Geometrically Ordered Design: The Big Ten
By: Dustin Pike
This is my tenth article pertaining to the design field and its relationship with mathematics. Design in essence cannot be accomplished without specific degrees of control, and almost always has a definitive point to make. How well the ‘point’ can be made is attributed to how well the design was carried out. This cannot be said about all art-forms. Art can be about anything or nothing at all, which makes art primary, and design secondary. In this respect design can be seen as separate from other art forms, because the designer has a precise goal. In order to understand any design language at its core, the viewer must understand visual acoustics on multiple levels. The level I have chosen to start with is numbers. I will show their relationships with each other through geometric and proportional means, and describe how numbers can be ‘seen’ and ‘produced’ through artistic expression. Design language cannot be truly understood without awareness of this knowledge. Not only is this the groundwork for every art form, but it is also the chosen architectural language of the natural world.
Our previous article on the #9 was shown to be last of the digits in the singular tense and embodied the maximum progression of its kind. This created a sort of mathematical boundary plane, beyond which (as we will see) is nothing or, more properly, no-thing. In a sense, the numerical system at this point finds itself back at its beginning upon ‘another level’. Yet how can this be so? Indeed it does appear that the #10 and the #1 are different, so let us examine their numerical difference closely.
The ‘digital-rooting’ system introduced in the previous article highlighted the repetitive nature of certain number sequences when taken down to their singular ‘root’. Thus the #10 can easily been seen as a disguise for the #1 since 1 + 0 = 1. Here then is introduced the Zero, which when given some thought actually is the true agent responsible for creating our entire system.
From time immemorial, this Zero has been worshiped and studied under the familiar symbol of the circle (easily suggested by the shape). The visual phenomenon of infinite movement inherent in its curve is often too simple a thing to spend time considering for most people. The mind becomes confronted with an obvious juxtaposition: what is this ‘infinite’? How can it ‘be’? Certainly the brightest minds of the past have pursued these questions at length, but most end up realizing that they are chasing a ghost (or more figuratively, their own tail; See Ouroboros Image). This so-called eternal ‘Idea’ given by the circle, when divorced from its material partner, cannot be said to have an identity at all since it is non-dual. This ‘non- dual’ is perfectly primed and receptive of any influence thrust upon it, and can be seen as the Orphic Egg of the Greeks (See Orphic Egg Image).
All of these explanations seem quite fantastic and outlandish, unless it is understood that we are attempting to explain something unexplainable. Here I am reminded of the words of H.P. Blavatsky: “Divine thought cannot be defined, or its meaning explained, except by the numberless manifestations of Cosmic Substance in which the former is sensed spiritually by those who can do so.” In this light, Zero can be seen as ‘possibility’ (which forms the base of all things possible). Even the quantum physicists of today, who ironically find themselves in agreement with ancient Buddhist philosophical ideals, tell us that the total energy of the universe equals Zero. This is not an easy concept for the western mind to digest, due to the overwhelming amount of Christian dogmatism most of us are brought up with. The emptiness of a Buddhi during ‘Parinirvana’, when technically considered, is not unlike that of a dreamless sleep (before being annunciated by the dream). Mathematically, we could view this as an ‘empty set’ whose elemental properties have not yet been established. Biblically, it is the ‘darkness upon the face of the deep’.
Having considered all the previous numbers we have delved into, and their accompanying symbology, I shall now reveal what is known as the Tree of Life (See Tree of Life Image). The amount of knowledge contained within this diagram alone has occupied many individuals for thousands of years, if not more, and so I will but break the surface for the layman. Immediately it is noticed that there are 10 points of aggregation known by the Jewish mystics as Sephirot, meaning ‘emanations’ (these are the 10 numerical digits). Through these emanations, Ein Sof (the infinite) reveals itself out of nothingness. To make an even a greater leap, the mystic is to view these ‘points of aggregation’ as living and breathing intelligences with a universe unto themselves quite distinct from their neighbors.
One should also notice that there are 22 connecting paths in-between these points. They serve as a sort of communication link between the numbers, and find their origin in the Hebrew alphabet (each link associating itself with one of the 22 letters). As if this wasn’t enough, the 22 letters themselves also have numerical associations assigned to them. It is futile to delve further into this due to its complexity, but I would have the reader know that systems such as the Tarot and I-Ching are based upon this structure. However, anyone who is remotely interested in these systems can rightly guess that it calls for great dedication and patience.
Another idea in service of the #10, which has served its time in history, is the Greek Tetractys (See Tetractys Image). Using so-called ‘triangular numbers’ sequentially, 10 spheres are created during the 4th, and in this concept, final addition (1 + 2 + 3 + 4 = 10). It is here useful to note the simplicity inherent in this type of abstract symbol. Simplicity is, ironically, perhaps the most wide-ranging idea of all. The Greeks, or more specifically, the Pythagoreans attached an enormous amount of knowledge into the Tetractys and literally protected this with their lives. One of the embedded systems in place is of course the 4 Elements, and their associations with space:
Uppermost Circle = Fire (Zero-dimensional point)
Second Row = Air (One-dimensional line)
Third Row = Water (Two-dimensional plane)
Fourth Row = Earth (Tree-dimensional shape)
In fact the Pythagoreans held this symbolism is such high regard that they announced its presence with a prayer:
“Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all”
This article marks the last of the 10 digit system and with it came the idea of unity restored. The #1 is upon higher ground, and further progression is due. I should not digress into information pertaining to the #11 and beyond due to the fact that this would extend unto forever. However, I do plan to continue the Geometrically Ordered Design articles in the coming months with an aim towards modern design theory and practice. In this way I will take a step forward out of history and partake of the ‘now’.