In Part I, we introduced an important symbol known as the enneagram. In this part, we will continue to explore the occult aspects of this symbol and how they relate to the Natural Laws that govern the universe and all within it.
Thus, we begin our journey with the circle of the enneagram, the circle of space in which all things may manifest.
THE CIRCLE AND THE MONAD
In sacred mathematics, the number zero is the antithesis of all and is not a number but rather the absence of anything, the uncreated, the central point about which everything else revolves. This idea can be graphically demonstrated using the geometer's compass, wherein a circle is drawn about a fixed point.
Describing a circle around a fixed point is a sacred act of creation. It symbolizes two extremes of the Absolute: absolute-nothingness represented by the point, and absolute-all-ness, illustrated by the circumference. Within the extremes of nothingness to all-ness exists the entirety of the universe. The ancients viewed the circle as the monad, and from this unity, all other manifestations are made possible.
There are several remarkable features regarding the monad, which the student of The Eminent Way should come to appreciate. For example, consider that every other number can be constructed with the addition of unity to itself (i.e., 1+1+1+1+1 = 5). In contrast, unity cannot be described using any whole number other than itself. Thus, it is considered the undefinable creator, the hidden god.
Furthermore, when a series of unities is multiplied by itself, the creation of every other number in the natural sequence of 1 – 9 may be obtained, which always returns to unity:
11 x 11 = 1-2-1
111 x 111 = 12-3-21
1111 x 1111 = 123-4-321
111111111 x 111111111 = 12345678-9-87654321
Thus, all of creation is considered a reflection of the one.
Further, we can see that when multiplied or divided, unity always preserves the identity of all it encounters. For example, any number multiplied by one equals the original number, and any number divided by one also equals the original number.
Thus, it can be said that every number is but an outward expression of the monad.
Although every circle is identical in every way other than size, there is more to every circle than meets the eye. Every circle is a profound statement about the ethereal nature of the universe. Expanding from the nothingness of its dimensionless center to the infinite points of its circumference, a circle implies the mysterious transition from void to all.
Moreover, its radius and circumference are never measurable simultaneously due to their unique relationship to the irrational number Pi (3.1415926…). When either the circumference or radius is measured in whole units, the other becomes infinitely unmeasurable and unknowable.
Thus, the monad is the unknowable one.
Moreover, the circle, or sphere, is the universe's most balanced and natural shape. If allowed to do so, all shapes will resolve into the form of a circle or sphere, as can be seen in the case of soap bubbles blown from a wand; all seek to return to the state of unity.
"The one godhead, secret in all beings, all-pervading, the inner self of all, presiding over all action, witness, conscious knower and absolute… the one in control over the many who are passive to nature, fashions one seed in many ways" – Swetaswatara Upanishad
THE TRIANGLE AND THE TRIAD
In contrast with the circle, which encloses the greatest area within the smallest perimeter, the triangle encloses the smallest area with the greatest perimeter. This property can be demonstrated using a piece of string and a sheet of graph paper by shaping the string into a circle on the graph paper and counting the number of squares it encloses. Next, form the string into a triangle, and again count the number of squares enclosed within the shape. You will note that even though the same string length is used, the number of squares occupied by the string in the form of a triangle is significantly less than that of the circle. In this way, they may be considered opposite properties, just as space and matter have opposite properties.
Moreover, the triangle is the only structure that is rigid by the right of its geometry alone. This self-rigidity feature is used in load-bearing structures such as the arch of a cathedral entrance which can support significant weight. Triangles bestow strength, balance, and efficiency of space to any form.
Protons, electrons, and neutrons comprise the subatomic world upon which all atoms are formed. And indeed, it is impossible to describe an object's size and shape without referring to the three dimensions of space it occupies.
The human body is a three-part structure consisting of top, middle, and lower segments and is further divided into the components labeled body, soul, and spirit.
When unity is divided by three (1/3), an endlessly repeating decimal (.333) is obtained, which is irresolvable back to its unity in that the reverse process, multiplication, will never yield 1, but only a never-ending approximation of it (.333 x 3 = .999).
There are six ways around a triangle. For example, if one were to label the three points of a triangle as 1, 2, and 3, respectively, the six possible ways to trace the triangle would be:
These six ways or processes correlate to the next element of the enneagram, the hexagram produced by dividing unity by the septenary, or 1/7, which forms the recurring six-digit decimal .142857
"The triad has a special beauty and fairness beyond all numbers, primarily because it is the very first to make actual the potentialities of the Monad" -Iamblichus (c. 250)
There is a mysterious relationship between the numbers six and seven, but an even stronger bond exists between the hexagram, the triangle, and the circle. The number six is the first number that can be obtained by multiplying two separate numbers (other than unity):
1 = 1x1
2 = 2x1
3 = 3x1
4 = 4x1, or 2x2 (same)
5 = 1x5
6 = 1x6, or 2x3 (different)
Thus, the hexad is composed of two trinities, and because it is the doubling of three, it partakes of the triad's principles of balance and strength. The ancients also called it a perfect number because it is both the sum and product of its parts (i.e., 1+2+3=6, 1x2x3=6).
The number 6 and the corresponding number 60 encompassed the most accurate way to measure time to the ancient Sumerians. The base-60 measurement of time is practical because 60 has the greatest number of whole devisors, which allows us to count time in many units. For example, because 60 is divisible by 2, we can account for time in half-hour increments. Similarly, because it is also divisible by 4, we can count time in 15-minute increments—the divisibility of 60 by 12 yields 5-minute increments, and so on. Even today, we use the ancient Sumerian system of timekeeping, based on the number six. Therefore, is it any wonder that the enneagram's inner symbol, representative of time, is a six-pointed hexagram?