I. 17
NUMERI SACRI
3 4 7 10 12 40
Unde ratio numeri contemnenda non est, quae
in multis sanctarum scripturarum locis quam
magni aestimnanda sit eluced diligenter
intuentibus. Nec frustra in laudibus Dei dictum est:
Omnia in mensura et numero et pondere
disposuisti.
Augustinus, De Civitate Dei,
liber XI, cap. 30
Thus we see that we should not underestimate
the significance of numbers, since in many
passages of sacred scripture, numbers have a
meaning for the conscientious interpreter. Not
without reason has it been said to praise God:
THOU HAST ORDERED ALL THINGS IN MEASURE,
NUMBER, AND WEIGHT.
Augustine, The City of God,
Book XI, chap. 30.[426]
Throughout the Middle Ages sacred numbers, conceived
as an expression of divine order pervading the created
world, formed an integral part of theological and secular
thought.[427]
Recent studies have shown, with increasing
strength of evidence, that they played an important role in
the thinking of medieval architects.[428]
The Plan of St. Gall
confirms these findings. It offers persuasive proof that
sacred numbers were a decisive factor in the conceptual
organization of the Plan as a whole, the proportioning of
its major building sites and the dimensioning of the
individual buildings. Throughout the entire width and
length of the Plan there are signs of the recurrent use of
certain favorite numbers, in both the manipulation of
straight numerical sequences as well as the management of
a variety of modular scale relationships.
Predominant in the mind of the designing architect, as
this analysis will show, are the numbers three, four, seven,
ten, twelve, and forty—all associated with eminently sacred
connotations.
THREE: This holiest of all holy numbers is encountered
in a variety of pagan religions where triads of deities
acquired a pre-eminent position.[429]
The Babylonian triad
Anu, Bel, and Ena; the Indian triad Brahma, Vishnu, and
Siva; the Greco-Roman triad Jupiter, Juno, and Minerva
found a Christian counterpart in the doctrine of the Holy
Trinity (Father, Son, and Holy Spirit). Both the Old and
New Testaments abound with references to the sacredness
of this number. God created the world by dividing it into
its three constituent parts, land, water, and air. He spoke to
Moses in the desert of Sinai on the third day of the third
month and gave the law on the same day. Christ was
tempted thrice and spent three days in the tomb. In the
Christian liturgy the number is reflected in such devotional
formulae as the triple
Agnus dei, the triple
Mea culpa, the
triple
Dominus non sum dignus, that have parallels in the
Greek and Roman ritual (triple libation, triple pronunciation
of the mystical words, triple circumambulation,
lustratoria and others).
On the Plan of St. Gall the number three is used in the
organization of the basic site divisions (figs. 75 and 76).
There is an eastern tract, a central tract, and a western tract
(fig. 75). The central tract, which has twice the surface area
of tract 1 and 2, is internally divided into a straight plot on
the northern side of the Plan, a P-shaped plot in the center,
and an L-shaped plot to the south (fig. 76). The northern
plot is internally divided into three building sites (Abbot's
House, Outer School, House for Distinguished Guests),
the L-shaped plot to the south is comprised of six building
sites—three in the vertical stem of the L (Granary, Great
Collective Workshop, Monks' Bake and Brew House) and
three in the horizontal bar (Hospice for Pilgrims and
Paupers, House for Coopers and Wheelwrights, House for
Horses and Oxen; fig. 77).
The number three, as I have shown in my analysis of the
scale and construction methods used in designing the Plan,
played an important role in the arrangement of the 40-foot
squares that determined the layout of Church and Claustrum,
as well as the 160-foot squares that formed the basis
for the calculation of the overall dimensions of the monastery
site.[430]
The Church is inscribed into a grid of squares,
three 40-foot units wide and nine 40-foot units long (fig.
61); the cloister into a grid of squares three units wide and
six units long. The entire settlement is developed within a
grid of 160-foot squares, three units wide and four units long
(fig. 63).
Three multiplied by itself is nine. This figure, apart from
the instance just mentioned, is reflected in the nine interstices
of the nave arcades (fig. 55) and the two rows of
planting beds in the Monks' Vegetable Garden (fig. 64).
FOUR: The number four was associated, both in pagan
and Christian times with the basic divisions of matter,
time, and space: the four humors of the body, the four
winds, the four seasons, the four rivers of paradise, the
four cardinal virtues, the four horsemen of the Apocalypse,
the four main prophets, and the four evangelists.[435]
On the Plan of St. Gall it determines the internal layout
of the most important building site, namely the P-shaped
central plot of land that accommodates the Church and the
three principal claustral structures. Moreover, it played a
crucial role in the calculation of all the basic modular values
used in constructing the Plan.[436]
SEVEN: In Sumerian and Babylonian times this figure
was associated with celestial bodies and spiritual forces:
the seven planets, the seven evil spirits, the seven levels of
the ziggurat and others.[437]
In the biblical tradition, St. Augustine
writes, it was used to express "the whole or completeness
of anything." God created the world in seven days and
on the last of these, the seventh, he "did not wish to
sanctify his creation by any of his words but, rather by his
rest."[438]
In the later Christian tradition all human life is ordered
by series of seven. There are seven capital sins, seven
virtues, seven sacraments, seven requests in the Pater
Noster. Each man passes through seven ages, and the
world itself will last no more than seven periods.[439]
In
monastic life the number is observed in the seven daily
services to which the monks are held (Lauds, Prime, Terce,
Sext, None, Vespers, and Compline).[440]
On the Plan of St. Gall the numeral is reflected in the
seven buildings that form the cloister (three major and four
minor; fig. 79), the seven houses that lie in the western tract
of the monastery (fig. 80), the seven steps (septem gradus) by
which the presbytery is raised above the crossing (fig. 99),
the seven desks for the scribes in the scriptorium (fig. 99),
the seven tables in the Monks' Refectory (fig. 211), the seven
beds that are located in the abbot's dormitory (fig. 251)
besides that of the abbot and the seventy-seven beds in the
Monks' Dormitory (fig. 208).
TEN: "This number signifies perfection, in an even
fuller sense," St. Augustine writes, "because it is composed
of the number seven, which embraces all created
things, and the number three which stands for the Holy
Trinity."[445]
It found its most significant embodiment in the
Ten Commandments, composed of three precepts pertaining
to the love of God and seven to the love of neighbors;[446]
and it is reflected in Hebraic liturgy in the ten shores
of Egypt, the ten ropes of the tent of the tabernacle, the
height of the cherubs in the temple (ten cubits) and the ten
horns of the apocalyptic beast. It was on the tenth day that
Christ ascended to heaven.[447]
Ten is the number that forms
the basis of the decimal system and it is the universal ten
of the Pythagoreans.
All the principal dimensions of the Plan and those of
many of its larger subdivisions can be interpreted as
multiples of ten. The Church in the form in which it is
drawn has a length of 300 feet.[448]
An axial revisionary title
suggests that in actual construction this should be reduced
to 200 feet.[449]
The cloister yard, including its walks, has a
surface area of 100 by 100 feet.[450]
The square with the
savin tree in the center measures 20 by 20 feet.[451]
Ten is the
basic factor in all of the larger modules used in designing
the Plan. Multiplied by four it yields the 40-foot square,
[452]
and again by four the 160-foot square.
[453]
The number finds
specific mention in the explanatory title that defines the
distance (
pedes denos) between the piers that support the
covered porch of the semicircular atrium that gives access
to the Church.
[454]
TWELVE: The number twelve formed the basis of the
Sumerian and Babylonian numerical system, which was
duodecimal (the twelve signs of the zodiac, the twelve
months of the year, the twelve hours of the day). It played
a significant role in the number symbolism of the Jews (the
twelve gates of paradise, the twelve tribes of Israel, the
twelve bronze calves) and the Christians (the twelve
apostles, the twelve stars around the head of the apocalyptic
woman, the twelve days from Christ's birth to Epiphany).
On the Plan of St. Gall it is reflected in the twelve subdivisions
of the East tract (fig. 80), the twelve cubicles for
the students of the Outer School (fig. 407), and the twelve
feet (
bis senos pedes) assigned to the interstices of the
arcades of the Church in one of the revisionary titles of the
Plan.
[456]
FORTY: "I think that life itself is represented by the
number forty. . . . Not without reason did the Lord remain
on this earty forty days, after his resurrection, when he
conversed with his disciples in this life."[457]
For ages this
number, as I have already had occasion to point out in a
preceding chapter, had been associated in the biblical
tradition with periods of expectation and penitence.[458]
It is
the value assigned to the width of the nave of the Church
of the Plan[459]
and forms the basis of the grid of squares that
determines the proportions of Church and Claustrum[460]
as
well as the dimensions of the entire monastery site.[461]
It is
a crucial figure both for the planimetric organization of the
monastery site and for the proportions of the Church and
the claustral buildings.
This is an enumeration of the most obvious incidence of
the use of sacred numbers in the design of the Plan. There
are others,[462]
but perhaps one should not belabor the point.
Before abandoning the subject, nevertheless, attention
must be drawn to the existence of a broad range of different
manifestations of number symbolism on the Plan of St.
Gall, not so easily detected by the eye of modern students
of the Plan, and least of all by those who were reared in the
metric system. I am referring to all such cases where sacred
numbers are manipulated in modular, rather than in
straight, numerical sequence. The outer boundaries of the
monastery site, as has been shown in a preceding chapter,
were established in the proportion 3:4,[463]
laid down with
the aid of a regular straightedge, on which these lengths
were 30 and 40 Carolingian inches.[464]
The corresponding
distance on the ground was 480 and 640 feet,[465]
both
multiples of forty. The entire monastery site discloses itself
to be inscribed into a grid of twelve (=3 × 4) supermodules,
each representing a surface area of 160 × 160
feet.[466]
This area was internally composed of sixteen 40-foot
squares. On the Carolingian straightedge, with the aid of
which these dimensions were scaled on the Plan, this
supermodule corresponded to 10 × 10 inches.
[467]
In our analysis of the scale and construction method used
in designing the Plan we have shown that all of those installations
of the Plan that were too small to be expressed as
multiples of 40 feet (width of the nave of the Church) were
designed as multiples of a standard module obtained by
halving forty, four times in succession, and thus arriving
at a base value of 2½ feet, perhaps equivalent to an actual
Carolingian "pace."[468]
A modular sequence formed by
multiples of 2½ produces such imperfect numbers as 7½,
12½, 17½, 22½, 27½. These graduations appear peculiar to
anyone who is accustomed to think in sequences of full
numbers, but become meaningful once it is understood
that on the Carolingian straightedge used by the designer
in scaling the Plan, 7½ corresponded to three; 12½ to five;
and 17½ to seven standard modules. Typical examples are
the two enclosures, one of which serves as Henhouse, the
other as the Goosehouse (fig. 466). They are formed by
concentric circles, struck to diameters of 12½, 27½, and 42½
feet. On the scale used by the designer these values corresponded
to five, seven, and seventeen standard modules.
The House of the Fowlkeepers, which lies in the middle
between these two installations, covers a surface area of 35
feet by 42½ feet. On the straight edge these values corresponded
to fourteen (= twice
seven) and seventeen (=
ten
plus
seven) standard modules. Examples like these could be
multiplied by scores of others.
On the Plan of St. Gall, thus, we must conclude that
number symbolism is used on different levels: the modular
graduations of the Carolingian straightedge with the aid
of which the Plan was drawn, the number of feet which
corresponded to this module on the ground[470]
and the
number of actual Carolingian inches that furnished the
actual frame of reference for that modular scale. The author
of the Plan of St. Gall could switch from any one of these
three levels of thinking to any other with the same ease with
which a modern Anglo-Saxon carpenter switches from the
straight numerical sequence used in listing multiples of feet,
through the duodecimal system used in designating inches,
to the sixteen divisions used in designating fractions of
inches. Numbers meaningful in one system may be replete
with symbolism in any of the others.
In drawing attention to the use of sacred numbers in the
design of the Plan of St. Gall, we must emphasize that the
conceptual attitude reflected in this system should under
no circumstances be confused with the principle of carefully
regulated modular relationships discussed in our
chapter on the scale and construction methods used in the
Plan (above, p. 77ff). They have different historical roots
and different historical implications.
Number symbolism is cultural material of old vintage
transmitted to the age of Charlemagne in the form that it
had attained in the writings of the early Church Fathers.
It was the product of theological and biblical speculation
and an expression of the belief that the created world was
held together by a divinely ordered system of numerical
relationships, and that the continuance of life depended on
the perpetuation of that system. Sacred numbers, judiciously
selected, could be used for aesthetic purposes but
had in themselves no binding aesthetic implications. Of the
six intensely holy numbers used by the author of the Plan
(i.e., the numerals 3, 4, 7, 10, 12, and 40) four are not in any
modular relationship to one another (e.g., 3, 4, 7, and 10);
and 3, 7, and 12 are not in any modular relationship to 40,
the number holding the key position in the aesthetic
organization of the Plan. Only 4 and 10 are modules of this
crucial figure, 40. It is in the establishment of a coherent
aesthetic system between these three—4, 10, 40—and the
consistent application of that system to the layout of the
entire monastery site that a new principle of spatial composition
emerges in western architecture and planning. We
shall return to this subject in our discussion of the cultural
roots and architectural implications of the square schematism
of the Plan of St. Gall (below, pp. 212ff).
