15 Object Versus Symbol II: About Symmetry

The Symmetry of 1

“God said: You are a nomad, you know. Even on Earth, you are traveling in space, in what is called space. I say you are a nomad because you are a traveler. As a matter of fact, you hop from pillar to post. We can call the pillar Heaven and the post, Earth, even as space and place do not truly exist.

And, yet, for all practical purposes, that is, Earth purposes, you are somewhere, always somewhere, hither and yon, Heaven and Earth. You are on the rebound from one to the other. You are more constantly aware of Earth. It is like a bird’s nest in a tree. You call it home when your True Home is seemingly farther away from you even as Heaven is as close to you as I am, and that is very close indeed.” HL 4475 

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In this second blog on “Object Versus Symbol”, we will approach objects, symbols, and their relationships through the symbolic language of mathematics and geometry. But no technical or mathematical knowledge is a prerequisite. Observation of the surrounding world is all that is needed.

The symbolism of symmetry

Symmetry is a symbol, a geometric relation, a programmed organization of space and time by the mind.

In the relative world, we perceive symmetry (in Greek, sum-/sun- “together, like” + metron “measure” ) as the exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis. Symmetry is also associated with proportion, a part considered in relation to the whole.

Most human constructions are symmetrical, according to the above definition. And symmetry is interpreted by the mind according to the law of opposites:right-left, up-down along a dividing plane. It seems that the whole or unity of an object (especially objects constructed by the human) gets its reality or meaning from the addition, connection or relation of two halves ½ + ½ reunited on opposite sides of each other by an invisible, imaginary dividing line, plane or about a center or an axis.

And these two halves are a mirror-inverted reflection of each other. We can easily see those two horizontally mirroring halves reunited by the imaginary dividing perpendicular straight lines in the picture of the temple. It appears that everything in the world is produced by twoness (two halves) and unity is a result of twoness. This is the principle of duality: one is produced by two, it takes two to make one, but the premise is “two halves to start with”. But what is a ½ (half) by itself? Is ½ composed itself of 2 halves? Then the ultimate constituent of matter would be ½ -> ¼ -> 1/8 -> 1/16 -> … -> 1/∞ which, in mathematics, is equal to 0 (zero). One would then ask if there are such things as opposites or halves?  We could go even further and ask if two ultimate halves will yield 0+0=1.

Let’s go further and examine symmetry in a plane mirror (the vertically reflected image of the temple through the mirror of the water). When we place an object (source) in front of a plane mirror, the image seems to be on the other side of the mirror at an equal distance from the mirror as the object. The image is also inverted on the horizontal plane: what pertains to the left on the object in front of the mirror appears to pertain to the right in the facing image. Just think about the cat looking at itself in the mirror and going around the mirror to meet the “other” cat behind or on the other side of the mirror. An image does not oppose to the source because it is projected by the source. But the mind can trick itself by projecting a shift of location of its point of reference or point of observation to the plane of the mirror. We could say that the mind has the power to “split” itself, assuming a new observation position by eclipsing its original one. It is as if the mind momentarily decided to forget what it originally is to become a new observer, separate from, and even forgetting its original self. The mind starts dreaming of a new world of symmetrical forms ad infinitum not knowing it is the source of the spectacle. By this shift of the mind of its observation position towards the plane of the mirror, the illusion of depth and inversion through the mirror is generated. The mirror is a device used by the mind to project itself into seeming different entities that seem to oppose us by facing us but there is always only one source. There are no real opposites. Twoness does not really exist, only oneness is.

So what are the seeming two halves really made of? If opposites don’t really exist and there is only one,  it must be that one of the seeming opposites is not 1/2 but 1 and the other opposite is just a projection of the other. Hence it’s value is not 1/2 but 0 and 1+0=1, which is arithmetically consistent (more than 0+0=1). Symmetry in the outside world appears as an impossible 1/2+1/2=1 while the concealed symbol is 1+0. Furthermore, 0 is associated with the idea of absence, especially in the binary mathematics of computer 00011111000111000011  yet, in mathematics, 0 paradoxically expands the numbers: 1, 10, 100, 1000…

Could it be possible that what we perceive as an absence, a zero, is, in reality, a container, a void that can house a content which is 1? A house is made of a floor, a ceiling, doors, windows but it is the actual void inside the house that makes it habitable (TAO). A container must be an empty space if we want to be able to put something in it.

A symmetry without halves, without opposites

Let us take a look at the picture of the coffee bean below. Does the “dividing” line that we see on the coffee bean reunite the two sides or two halves of the bean? Is the coffee bean constituted by the reunion of its two halves on opposite sides of its dividing line? No, the bean has no halves and is not the result of assembling the two halves around an imaginary dividing line. The seeming dividing line is a curved, spiral 1, the oneness that creates the physicality of the coffee bean. The figure between the coffee bean and the Yin Yang symbol illustrates very well how the invisible 1 generates the symmetry of oneness, wholeness without the need of opposites. This figure is the symbol of what could be called the ultimate physical atom or the vitality globule which expresses the pure relation of Oneness with Itself. It also expresses life as a pure “internal” reality.                                       3 representations of the Symmetry of 1
[source of the image in the middle: C.W. Leadbeater, The Chakras, The Theosophical Publishing House, Madras, 1969]
The symmetry of the human body is not built along the reunion of its 2 opposite halves on opposite sides of an imaginary dividing line or plane but around this spiral 1 (the spinal cord perhaps?) that generates both the content and the container of the body. The zero (0, circle) is how the 1 extends itself. Zero has the morphology of a vibrating, spinning atom generating all the multiple forms of the Universe.

Since symmetry in nature is not built on twoness but on Oneness, what seems to be the reunion of two halves is, in reality, One winded up around itself, establishing a relationship with Itself. And this relation with Itself is called love, harmony, music, light, joy, peace, abundance. In music, all the 12 notes of the scale in an octave (the white and black keys on a piano) are generated from one single note (not two notes) or one unit string (let’s call it C). It is like clapping hands with only one hand. All the other notes are generated from this 1 note.  1 is the only Reality and it is the only real symbol, the only real sign of recognition, the only relation. The unit string, yet physical, is also a pure relation. A proportion of 2/3 of the unit string (the key C for example)  creates the string or note (G), which is the fifth note. Then G creates the string D, D creates A, A creates E, E creates B, B creates F#, F# creates C#, etc until we get the 7 white notes and 5 black notes of a scale in an octave on a piano (the chromatic scale). And if we reverse the ratio 2/3 of the fifth note (G), we obtain the frequency of the note G which vibrates 3/2 times faster than the note C. This is the symmetry in nature. It is produced by the number 1, not by the number 2. And curiously enough the core of the dynamic symmetry of nature is not the number 2 but the number 5. Some readers will already have guessed that I had in mind the golden number, the golden proportion, and the golden mathematical series like Fibonacci’s but we won’t discuss them in this blog.

Symmetry in nature is generated by Oneness where 1+0=1 appears in a multiplicity of forms based on sameness, likeness while the artificial symmetry in human constructions, perceived by the split or shifted mind, is based on twoness where 1+1=2 or ½+ ½ =1, seemingly based on unlikeness generating unlikeness. Imagine now that the “dividing” line we observe on the coffee been is not an imaginary line but the radiating axis, the pillar, along which the form of the coffee bean winds and weaves itself. It is the same invisible line that creates the vortex, the tornados or cyclones. It is also the eye of the cyclone, perfectly motionless while the surrounding world is spinning around. Symmetry in nature is not the reunion of two halves, it is a whole creating a whole. A relation is always ternary; it takes a minimum of two, and a mediator that connects 1 to 2. Let’s call the number 3 the “Holy Spirit” who provokes the “reaction” between 2 and 1 by dividing 2 by 3, the product of the division (in reality it is a multiplication) yielding (in music) the G key and subsequently the 12 major chromatic scales and 12 minor scales.  If we wanted to use the term “half” in the symmetry of nature, we would have to say that the first half is the content and the second half is the container. The content (idea) projects itself in a container creating the illusion of twoness. But it is only Oneness. The mind is tricked and thinks that duality is real. The mind has temporarily forgotten what it was, thinking that it is something else.

How the mind can trick itself

The mind tricks itself by believing in the absence or in the separation from 1, that is from its own source. Only the belief in absence or separation from 1 can fabricate the illusion of multiple separate objects in the world. This is done by thinking that 1/2+1/2=1 instead of thinking that 1+0=1. We think we were created from the outside or that we created ourself. To project this belief in absence or separation, we have said that the mind projects a shift in the location of its point of reference or point of observation to the plane of the mirror. Let us examine this shift of point of observation with the geometrical graphs below. These graphs represent what is called in geometry an asymptote. You won’t need to be a wizard in geometry to follow my reasoning. Just retain that an asymptote is a (straight) line whose distance to a given curve tends to zero but never intersects the curve (greek: a- “not” + sum- “together” +ptotos “falling” hence asumptotos means “not falling together, not intersecting”. [In contemporary mathematics, it is now said that it may or may not intersect its associate curve, but we will stick to the original meaning of the asymptote where it tends to zero without intersecting].

Let’s imagine that the curve (hyperbole) in the upper right quadrant of the perpendicular straight lines represents the Source, Oneness, number 1. The curve in the lower left quadrant is only a mirror image of the preceding one. It represents the universe of forms (earth). The x-axis and y-axis are asymptotes of the hyperbole XY). The system of coordinates, horizontal and vertical, classically named x and y-axis — let us forget a 3-D representation with the z-axis — represents the shift of location of the mind (its separation) in space and time coordinates which are defined by the plane of the mirror. The mind creates to itself the illusion that it is sitting or walking on the coordinate x-y lines between the two curves. It is as if the two perpendicular straight lines created a plain mirror where unity sees its image on the other side of the mirror at an equal distance from the mirror.

We seem to live in a metaphoric world and we effectively do. We think we are walking at the surface of the Earth. But are we really touching the ground? Walking on earth is really walking on a bunch of zeros and ones (0011000111100010…). Think for a moment that when you look at a web page, if you select the .html menu, you will see only cryptic codes. The image is entirely generated by programmed code in a specific computer language. Now think that the visible universe, including our bodies, is also an image (or multiple images) generated by a very highly sophisticated programming language (using light perhaps) used by the mind and interpreted through the five physical senses. The outside Universe is just an illusion created by a very powerful computer (the mind) with an incredible power of crunching numbers and binary code of 0s and 1s, or atoms and quanta.

So, in the relative world, we seem to walk on an asymptote, not really intersecting Heaven and not really intersecting the earth. We are literally in between. Our mind is split.  It seems that we are nowhere even if we hold mentally to the time/space coordinates of the earth.

We come to a point where we realize that it is impossible to stay in between. We have a choice to make. We cannot approach the outside reality (from behind the mirror) in order to find the Truth (the source in front of the mirror). We cannot touch the Spirit by touching the matter. We cannot touch the Truth by touching the illusion. We cannot even really touch the matter because it is only numbers and codes. Reality is not something. It is everything and nothing at the same time. It is 1. Objects in the outside world can approach Reality but without ever being able to touch it. This is probably the origin of the feeling of lack, separation from our Source. Either we traverse the mirror (“through the looking glass”) to join the image and continue experiencing the virtual reality of the personal self we created or we shift again our point of observation to where it was initially. Ultimately, death might be only the decision not to choose—that is choosing to stay behind the mirror!—. Or it is where and when we leave the asymptote to join the hyperbole 1, where we come from and from where we never really departed, only in a dream. The mind has to wake up from the dream and shift back to its original position: the center of everything.

“You call it home when your True Home is seemingly farther away from you even as Heaven is as close to you as I am, and that is very close indeed.” 

Written by Normand Bourque on Feb 19, 2013