Geometrically Ordered Design: Fantastic Four

July 29th, 2012  |  Published in Summer 2012



"The Canons of Vitruvius and Leonardo"

By: Dustin Pike

“The most incomprehensible thing about the universe is that it is comprehensible.”

-Albert Einstein

This is my fourth 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.

As we further our climb up the ladder of single digits, we come to the number 4. Last month I wrote of the number 3, and discussed its relationship with perception and planar geometry. Keep in mind that as of the last article we have yet to break into what is referred to as ‘physical geometry’, but with the introduction of the number 4 we do just that. If there is one idea that pertains to this number, let it be the very beginnings of physical solidification and stability forming what we call matter. Even the word matter comes from the Latin ‘mater’, meaning mother (which brings the term ‘Mother Earth’ to mind). Unlike the previous numbers, we now have something that is quite tangible. This is due in part to the fact that you need at least four points to manifest any three-dimensional object. The number 3 simply gives us our X, Y, and Z axis without the input of any usable data, but with the number 4 we begin importing data into our ‘reality’. As a simple example take the tetrahedron, which according to the Euclidean philosophers and mathematicians stands in as the first Platonic solid and rightfully represents fire (See Tetrahedron image).

So now that we know the underlying theme surrounding the number 4, where can we see this in artistic expression? All around us. Basically anything that you can sense or think of, which makes the number 4 easy to spot. Even simply thinking of something, although invisible to the naked-eye, creates a tree-dimensional sine wave that protrudes into space. This is why in societies, past and present, there has always been an emphasis on this particular digit (Main examples being North/South/East/West, Spring/Summer/Fall/Winter, Earth/Fire/Air/Water, etc.). The essence of this number provides us with the material necessary to manifest any desired action, but is not the action behind such manifestations. Action itself requires another step up the ladder to the number 5, which we will investigate in the next issue. Think of the 4 as being the canvas, paint, and paintbrush without the influence of the human hand in motion.

With the introduction of the tetrahedron, we also bring in the idea of the square (See Tetrahedron image). Of course, if we are to experience the square we must first construct one. There are many ways to do this, but to save some time I have supplied my favorite method (see the Construction of a Square image). When creating in this manner, I suggest imagining the square as an intelligent life-form of its own merit being birthed through the canal of the circle. In a purely metaphysical manner this helps to dissect the spiritual implications of the square. After having successfully constructed the square still yourself for a moment or so and take the form into your mind’s eye. Take note of the feelings and things that come to mind during this exercise, and focus on letting the form speak to you. The simplicity will often throw you out of focus, but do not be fooled for this is merely part of the square’s quadratic and imperial nature. It also helps to rotate the square 45º so that it appears more active or passive.

The Mathematical ideas that come along with the number 4 are too numerous to indulge in, but hopefully I can reveal one that may have escaped your notice. It has been said, due mainly to the interference of the ever elusive Pi or (3.1415…), that it is impossible to construct a circle with the same circumference as the perimeter of a square. It may come off as being unimportant at first, but it seemed to be important enough to drive artists like Leonardo da Vinci and his master Marcus Vitruvius into digging a bit deeper on the subject. (See the Canons of Vitruvius and Leonardo image). Without spoiling too much of their findings, there is a peculiar relationship between the circle/square when they are of equal proportion, and the triangle that is created from their marriage. As for those who still find this subject dull, this triangle just so happens to correspond precisely with the measurements of the Great Pyramid at Giza in Egypt (See the Proportion of the Circle and Square image). I won’t get into this idea too heavily as of yet since it strays us from the main point at hand, which is that the circle and the square share a mysterious mathematical relationship.

With any luck this article has at least sparked a fuse in the aspiring designer mind of the viewers out there. My hope is to let the everyday art lover in on some of the abstract secrets artists and designers use to employ their messages. Next month I delve into the aspect of the number 5, and with it the idea of physical motion.


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