When we look at the cosmos its beauty draws us in then leads us beyond itself to its Creator, whose mark it bears. The patterns and symmetry of the cosmos can be described mathematically. We are used to the idea that number denotes quantity. Science especially makes use of this property of number when it describes the physical properties of the cosmos. In the traditional study of mathematics, number also, is given a symbolic meaning. This article discusses the symbolic meaning of numbers and how they have been used in Christian culture, especially art. In this sense art and science are complementary, both describing the order of creation, but in different ways.
‘God has arranged all things in number, sequence and proportion.’
(Wisdom 11:21)‘Since God can only make things that are ordered according to their nature, since order presupposes number and number presupposes measure, and since only numbered things are ordered and only limited things are numbered, then God must needs have made things according to number, weight and measure.’
(St Bonaventure, Commentary on the Four Books of Sentences 1, 43, 1)
One ought to aim for discernment when interpreting the significance of numbers. When considering accounts in the bible, for example, it is as well to remember that when a writer refers to the number of times that an event occurred, it is possible that he is simply recording the observation without an intention of communicating any spiritual significance.
The application of number and proportion to the ordering of our work requires as much discernment. The symbolism must be in accord with the end to which that work is directed. So for example, employing the symbolism of 8, symbolizing the eighth ‘day’ of creation, is appropriate for the baptistry of Florence cathedral, but one might hesitate to say the same about an octagonal cowshed. Similarly, no matter how well the proportions of a building relate to each other, if the upper storey is so low that everyone who enters has to stoop permanently then there is a lack of integrity; and the is proportion is not due proportion.
Nevertheless, the words of the Book of Wisdom (11:21) should always be borne in mind: God has arranged all things in number, sequence and proportion. As with so many other things, the safest route is to allow tradition to guide us. The practice of the Fathers of the Church appears to be one of caution: there is greater confidence in the interpretation of number the more often it appears in the bible or is confirmed by one of the other disciplines, for example, arithmetic, geometry or music. Consider the number 7: its repeated occurrence in the bible gives greater credence to the idea that 7 is especially significant, and comparison of the occasions that it is mentioned has allowed for a greater understanding of what that significance is.
Boethius, in his book on arithmetic, approaches number from a philosophical point of view seeing the mind of God in the symmetry and order of number. He says that ‘the basic ordering of numbers has come about by careful consideration and through great constancy of divinity’1. In this book he ignores bibilical symbolism altogether.
This article contains a description of the numbers considered significant in the Christian tradition.2
Zero
Zero does not exist as a number in traditional arithmetic. The first number was always considered to be unity. Zero came from India and was introduced to Europe through contact with the Arabs in the Middle Ages. As Stratford Caldecott explains,3 this is seen by some as a reason for rejecting it in the context of symbolic meaning. I agree with Caldecott, who suggests that the fault is a failure to read it symbolically. So for example, he offers the idea that it could be the ‘ground of being and the symbol for the return to one’.
One – Unity, First and Last
Unity, in philosophical context means the unity of being – everything that is a ‘thing’ can be considered as such, rather than only as part of something else, because it is a unique entity. One is the number that when ‘squared’ that is multiplied by itself, produces itself. This number traditionally signifies the unity of being, transcending all that exists. It is often represented by a circle, or else by a point. Unity is the first and the last: one is the number that when “squared”, i.e. multiplied by itself, produces itself. Symbolically, the One is not merely the first in a series of numbers, but the number-beyond-number that includes all others, equivalent in that sense to the modern conception of Infinity. The ‘tondos’ or circular paintings of Raphael conform to this principle, for example the Alba Madonna, which depicts Our Lady, Our Lord and John the Baptist, which is in the National Gallery in Washington DC.
Two
This is the number of polarity and division. It is reflected in the language when we call someone duplicitous or two-faced. In a Christian context it has a negative aspect as the dualistic separation of matter and spirit. It can also symbolize the beginning of the process of creation, which in the Book of Genesis is described as taking place through a series of polarizations (heavens and earth, light and dark, etc.).
Three
The Triad, of course, is the number of the Trinity and manifested as a triangle. This presents a graphic image of how the number three can be seen as returning polarity to unity. The triangle and the circle together are used to indicate one God in three persons. An equilateral triangle has a particular significance in the natural order, as it is the simplest shape that can be repeated on a two-dimensional plane without leaving any space (just as the tetrahedron can be stacked in three dimensions without leaving space between). As such the triangle is one of the fundamental building blocks of patterned art, along with patterns based upon the square and hexagon, for similar reasons. In the bibilical context a threefold repetition of a phrase represents an absolute. This is often reflected in the language of the liturgy eg ‘Holy, holy, holy…’.
Four
Quaternity represents the earth, or the entire material order, and is manifested as a square. The four traditional “elements” of earth, water, air and fire seem to correspond not to the types of atom described by modern science (hydrogen, helium, etc.) but to the four basic states of matter which we call solid, liquid, gas and energy. (Sometimes plasma is used for the fourth state. Plasma is the state of matter in the sun, which is the source of our heat and light, ie energy, on earth.) St Augustine affirms the significance of the four Aristotelian elements from a Christian point of view in De Musica ((St Augustine, De Musica, Book VI, Ch 13)) he then describes the geometric argument for the significance of four as the number of the sensible world that occupies space, applying it to the element earth.
In the book of Genesis,4 the river of Eden split into four heads supplying the world. Four is also the number of the Evangelists whose foundational writings are spread throughout the four corners of the world. Christ tells us in Mark’s gospel of the coming of the Son of Man when he will ‘send out his angels, to gather his elect from the four winds, from earth’s end to heaven’s’.5 The symbols of the Evangelists: angel, bull, eagle and lion are derived from the four-faced figure described in the vision of Ezekial. The fourfold nature of the Gospels was established as a canonical principle by St Irenaeus in the second century. We see four represented in two-dimensional geometric patterns with four-fold symmetry. The Westminster pavement (a 13th century Cosmati floor), for example, contains many. Along with patterns based upon the triangle and the hexagon (sixfold symmetry) it is one of the basic units of repeated patterned art.
Five
Five is traditionally seen as the number of the flesh, of life and of love. It is manifested as a regular pentagon or a five-pointed star, and though the spiritual symbolism is strong in Christianity, it is perhaps more often used in Islamic art than Christian. Inanimate nature conforms to the order of four- and six-fold symmetry, as in crystal structures. Living nature, on the other hand, appears to be ordered more often by five. The traditional association is with the five senses and the five fingers on each hand (Bonaventure listed five spiritual senses in addition to the corporeal). There are numerous traditional devotions to the five wounds of Christ.
Six
Six is both the sum and the product of the first three numbers: one, two and three – the sum of its aliquot parts and as such is the first ‘perfect’ number. It is the number of days of the work of creation. It is represented geometrically as a regular hexagon. The hexagon, comprised of six equilateral triangles, is the third shape that can be repeated in a plane without leaving space. If equal sized spheres are allowed to stack along any plane they will form repeated patterns of either six-fold or four-fold symmetry. Sixfold patterns feature regularly in tiled floors or ‘cosmati’ pavements (named after the family that was most famous for making them in the 13th century) and at Westminster Abbey.
Seven
The seven days of creation (six days of work and one of rest) became the model for the seven days of the week. This number appears many times in Scripture, being a particular favourite of St John. There are seven sacraments, seven deadly sins and seven virtues seven gifts of the Holy Spirit. There are seven planets in the skies, as visible to the naked eye: the sun, the moon, Mercury, Venus, Mars, Jupiter and Saturn. The tradition regarding the significance of these planets is not undermined by the subsequent discovery of more planets. To the medieval mind these are significant precisely because they are easily visible. An aspect of our humanity is that we are able to see the thumbprint, so to speak, of the Creator in His Creation; just as an aspect of the creation is that it is made to reveal God to us through our perception of it.
The arrangement of tones in the Western musical scale is based upon the number seven also, with seven tones in the octave. The eighth being simultaneously the first note of the next octave.
Seven represents totality, since it is the sum of four, the number of the material order, and three, the number of the Trinity, and is related to twelve, which is the product of these same numbers. It appears in iconographic and Western naturalistic art as the combination of a square and a triangle. For example, the Transfiguration painted by Raphael. The simple geometric design of Raphael’s paintings convey a sense of calmness. Raphael was well aware of the arithmetic of Christian cosmology. In his fresco in the Vatican, The School of Athens, we see on the left, amongst the great philosophers of the past, the kneeling figure of Pythagoras holding a diagram explaining the numerical basis of musical harmonies; also included in this painted chalk board is representation of the tectractys – the triangular arrangement of 10 items. This will be discussed in greater detail in a later article about harmony and proportion.
Seven also translates into the liturgy in the weekly cycles and daily cycle of 7-times a day of the Benedictine cycle. St Benedict took his inspiration from the psalms. In each the liturgy, each sevenfold repetition is often associated with an additional 8th motion that as crucial in our understanding of what the liturgy is. This will be discussed under 8.
The fundamental significance of seven goes right back to God’s covenantal relationship with mankind. The American scripture scholar, Scott Hahn wrote about this as follows:
‘Where precisely, does God swear his covenant oath? He does so in the very act of hallowing the seventh day (Gen 2:2). The seventh day is itself God’s Great Oath.
‘While etymologies do not often make for good exegesis, the etymology of the Hebrew word for “seven” is essential for our understanding of the Genesis text. For it is from the “seventh day” of creation that all subsequent covenant oaths took their origin and inspiration.
‘The Hebrew word for the number seven, sheva, also has a verb form. Shava is the verb for swearing oath. Its meaning is “to seven oneself”. When human beings swear in this way, they follow the precedent set by God at the dawn of creation. Throughout the Old Testament, the number seven will recur many times in connection with the making of covenant sacrifices. For example, the place of Abraham’s covenant oath with Abimelech was later named Beer-sheva, which is alternatively translated as “Well of Seven” or “Well of the Oath”. It was there that Abraham swore his oath and gave seven ewe lambs as guarantee (Gen 21:22-34). In Genesis 2, the seventh day was the sign of the covenant that God had made with man and woman.’6
‘What the Apocalypse shows is the definitive consummation of the covenant. Thus the number seven dominates the book: seven churches, the seven spirits and seven torches of fire before the throne, the seven lampstands, the seven spirits of the son of man and the seven stars in his right hand, the seven seals, seven angels that stand before God, the seven horns and seven eyes of the Lamb, the seven horns and seven trumpets, and seven chalices of God’s wrath. The overwhelming message is that the son of man has definitively renewed the covenant. He has severed himself by the liturgical offering of his body, once for all.’7
Eight
The so-called eighth ‘day’ of creation sybolises the new order ushered in by the incarnation, passion, and death of Christ, culminating in his resurrection on Sunday, simultaneously the eighth and first days of the week. It is represented geometrically as a regular octagon. Traditionally baptismal fonts will be created in octagonal shape. The baptistry of the Duomo in Florence is an octagonal building that is separated from the main building. Eight, expressed as ‘7 + 1’ is a strong governing factor in the Church’s earthly liturgy. Sunday, the day of the Mass, is simultaneously the first day of the new 7-day week and the liberating eighth day of the last. It is the eighth day of the week that represents the new freedom from death through Christ. Without Christ, the passage of time could be represented by a self enclosed weekly cycle sitting in a plane. The eighth day represents a vector shift at 90° to the plane of the circle that operates in combination with the first day of the new week. It demonstrates in earthly terms that a new dimension is accessed through each cycle of our participation temporal liturgical seven-day week. This way time can be envisaged as a helix taking us forward to our heavenly destiny. Raphael’s, altarpiece, the so-called Mond Crucifixion, which is in the National Gallery in London, is a design based upon an octagon. The heads of the human figures around the cross sit on the lower four points, while the two outer feet and heads of each angel flanking the cross mark out the other four. The 7+1 liturgical form operates in the Divine Office too. For the psalmist, as quoted by St Benedict in Chapter 16 of his rule says:
As the Prophet said: “Seven times a day I have given praise to Thee”8, this sacred sevenfold number will be fulfilled by us in this way if we perform the duties of our service at the time of Lauds, Prime, Tierce, Sext, None, Vespers, and Compline; because it was of these day hours that he hath said: “Seven times a day I have given praise to Thee”9. For the same Prophet saith of the night watches: “At midnight I arose to confess to Thee”. At these times, therefore, let us offer praise to our Creator.“for the judgments of His justice”; namely, at Lauds, Prime, Tierce, Sext, None, Vespers, and Compline; and let us rise at night to praise Him.
The night office, Matins, is the eighth that is sung in conjunction with the 7 daytime Hours (in practice, many communities run Matins and Lauds together). This could be seen as paralleling the running together of the eighth and first days in the weekly cycle of the liturgy. Eight appears in the liturgy in the octaves, the eight day observances, of Easter and Christmas. They represent an overflowing of grace from these major feast days.
Nine
As the sum of three threes, nine echoes the Triad, indicating the impress of the Trinity on creation. It features most famously in the nine choirs of angels in the celestial hierarchy of Dionysius the Areopagite. It also appears liturgically in the nine days between the day of the Ascension and Pentecost and the medieval commentators connected the ninefold invocation of Kyrie that has remained in the Extraordinary form of the Mass to the nine choirs of angels. The Acts of the Apostles describes how Our Lady and the apostles prayed for nine days until the descent of the Holy Spirit (promised by Christ). From this comes the tradition of the novena, nine days of prayer.
Ten
The Decad or Tetractys is the sum of the first four numbers, and represented by an arrangement of ten points arranged in an equilateral triangle: one over two over three over four. This arrangement has been recognised as a significant, going back in time to the Pythagoreans.
In so far as it is composed of a one and a zero, it also represents the return to unity in another way. As a doubling of five, it echoes the form of the human being, or the symmetry of hands and feet. Stratford Caldecott describes how in the context of the Book of Revelation it represents authority, as in the 10 commandments or else simply a limited number (in contrast to 1,000). The notes produced by plucking strings of relative length 1, 2, 3 and 4 are the basis for the fundamental musical harmonies in Western music (octave, perfect fifth and perfect fourth) and so for harmonic proportions in art and architecture. (The harmonious combination of numbers will be discussed in more detail in a later article on proportionality.) We do see it represented in Christian art, though less often than other numbers. For example, the late 13th century fresco of the Dream of Innocent III by Giotto in the Basilica of St Francis of Asissi has a tectractys on the painted on the gable end of a building.
Twelve
Outside the Decad, twelve is probably one of the most richly symbolic of numbers – especially in a Christian context. There are twelve lunar months in the year, and the heavens have been divided into twelve signs of the zodiac. This is a Christian ‘liturgical’ division if the stars in the sky are thought of as participating in the heavenly liturgy. This natural division of the year has been passed down into a division of the day into twelve hours, and night into 12 hours. It is represented geometrically by a regular solid with twelve sides, the dodecagon, or by a twelve-pointed star composed of equilateral triangles. Arithmetically, it is the product of 3 and 4 and as such is linked to 7 (=3+4). This is the power of God, represented by the Trinity, being taken out to four corners of the world. There are 12 apostles, 12 patriarchs and 12 tribes. The signs of the zodiac do appear in Christian churches as a symbol of the universe participating in the heavenly liturgy. For example one of the main designs on the tiled floor of the church of San Miniato al Monte, just outside Florence contains a representation of each within a circle divided into 12 equal sectors, as part of an interior laden with geometric art.
Twenty-eight, 28
Twenty eight is the second perfect number being the sum of its aliquot parts: 1, 2, 4, 7 and 14. An idealised lunar month of 28 days is two phases (a waxing and a waning) and the 7-day week is half a phase. The moon is the symbol of the Church. When the Divine Office according the Roman Rite was revised after the Second Vatican Council, it was ordered around this 28-day cycle.
‘He made the moon also to serve in its season, to mark the times and to be an everlasting sign. From the moon come the sign for the feast days, a light that wants when it reaches the full. The month is named for the moon, increasing marvelously in its phases, an instrument of the host on high shining forth in the firmament of heaven.’10
1,000
1,000 is to denote a very large number or eternity. St Peter says, for example that ‘a day with the Lord is like a thousand years and a thousand years as one day’.11
Adding numbers
The addition of numbers combines properties of each into a single entity. For example, 7 is a special number in its own right and because it is the sum of 3 and 4. Also, the addition of 1 to a number represents overflowing or further liberation beyond an initial mark that is still identifiable; as in the case eight, when considered as (7+1) which can be considered meaning that which is beyond 7.
Multiplying numbers together
This is an operation of expansion which is an abundant unlimited extension of one number into another. So 3×4, produces 12 and which represents the celestial order, the spiritual animation of all that is material. In the Book of Revelation, there are 144,000 faithful in heaven. As Stratford Caldecott describes in his booklet on the interpretation of the Book of Revelation,12 this number is derived from 12x12x1000 which corresponds to an unlimited extension of the Tribes and the Apostles.
Perfect, superfluous and diminished numbers
Perfect numbers are those that are the sum of their aliquot parts. Six is the example we have discussed so far. Those numbers for which the sum is greater or less than the aliquot parts are called superfluous or diminished, respectively. Boethius explains that ‘perfect’ numbers are considered so as a consequence of their relationship with superfluous and diminished numbers: ‘Between these two kinds of number, as if between two elements unequal and intemperate, is put a number which holds the middle place between the extremes like one who seeks virtue.’13
Triangular numbers
These are numbers that can be arranged in a triangular patterns of dots: 1, 3, 6, 10…. Ten dots arranged in a triangle constitute the tectractys.
Square numbers
These are numbers that can be arranged in square patterns of dots: 1, 4, 9, 16…. Any adjacent triangular numbers combine to form a square number. So 6 + 10 = 16.
The appearance of these numbers in geometrical design
All of these numbers have regular application in different aspects of the Christian life. In geometry or art based upon geometric form the most commonly occurring examples are (1, 3, 4, 6, 7, 8; circle, triangle, square, hexagon, square + triangle, octagon respectively).
Example of four circles spinning out of a central circle is a common shape. This is interpreted as signifying the creation of the material universe by God, four spinning out of one. It has been suggested that it can also signify the end of time when all returns to God. We see this in the Westminster Pavement.
The vesica piscis is a shape created by the intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. The name literally means the bladder of the fish in Latin. The shape is also called mandorla (meaning ‘almond’ in Italian). The fish is the traditional sign of Christ. Some Christians believe that a second link between their religion and the fish symbol is seen in the Greek word for fish (ichthus, spelled: Iota Chi Theta Upsilon Sigma). That is an acrostic which has many translations in English. The most popular appears to be “Jesus Christ, Son of God, Savior“. It is often seen enclosing Christ, especially when depicted in his heavenly realm. So for example, Christ in Majesty where he is depicted as King on his throne will use this shape. Similarly, many depictions of the transfiguration, in which Christ’s appearance to the three apostles was transfigured in heavenly glory, will show Christ within a vesica.
Christ in glory, illuminated manuscript, 12th century
- Boethius, De Institutione Arithmetica, Book 1; tr Michael Masi, pub Rodopi press as Boethian Number Theory, NY, 2006, p81 [↩]
- For those interested in this field, I would recommend Stratford Caldecott’s CTS (Catholic Truth Society) booklet on the book of Revelation, which I drew on for this article, particularly in discussion of the mathematical operators eg addition or multiplication. [↩]
- Stratford Caldecott, Beauty for Truth’s Sake, Brazos Press, 2009, p63 [↩]
- Gen 2:10 [↩]
- Mark 13:27 [↩]
- Scott Hahn, Letter and Spirit, p60, Ignatius Press [↩]
- Scott Hahn, Letter and Spirit, p154, Ignatius Press [↩]
- Ps 118[119]:164 [↩]
- Ps 118[119]:62 [↩]
- Book of Ecclesiastes, quoted from Thursday Week 1, Office of Readings. [↩]
- II Peter 3:8 [↩]
- Stratford Caldecott, Companion to the Book of Revelation; CTS, London, 2008 [↩]
- Boethius, De Institutione Arithmetica; tr Michael Masi, pub Rodopi press as Boethian Number Theory, NY, 2006, p96 [↩]
