ether.”

Some eminent authorities have drawn attention to the intimate relationship that exists between the Royal Arch and the inner workings of the Installed Master’s ceremonial, deriving from the ancient ceremonies practised in the lodges of operative free masons. In this respect there also are connections between the Installed Master’s ceremonial and the degree of Most Excellent Master. The recognisable components of the Royal Arch work that are included in the installation ceremonials in some jurisdictions of speculative craft freemasonry, receive even greater emphasis in the ceremonials of the Royal Order of Scotland. The pentagram is a component of the jewel of the Deputy Grand Master in the Grand Lodge of England and of some other Grand Lodges that have an English heritage. The pentagram is also a central feature in the jewels of the Provincial and District Grand Masters and the Grand Superintendents in the English and Scottish jurisdictions. In several jurisdictions the pentagram is used as the basic element of the Past Master’s jewel.

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