SACRED GEOMETRY

New Discoveries

Linking The Great Pyramid to the Human Form

Copyright 1997 - 2000   CHARLES R. HENRY

Professor, Department of Sculpture

Virginia Commonwealth University

Richmond, Virginia

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For more than twenty years, I have been studying the image generating properties of reflective spheres stacked in 52 degree angle pyramids. The 52 (51.827) degree angle slope of the sides of The Great Pyramid in Cairo, Egypt embodies the Golden Mean which is the ratio that is used in Nature to generate growth patterns in space. Sacred Geometry studies such primal systems which reveal the unity of the cosmos by representing the relationships between numbers geometrically. The Vesica Piscis is one of the most fundamental geometrical forms of this ancient discipline and it reveals the relationship between the The Great Pyramid and the 2 dimensional expansion of a circle of one unit radius R as shown in Figure 1. This relationship is more completely described in The New View Over Atlantis by John Michell published by Thames and Hudson.

Figure 1         Vesica Piscis in 2 Dimensions

In the early 1970s, I became very interested in the three dimensional representation of this geometry and I visualized this as a three dimensional pyramid inside two intersecting spheres shown in Figure 2.

Figure 2          Vesica Piscis in 3 Dimensions

In an effort to visualize these 3D relationships in yet another way, I stacked reflective Christmas Tree balls in an inverted pyramid shell. I discovered that the patterns of multiple reflections created on the interior surfaces of reflective spheres stacked at this angle produce images that relate to the human form as photographed and shown in Figure 3 and Figure 4.

Figure 3

Figure 4

I made many pyramidal configurations of reflective spheres with different light sources and I photographed the patterns on the interior surfaces from many points of view. Another is shown here in Figure 5.

Figure 5

Then in 1977, I discovered one stacking structure and viewpoint that produced a very convincing image of an archetypal human face. This structure of 10 spheres (2 5-ball pyramids) forming a cluster is shown in Figure 6.

Figure 6

The face image is shown in the lower third of the pattern on one sphere inside this 10 sphere cluster and is shown in Figure 7.

Figure 7   When I made this photograph, the structure was enclosed in a mirrored pyramid.

Later, I realized that the most natural structure for enclosing would be another 10 sphere, 2 pyramid structure that would totally enclose a smaller but similar cluster.  I worked out the math to find that by multiplying the inner sphere's diameters by Pi gives the dimension for the outer sphere's diameters as shown in Figure 8.

Figure 8        One sphere is removed from the outer cluster to reveal the inner cluster. However, the inner cluster must be upside down with respect to the outer cluster to fit inside.

The expansion by Pi reinforced my suspicion that this 10 sphere cluster is a fundamental unit that is linked to the properties of three dimensional space.

Close-packed reflective spheres clustered in this concentric shell structure produce an optical distribution network that links the Golden Mean and Pi. The Golden Mean is expressed in the 52 degree angle pyramid structure and Pi is expressed in the ratio of the diameter to the circumference of each sphere of course; but it is also expressed in the ratio of the sizes of spheres in the 10 spheres within 10 spheres concentric shell structure that I discovered. This concentric shell structure could continue to expand with many shells and still retain the same ratio between shells. It was not until 1991 that I was able to build and photograph the images inside a ten-within-ten (2 shell) structure. I used 10 - 6" diameter spheres and 10 - 19" diameter hemispheres. The structure is shown here in Figure 9.

Figure 9

Figure 10  and Figure 11 are photographs of the interior of the 10 spheres within 10 spheres cluster shown in Figure 9.

Figure 10

Figure 11

The photographs that I made from this 10-within-10 sphere structure revealed the inherent limitations of photography for this work. The final images were not what I was seeing with my eyes while directly viewing the interior of the structure. But this approach did reveal a more complete face form and I also realized that I would need at least 10 more spheres (about 60" in diameter at \$1500 each) to complete the enclosure and remove the remaining gaps in the images. Also, the lighting system was limited to the exterior and it was very difficult to control the positioning, color and brightness. So, in 1992, I purchased a computer to model these structures with ray-tracing software which enabled me to investigate more thoroughly the relationship between this cluster geometry and the archetypal images generated therein. During this tour into cyberspace, I could take a camera into the sacred chamber central to the concentric shells of reflective spheres which are simulated by a computer program (Real 3D by Realsoft Oy, Finland) that most accurately renders the effects of real-world light sources and records the patterns generated by multiple reflections on metal surfaces. With this method of investigation, I am able to more conveniently control the many variables which led to these discoveries and conclusions:

1.) At least 40 spheres (4-10 ball shells) are necessary to enclose the central area and fill in the gaps in the images.

2.) Most of the lights should be point sources placed at the points of contact between the innermost spheres of the structure; although additional symmetrically-paired, point-lights are necessary in the central area.

3.) Some of the innermost spheres are reduced in size and they can float within certain areas in the central space. Figure 12 shows typical positions and sizes.

4.) The camera position and field of view as shown in Figure 12 produces the most convincing image of the human form.

Figure 12

5.) The image of this artificial anthropoid that is produced in these structures can be animated when the positions and sizes of certain spheres are modulated as shown in the three animations listed below.

animation 1            .8 MB ... estimated download time at 56k ... 3.5 min.

animation 2           2.4 MB ...  estimated download time at 56k ... 10 min.

Figure 13       Human Form From Sacred Geometry

The computer image in Figure 13 was made from the camera position and field of view shown in Figure 12.

Figure 14   is from the same camera position (shown in Figure 12) but the lens set at a very wide angle.

Figure 14

Figure 15 is from the same camera position (shown in Figure 12) with the camera lens set to zoom in.

Figure 15

Figure 16   is a stereo image and it shows the interior of the cluster in 3D. Stare through the images with your eyes focused at a distant point and the two images will turn into three images and the center image will appear in 3D.

Figure 16

In 1996, I produced an animation Sacred Spaces (6 minutes) which has been screened in many national and international film festivals and it has won some awards (see resume). I have also produced Flesh Tones (5.5 Minutes) another animation completed in 1997 and I have produced many high resolution images for prints/slides (some examples are shown in Figures 13 through 36) which I have presented with the video animations at lecture presentations. These images are stills from the animations and they demonstrate the variety of image generating that is inherent in this system. I have concentrated on exhibiting the videotape documentation of my work thus far because it is the most portable presentation format that describes this research most completely.

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Conclusion

This interdisciplinary research has taken me into many related areas of study.   Geometry, Optics, Ancient History of Art and Religion, Computer Imaging, Photography, Animation, Graphic Art and of course Sculpture are the major connecting disciplines that have contributed to this work.

I feel that I have rediscovered some of what was a highly developed understanding of Mankind's relationship to the Universe and this knowledge was utilized and documented in the geometry of ancient structures. Sacred Geometry, the study of the unity of the cosmos, demonstrates relationships between Number and Space and the Human Form. It was used in the construction of ancient glyphs and monuments thereby preserving the knowledge of these principles of Natural Law for future generations.   This construction of reflective spheres may embody the technology that produced the animated images of the deities in the temples of antiquity. The Tree of Life which is a graphic representation of the interaction between cosmic forces is shown in Figure 22. It is found in many ancient texts of the Kabbalah.

Figure 22.

I realized that The Tree of Life graphic can also represent the 10 sphere cluster made with 2 5-ball pyramids as shown in Figure 23.

Figure 23

The construction of this structure of clustered metal reflective spheres (offering bowls) is well within the capability of many ancient cultures and with the addition of a few glass lenses, these images could be projected onto walls or into smoke. Perhaps there is some Truth behind the smoke and mirrors of Ancient Religion ... perhaps it is geometry ... Sacred Geometry.

This research which is documented in four computer animations Sacred Spaces, Flesh Tones, Our Mothers and Sacred Spaces 2, in color computer prints, and in color slides has given me new insight into the motives that may have inspired the construction of The Great Pyramid.

1998 - 2000 update

The images shown in Figures 24 - 35 were made with 50 spheres and 144 point-light sources.  Each of these images was made with unique brightness, color and value settings for various groupings of lights.

Figure24

Figure25

Figure26

Figure27

Figure28 horizontal

Figure28 vertical

Figure29

Figure30

Figure31

Figure32

In Figure32,   the camera is aimed at the sphere opposite the face shown in Figure 31.  Figure 12 shows the camera position for Figure 31.  The image in Figure 32 was formed when the camera position was rotated 180 degrees around the vertical axis  shown in Figurre 12    and  zoomed in.   The face image (a child?) in Figure 32 is much smaller  than the face (mother?) in  Figure 31.

Figure33horizontal

Figure33vertical

Figure 34

Figure35 This is a stereo 3D image that requires shutter glasses to view and your monitor must be set to interlace mode.

Figure 36            Stereo Image for Cross-Eyed Viewing

With your monitor at arm's length away, focus on a point 6 inches in front of your nose (put your index finger 6 inches in front of your nose and focus on it). You will see a third image in 3D between the two images on the monitor (at the tip of your finger). Shift your attention from your finger to this third/middle image which will appear in 3D.

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The cross-eyed viewing method is perhaps the most effective way to put the viewer inside the cluster to see the human image as it would exist in 3D from the cameras position as seen in Figure 12. There are many more identifiable images in this clustering geometry viewed from this position and from other camera positions and even more images with other color settings for the point lights.

Figure 36 Large

Figure 36 Zoom-in  This is the image on the forehead of the face in Figure 36 Large.

Figure 36 Wide-angle Large

Figure 36 Very wide-angle Large

Figure 37          Rods connecting centers of nearest neighbors in 3 shells

I'm now very curious about the relationship between Sacred Geometry and Sacred Music and the Human Form. Number relates to all that science measures by virtue of the way that 3D Space is defined. Number is also used to measure Time ... and, as Pythagoras observed, Music is a manifestation of Number in Time. The distribution of sounds i.e. amplitude and frequency, may well find an idealized model in the 10 within 10 sphere, space-filling, close-packing geometric system. The representation of this geometry with sticks or strings or rods as shown in Figure 37 (in which the centers of nearest neighbor spheres in three shells are joined) may represent the ideal space-filling matrix of linear oscillating elements. It may also be used to define spatially distributed, hierarchical, cellular arrays.

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The camera positions on the symmetric planes within the cluster produce a bilateral symmetry that we identify with animal and human form. Naturally, we would expect this symmetry in the idealized images of higher life forms. The multiplicity of idealized beings in this cluster of reflective spheres suggests the presence of The Company of the Gods as described in many ancient Egyptian texts. It seems that the face images occur on a vertical plane linking the centers of spheres. There seem to be faces facing faces and faces within faces throughout this reflective environment. My guess is that the sacred part of what I have discovered is a result of the way the deity put the higher life forms in three dimensions.

This cluster geometry may have other properties that would be useful for spatial organization. The nesting of 10 reflective spheres within 10 reflective spheres geometry produces a distribution system that could be used for processing of optical information between the interior to the exterior of the structure. Because of the spatial distribution of the reflective spheres in two concentric shells of ten each, optical information must be reflected and diverged in order to enter or exit the system with the exception of a few radially arrayed directions. The system becomes a more selective filter of optical information as more shells are added to the structure. This inside-to-outside transformation/translation should have many practical applications in pattern recognition tasks. For example, any point source of coherent light (laser light) anywhere outside the two-shell cluster will produce a unique light distribution pattern on the inside as viewed from the center area of the cluster. This pattern could be recorded in a holographic medium and the exterior point source could then be reconstructed using conventional holographic means.

Is Number (Geometry and Time) the link between Art, Science and Religious experience? The language of number is perhaps the most convincing form of expression between humans and between humans and the Gods. We think and imagine in visual forms. Einstein constructed his mathematics based on mental images. He said that he would first try to visualize a space/time image and then mathematize it. We use mental images to construct possible scenarios of the future so that we don't have to live out each one in "reality". Words and pictures and mathematical formulas are ways to document, test, realize, and communicate these visions. Although there is seldom a need to mathematize images, we sense that it would be possible. We know that we could count and number the grains of sand on the beach. The geometry of our visions is what makes them real to us and it allows us to mentally work on them and to integrate them convincingly into our life here in 3D.

I'm not quite sure how the physical human form fits into the grand scheme of things but it does seem to be a result of the space-filling, spherical, close-packing geometric system that I've discovered and it is indeed "Sacred Geometry" by virtue of the definition God gave to three dimensions. I don't think this geometric system is the matrix for all life systems but I think it can serve as a model for the interactions between the various dimensional realities in which we are immersed. It may also guide us in our attempt to develop new sciences and technologies that utilize the forces that operate in the regions that we now call consider paranormal.

According to contemporary Superstring Theory as described by Dr. Michio Kaku in his many recent writings, the mathematics that most appropriately describes the forces of nature requires an expression in ten dimensions. Einstein tried to describe the forces of nature in the mathematics of 3D and Time and found that the formulas were not broad enough to include all of the forces. We can perceive 3D and Time. The other 6D in Superstrings are hidden from our normal senses due to their incredibly small size according to Dr. Kaku. Our instincts inform us that there are more than 3 Dimensions and Time in the universe and the possiblity that something else exists mathematically beyond our perceptual horizon drives my curiosities about our possible links to these worlds. The new science of parapsychology has discovered many ways that humans can perceive by means beyond the physical senses and it has found that there are some people that are more capable of extrasensory perception than others. It may well be that our only contacts with this duality of nature are through numbers and mathematics on one hand or through dreams, remote viewing, telepathy, Ouija boards and tarot cards on the other. This would certainly confirm the existence of a God with a sense of humor

I am interested in any information relating this technology to ancient religious traditions.  Any references that you send will certainly be appreciated and I will certainly credit any references in future publications.

A more detailed version of this research is now available on CD-ROM and it includes the 10 minute animation Sacred Spaces 2 in streaming format.

I am also making available unlimited editions of selected images on this website which will be printed in very high resolution on archival paper with archival inks.

For more specific information about the availability, formats, sizes and pricing of the prints and CD relating to this work you may contact me at:

<crhenry1@verizon.net>

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