Geometrically Ordered Design: The Wholly Trinity

June 17th, 2012  |  Published in *, June 2012  |  1 Comment

"Recursive Triangle", Dustin Pike

By: Dustin Pike

“The triad is the form of the completion of all things.” -Nichomachus, Pythagorean philosopher

This is my third article pertaining to the design field and again it is necessary to distinguish between art and design. 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 art. Art can be about anything or nothing at all, which makes design a subdivision of art. In this respect design can be seen as separate from other art forms, in that there is a singular goal in the mind of the designer. In order to understand any art form at its core, the viewer must understand visual acoustics on an elementary level. The level I have chosen to start with is numbers and their relationships with each other through geometry and proportion. Design cannot be truly understood without attaining this knowledge. Not only is this the basis for every art form, but it is also the architecture of the natural world. Also to aide the reader, I will be referencing specific visual instances where the number or geometry in question can be better understood.

As stated in my first article ‘Design Intervention’, the goal of these next articles will be dedicated specifically to understanding our numerical system through the process of Sacred Geometry. I will be breaking down each of the single digit numbers from 1-9, and end with zero. Of course, if we are talking about numbers, the best place to start is technically zero, but I think saving the best for last is appropriate for this kind of approach.

We have now made it to the number three on our journey through the numerical digits. Last month I wrote of the number 2 and its polar/dual nature, but with the number three we break through the polar barrier. Even when we catch ourselves saying “One, Two, Three” our minds are collapsing the forces of dualistic thought into an apparent sequence of infinity. As some of you may well know, this marks a special place in our free creating reality. To the Greek mathematicians the digits one and two were the parents of all numbers, just like a mother and a father produce a child. Three is what actually began perspectival consciousness. This makes sense when we realize that the essence of the number three carriers with it a bridge that connects our conscious realm of thought to our emotional awareness. In this perfected balance of opposites it is said that our core ‘being’ can be found, just like the cerebral hemispheres of our brain are forced to have a middle ground in the so-called corpus callosum.However, I must advise that labels such as “thought” and “emotion” must be treated carefully due to the fact that in truth thought and emotion are but polar pairs of the same being and are thus one.

In simple artistic terms the number three is the comprehension of triadic activity such as black/white/grey, past/present/future, situation/conflict/resolution and various other scenarios. The most common and obvious example would be a simple triangle. Looking at a triangle is one thing, but if we are to learn from it we must construct one. Building a triangle is as simple as intersecting two circles, then dividing and connecting both of their midpoints (Shown in the Triangle Construction image). Seeing such a basic form might not be as enthralling to someone who can’t bear witness with fresh eyes from time to time, but for the few who don’t mind, try staring at a triangle for a number of minutes. A very core understanding of the number three can be felt from this experience alone. Countless artists, mathematicians, scientists, and religious scholars throughout history have referenced the triangular form as being of great importance, and for good reason. The form has been long known to hold a great many truths, and I encourage you to search them out. (I’ve included an illustration of what is called a recursive triangle, which is just a fancy way of saying self-similar replication, for contemplative purposes).

Mathematically speaking, having three separate integers signifies planar geometry and gives birth to mind’s idea of perspective. However, it would be wise to note that a ‘plane’ is purely theoretical and as such is merely the platform of what we perceive as substance, and not the substance of which it is a platform. This is of significance if we are to imagine this planar geometry in our minds. At this stage of creation perceivable dimensionality hasn’t yet taken place, but the architectural groundwork has been laid. Consider it an impossibly thin piece of paper stretched completely flat to a horizon of infinity. There are no hills or mountains, no valleys or brooks. In fact no compression or decompression of any kind exists on the surface, because in essence that’s all it really is, surface and nothing more. Distinctive attributes would require a further dimension for them to perceivably materialize (this will be discussed on the next article regarding the number four).

For concepts that are purely theoretical applying math is an easy way to gain insight. We might see that a triadic experience is simply a positive integer balancing out a negative integer by mutual negation and becoming zero (as shown in the Mutual Negation image included). This is about as simple as it gets. Three is then equal to zero in that it is the fulcrum of balance between the positive and the negative integer. This may seem a little arbitrary, but to the mind of the designer this subtle information is vital to understanding how not only we create, but how Creation creates.

I hope this article gave at least some positive insight into the workings of the designer mind. It may seem that we are going somewhat slowly in the process of these articles, but bear in mind that each step of this numerical process is necessary to explain how idea takes form, and thus how the mind understands that idea through form. Next month, we introduce the number four and physical manifestation.



  1. Cynthia Kukla says:

    June 19th, 2012at 11:01 am(#)

    This is fabulous. Are you familiar w/ Cecil Balmond, the engineer/architect? He examines design from a really fundamental way. Your work and thinking have a similar spirit.