Spheriphor = Tetrahelix + Triskele + Trimurti + Jewel in the Lotus

I created the geometry for the Spheriphor digital art work as an investigation into spherical spirals, but this figure has also led me down deep into multiple levels of insight meditation. If you have been following my blog, you may know that I believe that the root essence of existence is the spiral. I talked about this with my Maori artist collaborator Kura Puke (for I. She also believes spirals to be at the heart of all things.
 

Just recently, during a Vipassana meditation session, I had an insight that emerged from contemplation of the tetrahelix (spiral based on the tetrahedron). I visualized the tetrahelix emerging from a set of 3 vectors that propagate through space. These 3 vectors are the primary (active) system of all phenomena. There is a set of 3 complementary vectors that are secondary (reactive), and together with the primary set of 3 vectors, the tetrahedron (minimum system of Universe) is formed (as per Bucky's Synergetics).
 

Then, I arrived at an internal visualization of the relationships between the 3 primary vectors. This visualization involved a spiraling propagation through space based on 3 parameters: length, angle and twist. I could see that these 3 parameters were the true 3 dimensions of Universe (as opposed to width, height and depth). I made a mental note to create an mathematical computer generated visualization based on this concept.
 

Then all of a sudden the visualization shifted to the Hindu Trimurti. My mental energy shifted from left hemisphere to right hemisphere; the wonders of the corpus callosum.
 

From Wikipedia:

The Trimurti (English: 'three forms') is a concept in Hinduism in which the cosmic functions of  creation  ,  maintenance  , and  transformation  are personified by the forms of Brahmāthe maintainer or preserver Vishnu the creator and Śhiva the destroyer or transformer. These three deities have been called "the Hindu triad" or the "Great Trinity", often addressed as "Brahma-Vishnu-Maheshwara."

Next came the realization of the equivalence of Hindu and Tibetan Buddhist trinities:

1. Vishnu = Sunyata
2. Brahma = Amitabha
3. Shiva = Chenrezig

 

The visualization then shifted again. This time the triad transformed into the Mani; the most beneficial mantra, "Om Mani Padme Hum". I saw the following: 

1. the clear light of creation (Om) radiating from within 
2. the jewel maintaining (Mani) all phenomena
3. sitting on a lotus transforming (Padme) all dualistic views
4. within my human heart (Hum) the most fortunate of all incarnations

In this meditation I attained the most in-depth understanding of the Mani that I have ever realized.

The visualization which emerged from my contemplation of the tetrahelix now circled back to my 4 colored, Triskele version of the Spheriphor. The Spheriphor contains both the 3-way symmetry of the Trimurti and the 4-colored aspects of the Mani. The Spheriphor is truly an all-encompassing spherical-metaphor that represents the complete Hindu-Buddhist psycho-cosmology. 

 
Spheriphor by Tom Greenbaum

 

You can view my Spheriphor study at http://karmatetra.com/ISDE5/spheriphor_study03.htm

Also on the Spheriphor Study 03 page are alternative views of the figure based on a spherical octahedron. The 3 views are based on vertex, face-centered and edge centered perspectives:

• http://karmatetra.com/ISDE5/Images/Spheri-Spiral_50.jpg  My 4 colored Triskele (Celtic triple spiral) version. Do you think that the Celtic mystics were actually peering into the vertex of a spherical octahedron wrapped in spirals like I was?  Also, Hans-Peter Welke fell in love with this image and asked me for permission to use it for the cover of his brochure on the "Corporate Identity Development Process"  See the attachment for the brochure. Hans-Peter credits me for the image on the last page.
• http://karmatetra.com/ISDE5/Images/Spheri-Spiral_52.jpg
• http://karmatetra.com/ISDE5/Images/Spheri-Spiral_49.jpg

 

I would love to make this figure out of glass. I have thought of possible ways to make it out of glass, but it would be a major challenge.

Trinity: Dividing the Universe into Three

How do trinities work? This is a very deep question with answers on many levels. The levels exist in many domains of human experience and knowledge. It would take a lot of words to answer this properly.

The mind naturally divides the universe into three parts:

1. The subject or thought that our mind is considering in the moment, which is actually a set or collection of things.
2. Everything that we think is included inside this thought, or within this consideration set.
3. Everything that is excluded from our current thought, or outside the consideration set.

Because of this mental process our mind creates trinities. Every time we think about something we divide the universe into three parts. When we later recall our thinking process, we tend to generalize and think about the big picture which is the trinity of the situation. We think about the 'system' that our mind created when we thought about that particular consideration set. We look at the way we divided the universe with our thought. This is mostly not a conscious phenomena, but it is operational nonetheless.

One of the most powerful examples of how this innate dividing of the universe into three parts is Earth, Heaven and Hell. Primitive Human experience thought of their world as a flat plane that extended infinitely in all directions. Naturally this divides the universe into three parts: The Earth on which lives Humans and all creatures, Hell below and Heaven above.

Primitive Humans knew about the Earth on which they stood. They thought about their Earth intently and with great curiosity because their survival depended upon this knowledge. However, when they had time to think about the 'big' picture, they considered how the the universe must be divided into three distinct regions: Earth, Heaven and Hell. They imagined that beings must exist above and beneath the Earthly plane. They placed themselves in the 'big' picture and thought of a cycle of existence that must include the possibility of traveling to these other planes of existence, etc.

There are so many trinities that Humans throughout history have created that it is impossible to catalog them all. Searching the Internet for 'three' yields some interesting results. There is a very interesting website written by Michael Eck who has devoted his life to cataloging threes, see www.three.com and The Book of Threes.

From Wikipedia (and other sources) some interesting facts about three.

In Mathematics:

• Three of the five regular polyhedra have triangular faces — the tetrahedron, the octahedron, and the icosahedron. Also, three of the five regular polyhedra have vertices where three faces meet — the tetrahedron, the hexahedron (cube), and the dodecahedron. Furthermore, only three different types of polygons comprise the faces of the five regular polyhedra — the triangle, the quadrilateral, and the pentagon.

In Nature:

• A human ear has three semicircular canals.
• Humans perceive white light as the mixture of the three additive primary hues: red, green, and blue.
• Genetic information is encoded in DNA and RNA using a triplet codon system.
• Atoms consist of three constituents: protons, neutrons, and electrons.
• We perceive our universe to have three spatial dimensions.

In Religion:

• The Christian Holy Trinity: Father, Son and Holy Ghost.
• The Hindu Trimurti: Brahma the Creator, Vishnu the Preserver, and Shiva the Destroyer.
• In Hinduism the three Gunas underlie action, in the Vedic system of knowledge.
• The Hindu Tridevi.
• The Three Jewels of Buddhism.
• The Three Pure Ones of Taoism.
• In Kaballah the trinity is God, Torah and Israel.
• The three Patriarchs: Abraham, Isaac, and Jacob.
• The Jewish Bible, the Tanakh has 3 sections: Torah, Nevi'im, and Ketuvim.
• There are three main divisions of Jews: Kohen, Levi, and Israel (Israelite).
• According to the prophet Muhammad, there are three holy cities of Islam (to which pilgrimage should be made): Mecca, Medina, and Jerusalem.
• The Wiccan Rule of Three.
• The Triple Goddess: Maiden, Mother, Crone; the three fates.
• Gurdjieff's Three Centers and the Law of Three.
• The three Doshas (weaknesses) and their antidotes are the basis of Ayurvedic medicine in India.
• Hegel's dialectic of Thesis + Antithesis = Synthesis creates three-ness from two-ness.
• Saccidānanda, Satchidananda, or Sat-cit-ānanda is a compound of three Sanskrit words, Sat, Cit, and Ānanda, meaning truth, consciousness, and bliss respectively. The expression comes from Hinduism and is used in yoga and other schools of Indian philosophy to describe the nature of Brahman as experienced by a fully liberated yogi or saint.

It is no surprise that most of the major religions have a highly significant trinity in their teachings. What I find curious is that perhaps the most significant trinity of Human existence: Father - Mother - Child is not represented. The Christian Holy Trinity: Father, Son and Holy Ghost comes close. Do you think that the Holy Ghost is a substitute for Mother? Some reports state that the Blessed Virgin Mary is venerated more than Jesus Christ as a Christian Deity.

An interesting web page The Christian Goddess talks about this issue. See http://www.northernway.org/goddess.html  (My highlight below).

Many theologians and scholars believe the Holy Spirit written as, Pneuma in Greek every time it appears in the New Testament, is a feminine being.  Note that Pneuma is a neuter word in Greek, but in Hebrew the word Ruah (Spirit) and in Aramaic the word Shekinah (Presence) are feminine words and imply a feminine divine presence.  The Holy Spirit is possibly a Christian Goddess, not a mysterious invisible member of an all-male Trinity "club."

Plato also conceived of a triad consisting of Beauty, Symmetry and Truth. Bucky Fuller talks about this in Synergetics.

Fig. 542.02 Tetrahedral Analysis of Plato's Triad: The triadic concept of Beauty,Symmetry, and Truth inadvenently omitted the function of the observer. The tetrahedron is the unique symmetrical set of minimum interrelationships.

Copyright © 1997 Estate of R. Buckminster Fuller