The
Tetractys (
greekGreek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical...
Τετρακτύς) is a
triangular figureA triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number...
consisting of ten points arranged in four rows: one, two, three, and four points in each row. As a
mysticalMysticism is the pursuit of communion with, identity with, or conscious awareness of an ultimate reality, divinity, spiritual truth, or God through direct experience, intuition, instinct or insight. Mysticism usually centers on a practice or practices intended to nurture those experiences or...
symbol, it was very important to the secret worship of the Pythagoreans.
- The Tetractys symbolized the four elements
Many philosophies and worldviews have used a set of archetypal classical elements, most developed sets of the simplest essential parts and principles of which anything consists or upon which the constitution and fundamental powers of anything are based...
— earthEarth is the third planet from the Sun. It is the fifth largest of the eight planets in the solar system, and the largest of the terrestrial planets in the Solar System in terms of diameter, mass and density...
, air, fireFire is the rapid oxidation of a combustible material releasing heat, light, and various reaction products such as carbon dioxide and water. If hot enough, the gases may become ionized to produce plasma. Depending on the substances alight, and any impurities outside, the color of the flame and the...
, and waterWater is an ubiquitous chemical substance that is composed of hydrogen and oxygen and is essential for all known forms of life.In typical usage, water refers only to its liquid form or state, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam. Water covers 71%...
.
- The first four numbers also symbolized the harmony of the spheres and the Cosmos
In its most general sense, a cosmos is an orderly or harmonious system. It originates from a Greek term κόσμος meaning "order, orderly arrangement, ornaments," and is the antithetical concept of chaos. Today the word is generally used as a synonym of the word Universe . The words cosmetics and...
.
- The four rows added up to ten
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, which was unity of a higher order (in decimalThe decimal numeral system has ten as its base. It is the most widely used numeral base.- Decimal notation :...
).
- The Tetractys represented the organization of space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional...
:
- the first row represented zero-dimension
In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s (a pointIn geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue. Thus, a point is a 0-dimensional object...
)
- the second row represented one-dimension (a line of two points)
- the third row represented two-dimensions (a plane defined by a triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
of three points)
- the fourth row represented three-dimensions
Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth , although any three mutually perpendicular directions can serve as the three dimensions....
(a tetrahedronIn geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
defined by four points)
A
prayerPrayer is the act of addressing a god or spirit for the purpose of worship or petition. Specific forms of this may include praise, requesting guidance or assistance, confessing sins, as an act of reparation or an expression of one's thoughts and emotions...
of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.
- "Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all".
As a portion of the secret religion, initiates were required to swear a secret oath by the Tetractys.
The
Tetractys (
greekGreek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical...
Τετρακτύς) is a
triangular figureA triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number...
consisting of ten points arranged in four rows: one, two, three, and four points in each row. As a
mysticalMysticism is the pursuit of communion with, identity with, or conscious awareness of an ultimate reality, divinity, spiritual truth, or God through direct experience, intuition, instinct or insight. Mysticism usually centers on a practice or practices intended to nurture those experiences or...
symbol, it was very important to the secret worship of the Pythagoreans.
Pythagorean symbol
- The Tetractys symbolized the four elements
Many philosophies and worldviews have used a set of archetypal classical elements, most developed sets of the simplest essential parts and principles of which anything consists or upon which the constitution and fundamental powers of anything are based...
— earthEarth is the third planet from the Sun. It is the fifth largest of the eight planets in the solar system, and the largest of the terrestrial planets in the Solar System in terms of diameter, mass and density...
, air, fireFire is the rapid oxidation of a combustible material releasing heat, light, and various reaction products such as carbon dioxide and water. If hot enough, the gases may become ionized to produce plasma. Depending on the substances alight, and any impurities outside, the color of the flame and the...
, and waterWater is an ubiquitous chemical substance that is composed of hydrogen and oxygen and is essential for all known forms of life.In typical usage, water refers only to its liquid form or state, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam. Water covers 71%...
.
- The first four numbers also symbolized the harmony of the spheres and the Cosmos
In its most general sense, a cosmos is an orderly or harmonious system. It originates from a Greek term κόσμος meaning "order, orderly arrangement, ornaments," and is the antithetical concept of chaos. Today the word is generally used as a synonym of the word Universe . The words cosmetics and...
.
- The four rows added up to ten
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, which was unity of a higher order (in decimalThe decimal numeral system has ten as its base. It is the most widely used numeral base.- Decimal notation :...
).
- The Tetractys represented the organization of space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional...
:
- the first row represented zero-dimension
In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s (a pointIn geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue. Thus, a point is a 0-dimensional object...
)
- the second row represented one-dimension (a line of two points)
- the third row represented two-dimensions (a plane defined by a triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
of three points)
- the fourth row represented three-dimensions
Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth , although any three mutually perpendicular directions can serve as the three dimensions....
(a tetrahedronIn geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
defined by four points)
A
prayerPrayer is the act of addressing a god or spirit for the purpose of worship or petition. Specific forms of this may include praise, requesting guidance or assistance, confessing sins, as an act of reparation or an expression of one's thoughts and emotions...
of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.
- "Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all".
As a portion of the secret religion, initiates were required to swear a secret oath by the Tetractys. They then served as novices for a period of silence lasting three years.
The Pythagorean oath also mentioned the Tetractys:
- "By that pure, holy, four lettered name on high,
- nature's eternal fountain and supply,
- the parent of all souls that living be,
- by him, with faith find oath, I swear to thee."
The Pythagorean SourceBook claimed that there were 2 quaternaries of numbers, one which is made by addition, the other by multiplication; and these quaternaries encompass the
musicMusic is an art form whose medium is sound. Common elements of music are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
al,
geometricGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
and
arithmeticArithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations, such as addition, subtraction, multiplication and division...
ratios of which the harmony of the universe so composed. The first quaternary is 1,2,3,4. There are 11 total quaternaries. And the perfect world which results from these quaternaries is geometrically, harmonically and arithmetically arranged."
It is said that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of
4:3The Diatessaron is the most prominent Gospel harmony created by Tatian, an early Christian apologist and ascetic. The term "diatessaron" is from Middle English by way of Latin, diatessarōn , and ultimately Greek, dia tessarōn The Diatessaron (c 160 - 175) is the most prominent Gospel harmony...
(perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths (in a 4:3 relation), pure fifths (in a 3:2 relation), and the simple ratios of the unison
1:1-Interval of the unison:Unison may refer to the pseudo-interval formed by a tone and its duplication , for example c-c, as differentiated from the second, c-d, etc. In the unison the two pitches have the ratio of 1:1 or 0 half steps and zero cents...
and the octave
2:1In music, an octave , is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon which has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." It may be derived from the...
. Note that the
diapasonDiapason may refer to:* Diapason , a just interval in Pythagorean tuning* Diapason , a tonal grouping of the flue pipes of a pipe organ* Diapason , a French classical music magazine...
, 2:1 (octave), and the diapason plus diapente, 3:1 (compound fifth or perfect twelfth), are consonant intervals according to the tetractys of the decad, but that the diapason plus diatessaron, 8:3 (compound fourth or perfect eleventh), is not.
Quote:
- "The Tetractys [also known as the decad] is an equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°...
formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematicalMathematics is the science and study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions....
idea and a metaphysicalMetaphysics investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world...
symbol that embraces within itself—in seedlike form—the principles of the natural world, the harmonyIn music, harmony is the use of simultaneous pitches, or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
of the cosmos, the ascent to the divine, and the mysteries of the divine realm. So revered was this ancient symbol that it inspired ancient philosophers to swear by the name of the one who brought this gift to humanity — PythagorasPythagoras of Samos was an Ionian Greek philosopher and founder of the religious movement called Pythagoreanism. He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy...
."
Kabbalist symbol
There are some who believe that the tetractys and its mysteries influenced the early kabbalists. A Hebrew Tetractys in a similar way has the letters of the
TetragrammatonYahweh is the English rendering of יַהְוֶה , a Hebrew vocalization of the Tetragrammaton that was proposed by the Hebrew scholar Wilhelm Gesenius in the 19th century. Although this vocalized Hebrew spelling יַהְוֶה is found in no extant Hebrew Manuscript, several English Bibles use the spelling...
(the four lettered name of God in Hebrew scripture) inscribed on the ten positions of the tetractys, from right to left. It has been argued that the Kabbalistic
Tree of LifeThe Tree of Life , in the Book of Genesis is a tree planted by God in midst of the Garden of Eden , whose fruit gives everlasting life, i.e. immortality. Together with the Tree of Life, God planted the Tree of Knowledge of Good and Evil...
, with its ten spheres of emanation, is in some way connected to the tetractys, but its form is not that of a triangle.
Tarot card reading arrangement
In a Tarot reading, the various positions of the tetractys provide a representation for forecasting future events by signifying according to various occult disciplines, such as Alchemy.
http://www.cs.utk.edu/~Mclennan/BA/PT/D-tet.html Below is only a single variation for interpretation.
The first row of a single position represents the Premise of the reading, forming a foundation for understanding all the other cards.
The second row of two positions represents the cosmos and the individual and their relationship.
- The Light Card to the right represents the influence of the cosmos leading the individual to an action.
- The Dark Card to the left represents the reaction of the cosmos to the actions of the individual.
The third row of three positions represents three kinds of decisions an individual must make.
- The Creator Card is rightmost, representing new decisions and directions that may be made.
- The Sustainer Card is in the middle, representing decisions to keep balance, and things that should not change.
- The Destroyer Card is leftmost, representing old decisions and directions that should not be continued.
The fourth row of four positions represents the four Greek elements.
- The Fire card is rightmost, representing dynamic creative force, ambitions, and personal will
Will, or willpower, is a philosophical concept that is defined in several different ways.-Will as internal drive:Friedrich Wilhelm Nietzsche defines will similarly to the "any internally motivated action" usage, but more narrowly. In this sense, will is more a "creative spark," a certain...
.
- The Air card is to the right middle, representing the mind, thought
Thought and thinking are mental forms and processes, respectively . Thinking allows beings to model the world and to deal with it according to their objectives, plans, ends and desires. Words referring to similar concepts and processes include cognition, sentience, consciousness, idea, and...
s, and strategies toward goals.
- The Water card is to the left middle, representing the emotion
An emotion is a mental and physiological state associated with a wide variety of feelings, thoughts, and behavior. Emotions are subjective experiences, often associated with mood, temperament, personality, and disposition. The English word 'emotion' is derived from the French word émouvoir...
s, feelings, and whims.
- The Earth card is leftmost, representing physical realities
Reality, in everyday usage, means "the state of things as they actually exist." Literally, the term denotes what is real; in its widest sense, this includes everything that is, whether or not it is observable or comprehensible. Reality in this sense includes being and sometimes is considered to...
of day to day living.
Other symbols
- An archbishop
In Christianity, an archbishop is an elevated bishop. In many Christian Churches, this means that they lead a diocese of particular importance called an archdiocese, or in the Anglican Communion an Ecclesiastical Province, but this is not always the case. An archbishop is equivalent to a bishop in...
's coat of armsA coat of arms, more properly called an armorial achievement, armorial bearings or often just arms for short, in European tradition, is a design belonging to a particular person and used by them in a wide variety of ways. Historically, they were used by knights to identify them apart from enemy...
shows two tetractys designs.
- The tetractys is the fourth triangular number
A triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number...
's geometrical representation.
- Coincidentally, the pins in ten-pin bowling
Ten-pin bowling is a competitive sport in which a player rolls a bowling ball down a wooden or synthetic lane with the objective of scoring points by knocking down as many pins as possible.-Summary:The wide, lane is bordered along its length by "gutters”— semicircular channels designed to...
are ordered in the tetractys pattern.
In literature and popular culture
- Tetraktys is the name of a Pythagorean cult in the mystery novel The Night Villa by Carol Goodman.
- Samuel Beckett
Samuel Barclay Beckett was an Irish writer, dramatist and poet. Beckett's work offers a bleak outlook on human culture and both formally and philosophically became increasingly minimalist....
's novelMurphy is an Anglicized version of two Irish surnames Ó Murchadha , and Mac Murchaidh derived from the Irish personal name Murchadh, which meant "sea-warrior" or "sea-battler"...
has a mention to the tetrakyt in its opening pages.
- The Tetraktys is also the name of an underground psychdelic folk band based in Calgary
Calgary is the largest city in the Province of Alberta, Canada.The Calgary census metropolitan area is the third most diverse in Canada in terms of visible minorities after Toronto and Vancouver when considering only CMAs with population greater than 200,000...
- The Tetraktys is mentioned in the novel "Crímenes Imperceptibles"
The Oxford Murders is a novel by the Argentine author Guillermo Martínez, first published in 2003. There is a 2005 translation by Sonia Soto....
, by Guillermo MartínezGuillermo Martínez is an Argentine novelist and short story writer.Martínez was born in Bahía Blanca, Argentina. He gained a PhD in mathematical logic at the University of Buenos Aires....
. The novel was turned into a movieThe Oxford Murders is a 2008 thriller film adapted from an award-winning novel of the same name by the Argentine mathematician and writer Guillermo Martínez, directed by Álex de la Iglesia and starring Elijah Wood, John Hurt and Leonor Watling.-Plot:...
.
- The 2009 novel Tetraktys, by RSA senior scientist Ari Juels, pits a classicist turned computer scientist against an ancient Pythagorean cult.
- True Worshipers of the Ineffable Tetractys, or T.W.I.T., is the name of a secret organization in Thomas Pynchon
Thomas Ruggles Pynchon, Jr. is an American novelist based in New York City and noted for his dense and complex works of fiction. Hailing from Long Island, Pynchon spent two years in the United States Navy and earned an English degree from Cornell University...
's novel Against the DayAgainst the Day is a novel by Thomas Pynchon. The narrative takes place between the 1893 Chicago World's Fair and the time immediately following World War I and features more than a hundred characters spread across the United States, Europe, Mexico, Central Asia, and "one or two places not strictly...
.
Further reading
- von Franz, Marie-Louise. Number and Time: Reflections Leading Towards a Unification of Psychology and Physics. Rider & Company, London, 1974. ISBN 0-09-121020-8
See also
- Monad
- Dyad
The Dyad is a title used by the Pythagoreans for the number two, representing the principle of "twoness" or "otherness".Numenius said that Pythagoras gave the name of Monad to God, and the name of Dyad to matter...
- Triad
The Triad is a Pythagorean title for the number three. According to Priya Hemenway they considered it the most beautiful number, as it is the first number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.-See also:*...
- Tetrad
The tetrad or number four is the first number formed by the addition and multiplication of equals. To the Pythagoreans, this symbol and number represented justice as it is the first number that is divisible every way into equal parts.-See also:*Monad*Dyad...
- Decad
The decad was seen by the Pythagoreans as an "assembly point" and a symbol of earth and heaven. They regarded the decad as something perfect, which embraces the whole nature of number.-See also:*Monad *Dyad...
- Pentad
The pentad was a Pythagorean term for the number five. A pentagram, symbol of the pentad, was used by the Pythagoreans as a secret sign to recognize each other.In a passage from Lucian, he refers to the pentagram as the secret sign of brotherhood between the Pythagoreans. It represents the...
External links