Tuesday, May 15, 2018

Sacred Geometry and the Human Body - Realizing the Cosmic Significance of Our Biological Design


Why is it that we consider the human body to be such a beautiful thing? We see its amazing capacity for strength, flexibility and its ability to do seemingly impossible things, but what is it that makes the human form seem so aesthetically balanced and naturally harmonious in appearance?


Most seem to agree that the human body is a work of art in form and performance. Though in one sense, we may consider the female form to be more aesthetically pleasing, in general, we can agree that the body, at its best, is an amazing thing.

If we look at the psychology behind our preference for that which is aesthetically pleasant about nature (as opposed to artificial industrial structures), we may notice there is a distinction within natural forms. In fact, there are several factors and actual mathematical consistencies which we can observe in the natural world which create aesthetic appeal as well as universal harmony in our human perception. These factors appear to be finite in nature, and yet they seem to appear in countless contexts throughout the universe.

What are these factors, you might ask? Let's explore.


The Golden Mean

We call it the Fibonacci spiral, the Golden ratio, phi ratio, the Golden mean, and other titles, but what is this geometric phenomenon? Why is it significant, and why does it continually manifest in so many iterations throughout the universe?

Whether we are familiar with the equation or the graphical representation, the Golden mean seems to be expressed in countless context in nature—both on our planet and beyond. At the same time, this ratio seems to be etched into the our human psyche at the foundational level.


For our exploration of the mean's significance in the human body, let's consider a few details.

The Golden mean seems to express itself in virtually every facet of the human form. We might keep in mind that this ratio only represent the ideal human body and may not be expressed in exact proportions. However, in general, it seems that our bodies follow this mathematical template rather well. To demonstrate, here is an interesting article by the website Sacred Geometry on the intricate expression of geometry in the human form.

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Source: Sacred Geometry

Published: July 2012

By: Jordi SolĂ -Soler 

Phi in the human body

1. Introduction

Marcus Vitruvius Pollio, Roman architect (c. 25 B.C.), remarked a similarity between the human body and a perfect building: "Nature has designed the human body so that its members are duly proportioned to the frame as a whole." He inscribed the human body into a circle and a square, the two figures considered images of perfection. It is widely accepted that the proportions in the human body follow the Golden Ratio. In this article we will review some studies on the subject. We will show the nineteenth century findings of the Golden Ratio in the human body by Adolf Seizing, actually approximated by a Fibonacci sequence of measures. Then we will examine the Golden proportions of the human body proposed by architects Erns Neufert and Le Corbusier in the twentieth century. Finally we will show how a common study with a German and an Indian population samples confirmed the presence of the Golden Ratio in some proportions of the human body.



2. Golden proportions in the human body found by Adolf Zeising

Adolf Zeising's main interests, back in the nineteenth century, were mathematics and philosophy. But after having retired he began his researches on proportions in nature and art. In the field of botany, he discovered the Golden Ratio in the arrangement of branches along the stem of plants, and of veins in leaves. From this starting point he extended his researches to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, etc., and finally to human and artistic proportions. The title of his first publication in 1854 declares his program: New theory of the proportions of the human body, developed from a basic morphological law which stayed hiherto unknown, and which permeates the whole nature and art, accompanied by a complete summary of the prevailing systems [1]. That universal law was, in efect, the Golden Ratio. There he presents his own proportional analyses of the human body (Figure 1).

Figure 1: Golden proportions in the human body found by Zeising [1].

Zeising divides the total height of a man's body into four principal zones: top of head to shoulder, shoulder to navel, navel to knee, and knee to base of foot. Each zone is further subdivided into five segments, which are arranged symmetrically within each zone: either following the pattern ABBBA or the pattern ABABA, but always summing up 2A+3B. By the way, the 3/2 proportion in each zone is a Perfect Fifth in the equal temperament musical scale. Is music involved in the design of our own body?

On the right of Figure 1 you can see the Golden proportions present in each of the segments, and between them, at different scales. Zeising's proportions of the human body are a beautiful example of how Nature closely approximates the Golden Ratio by means of a Fibonacci sequence of measures. Zeising erroneusly substitutes 90 for 89 in his measures, but we have used the exact value in the following calculations. The Fibonacci numbers present in his scheme, explicitly (green) or implicitly as grand totals (magenta), are the following:


Grouping consecutively each pair of adjacent measures one obtains an iterated division of the big segment (987) into consecutive Fibonacci numbers that closely approximate the Golden Ratio (Figure 2a). This reminds us the power of the Golden Ratio for consecutively dividing a segment with simple additions and substractions after the first split (Figure 2b). This sequence of Golden Ratio divisions also reminds us of the fractal nature behind the design of our body, because the same Golden proportion is repeated at all scales.

(a)

(b)
Figure 2: Iterated division of a segment according to (a) the numbers in the Fibonacci sequence and (b) the Golden Ratio.


3. The Golden proportions proposed by architects Neufert and Le Corbusier

In the twentieth century the architect Erns Neufert (1900-1986) propagated the Golden Ratio as the architectural principle of proportion in the human body. Neufert did not strictly follow Zeising's human Fibonacci proportions, but introduces the exact Golden Ratio instead [2] (Figure 3). For him, the Golden section also provides the primary link between all harmonies in architecture.

Figure 3: Golden Ratio proportions of the human body after Ernst Neufert [2].


There is another great system of body proportions of the 20th century known as the Modulor, proposed by Le Corbusier (1887-1965). In his manifesto Vers une architecture, he presents the Golden Ratio as a natural rhythm, inborn to every human organism. For details on the historical origin and developement of Modulor I and II systems you can examine the excellent summary by architect Manel Franco [3]. Figure 3 shows the essential proportions proposed by Le Corbusier for the human body:

Figure 3: Simple sketch and main Golden proportions in the human body proposed by Le Corbusier [3].

In his final version, the Modulor II system proposes two Golden progressions of measures for the human body (Figure 4a). Returning to the style of Zeising, these progressions are actually two Fibonacci sequences of measures (Figure 4b). That is to say, each measure is obtained by the sum of the two preceding ones. Therefore, the ratio of any pair of consecutive values in these progressions closely approximates the Golden Ratio.

(a) Golden proportions in the human body proposed in Le Corbusier's Modulor II.
(b) Detail of the red and blue progressions (in mm) in Modulor II. The ones in italic
slightly deviate (1mm) from an exact Fibonacci sequence
Figure 4

Read more at: Sacred-Geometry.es

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The diagrams above represent an astonishingly consistent pronunciation of the Golden mean and phi ratio within various comparisons of dimensions in the human form.

These proportions seem to be consistent within the male and female anatomy, though these expression do vary. It does seem that the female form has a greater expression of the Fibonacci spiral than the male form. This does not only manifest in the form of proportions, but seems to appear with a greater level of overtness within the female body, as though nature is somehow showing off.

We will not display the images here, but anyone can google the topic of the Fibonacci spiral and female anatomy and they will see the ways in which the spiral itself is the main component which makes the female form so visually appealing. The male form does not have the same overt expressions of the Fibonacci spiral, and this may be why in a visual sense, the male form is not as attractive as the female.

We have seen extensive evidence that the human form is much more than a randomly generated expression of happenstance. More so than anything, this pronunciation of phi ratio appears to be a universal and mathematical constant, expressing itself in countless ways in our perceived reality. But how could a mathematical form be so common and yet be so various in its expressions throughout nature?

The answer may lie in resonance.


Frequency and Form

By now, most are familiar with the study of cymatics. This is the science which observes the effects of harmonic tones of sound on fluid systems such as water combined particles of sand. The fact is that when perfect harmonic tones are generated into a fluid system (such as the notes on a musical instrument), they produce consistent geometric structures manifesting in fractal patterns throughout the fluid. From these experiments it was learned that sound and frequency have the ability to create geometric forms without any other input into the fluid system.

3-dimensional, cellular patterns created with sound, sand, and water

Demonstration in the study of cymatics

It was theorized by Dr. Hans Jenny—a Swiss medical doctor and creator of the study of cymatics—that matter was somehow sustained by this sound or by wave-forms of some kind. Richard Buckminster Fuller (the famed architect, systems theorist, author, and designer) and Sir Roger Penrose (physicist, mathematician, and philosopher) were two other established scientific figures who studied this phenomenon of regularly occurring geometric patterns in the universe. When we combine the studies of these three figures, we will likely come up with a new universal observation.

It may be that the fabric of spacetime itself is similar to a fluid substance. It may also be that the reason matter exists within this universe is that matter is continually sustained by some universal geometric constant or frequency. Further, it is possible that this universal force of frequency initiated the beginning of the universe and continually creates and sustains the material structures we see distributed throughout it.

Adding to the theory of a geometric universe are two Prinston physicists—Nima Arkani-Hamed and Jaroslav Trnka. In a groundbreaking research endeavor, these two physicists built on the worked of Sr. Roger Penrose and made a discovery that may have very well changed the field of quantum physics forever. Here is a description of their achievement from Discover Magazine.

“A new computational insight in 2004 dramatically reduced the amount of paper required to describe a collision, and these new formulas combined multitudes of Feynman diagrams into a single mess of math. Last year, Princeton physicist Nima Arkani-Hamed was analyzing the formulas in search of a better way to simplify these quantum calculations. Using only pen and paper, he discovered a new kind of geometric shape called an amplituhedron — one that hints at a new way of seeing the universe.

Arkani-Hamed noticed the formula could be rearranged and still yield the same answer. Like paleontologists brushing away dirt to reveal a fossil, he and his colleagues found the pieces of a shape within the math — pieces that together form a multidimensional amplituhedron. The shape’s dimensions — length, width, height and other parameters (hence “multidimensional”) — represent information about the colliding particles, and the equation describing its volume also describes the particles that emerge from the collision.

This result, the volume, is a single term that fits on a space the size of a napkin.”


Each of the figures discussed above have gathered a plethora of mind-expanding knowledge, and their work deserves adequate attention in order to be fully appreciated. However, for the sake of time, we will spare the finer details.

If we are familiar with the work of the late Richard Feynman, we will be familiar with the concept of the Feynman diagrams. These equations are designed to calculate all of the possible trajectories of quarks (sub-atomic particles) during experiments in quantum physics. To put things into perspective, these Feynman equations are so complex that they literally take 90 to 100 pages in order to solve just one. However, Arkani-Hamed and Trnka just happened to find a simple geometric form that helped to solve every last permutation of the Feynman equations.

Graphical representation of the amplitudedron

The findings of Arkani-Hamed and Trnka served as proof that it the fundamental level, the universe is actually founded upon sacred geometric patterns repeating in regular intervals, much like a crystal. This discovery had profound implications for both quantum and astrophysics, and may even help to prove our point here.

If we are familiar with the scholarship of researcher, public speaker, and author, David Wilcock, we will be familiar with the relationship which the amplituhedron has with sacred geometry. As we can see, the amplituhedron (above) is formed of four tetrahedrons.

The star tetrahedron


When four amplituhedrons are combined, they form a perfect star tetrahedron (a manifestation of the Platonic solids), and as we may know, according to the frequency-based theory of the universe, whenever one iteration of the Platonic solids manifests, the rest tend to show up as well.

This manifestation of spherical geometry as the foundational form of the entire quantum universe further supports the theory that the universe—from its most minute infinitesimal scale to the broadest aspects of the cosmic infinity—is governed by sacred geometry.

We see this trend quite often in modern science. In virtually every field of study, the most complex and tedious work in which scientists spend years to simply understand the nature of the universe, all of the most astronomically complex problems wind up being solved simply by applying the concept of sacred geometry to them. So what does this have to do with the human body? The answer is quite simple and yet exceptionally profound.


Close-Packed Spheres

Back in school, many of us studied the scientific concept of close-packed spheres. This explanation is typically used to describe the relationship between atoms and molecular arrangements in solids. However, as we may have observed, the subject of sacred geometry and Platonic solids is much more complex than public education reveals to us.

As we may know, the connection between the Platonic solids, close-packed spheres and the Fibonacci's curve is quite consistent in a number of ways. At the fundemental level, phi ratio is written into Platonic geometry. 


The relationship between phi ratio and and Platonic geometry

Also, as the Platonic solids are interwoven (as each of these solids fit inside the others with striking symmetry), their relationships reveal clear instances of phi ratio. And as we know, these geometric solids are fractal and spherical in nature. As they fractalize outward, they form an arrangement of close-packed spheres.

Note the sides of the tetrahedron bisected by the blue line.

"Given an equilateral triangle ABC, erect a square BCDE externally on the side BC.
Construct the circle, center C, passing through E, to intersect the line AB at F.
Then, B divides AF in the golden ratio."
Segment AC is bisected by line BD.
 The intersection created depicts the golden mean for both segments.

These spherical arrangements (in that all of them fit perfectly inside of a sphere) appear to be the fundamental aspect of all of physical reality.  From the quantum level to the cosmic scale, everything which exists appears to have a form to which close-packed spherical arrangements can be applied. And of course, this arrangement also applies to the development and anatomy of the human body.

As it turns out, close pack spherical arrangements manifest from the first moment of conception in the ova cell. After fertilization takes place, the ova cell begins mitosis. Following the second cellular division, a clear tetrahedron is formed from the spherical cells.



As the process of mitosis continues, the cells may form a star tetrahedron. This star tetrahedron then becomes a cube octohedron. From this point, the embryo begins to complexify, and baby develops from then on.


 


The Fibonacci's curve also appears to be expressed indirectly through the development of a child. Throughout the development of a human being into adulthood, the form of close-packed spheres is apparent, though it can be easily missed if we do not know where to look.

Many of us may actually be aware of this form, though it is rather rare that this form would be related to the human body in the way we are referring to.

The flower of life

We might be aware that the flower of life is a two-dimensional expression of a three-dimensional pattern of close packed spheres. The shapes which are expressed within this pattern are numerous. However, the overall idea is consistent no matter the arrangement. In essence, the pattern of close-packed spheres may extend outward into infinity, but for our purposes the pattern only needs to fractalize inward.


Flower of life and human dimensions - simplified for visual comprehensiveness

The above image shows just how much significance the flower of life has on the overall form of the human body. When we take the diameter of the circle formed by the major points of the body (the largest circle a the center), and then continually divide these circles by two (forming smaller iterations of the flower pattern), we begin to see the geometric correlation between these measurements and the anatomy of the body. Though these relationships are not always exact, the striking adherence to the geometric design of the flower of life is remarkable.

Starting in the head, we can see the beginning of where the eye-line would be in a human being. We may note that this is also the line at which the third eye is located. This line is the convergence of where all three sizes of circle occurs.

Moving downward, we see the center of where the next smaller circle rests. This is where the throat chakra is located. It is also the shoulder level and a major point of structural support for the head and neck.
Next is the level of the heart and heart chakra. This level is not defined by the center of the figure like the others, but by the intersections of the upper-most small circles which flank the central column of small circles. So this level appears to define the heart-space.

Moving downward to the next point of intersection is the solar plexus. This is where the third chakra is located and is also around the area where the esophagus ends and the stomach and following aspects of the digestive system begin.

Going down the body, we can see that at virtually everywhere these various sizes of circles intersect, there we have significant aspects of the body. The elbows, the navel, the second chakra, and hips, groin and many other aspects of the human anatomy correspond to these intersections. One particularly interesting aspect of this relationship is that the major aspect of the flower of life pattern appears to incorporate the body from the ankles to the third eye, but does not necessarily include the soles of the feet or the top of the head. This is with regard to the main, central circle.

We may keep in mind the fact that these circles are not actually circles, but are spheres interwoven at the edges and centers. The entire pattern creates an expression of sacred geometry, and depending upon how far the pattern stretches outward, the various Platonic solids can be formed. This particular instance of closed packed spheres forms the geometry of the cube octahedron—also known as the vector equilibrium.



If we remember, it was the cube octahedron which was clearly manifested in the form of the embryo. As we have it, the human body seems to take the energetic shape of the cube octahedron not only immediately after conception, but into adulthood as well.

We may also be aware of the fact that the cube octahedron geometry perfectly nests a star tetrahedron within it. This is one of many manifestations of the merkaba within the human form as well as virtually all other objects in the universe, from plants and animals, to planets, stars, and galaxies. This relationship may mean that the same laws which govern the anatomy of the human form are the same as those which govern the largest cosmic objects in existence.


Implications of Universal Geometry

These characteristics of the sacred geometry, the Platonic solids, the Fibonacci's spiral, phi ratio, and close-packed spheres all seem to be foundational components within our world and universe. These characteristics seem to suggest some all-encompassing principle which maintains universal structure and order.
It may even be that this force—whatever it may be—was the driving energy which brought the universe into being and which initiates and promotes the process of evolution. If this is the case, and this force is universal as it appears to be, this means that life and evolution are not only taking place here on planet Earth, but that it may be occurring and virtually every corner of the universe where conditions are suitable for it.

This regularity of life within the universe would also suggest that the general anatomy of the form of organisms follow the same general principles and the same anthropomorphic blueprint. This could mean that eventually, all life within the universe would assume a general form much like our current human bodies. However, with this possibility of evolution being continual and universal, we must also accept the possibility that eventually, we as homo sapien sapiens, will evolve beyond our present state as well.


The geometric relationship between conscious beings and cosmic bodies such as stars, planets and galaxies suggests that at some level these heavenly bodies are conscious as well, or perhaps even alive. If this is true, it means that at some level, evolution is affecting everything in the universe in an orderly and geometric way.

As the cosmos change, we as expressions of the cosmos change. It may even be that as conscious members of the cosmos, we—though we seem small in scale—may have the ability to affect the cosmos. If the cycles of solar systemic rotation can affect our sleep cycles, moods, and life-spans, perhaps the energetic influence flows both ways.

Is it possible—if the bodies within our solar system and the evolutionary alterations within the cosmos have an effect on Earth life—that we as the conscious collective of humanity have the ability to affect certain aspects of the cosmos with our collective intent?

It may be that through our collective will, that we as conscious humanity hold the massive potential to determine the evolutionary path of our own population as well as steer this path to more prosperous outcomes. This may very well be within our ability and if, in fact, it is, the implications would be galactic in scale.
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