continuous creation

The Talmud, expanding on the Biblical account, tells us that Abraham discovered the One-God while he lived in the house of his father Terach. Terach, we are also told, was an educated professional knowledgeable in the skills, philosophies and spiritual practices known in his homeland in "Ur of the Chaldees," a civilized and sophisticated city-state in "Babylonia."

The Talmud is the "oral" Torah given to Moses with the written Torah - The Five Books of Moses - at Mt. Horeb-Sinai. From: The Handbook of Jewish Thought, by R. Aryeh Kaplan (Brooklyn, N.Y, Maznaim Publishing Co., ©1979) page 42, and Kaplan's footnotes, bottom page 42 (see Note 1).

"It was into this pagan atmosphere that a most unique individual was born. From his earliest childhood, Abraham transcended his pagan environment and recognized that the world was governed by one Supreme Being. As one of the greatest geniuses of his time,35 Abraham was able to use his keen mind to see through the sham and falsehood of the values of his generation,and understand the true purpose of creation."1
Abraham is at home. He is reflecting on the many idols of metal and stone and wood that his father makes and sells. He has a realization that these idols are dead and inert and he "discovers" the One-God. This is a paraphrase of the traditional story. How are we to understand it?
If we, as our scholars, assume that this story is to be taken literally, then Abraham realizes that the idols his father makes and sells are not alive, and thus not able to have any effect in the world no matter what or how they are prayed to and no matter what sacrifice is offered to them. We are assuming that a man whom we are told is educated and sophisticated would make and sell inert effigies as deities. If we met an educated and sophisticated person today we would not find it plausible that they would be in the business of selling idols. Why should we make that presumption about Terach?

Consider instead the following scenario. Terach, as an educated and worldly man, would know and appreciate the arts, sciences and spiritual beliefs of as many different peoples and cultures as were known in his world. We assume this of educated persons today. If this is so, then the "idols of metal and stone and wood" referred to in the traditional story are really the particular cultural embodiments of the arts, the sciences, and the sacred as they are known in various different cultures.

The "idols" of a sophisticated person are not, literally, stone effigies and statuettes. These "idols" are the cultural, political, social, and scientific paradigms comprising the world-views of the societies in which they (and we) live.

When we examine the spiritual beliefs and cosmologies of many ancient and modern cultures we find that they all include excellent models of certain essential qualities of life - albeit each in its own cultural context with its own particular perspective, emphasis and physical analogs.

The ancient Chinese developed a cosmology and an original ideographic alphabet based on the 28-mansions of the lunar zodiac.
The Greeks and the Persians modeled the cyclicity of life by a pantheon of gods, goddesses and their familial relationships based on the 12-houses of the solar zodiac.2
The Druids of northern Europe modeled the self-propagation of life on the life cycles of trees and other growing things.
Each and every culture has made accurate and effective models of the cyclic, self-propagating and self-referential nature of all life in terms appropriate to its needs and experience. These different cultural embodiments of the same universal principles underlying all life are referred to as "idols of metal and stone and wood." These "godlet" cultural paradigms are honored (and, literally, stone statues of these "idols" are worshipped) by the society that makes use of them.
All cultures model the same processes of the same overall unity of the natural world and each uses a different physical example to do it.
Abraham, seeing through each example to a Singular archetype, DEFINED the One-God as the Unity underlying all of them.
Abraham, in this view, acts as a mathematician: he postulates a meaningful and functional definition of Unity. The mathematician's model makes use of none of the "garments" of the many different cultural embodiments. Even though it is a mathematical model that must make use of geometry and form (or formalism) to be expressed, it (the model, not the sacred) MUST be understood as a complete abstraction without physical embodiment. A good mathematician tolerates no unneeded embellishments.

This perspective suggests why the Abrahamic faiths absolutely prohibit "graven images" of God. Any "graven image" would be a physical representation of only one culture's iconography during one historical period - it could never be a timeless model of a universal underlying Unity.

Once we understand this mathematician's idea of God as a DEFINITION necessary for universality we can, perhaps for the first time, see how and why it is possible that the Abrahamic faiths' insistence that God is the ONLY-GOD could be literally true, and not just the chauvinistic religious puffery of these faiths - and in a way that does not impugn the validity of other religions. The definition of Unity is in no way prejudicial to any other view.

Even before Moses was given the Torah, it is possible that Abraham realized that this ultimate, Singular, definition of the universal One-God is also identical with the personal meditational experience of God. That the Immanence of All-There-Is and the Transcendent Singularity in our experience of meditation are one and the same may be the basis of Abraham's understanding of and belief in the One-God.

This suggests the truly extraordinary possibility that our ancient sages also realized that there is one particular mathematical definition of Unity that is also a model of the sequence of feelings, the "Yoga" and the "Hero's Journey", that leads to the meditational experience of Unity. The meditational experience may be the gnosis that personally validates and empowers these spiritual tradition(s).

Further, although the particular details and depth of understanding of the idea of an explicit definition of the Unity of God may have been most fully developed by the Abrahamic faiths, the principle was known and considered fundamental in other cultures as well. Terach and Abraham did not live in a cultural vacuum.

MODELS OF WHOLENESS, SINGULARITY AND HIGHEST CONTRAST

How are we to model this ultimate, exquisite, unknowable UNITY representing our unique definition of the Singularity of the One-Living-God? Is there an entirely abstract - non-idolatrous - mathematical model that incorporates Singularity, Uniqueness, Self-organization, Universality, Infinitude, Elegance and Simplicity?

What is the most elegant and exquisite model of "highest contrast"?
Could this same model also represent the meditational process or the path and goal of the "Hero's Journey?"
In The Laws of Form, mathematician G. Spencer-Brown proposes the "mark of distinction" archetypally distinguishing INSIDE from OUTSIDE as a definition of maximal contrast. Mathematicians have shown that all of formal logic can be derived from G. Spencer-Brown's "mark of distinction." The following is from The Laws of Form, p. xxix (emphasis added):
"The theme of this book is that a universe comes into being when a space is severed or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can begin to reconstruct, with an accuracy and coverage that appear almost uncanny, the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance.
"Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe. It is this sameness, the idea that we can find a reality which is independent of how the universe actually appears, that lends such fascination to the study of mathematics."
The distinction between archetypal Symmetry and Asymmetry is also primary and of absolute contrast. Each co-defines the other. Without a representative standard of asymmetry how could we unambiguously define symmetry?

Archetypal symmetry can be represented by the most compact structural forms (in any given dimension). The five Platonic solids (Tetrahedron, Cube, Octahedron, Icosahedron, and Dodecahedron) and the Archimedian semi-regular solids can define fundamental symmetries in 3-dimensions. (Mathematicians and physicists derive the formal symmetry groups that they use from these polyhedral archetypes.)
Archetypal asymmetry can be represented by a dynamic form that continuously breaks symmetries as it unfurls. Meru Foundation research suggests that this form is a particular, explicit vortex, which we call "Naked Recursion" ("naked" in the mathematical sense - unadorned, without any other quality) and which has been traditionally associated with "the flame of consciousness", the archetypal living process of a "fruit tree yielding fruit whose seed is inside itself" (Genesis I.11.), and with its highest human embodiment - our hands.

As we will see later, besides its traditional association with the heart Chakra, what is most astonishing about the vortex-shaped model HAND is its direct relationship to both our personal consciousness and to our cosmological model of Unity, Singularity and Wholeness.

Confirmation, The Meruba Ashurit Rabbinic Hebrew Alphabet—also Greek and Arabic
When we combine the these two natural models of the source of information—the sun-sky source model that informs us, and the subjective mind-objective world model which we use to inform the world—we find the same form: our hands. When we place the sun-sky Dirac model hands on our real hands and then point to what we want, we see distinct 2-dimensional outlines of each of the letters of the fluid rabbinic form of the traditional "sacred" Meruba Ashurit Hebrew alphabet. (It is likely that this same abstract hand form also generates the letters of particular Greek and Arabic alphabets, using either the full Dirac String orbit or half of the orbit. This has been demonstrated only casually, but based on text references, it is highly plausible.)

When we see the outline of a particular Hebrew letter, we are making a left-right pair of gestures whose natural universal (human) meaning is the same as the meaning of the name of the letter. In this case, form and function are intrinsically linked by the geometry of choice (information) and by how we express our conscious choices (how we inform, in turn).* Thus, the shapes of these "sacred" Hebrew letters may not be arbitrary; their shapes may carry natural meaning in themselves, as is traditionally claimed. Each articulation of the model of the source of information represents a distinct pointing direction and gesture whose natural meaning is the name of the letter that is displayed.

When we spell Hebrew roots by means of the gestures that make the letters of the root, we (often) see a more complex, compound gesture that has the same universally recognized visual meaning as the Hebrew root.

For example, when we point to our mouth using the standard shouting "megaphone" gesture, thumbs in, fingers flared, we see an outline of the Hebrew letter Pe; Pe means "mouth" or "speak." When we outline the shape of a globe, melon, or basketball in our hands in order to designate something "round," we see, in sequence, the Hebrew letters Gimel and Lamed which form the root GaL, meaning "round."

It is highly unlikely that this constellation of results would occur if these "sacred" letter shapes were arbitrary, or the result of orthographic convenience alone. The letters are not orthographically reasonable: words are written right-to-left, while letters are drawn left-to-right; thus, without explicit care, the writing hand smears each new letter. It is important that these findings and conclusions be tested with native speakers, with many more examples, and to see if arbitrary letter shapes could reasonably be expected to enable the same results.

One confirmation that this model for generating the shapes of the Hebrew letters was known in the past can be found in the Sefer Yetzirah, the "Book of Formation." The Sefer Yetzirah is universally believed to be about the Hebrew letters. But, even though the title of the book (Yetzirah = "form") tells us that it is about "form," nowhere in any translation (nor in any extant commentary by academic or religious scholars, who read the original language) does any discussion of the form of the letters occur. This unsatisfying standard of translation would not be accepted in any other field of scholarship. No modern scholar would take seriously the translation of a book titled Chemistry, for example, that did not contain any reference to chemistry. This tolerance for illogic is one example of how some scholarship "damns by faint praise." Clearly there is a risk of demeaning traditional accomplishments when we accept traditional claims on lower standards than we insist on today.

When the half-orbit spiral vortex model (and related geometry) is identified with controversial and obscure terminology in the Sefer Yetzirah, the text immediately "reads clear," and the form of the letter-generating spiral vortex—the apple-based model hand—is readily apparent and seen to have been described and specified with extraordinary (technical) elegance in the text, all along.*

The Sefer Yetzirah outlines the model hand by describing its minimal, essential, symmetry qualities in 1-, 2-, and 3-dimensions. Simultaneously meeting these three simple dimensional criteria immediately and elegantly defines the letter-generating model hand spiral vortex forms. It is clearly unrealistic to expect scholars not comfortable with geometry to recognize so elegant a set of geometric metaphors. (For details see Note 2.)

Idealized Apple, Sufi Dancer, and Conservation of Momentum
This Idealized Apple can be represented by a dimpled-sphere torus, with the womb and seeds in the center hole, the stem and trunk identified with the fruit at its stem end, and the entire fruit identified with the whole sphere. The seed-tree-apple life-process spans from the torus’s hole to the whole torus—from an in-sphere (womb with seeds) to an out-sphere (fruit). This mini-sun (womb and seeds) in a surrounding mini-sky (fruit) recapitulates the form of the source of the information that informs the life of the apple-tree system. They are "made in the image of" the source that informs them. Notice also that this relationship-topology is the same as the traditional religious claim that humans are "made in the image of God."

The dimpled-sphere torus (Edenic and Apollo "apple") had specific cosmological significance in the ancient world. Indeed, the word "world" is related to the idea of a "whirl", and the presence of consciousness in the whirled with the "whirlwind."

The spiral vortex on the dimpled-sphere torus—which strings out the 7 regions that topologically define the self-reference-modeling 2-torus—can also model the conservation of angular momentum. Again, Arthur Young shows how this self-referential process topology is useful in understanding angular momentum, and he suggests that these toroidal models are meaningfully related to the quantum mechanical unit of angular momentum, Planck’s constant, h, and to a "quantum" or "bit" of conscious volitional choice. [3]


A Universal Hand

Obviously, we, and perhaps some of the other primates, are the only self-aware beings that have human (or human-like) hands. This is one reason why an accurate, 3-dimensional, photo-realistic human hand is not good enough to be universal. In order to form the letters of a natural pointing alphabet suitable for extra-terrestrials, we must make use of an idealized model hand based on the natural form of the source of information, not a realistic human hand. (I’m guessing that the "hand" of any being with a self-aware volitional consciousness similar to our own—no matter what its form, substance, or medium in which it can point—would have to be topologically equivalent to our hand, and would have the ability to move and point in a space with the same degrees of freedom, as befits its similar mental dexterity.)

Likewise, if we were to attempt to investigate whether this symbol system could be of use with dolphins, who do not have physical hands but instead use acoustic pulses as their pointing, probing, and gesturing system, we would have to adapt these principles to the shape of acoustic pulses instead of physical human hands. (In this case, the connection may be fairly simple. Acoustic pulses can travel like soliton-tori, which might plausibly be represented by the Dirac half-orbit form(s). This experiment needs to be performed.)

Recent published reports by:

1. Anthropologists now tell us that pre-humans used gesture language before developing speech; [4]
2. Child development psychologists tell us that infants can learn to gesture meaningfully to their parents before they develop spoken language (and spoken language naturally flows from their earlier gesture language); [5]

3. Scholars investigating natural language tell us that persons blind from birth make gestures that they have never seen, even while speaking to other blind people who cannot see their gestures, and that these gestures are essentially the same as those used by sighted persons.[6]*

4. Other recent published work discusses the likelihood that all cognition is based on body movements and gestures and their results.[7](Also see Note 3)

The concept for the design of an elegant, natural, universal pointing gesture alphabet discussed here relies on the reasonable assumptions that self-aware volitional creatures evolve on a planet-like body in a solar-like system (with electron physics as described by Dirac), and that they have a bodily means of projecting their personal will into the consensus world.
I would like to propose the investigation of this system for finding abstract communications forms (letters, numbers, etc.) suitable for communication with extra-terrestrials. We could start by investigating the usefulness of these ideas for communication with our self-aware companions here on Earth.

Notes

1. We are neglecting second order effects that are also part of the information source system. For example, not only is there contrast between sun and sky; the earth between them is in yearly orbit, and rotates on a 24-hour day-night cycle. The day-night cycle rhythmatizes the sun-sky contrast, and this in turn provides a clock-and-carrier for the information. Rotation at this level recapitulates, and is represented by, angular momentum at the fundamental-particle level.

2. The pairing pattern of letters at the beginning of B’reshit (Genesis) leads to the Continuous Creation model, which consists of exactly six model "hands".**

The Continuous Creation model can be described with unusual and extraordinary elegance and precision by examining its 1-, 2-, and 3-dimensional symmetries. There is no more mathematically elegant and compact way to describe a fundamental form than to take but 3 "snapshots" of it, one in each of the three spatial dimensions. This is perhaps one of the most elegant mathematical descriptions possible, and to mathematicians it’s immediately striking.

This is a unique identification. It includes identification of the descriptive words, T’li, Gal-Gal, and Lav, as well as their unique geometric relationship to the three numbers, 3, 7, and 12.

3. In the February 2002 issue of Scientific American, Steve Mirsky reports on research published in the November 29, 2001 issue of Nature, as follows: "...A region within Broca’s area known as Broadmann’s area 44, critical for the power of speech, is larger in the left hemisphere of humans than in the right. A study has now found that the same asymmetry exists in other great ape species: chimpanzees, bonobos and gorillas. [...T]he Emory University researchers conjecture that the area may have originally been associated with the production of gestures used by apes for communication. This area eventually became used as a source of speech in modern humans." [10]

References:

1. Penrose, Roger, The Emperor’s New Mind, Oxford University Press, 1989

2. Jaynes, Julian, The Origin of Consciousness in the Breakdown of the Bicameral Mind, 1976

3. Young, Arthur M., The Reflexive Universe, Anodos Books. Available through the Arthur Young website at www.arthuryoung.com/aybooks.HTML

4. Corballis, Michael, The Gestural Origins of Language, ©1999 Michael Corballis, published in The American Scientist, March-April 1999. This article is available at www.amsci.org/amsci/articles/99articles/Corballis.html

5. Acredolo, L. & Goodwyn, S. (1993). Symbolic gesture versus words: Is there a modality advantage for onset of symbol use, published in Child Development, 64, 688-701.

6. Iverson, Jana, and Goldin-Meadow, Susan, Why People Gesture When They Speak, published in Nature, Nov. 19, 1998. Excerpts available at www.meru.org/3220lecture/blndgest.html

7. Iverson, Jana, and Thelen, Esther, Hand, Mouth and Brain: The Dynamic Emergence of Speech and Gesture, published in the Journal of Consciousness Studies, Vol. 6, Issue #11-12, Nov/Dec 1999. Also see other published work linked to at www.meru.org/Gestures/gestures.html

8. Tenen, Stan, Man Bites Dog, published in the Noetic Journal, Vol. 2, No. 2, p.203, as an appendix to the essay The God of Abraham: A Mathematician’s View (see below).

9. Tenen, Stan, The God of Abraham: A Mathematician’s View, published in the Noetic Journal, Vol. 2 No. 2, p. 192.

10. Mirsky, Steve, Parts of Speech, published in Scientific American, February 2002, page 28.

Internet URLs and Links

Man Bites Dog
www.meru.org/manbitesdog.html

The God of Abraham, A Mathematician’s View
www.meru.org/GodofAbe/onegdpix.html

Squaring the Circle: The One and the Many, Mind and World
www.meru.org/3220lecture/contents.html

The Dirac String Trick: First Hand
www.meru.org/dirac.html

The Light in the Meeting Tent (poster)
www.meru.org/Posters/ColorLightinTent.html

The Light in the Meeting Tent (Meru Archive Draft Article: 1986)
www.meru.org/lightintent/lightin.html

Unity and Wholeness
www.meru.org/Posters/Unitywho.html

The Geometry of Rumi’s Description of the Mevlevi Sufi Round Dance
www.meru.org/Sufi/rnddance.html

An Idealized Embryonic Fruit and a Dancer’s Exchange of Angular Momentum
www.meru.org/Posters/angumomt.html

Hebrew Alphabet Hand Gestures
www.meru.org/Gestures/Atbashgest.html

Why People Gesture When they Speak (Excerpts) by Jana Iverson and Susan Goldin-Meadow
www.meru.org/3220lecture/blndgest.html (see Reference 6 above)

The Gestural Origins of Language, by Michael Corballis,
www.amsci.org/amsci/articles/99articles/Corballis.html (see Reference 4 above)