Introduction to The Secret of the Luo Shu, Numerology in Art and Architecture
If
numbers can be considered the letters of a universal alphabet, then the perfect
arrangement of numbers that can describe the formulas of mathematics correspond
to heavenly statements of mathematical fact.
(This represents the only pure truth of our universe).
When
humankind discovers these mathematical equations and can apply them to daily
life, society reaps the benefits of evolution and prosperity. It would be a
natural progression for symbols to be born, symbols that are directly related
to the advancement of humankind. The
integration of these math symbols with art and architecture can then tell the
story of civilization. The Chinese magic
square is one such symbol.
This
paper is dedicated to the basic elements of numerology, i.e. the symbolism of
numbers based on the Chinese magic square of three, otherwise known as the Luo
Shu.
The
Luo Shu represents the ideal model of time and space: time as in the numbers of
the calendar and space as in the Pythagorean Theorem, the most important
mathematical relationship to ancient civilization. Hence, the Luo Shu was the basic model the
early Chinese determined as their concept of the world and was incorporated
into art, architecture, city design, royal tomb design, and served as an
important correspondence to a select group of Chinese pictograms.
As
time unfolded, different cultures would adopt the model of the Luo Shu with
usage of its perfect symmetrical template to be found in Roman mosaics, early
Christian art and architecture, Islamic pottery, tiles and textiles, and Italian
Renaissance art.
The
magic square is represented by the quincunx design, or quincuncial composition,
which is based on the arrangements of numbers within the magic square and the
powerful math that lies within its manifestation. The model of the magic square became a motif
repetitive in art and architecture which represented the implementation of math
to establish order on earth.
Christianity
incorporated magic square symbolism in its early church design, illuminated
manuscripts, textiles and more. The
walls, windows, pavements, and mosaics of the church were adorned with this
motif. In fact, the cross and square
ground plan, also known as the nine-bay church ground plan also known as the
quincunx ground plan, was the most popular church design in Medieval times.
Why
the Magic Square?
Table
1. The first magic square and the
corresponding formula; in the example of an order 3 magic square, X = 3 and Y =
5. A magic square is defined as an
arrangement of numbers in a square such that the sum of any row, column, or
major diagonal will yield a singular result, in this case 15. Pythagorean triads highlighted in green. (Note: it is necessary to use Y as a means to
express the fraction
(X2
+ 1) ÷ 2 for an easier visual processing of the formula).
The formula above allows the generation of higher order
magic squares in the Luo Shu format as long as X is odd and greater than
one.
To understand the wisdom
that the Luo Shu offers, one must consider that the Luo Shu represents a “set
of magic squares” based on a common formula that can be expanded to include
higher order magic squares; the Luo Shu is not limited to just the 3x3 magic
square. A “set” of magic squares
traditionally used in alchemy would include the odd and even magic squares up
to order nine; this author considers the Luo Shu set of magic squares to
include only odd magic squares up to the order twenty-seven. Examination of the math of the higher order
magic squares will give insight to the various mathematical properties
associated with magic squares in the Luo Shu format.
The fraction (X2 + 1) ÷ 2 will be
represented by Y and will always equal the center number of the
corresponding magic square. X and
Y will always be the odd components of a Pythagorean triad, (X)(Y)
will equal the magic constant, and X2Y will equal the sum
total of all the numbers in the square, or ∑X2.
Table 2.
The first three magic squares of the Luo Shu demonstrating the
Pythagorean Theorem in the form of Pythagorean triplets of numbers (in green)
in the shape of a gnomon or right angle.
The first significant
feature of the Luo Shu is the Pythagorean triad of numbers in the shape of the
carpenter’s square or gnomon, an important symbol that is closely associated
with the Luo Shu as it also represents time and space as well as applied
mathematics (see table 2).
The second outstanding feature of magic squares in the Luo Shu format is
the cross of odd numbers that run through the horizontal and vertical axis with
a center point of reference.
Table 3.
Example of the cross of odd numbers that will appear in every magic
square in the Luo Shu format. Here, the 9x9 magic square. 9, 40, and 41 satisfy
the Pythagorean or Right-Angle Triangle Theorem. (X)(Y) = 9 x 41 = 369, the magic
constant. In alchemy, this square
corresponds to the moon.
The third important feature of the 3x3 magic square are the quincuncial
relationships of even and odd numbers around the center number. A quincunx is defined as an arrangement of
five things with one at each corner and one at the center of a square. The even
numbers of the first nine numbers will occupy the corners (or four quadrants)
and the odd numbers will form a cruciform with the number five at the center;
this is known as a double quincunx.
Table 4. All
magic squares in the Luo Shu format will have a cross of odd numbers that run
through the vertical and horizontal axis.
The ya cartouche 亞 – cosmic temple – reflects
this important feature of the Luo Shu.
The odd numbers equate to the heavenly yang force, the four
cardinal directions and the center; the even numbers represent the earthly yin
force.
The early Chinese believed these squares were a communication from
Heaven because of the wisdom contained within.
As these squares exhibit the Pythagorean Theorem, a center, and a cross
of odd numbers that separates the square into four quadrants, the “luo shu”
squares became a perfect model to represent Heaven and earth in microcosm, to
be used in art and architecture while at the same time communicate a wisdom of
mathematics that would remain hidden, known only to the intelligentsia. This explanation can help to understand why
this pattern shows up across a diversity of cultures, beginning with the early
Chinese and continuing thru the Renaissance era. This model, or symbol, of numerology would
therefore be transformed into an artistic composition of motifs beautifying
tiles, pavements, mosaics, books, and textiles to mark structures and objects
of religious or political import.
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