13 Numerology

Numerology, or the science of the symbolic meaning of numbers, was applied in the Renaissance to three different subjects: the cosmos, the Bible and the work of art. God was believed to have created the world on numerical principles and to have given the Bible an additional layer of meaning by filling it with symbolic numbers. The initiate into the mysteries of numerology could ‘read’ both God’s books, the Book of Works (the universe) and the Book of Words (the Bible). The artist could imitate the divine process of creation by organising his work on numerical principles; the harmonious construction of the work would thus reflect the harmony of the universe not because it was an imitation in a simple sense but because it was created by the same method.

The idea that the basis of the world is number derives from the Pythagorean and Platonic tradition. Our knowledge of the beliefs of Pythagoras, a Greek philosopher and mathematician of the sixth century BC who founded a religious community in southern Italy, is entirely second-hand: it comes from a hostile critic, Aristotle (1), and from sympathisers such as Plato and the Neoplatonists. Because the Pythagoreans expressed numbers spatially, as groups of points, they came to think of numbers as having concrete existence. The two most important groups of numbers are the Tetrad (4) and the Decad (10). The Tetrad can be expressed geometrically: 1 as a point, 2 as a line, 3 as a triangle, 4 as a pyramid. The Tetrad is the basis of the Decad because 10=1+2+3+4. This relationship is expressed in the Tetractys, which consists of the points of the Decad arranged triangularly: Each number in the Decad has a particular meaning, which is not merely symbolic. Pythagoras discovered that the musical scale can be expressed in terms of numerical proportion, and this discovery led to the belief that everything in the universe can be similarly expressed: things are numbers (1). The opposition between odd and even numbers was regarded as underlying all contraries: limit and the unlimited, male and female, light and dark, good and bad. The monad (1) represents unity, the dyad (2) excess or defect, the triad (3) reconciliation of opposites, the tetrad (4) equilibrium and justice (hence, for example, the emphasis in antiquity on 4 humours, 4 elements, 4 virtues). The numerical and musical theories in Pythagoreanism are closely linked: there is an underlying harmony between man and the cosmos, the microcosm and macrocosm, which can be expressed in terms of both number and music (for these theories see Chapter 6).

Some Pythagorean ideas were taken up and elaborated by Plato. The importance Plato attached to mathematics can be judged from the educational scheme he designed for his Guardians, the ruling class in the Republic, who are required to study this subject from the age of 20 to that of 30 (2). Numbers have aesthetic and moral significance. The Timaeus (31–6) describes how God first created the world’s body as a geometrically perfect sphere (3), and then created its soul in arithmetical and musical proportions according to a design known as the Platonic Lambda (because it resembles the Greek letter 1):

Thus universal harmony can be measured. There was an extremely influential application of this idea by the Roman architect Vitruvius. Vitruvius argues in On Architecture III i that the proportions of the perfect human body can be calculated mathematically, and that a man with arms and legs outspread exactly fits a circle and a square. These principles can then be applied to the design of buildings (4). Thus the mathematical proportions on which micro-and macrocosm are constructed become an objective aesthetic standard.

In the Pythagorean and Platonic tradition the first ten numbers are especially significant; in the biblical tradition, which goes back to Babylonian astrology, certain numbers assume meanings because of their associations. Some significant numbers in the Old Testament are 7 (God’s day of rest after the Creation), 10 (the Commandments), 12 (the tribes of Israel), 40 (the years spent by the Israelites in the desert), 70 (the number of the patriarchs). Numbers in the New Testament which echo significant numbers in the Old Testament form a system of numerical typology (on the functioning of typology see Chapter 10). Thus the 40 years in the desert typify Christ’s 40 days of fasting, the 70 patriarchs typify the 70 disciples appointed by Christ to assist the 12 Apostles (themselves typified by the 12 tribes). With the beginnings of Biblical exegesis in Alexandria Pythagorean and Platonic methods were introduced by Philo Judaeus to help interpret biblical numbers. In the hands of Augustine numerical exegesis became a sophisticated technical skill (5, 6). Augustine associated the divine geometer of Timaeus with the Christian God; the statement in the Apocryphal Book of Wisdom 11:20 ‘thou hast ordered all things in measure and number and weight’ became the basis of the view that God had created the world by number. Numerical exegesis went far beyond interpretation of the obviously significant biblical numbers. Every number used in the Bible in however seemingly trivial a context was scrutinised for its meaning. In Books XI and XII of The City of God we can see how far this process was taken. A single number could be interpreted in many different ways, according to how it was divided. The Pythagorean Decad acquired new Christian connotations, and numbers not necessarily stressed in the Bible became significant, for example 3 (the Trinity—a non-biblical doctrine perhaps influenced by Pythagoreanism), 4 (the gospels), 33 (the years of Christ’s life).

The Pythagorean and Platonic tradition of number symbolism was also transmitted independently from biblical numerical exegesis by the encyclopedists of late antiquity and the early Middle Ages. The more influential works are Macrobius’ Commentary on the Dream of Scipio, Boethius’ The Principles of Arithmetic, Martianus Capella’s The Marriage of Philology and Mercury (Book VII), and Isidore’s On Number. Some of these works are arithmological, that is they expound the meaning and powers of specific numbers in the Decad. Thus Macrobius (I vi) discusses at length the significance of the number 7. The impetus behind these works was pedagogical, the desire to transmit the traditions of classical culture; thus they simplified and passed on to generations of readers a basic knowledge of the principles of numerology. The classical attitude to number was perpetuated in the medieval curriculum of the Seven Liberal Arts, the elementary Trivium (three ways) consisting of literary studies, grammar, rhetoric and dialectic, and the advanced Quadrivium (four ways) consisting of mathematical studies, arithmetic, geometry, astronomy and music. Boethius (who first gave the Quadrivium its name) regarded arithmetic as the basis of the other sciences; in this he was following a tradition going back to Pythagoras.

In the Renaissance numerology was approached rather differently. The encyclopedic tradition of late antiquity and the Middle Ages was concerned with expounding the basic principles. Renaissance writers on numerology, most of them Neoplatonists, regarded it as a mystery whose secrets were the property of the initiated. (This esoteric attitude had been characteristic of the early Pythagorean community.) Renaissance numerologists combined traditional sources—Pythagorean/ Platonic and exegetical texts—with sources which were acquiring new interest—the Jewish Cabala, the Orphic and Hermetic writings (8, 9). Significant Italian numerological works include Pico’s Heptaplus (a sevenfold interpretation of the seven days of creation), Giorgio’s Harmony of the World and Bongo’s On the Mystery of Numbers. It is difficult to assess the knowledge or acceptance of the Italian Neoplatonist numerological tradition in England. Donne’s attitude in Essays in Divinity is revealing. He refers to Giorgio as ‘that transcending wit’, yet he seems embarrassed by the excessive application of Pythagorean number symbolism to the Bible (7). Three seventeenth-century authors, Henry Reynolds, Sir Thomas Browne and Henry More, seem to have accepted it wholeheartedly. In Religio Medici Browne describes God as ‘a skilful geometrician’, and he sees man’s task as the unravelling of God’s difficult designs in nature, the Bible and history. Browne performs an elaborate piece of numerological detective work in The Garden of Cyrus, identifying the repeated uses of the number 5 in nature and art. Reynolds, following Pico, makes an impassioned plea in Mythomystes for the mysteries of number to be properly studied, yet the defensive tone of the work suggests that he felt his position to be an unpopular one (9).

Numerology was more than a means of interpreting the universe and the Bible; it was a principle of artistic composition. Biblical number symbolism was used in the construction of Gothic cathedrals, and in the Renaissance architects like Alberti and Palladio, following Vitruvius, designed their churches to reflect on the one hand the proportions of the human body and on the other the proportions of the universe. Italian humanist architectural theory, made available in England in the early seventeenth century by Inigo Jones and Sir Henry Wotton, is reflected not only in English Palladian architecture but in country house poetry. Numerology was used as a principle of literary organisation by Augustine; The City of God, for example, has 22 books, reflecting the number of letters in the Hebrew alphabet. Augustine thus expounded the principles of number symbolism in his text, and illustrated them in his structure. The numerological organisation of a literary work enables a writer to express meaning through form; it is in effect a kind of allegory. The most important practitioner of numerical composition in the Middle Ages was Dante. Both The New Life and The Divine Comedy have complex numerical structures, the most important numbers being 3 and 9. The Divine Comedy has 3 books (symbolising the Trinity) and 100 cantos (one is introductory, leaving 99). Nine is the number associated with Beatrice; it is divisible by 3, thus indicating her divine nature. Dante’s numerical structures, though difficult to unravel, are not secret; Dante constantly draws attention to how his poems are composed and to be read (e.g. The New Life xxx), comparing his methods with those of divine creation.

To what extent were such numerological methods of composition used by English Renaissance poets, and how can we identify them? Two kinds of poetic numerology have been distinguished: ‘substantive’, in which number symbols are themselves the subject of a work, and are expounded and illustrated by the poet, and ‘formal’, in which the symbols are contained in the structure, so that the numbers of lines in a stanza or stanzas in a poem have symbolic meaning. The first kind of numerology is usually self-explanatory; the second is more difficult to detect. Readers are faced with the question of whether numerological composition was a habitual or an esoteric practice. Poets conversant with Neoplatonism, such as Spenser, Chapman (14), Milton and Henry More, were certainly familiar with numerological theory and are the likeliest practitioners of numerological composition. Some aspects of numerology were common knowledge among educated men, and were often explored in poetry: for example, the ideas of God as a geometer creating by number, of the proportion between the human body and the cosmos, of the circle, the most valued geometric form, representing both physical and moral perfection. God in Cowley’s Davideis I (Ch. 6.21) and in Paradise Lost VII (10) creates the world according to geometrical and musical proportion. Country house poems such as Marvell’s ‘Upon Appleton House’ stress the correspondence between the good man and the architectural proportions of his estate (12). Jonson took a broken compass and an incomplete circle as his motto (thereby indicating his awareness of his own moral limitations), and in his celebratory poems, such as the ode on Henry Morison, used the describing of a circle as an image of moral perfection (11). In addition to such allusions to the theory of numerology, we find ‘substantive’ number symbolism in many poems (13, 14), the best example being The Faerie Queene. Thus in Book I Spenser uses the Pythagorean system of contraries in his pairing of opposite characters such as Una and Duessa; sometimes these opposites appear as triads, such as Fidelia, Speranza and Charissa (Faith, Hope and Charity), the opposites of Sansfoy, Sansloy and Sansjoy (Faithless, Lawless and Joyless).

Such geometrical and numerical patterns are evident to patient readers, and would not have seemed mysterious in the Renaissance. ‘Formal’ numerology is another matter. Critics have only recently begun to investigate ‘formal’ numerological composition, by counting word, line or stanza totals to discover whether there is a correspondence between the symbolic meaning of these numbers and the poem’s content. This procedure is fraught with difficulties, one being that the critics may read meanings into the numbers they arrive at, another being that three different systems of number symbolism were available to the poet, Pythagorean, Biblical and temporal (the ways in which time could be divided, for example 24 hours, 7 days, 52 weeks, 12 months, 365 days). Thus the number 4 might represent justice, or the gospels, or the seasons; the context would confirm which meaning if any was intended. Two poems which have been convincingly shown to use ‘formal’ numerology are Spenser’s Epithalamion and Milton’s ‘Nativity Ode’. Spenser uses temporal symbolism; his poem illustrates through its stanza and line numbers the passing of the 24 hours of the day and 365 days of the year. Milton’s numbers are biblical and Platonic: the ode’s introduction has seven-line stanzas, the ‘Hymn’ eight-line, indicating the transition from time to eternity, from discord to harmony. Indeed it has been argued that the basis of the poem’s numerical organisation is the Platonic Lambda. Such complex schemes are probably meant to be secret, to be legible only by God, the poet and the initiate, as with the highest level of allegory. Mundane readers can appreciate the formal symmetry of a poem without realising that the symmetry itself expresses the poem’s meaning. ‘Formal’ numerology is thus an enigma; the danger for modern readers is that they may be so teased that they will track down numerical composition where it was never intended.

PYTHAGOREAN/PLATONIC NUMEROLOGY

1 The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything. And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analogues of what is and comes into being—such and such a property of number being justice, and such and such soul or mind, another opportunity, and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers, and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion of number.

Aristotle Metaphysics I v

2 Number is the subject of the whole art of calculation and of the science of number; and since the properties of number appear to have the power of leading us towards reality, these must be among the studies we are in search of. The soldier must learn them in order to marshal his troops; the philosopher, because he must rise above the world of change and grasp true being, or he will never become proficient in the calculations of reason. Our Guardian is both soldier and philosopher; so this will be a suitable study for our law to prescribe. Those who are to take part in the highest functions of state must be induced to approach it, not in an amateur spirit, but perseveringly, until, by the aid of pure thought, they come to see the real nature of number. They are to practise calculation, not like merchants or shopkeepers for purposes of buying and selling, but with a view to war and to help in the conversion of the soul itself from the world of becoming to truth and reality.

Plato Republic VII 524

3 Now anything that has come to be must be corporeal, visible, and tangible: but nothing can be visible without fire, nor tangible without solidity, and nothing can be solid without earth. So god, when he began to put together the body of the universe, made it of fire and earth. But it is not possible to combine two things properly without a third to act as a bond to hold them together. And the best bond is one that effects the closest unity between itself and the terms it is combining; and this is best done by a continued geometrical proportion… So god placed water and air between fire and earth, and made them so far as possible proportional to one another, so that air is to water as water is to earth; and in this way he bound the world into a visible and tangible whole. So by these means and from these four constituents the body of the universe was created to be at unity owing to proportion; in consequence it acquired concord, so that having once come together in unity with itself it is indissoluble by any but its compounder.

Plato Timaeus 31–2

4 The planning of temples depends upon symmetry: and the method of this architects must diligently apprehend. It arises from proportion (which in Greek is called analogia). Proportion consists in taking a fixed module, in each case, both for the parts of a building and for the whole, by which the method of symmetry is put into practice. For without symmetry and proportion no temple can have a regular plan; that is, it must have an exact proportion worked out after the fashion of the members of a finelyshaped human body… Now the navel is naturally the exact centre of the body. For if a man lies on his back with hands and feet outspread, and the centre of a circle is placed on his navel, his fingers and toes will be touched by the circumference. Also a square will be found described within the figure, in the same way as a round figure is produced. For if we measure from the sole of the foot to the top of the head, and apply the measure to the outstretched hands, the breadth will be found equal to the height, just like sites which are squared by rule. Therefore if Nature has planned the human body so that the members correspond in their proportions to its complete configuration, the ancients seem to have had reason in determining that in the execution of their works they should observe an exact adjustment of the several members to the general pattern of the plan.

Vitruvius On Architecture II i 1–4

NUMERICAL BIBLICAL EXEGESIS

5 The works of Creation are described as being completed in six days, the same formula for a day being repeated six times. The reason for this is that six is the number of perfection. It is not that God was constrained by the intervals of time, as if he could not have created all things simultaneously, and have made them afterwards conform to temporal succession by appropriate movements. No, the reason was that the completion or perfection of the works is expressed by the number six. For six is the first number which is the sum of its parts, that is of its fractions, the sixth, the third, and the half, for one, two and three added together make six… Hence the theory of number is not to be lightly regarded, since it is made quite clear, in many passages of the holy Scriptures, how highly it is to be valued. It was not for nothing that it was said in praise of God, ‘Thou hast ordered all things in measure and number and weight’ [Wisdom 11:20].

Augustine The City of God XI xxx

6 The significance of 40 days of fasting:

It is composed of four times ten; as it were, the knowledge of all things joined together by time. The course of the day and year are accomplished through the number four; the days are carried through in intervals of hours: morning, noon, evening, and night; the years, by the spring, summer, autumn, and winter months. But, while we are living in time, we must abstain and fast from all pleasure in time because of the eternity in which we hope to live; although, by the passage of time, that very doctrine of despising temporal things and striving for eternal goods is recommended to us. Further, the number ten symbolises the knowledge of the Creator and the creature. For a trinity is present in the Creator, while the number seven signifies the creature, by reason of his life and body. In the case of his life, there are three commandments to love God with our whole heart, our whole soul, and our whole mind; with regard to the body, there are four very discernible elements of which it is composed. So, while the number ten is being impressed upon us in the sense of time, that is, multiplied by four, we are being instructed to live virtuously and temperately, free from the delights of time—in other words, to fast for forty days.

Augustine Christian Instruction II xvi

7 In a few words we will consider, whether any mystery reside in that chosen number [70]; the rather because very many remarkable things, and passages in history, seem to me to have been limited in that number, which therefore seems more periodic than any other. But because any over-curious and mysterious consideration of this number 70, though it be composed of the two greatest numbers (for ten cannot be exceeded, but that to express any further number you must take a part of it again; and seven is ever used to express infinite), be too Cabalistic and Pythagoric for a vulgar Christian… because I am one, and in a low degree, of the first and vulgar rank, and write but to my equals, I will forbear it, as misinterpretable; since to some palates it may taste of ostentation; but to some, of distraction from better contemplations, and of superstition to others: yet, we may, as well with reverence to the things, as respect to the number, rest a little upon those works of God, or his servants, which this number, at least, reduces to our memory. First therefore, those fathers of the world, to whom God affords a room by name in the 10th of Gen. from whom are derived all nations…are reckoned there to be 70… And in that great captivity of Babylon…the chosen people of God were trodden down 70 years. To which foreign sojourning, for many concurrences, and main circumstances, many have assimilated and compared the Roman Church’s straying into France, and being impounded in Avignon 70 years… Then, those disciples, suppliers and fellow-workers with the Apostles…whom our most blessed Saviour instituted, were also of this number, 70. And so having refreshed to your memory, upon this occasion of the number 70, these stories out of the Bible, we will end with this observation, that when God moved Ptolomeus to a desire of having the Bible translated [from Hebrew into Greek], he accited from Jerusalem 72, for that glorious and mystic work; and these, though they were 72, either for affection to conform themselves to a number so notorious, or for some true mystery in it, or for what else, God knows, have ever retained the name of Septuagint [i.e. 70].

Donne Essays in Divinity II ‘Variety in the Number’

RENAISSANCE ATTITUDES TO NUMEROLOGY

8 The ancient system of philosophising through numbers…was held to by the early theologians, by Pythagoras in particular, by Aglaophamus, by Philolaus, by Plato and the early Platonists. But in this age, this doctrine, like other famous ones, has so passed out of use by the negligence of posterity, that scarcely any traces of it are to be found. Plato writes in the Epinomis that among all liberal arts and theoretical sciences the science of numbering is chief and most divine. Again, asking why man is the wisest animal, he answers that it is because he knows how to number… These things could not in any way be true if they had understood by the art of numbering that art at which now the merchants are expert above all. Plato also witnesses this, warning us in a loud voice not to confuse this divine arithmetic with mercantile arithmetic.

Pico della Mirandola On the Dignity of Man (compare 2)

9 Now, from this means that the first ancients used of delivering their knowledges thus among themselves by word of mouth, and by successive reception from them down to after ages, that art of mystical writing by numbers, wherein they couched under a fabulous attire those their verbal instructions, was after called scientia Cabalae, or the science of reception— Cabala among the Hebrews signifying no other than the Latin receptio: a learning by the ancients held in high estimation and reverence, and not without great reason; for if God (as the excellent John Picus rehearses) …did nothing by chance, but through his wisdom disposed all things as in weight and measure, so likewise in number; and which taught the ingenious Salluste [du Bartas] to say that:

Sacred harmony

And law of number did accompany

The Almighty most, when first his ordinance

Appointed earth to rest and heaven to dance, [trans. Sylvester]

well might Plato consequently affirm that, among all the liberal arts and contemplative sciences, the chiefest and most divine was the scientia numerandi… And I am fully of opinion…that the ignorance of this art, and the world’s maim in the want or not understanding of it, is insinuated in the poets’ generally-sung fable of Orpheus, whom they feign to have recovered his Euridice from hell with his music, that is, truth and equity from darkness of barbarism and ignorance with his profound and excellent doctrines; but that in the thick caliginous way to the upper earth she was lost again, and remains lost to us that read and understand him not, for want merely of the knowledge of that art of numbers that should unlock and explain his mystical meanings to us.

Henry Reynolds Mythomystes

GOD AS GEOMETER

10 Silence, ye troubled waves, and thou deep, peace,

Said then the omnific Word, your discord end:

Nor stayed, but on the wings of cherubim

Uplifted, in paternal glory rode

Far into chaos, and the world unborn;

For chaos heard his voice: him all his train

Followed in bright procession to behold

Creation, and the wonders of his might.

Then stayed the fervid wheels, and in his hand

He took the golden compasses, prepared

In God’s eternal store, to circumscribe

This universe, and all created things:

One foot he centred, and the other turned

Round through the vast profundity obscure,

And said, Thus far extend, thus far thy bounds,

This be thy just circumference, O world.

Milton Paradise Lost VII ll. 216–31

PROPORTION AS MORAL PERFECTION

11 All offices were done

By him, so ample, full, and round,

In weight, in measure, number, sound,

As though his age imperfect might appear,

His life was of humanity the sphere.

Jonson ‘To the Immortal Memory and Friendship of that Noble Pair, Sir Lucius Cary and Sir H. Morison’ ll. 48–52

12 Within this sober frame expect

Work of no foreign architect,

That unto caves the quarries drew,

And forests did to pastures hew,

Who of his great design in pain

Did for a model vault his brain,

Whose columns should so high be raised

To arch the brows that on them gazed.

……

But all things are composed here

Like Nature, orderly and near:

In which we the dimensions find

Of that more sober age and mind,

When larger-sized men did stoop

To enter at a narrow loop;

As practising, in doors so strait,

To strain themselves through heaven’s gate.

……

Humility alone designs

Those short but admirable lines,

By which, ungirt and unconstrained,

Things greater are in less contained.

Let others vainly strive to immure

The circle in the quadrature!

These holy mathematics can

In every figure equal man.

Marvell ‘Upon Appleton House’ stanzas 1, 4, 6

‘SUBSTANTIVE’ NUMBER SYMBOLISM IN POETRY

13 Upon this primrose hill,

Where, if heaven would distill

A shower of rain, each several drop might go

To his own primrose, and grow manna so;

And where their form, and their infinity

Make a terrestrial galaxy,

As the small stars do in the sky:

I walk to find a true love; and I see

That ‘tis not a mere woman, that is she,

But must, or more, or less than woman be.

Yet know I not, which flower

I wish; a six, or four;

For should my true love less than woman be,

She were scarce anything; and then, should she

Be more than woman, she would get above

All thought of sex, and think to move

My heart to study her, and not to love;

Both these were monsters; since there must reside

Falsehood in woman, I could more abide,

She were by art, than nature falsified.

Live primrose then, and thrive

With thy true number five;

And women, whom this flower doth represent,

With this mysterious number be content;

Ten is the farthest number; if half ten

Belong unto each woman, then

Each woman may take half us men;

Or if this will not serve their turn, since all

Numbers are odd, or even, and they fall

First into this, five, women may take us all.

Donne ‘The Primrose’ (a true love is a flower with four or six petals; the primrose has five petals; five, the number of marriage, is assumed to be the number of women, and ten the number of men)

14 The marriage of Hymen and Eucharis:

Next before her [Eucharis] went

Five lovely children decked with ornament

Of her sweet colours, bearing torches by;

……

The odd disparent number they did choose,

To show the union married loves should use,

Since in two equal parts it will not sever,

But the midst holds one to rejoin it ever,

As common to both parts: men therefrom deem

That equal number gods do not esteem,

Being authors of sweet peace and unity,

But pleasing to the infernal empery,

Under whose ensigns wars and discords fight,

Since an even number you may disunite

In two parts equal, nought in middle left

To reunite each part from other reft;

And five they hold in most especial prize,

Since ‘tis the first odd number that doth rise

From the two foremost numbers’ unity,

That odd and even are: which are two and three,

For one no number is, but thence doth flow

The powerful race of number.

Chapman Hero and Leander Sestiad V ll. 317–19, 323–40