nature's word : musings on sacred geometry

The Square Root of Two in Nature

The Square Root of Two in Relation to Uroboros, or the Division of Unity

To understand the idea of unity dividing, yet retaining its unified state, it is possible to try to learn more by looking at the original generating moment in the existence of a Human being. We look to the generating moment in a Human’s life to find a correlation between it and the generating moment of all creation. Both of these processes are intrinsically linked to one another, because both are governed by the generative archetype. The generative archetype encompasses the division of unity on any level – be it embryonic division to produce a new being, division of a plant’s seed to give birth to the greater plant (pictured at left), division of a perfect square to produce a new square, etc. This generation of many from unity is an undeniably huge part of the universe that we perceive, and thus the generative archetype (and the square root of two) is a huge part of our Human perception.

In quantum physics, a metaphor which is often used for explaining the movement and growth of the universe is that of a gradually inflating rubber balloon. If one were to take a rubber balloon whose surface was covered with dots and gradually inflate it, the dots would grow further and further apart from one another. At the same time, the dots themselves would be stretching out, expanding and becoming wider as the process continued. If we consider the dots to be groupings of dense matter, such as galaxies or solar systems, then we can see how the universe is continually expanding in all directions simultaneously.

Also in quantum physics there is a theory of a certain anti-matter particle which acts on the surface of this rubber balloon (the surface of the expanding universe) in a rather odd way.

It is believed that it is the nature of this anti-matter particle (symbolized by the small dot in the images) to cause the rubber surface to stretch inward, similar to the idea of one pushing their finger into the outside surface of the balloon (Step 2). This single, excessively tiny, particle continues to stretch the surface of space inward (Step T3), until eventually the surface of the balloon closes behind it – leaving the particle inside its own tiny “rubber” sphere, completely cut off from the original universe from whence it came (Step 4). The particle is now alone inside its own universe, yet within the sphere of the greater universe to which it originally belonged. A new separate and whole universe has been created within a greater universe.

This new universe contains only the matter of the anti-matter particle, and that matter (for reasons which quantum physics cannot yet explain) begins to expand. The expansion causes the surface of the sphere it is contained in to expand just as the original balloon metaphor above illustrates. The process continues, and the smaller universe expands just as the larger universe encasing it expands as well. At some point, another anti-matter particle affects the surface of the smaller universe, and causes the generation of another smaller universe within our new universe. It is believed that this process of universes generating new separate universes within themselves is occurring continuously, throughout our universe, the universes that spawned it, and the universes that it has spawned.

Now, with that in mind, let us look at the process of generation which occurs in the female reproductive system.

An egg is released from the ovary and becomes fertilized by the male’s sperm at some point in its decent through the fallopian tubes to the uterus. Upon fertilization, the chromosomes within the egg mix with those introduced by the sperm’s presence. The two sets of chromosomes combine, reproduce, and separate, moving to opposite poles of the spherical egg’s interior environment. Notice the polarization here – a perfect representation of a forming duality.

Then the magical moment occurs – the single cell of the egg divides down the center, creating two separate yet identical cells, both of which contain exact duplicates of the original set of combined male and female chromosomes. The process of chromosomal replication and division repeats in both new cells simultaneously, and the two cells each divide at the same moment, creating four exact copies of the original cell. The four divide to become eight, which divide into sixteen, then thirty two, sixty four, etc.

As the cells reproduced by the power of two, they begin to differentiate, with some cells becoming building blocks of the internal organs, while others become muscle, bone, tendons, and all other types of cells within the body. Despite this differentiation of cell type, all of the cells in their central nucleus retain exact duplicates of the genetic information which was housed in the set of chromosomes produced by the original generative moment when egg and sperm combined.

Now let us see the possible similarities between this generative process and the greater generative process of the quantum physics theory discussed above.

For this comparison, we will consider the anti-matter particle and the sperm to fulfil the same role – that of fertilizer. Both enter into a separate spherical realm which is primed for generation, yet requires the addition of an outside element to initiate the generative process. In the generation of an animal, the separate fertile environment is, of course, the egg. In the generation of a new universe, the fertile environment is that of the universe itself – that is, the “rubber surface” of the new universe, which is made up of material from the original universe that spawned it. This “rubber surface” material is clearly fertile, if it is considered that it consists of the basic universal stuff that our universe consists of, which is forever generating new phenomena as it moves and grows.

It is the basic nature of both egg and universal material to grow and produce new life, yet both require the fertilization of an alien “other” – the male seed. Once this initial fertilization has taken place, the male power has served its purpose, which is that of allowing the fertile material to reproduce and grow. The individual unity that is the egg or the new, egg-like universe, reproduces not by strict division (which would leave only half the original material in each new cell), but by multiplication. It is here, once again, that we witness the paradoxical miracle of the square root of two – generation which creates not by dividing unity into two separate unities alone, but by multiplying unity within the original unity.

It is this very miracle that the quantum physicists have not grasped in relation to the unexplained expansion of their theory of generation of a new universe from an anti-matter particle. The answer is nowhere to be found, just as the answer to why a single cell divides and reproduces in the way it does cannot be found, and just as a definite value cannot be assigned to an irrational number such as the square root of two. In both cases, we can observe the process which occurs, but our intellectual minds cannot perceive the mystery which lies behind the process. Instead, we must grasp with our wisdom and intuition that it is simply the intrinsic nature of the fertile universe to grow and expand once it has been fertilized, just as is so with an embryo. If we can see the connection that any universe is nothing other than an embryo on a greater scale, then it only makes sense that the newly created universe would begin to reproduce from itself and expand into an entire, complex, differentiated yet wholly unified being.

This example is the best that I can offer to describe the generative power that is expressed in the square root of two. The square root of two is the division of a single unified seed that leads to multiplication within the seed, and creates an ever expanding unity that never separates from the original seed that gave birth to it. Thus it is possible to perceive a universe divided into countless individual forms, all of which are intrinsically tied together into a single unity by the seed from which they came.

To see this generative power at all levels in the world around and within you is to understand the square root of two at its core. To feel the relation of all differentiated forms generated by the square root of two to the original seed from whence they came is to understand the power of one-ness, or universal unity. We will explore in Lesson Four how the number Phi is the vehicle through which we can understand the relationship between differentiated form and the encompassing whole.


Duality and the Growth of Human Consciousness

Now let us turn our attention to what the square root of two means to the human consciousness – not as a geometric figure, but as a fundamental part of human perception and understanding.

The most direct interpretation of the line that measures the square root of two is that it is that which divides unity into two perfect, apparently opposite halves. With the spanning of the square’s diagonal, we have created two triangles – exactly similar in every measure, yet opposite and separate from one another.

The ramifications of the simple act of dividing unity into duality is so vast as to be barely comprehensible. At the most basic level humans perceive and understand their environment by comparing and contrasting opposites. In the human consciousness, with the exception of a few states of being – specifically understood as spiritual or religious states – every time a quality is perceived, there is an immediate juxtaposition against the opposite quality which is automatically effected long before conscious perception occurs. Thus we derive our understanding of everything by observing how much of one quality, as opposed to it’s opposing quality, a thing possesses.

Everything that we take in from our environment comes through this filter of duality, and it is the basic creation of dualistic perception which leads to the eventual growth of individual intelligence and personality as it is known to exist in humans today. In this way it becomes very clear why the square root of two is known as the “Generative function” – the square root of two generates the universe as it is perceived in the human realm.

The number of pairs of dualities that the human mind employs in its search for understanding the phenomena which manifest around and within it are literally infinite – no list could ever begin to scratch the surface of possibilities. But certain pairs are more archetypal than others – dualistic motifs that come up over and over in every human experience. All of these pairs appear very simple on the surface, but it would seem that it is these simplicities which can effect our experiences the most. Examples include day and night, light and dark, life and death, summer and winter, male and female, good and evil, love and hate, earth and sky, passivity and aggression, creation and destruction, spirituality and materialism, and inner self versus outer world. The list could continue without end.

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4 Responses to “The Square Root of Two in Nature”

  1. Farzana says:

    The dot in the image shown above cannot be called an anti-matter. It is an external matter particle indeed that approaches the balloon like substance and comes in contact to it.

  2. Kias says:

    Thanks for the awesome read :) really enjoying your site.

  3. Leslie Taylor says:

    “Once this initial fertilization has taken place, the male power has served its purpose, which is that of allowing the fertile material to reproduce and grow.”

    Let me see if I can guess … a man a wrote that.

  4. Mon Soon says:

    Not only is the knowledge freely shared, it is very well guided towards a comprehensive understanding of the broadening subject matter. Congratulations!

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