As I pointed out in my previous article, fitting the human form into a circle and a square is a geometric proof that we are both spiritual and physical. The main purpose of this endeavor was to transform the individual from a body with the spirit hidden on the inside into one who outwardly expressed the spirit. This was the goal of the Mysteries (which are the source of our word mystical), and this became the quest of the alchemists and other mystics. It was described as the squaring of the circle.
In the first article, I said that Leonardo was able to solve this problem by drawing a beautifully proportioned figure and then finding these truths within the figure. To understand this statement fully we have to understand the significance of ratios.
The common understanding of Pythagorean number mysticism seems to be that the Pythagoreans thought of the whole numbers as symbols that were equated to specific qualities as well as quantities – one was unity, two polarity, three the beginning of form, etc. This is true; however, the most powerful way that numbers were seen to impact on reality was as ratios. Ratios are relationships between numbers. For example, we can see that 4 relates to 8 the same way that 1 relates to 2 – they are the same ratio. The Pythagoreans found that music could be expressed as ratios, that the ratio 1:2 described the whole note, 2:3 the perfect fifth, and 3:4 the perfect forth, These realities underlie all musical harmony. Every culture has to find these same notes and create their musical scale around them in order to have music. Beauty has this objective aspect as well as a subjective aspect. Pythagoras believed that the universe was ordered in this same way. Because there were seven planets that he knew of, he created seven notes to correspond to them. He called the universe a cosmos, which meant that it was a beautiful, musical harmony – music of the spheres.
Classical artists used the same principal to develop the perfect figure, and ratio is what Leonardo made use of also. By this, we mean that we have to find a way of measuring the figure by making use of relationships within the figure – not by measuring it with an external scale such as inches or any other external system. The unit of choice was the head. Leonardo’s figure has a one 1:8 ratio with its own head. In other words, it is 8 heads tall.
You will notice that Vitruvian Man has dividing lines drawn on his body. There is a line at the chin that indicates the limit of the 1 head unit, a line at the nipples that marks the length of 2 heads, a line at the groin that marks 4 heads, a line below the knees that marks 6 heads, and the base line the marks 8 heads. The base line forms the bottom of the square and the top rests on his head. Therefore, the square is 8 heads tall. Notice that the man’s lower set of extended arms touch the square on both sides. Because the width of a square is equal to its height, the length of the arms has to be 8 heads as well. In other words, our extended arms are the same length as our body from head to toe. Try measuring your friends; you will find that this is true with only a slight variation. The vertical lines on the shoulders of Leonardo’s figure measure the 2 head width of the torso at the shoulders; the line at the joint of each arm measures an additional 1 head in each direction; and then we jump another 2 heads on each side to the fingers and the sides of the square. However, the dividing line between the hand and the forearm stems from a different unit of measure. This is called the “golden proportion.” Proportion is a relationship between two ratios. The Pythagoreans noticed that there are three different levels of complexity of proportion.
The most complex described a relationship of four items: A is to B as C is to D; 4:8 = 1:2. This was called discontinuous proportion. Next was continuous proportion, which involved three items: A is to B as B is to C; 1:3 = 3:9. The most sacred proportion involved two items, thereby drawing us back to primal duality. This was called the Golden Portion: A is to B as B is to A+B. Expressed mathematically as 1to the irrational number 1.61803commonly referred to by the Greek letter Phi. In Vitruvian Man, the length of his hand relates to his forearm in the same way that his forearm relates to the length of the forearm and hand combined- the golden portion.
These measures are then related to other parts of the figure. Notice how Leonardo conveniently shows us the man’s left foot in profile. He even places the heel in front of the big toe of the right foot so that we can see the full length. The length of the foot is the same as the length of the forearm – demonstrating a golden relationship between the hand and the foot. The length of the hand can be related to the measurement of the face – from the chin to the hairline. The face in turn is divided into thirds, which coincide with the eyebrows and the tip of the nose – echoed in the length of the ears. The line at the eyebrows is the golden division of the entire head.
The golden relationship is the key to the proportions of the entire figure. For example, if we examine the length of the arm from the top of the shoulder to the tip of the fingers, we find that the elbow is the golden division. If we examine the length from the elbow to the fingers, we find the base of the hand at the wrist is the golden division. If we measure the hand, the fingers begin at the golden division, and fingers themselves are composed of segments with a golden relationship to each other. We can find the same pattern of proportion in the legs, feet, and torso. However, the most dramatic illustration of the golden portion is the division of the body at the navel. The relation ship of the distance from the top of the head to the navel is to the distance from the navel to the feet the same as the navel to the feet is to the entire height of the figure.
If we divide the square in half, we will find that the middle falls right at the line drawn through the groin. At the level of sexuality, we are centered in the physical. To find the center of the circle, the spiritual, we have to move up to the navel – the golden division. If we extend the horizontal line at the groin until it divides the square into two equal rectangles and then we draw diagonal lines connecting the corners of these rectangles. We will find that the diagonals intersect the circle as it extends through the center of each hand and foot. The pattern that is formed, with four equidistant points radiating out of a central fifth point (the navel where we were once connected to our life giving mother) is called a quincunx. This is a powerful archetypal symbol for sacredness that can be found in all cultures, and this is the same symbolic structure that is found on the World card in the Tarot.
The World card in the Tarot illustrates the same squaring of the circle. It depicts a sacred figure in the center; the archetypal Great Mother identified with the Navel of the World. To the alchemists, Hermeticists, and Neoplatonists, she is called the Anima Mundi, the Soul of the World. She forms a quincunx in relationship to the four figures in the four corners of the card – the four Evangelists, who through their relationship to the four fixed signs of the Zodiac relate to the four elements, the four directions, and the four seasons. The entire Tarot deck shares in this structure. The four minor suits relate to the square – the four elements, seasons, and directions. The trumps that move us along a spiritual journey of triumphs, that start with the four fold mundane world, take us through the hero’s journey of death and rebirth, and back to the world – only now with the spirit exposed – the naked truth – are the circle. The message of the Tarot is the squaring of the circle.
(The remainder of this article is in response to questions to the author.)
The more orthodox Christian symbol for the spirit in matter is Christ, which the alchemist sometimes used instead of the female figure. They also sometimes use the male figure of Hermes. However, all of these figures symbolize the same thing the spirit in matter. Buddhists use an image of Buddha for the same purpose.
I only know of one French Tarot deck, the Jacques Vievil’s deck, that used Christ on the World card. There are two putti on the Visconti-Sforsa deck’s World card and on another hand painted deck that follows the same model. There is a 15th century printed deck in Paris and the Tarocchini di Bologna that have a figure that is possibly Hermes. Most of the earliest printed decks, of which there only a few, like one that I have inspected in the Metropolitan Museum, have angels that are androgynous leaning toward female. All the other early hand painted and printed decks that I know of show a female figure.
My description is of the French model that led to the Tarot of Marseilles. The symbolism on the other World cards is not necessarily a quincunx. However, it consistently represents the spirit or soul of matter, most often as female, next comes androgynous (in alchemy Hermes is also at times considered androgynous), then male. Often the figure relates to the world as an axis mundi or Sovereign of the sacred center, which although not being a quincunx is a related symbol. The World is always exposing the truth that the World is sacred. This is the philosophy; this is the wisdom.
As I pointed out in my comments on Leonardo’s Vitruvian Man, Leonardo consciously used the Golden Ratio to proportion his figure and made the Golden Ratio of his figure the sacred center of the symbol. Showing that this ratio was the key to leading us to a realization of our spiritual identity.
Since I first learned about the Golden Ratio in college, I have noticed that almost all good paintings make use of this proportion in their composition. Unlike Leonardo, most artists are doing this intuitively because it just feels right. I was using it myself before I knew what it was. Finding the Golden Ratio in a work is not proof of an esoteric doctrine. However as I said before, I believe that beauty, no matter how the artist arrives at it, is the greater mystical truth.