To begin our study of sacred geometry, also know as Contemplative or Philosophical Geometry, it is only logical that we start with the beginning. For sacred geometers, that means starting with the number one.
In order to understand how sacred geometry views the number one, or any number for that matter, we must come to understand the essence of one-ness. That means that when pondering the true meaning of a number, we must consider not only the literal meaning of it (in this case the number one – one thing, one actual physical object), but instead we must consider three separate forms of it. Those forms are the typal form, the ectypal form, and the archetypal form.
The typal form is the literal, actual form of one. As stated, it means one physical thing that exists as an actual tangible object. The typal form is the most diverse and variable of the three forms, because there are an infinite variety of physical things that we could label as “one thing.” Thus the typal form tells us the least information about what is at the essence of one-ness.
The ectypal form is that which exists as an unmanifest idea – in other words, the idea that there is one thing. Because of its very nature as a product of abstract consciousness, the ectypal form is a much more formal and pure form than the typal form. The ectypal form of one does not have nearly as many possible variations and diversifications as the typal form has, and that is why we can say that the ectypal form is closer to defining the essence of one-ness.
The archetypal form represents the universal process associated with the number, and it is this form which is the most profound and important to us as students of sacred geometry. The archetypal form is certainly the most abstract form of the number, and yet at the same time it relates directly to processes which occur in the typal realm. It is precisely this dual application which gives the archetypal form its “sacred” nature. By claiming that there is a universal process associated with a number, we are saying that one-ness applies to everything – that nothing is exempt – and it is simply for us to come to understand how everything that is relates to the true essence of one-ness.
The archetypal form is that form that leads us to the fullest understanding of the essence of number. It is important to understand, however, that even the archetypal form does not ever lead us to a final answer, but instead simply starts us down the path of understanding.
It is easy to comprehend why this is so, if one considers that when pondering the archetypal form of a number, one is considering how that number relates to all things. Thus, there will always be more to relate to, and therefore one’s understanding can continue to grow in depth for as long as one is willing to take the time to look for relations.
Once again, the nature of this continual contemplation and growth speaks volumes to why the term “sacred” has been applied to this particular study of number. In sacred geometry, an expression such as 1+2=3 never expresses something easily definable and finite. Instead, this equation would be viewed as a starting point to expand one’s understanding of a universal truism, i.e., one-ness added to two-ness creates three-ness.
If one understands the basic symbolism behind the three numbers in this equation, an eternity could be spent coming to understand just how true it is that in all aspects of the changing universe, one-ness added to two-ness creates three-ness. It is simply a matter of how deep the geometer wishes to delve into a particular idea. Our example in this case is a bit of an over-simplification of the philosophy behind sacred geometry, but the truth which it points to is sound.
That brings us most directly to another very important definition of sacred geometry – that being that sacred geometry is simply a filter, a vehicle, which we can use to approach our lives with an attitude of reverence. If we wish to gain insight into the nature of life, then the answer is within the word “insight” itself – in-sight. Look in. Look at your life. Anyone who wishes to learn need only look. When we begin any geometric exploration in sacred geometry, we always begin with one point. From that point we grow outwards using compass and straightedge, and by doing so can create complex interrelations, all of which relate back to our original point of origin and unity. In the same way we can explore our experiences of reality – by using sacred geometry as our initial point of reference, to which we can always refer back to as our journey of exploration continues.
We as human beings have a consciousness firmly based on two-ness (we will return to this later) and consequently we have a hard time perceiving the fact that all things are in fact unified, i.e., one thing. But it is indeed true that all things are unified, and it is possible to come to a true understanding of how and why this statement is true. Actually, the foundation of most, if not all, schools of mysticism is the idea that we can come to perceive directly the unity of all things, although some schools state this fact a bit more blatantly than others.
Before moving on, it is important to address the issue of zero. When reading the first paragraph of this chapter, some people might have thought, “But number does not start with one. It starts with zero.” Unfortunately, as sacred geometers, we must deny the value of zero completely.
Zero is a comparably late add-on to mathematics which was brought to the west from the nihilistic Shankara (Hindu) and Narayana (Buddhist) tradition of India in the 1600′s. It serves nicely as a place-holder in our Arabic numeral system, but in fact zero has no place in reality what so ever, and thus it has no place in sacred geometry.
Zero is not a true number because it possesses only one of the three forms we use to understand number in sacred geometry. In the typal realm, zero has no meaning because there is no such thing as “nothing” in the manifested world. Modern physics proves beyond a doubt that there is no such thing as a vacuum or a void – the absence of everything, or zero – anywhere in the universe. No matter how empty a space may appear, there is always something in it, even in the deepest, darkest regions of space.
There is no archetypal form of zero, either. It is impossible to say that there is a process of nothingness which effects all things, because even if there were such a process, that process would still be a process, and thus it would be something. For example, let us take a look at the process known as decay. Decay could be said to be a process of nothingness – the negation of something, and thus a process of nothingness. But decay actually is a process of breaking one thing down into another thing. The things involved never cease to exist completely, but instead simply change from one form to another. Thus, there is no nothingness which is ever achieved – only change.
So we are left with the ectypal form of zero – that is, the abstract idea of nothingness. The reason that the ectypal form of nothing exists is because of the dual nature of human consciousness. If we can perceive that there is something, than we can imagine the exact opposite, in this case that there is nothingness. But, unfortunately, there is no such thing as no-thing, and it is only because we have been misled by our educators, purposefully or not, that we as a culture put so much stock in such an idea.
all materials copyright 2010, Aidrian O'Connor