In a former life (30 years ago), I was a math geek. I loved the perfect structure of shapes, the laws of number relationships, and dabbled in the ontological possibilities of mathematical philosophy (the study of being, becoming, and reality through the lens of mathematics). I’ve been thinking about these things again in relation to other issues, letting my mind wander nostalgically to an old playground.
Walk with me for a spell, my friends.
Pythagoras, who had some eccentric ideas about beans being bad for us and the transmigration of spirits, had some very interesting ideas about numbers. The latter turn out to be quite fascinating. The father of the Greek teachers (born in 580 BC), he taught that reality was essentially mathematical in nature. In fact, he constructed a philosophy with the simplest of tools: a compass, a straightedge, and a writing utensil.
The simplest shape that can be constructed is a circle, whose essence is a center from which a line can be drawn at every point equidistant to it. This is called a monad. It connotes beginning, stability, and unity, and is the geometric representation of One. It preserves the essence of any number with which it works (a number multiplied by one is itself; a number divided by one is itself), and the Greeks thought of it as a standard of measure of unspecified dimension, not a number in and of itself. In other words, it was the foundation of all numbers, which were merely multitudes of One.
By contemplating itself (examination in a mirror), the circle could be duplicated, producing a dyad. It connotes otherness, duality, and balance, and is the geometric representation of Two. Greek philosophers referred to it as “audacity” (a boldness to separate from the One) and “anguish” (a desire to return to the stability of the One.) It’s the only number whose sum equals its product (2+2=2×2). Separated by a line that connects the two centers, it is characterized by repelling and uniting, separating and returning, and wisdom as well as truth. It is the door between One and Many. Also not considered by the Greeks a number, Two is the complement and mirror of One, and together they are the parents of all other numbers.
The creation of the second from the first produces a vesica piscis. Shown here in yellow, it is the area shared by both circles when each touches the center of the other. As all other shapes can be constructed from these, this shape is a passageway into being, both spiritually and physically, and the area is the sacred space of creation, and a shape that shows up in much early Christian art associated with Mary and Jesus.
The first shape created from the union of One and Two is the triad, sometimes called the Firstborn, formed by the three lines connecting the centers and one of the intersection points between the circles. The triangle connotes stability and wisdom, harmony and peace, strength and balance, combining the traits of its parents. It is the only number equal to the sum of the parents (1+2=3), and the shape has the largest perimeter with the smallest area of any that can be constructed. It is also the only number whose sum (with parents) is the same as its product (with parents), as 1+2+3=1x2x3.
Extending lines from the triad, more complex shapes can then be constructed, with the tetrad and the pentad following, constructed within the vesica piscis.
There are fun things one can do with phi, as shapes of exact proportion can be produced within each of these shapes in precise increments, but I’ve been pondering the ontological truths we can find hidden within the numbers 1-3.
While we know that we do not derive doctrine from natural phenomena or the laws of mathematics, like parables, they “are a call to investigate the truth; to learn more; to inquire into the spiritual realities, which, through them, are but dimly viewed.” (Bruce R. McConkie, The Mortal Messiah, vol. 2, From Bethlehem to Calvary (Salt Lake City: Deseret Book, 1980), 245.)
In the story of the creation of Adam and Eve, we have a very interesting study in dualism. Adam was created of the dust of the Earth, but Eve was created from Adam, a reflection or mirror of him, we might say. Neither was created from an embryo to which others similar had contributed, as their subsequent children would be. The only union of One and Two that produces Many is one that creates Three, and that is only possible if that union involves each touching but not overshadowing the center of the other. Thus, their marriage (and ours, as they represent us) was ideally one of perfect balance allowing Christ to be nurtured first at the center.
Eve chose to eat of the fruit (signifying her audacity to be separate from the One from whom she was created), and was then informed by the Creator that her desire would be to her husband (signifying her yearning to be one with him again). The tension of her being (as with all women) entails both separateness and unity, producing a harmony that makes possible mortal life, as Adam followed her, acquiescing to the wisdom of creation through his choice to maintain the integrity of his connection to her center. Within her grew the seed of the One, their union producing the Firstborn, who made possible all others.
The same overlays can be made with the mortal birth of Christ, the fruit of the divine One uniting with the mortal Two, she (Mary) also a reflection of the divine in her purity. Out of their union the veil (which can be seen as both a separation and a means of joining, note the contradictory meanings of the word cleave) between two realms was broached, allowing the spiritual and the mortal to coexist for a discreet time and space.
While many see dualism in a fight between good and evil, between Christ and Satan; this opposition is not a true dualism because one is clearly superior to and will triumph over the other. True dualism is a oneness composed of fit (meet) companions, and is eternally balanced and coexistent.
This vesica piscis could also be said to occur in temples, where veils cleave realms.
With thanks to Jim Wilson.