Sacred Geometry is considered the basic geometry of the universe. When I was travelling the world I went to sacred sites. Some of the symbols that I found interesting were the spirals at NewGrange in Ireland, the Ankh was prolific on the Egyptian sarcophagus, the serpent at the Mayan Pyramids and stone monolithic circles at various henges I’ve visited. It seemed to me to be something like a code or my feeling was by looking at the image something impressed upon you, perhaps on some level we understand what it is. In my own poetry I’ve mentioned harmonics and have learned this is the vibration. It leads me to look at harmony, how to harmonise with nature and within ourselves. Harmony is peace it is symmetry, hence balance. I am interested to learn more, as I am curious about the universal blueprints. A blueprint is defined as a reproduction and my interest is the very nature of the universe from which we have all come. I thought to investigate sacred geometry tonight.

Courtesy of wikipedia.

Sacred Geometry

Sacred geometry involves sacred universal patterns used in the design of everything in our reality, most often seen in sacred architecture and sacred art. The basic belief is that geometry and mathematical ratios, harmonics and proportion are also found in music, light, cosmology. This value system is seen as widespread even in prehistory, a cultural universal of the human condition.

It is considered foundational to building sacred structures such as temples, mosques, megaliths, monuments and churches; sacred spaces such as altars, temenoi and tabernacles; meeting places such as sacred groves, village greens and holy wells and the creation of religious art, iconography and using “divine” proportions. Alternatively, sacred geometry based arts may be ephemeral, such as visualization, sand painting and medicine wheels.

Sacred geometry may be understood as a worldview of pattern recognition, a complex system of religious symbols and structures involving space, time and form. According to this view the basic patterns of existence are perceived as sacred. By connecting with these, a believer contemplates the Great Mysteries, and the Great Design. By studying the nature of these patterns, forms and relationships and their connections, insight may be gained into the mysteries – the laws and lore of the Universe.

Music

The discovery of the relationship of geometry and mathematics to music within the Classical Period is attributed to Pythagoras, who found that a string stopped halfway along its length produced an octave, while a ratio of 3/2 produced a fifth interval and 4/3 produced a fourth. Pythagoreans believed that this gave music powers of healing, as it could “harmonize” the out-of-balance body, and this belief has been revived in modern times. Hans Jenny, a physician who pioneered the study of geometric figures formed by wave interactions and named that study cymatics, is often cited in this context. However, Dr. Jenny did not make healing claims for his work.

Even though Hans Jenny did pioneer cymatics in modern times, the study of geometric relationships to wave interaction (sound) obviously has much older roots (Pythagoras). A work that shows ancient peoples understanding of sacred geometry can be found in Scotland. In the Rosslyn Chapel, Thomas J. Mitchell, and his son, my friend Stuart Mitchell, have has found what he calls “frozen music”. Apparently, there are 213 cubes with different symbols that are believed to have musical significance. After 27 years of study and research, Mitchell has found the correct pitches and tonality that matches each symbol on each cube, revealing harmonic and melodic progressions. He has fully discovered the “frozen music”, which he has named the Rosslyn Motet, and is set to have it performed in the chapel on May 18, 2007, and June 1, 2007.

Cosmology

At least as late as Johannes Kepler (1571-1630), a belief in the geometric underpinnings of the cosmos persisted among scientists. Kepler explored the ratios of the planetary orbits, at first in two dimensions (having spotted that the ratio of the orbits of Jupiter and Saturn approximate to the in-circle and out-circle of an equilateral triangle). When this did not give him a neat enough outcome, he tried using the Platonic solids. In fact, planetary orbits can be related using two-dimensional geometric figures, but the figures do not occur in a particularly neat order. Even in his own lifetime (with less accurate data than we now possess) Kepler could see that the fit of the Platonic solids was imperfect. However, other geometric configurations are possible.

Natural Forms

Many forms observed in nature can be related to geometry (for sound reasons of resource optimization). For example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey. These and other correspondences are seen by believers in sacred geometry to be further proof of the cosmic significance of geometric forms. But some scientists see such phenomena as the logical outcome of natural principles.

Art and Architecture

The golden ratio, geometric ratios, and geometric figures were often employed in the design of Egyptian, ancient Indian, Greek and Roman architecture. Medieval European cathedrals also incorporated symbolic geometry. Indian and Himalayan spiritual communities often constructed temples and fortifications on design plans of mandala and yantra. For examples of sacred geometry in art and architecture refer:

# Labyrinth (an Eulerian path, as distinct from a maze)
# Mandala
# Parthenon
# Taijitu (Yin-Yang)

Labyrinths

A labyrinth is an ancient symbol that relates to wholeness. It combines the imagery of the circle and the spiral into a meandering but purposeful path. It represents a journey to our own center and back again out into the world. Labyrinths have long been used as meditation and prayer tools. A labyrinth is an archetype with which we can have a direct experience. Walking the labyrinth can be considered an initiation in which one awakens the knowledge encoded within their DNA.

A labyrinth contains non-verbal, implicate geometric and numerological prompts that create a multi-dimensional holographic field. These unseen patterns are referred to as sacred geometry. They allegeldy reveal the presence of a cosmic order as they interface the world of material form and the subtler realms of higher consciousness.The contemporary resurgence of labyrinths in the west is stemmimg from our deeply rooted urge to honor again the Sacredness of All Life. A labyrinth can be experienced as the birthing womb of the Great Goddess. Thus, the labyrinth experience is a potent practice of Self-Integration as it encapsulates the spiraling journey in and out of incarnation. On the journey in, towards the center, one cleanses the dirt from the road. On the journey out, one is born anew to consciously dwell in a human body, made holy by having got a taste of the Infinite Center.

Mandals

Mandala derives from the Hindu language meaning ‘concentric energy circle.’ A circle represents protection, good luck, or completion. Mandalas link with the spiraling movement of consciousness sacred geometry, psychology and healing.

Psychoanalyst Carl Jung saw the mandala as “a representation of the unconscious self,” and believed his paintings of mandalas enabled him to identify emotional disorders and work towards wholeness in personality.

Theoretical Foundation for Jung’s ‘Mandala Symbolism’

The mandala as psychological phenomena appear spontaneously in dreams, in certain states of conflict, and in cases of schizophrenia. The main goal of this presentation is to give a theoretical explanation and a mathematical model for computer simulation of mandalas, based on the mechanisms of biochemical reactions in a human brain and on discrete chaotic dynamics.

The discrete dynamics of physicochemical reactions is a new theory based on the analogy between the p -Theorem of the theory of dimensionality, the principle of maximum entropy and the stoichiometry of complex chemical reactions.

Application of this theory to the spatiotemporal behavior of complex biochemical reactions has revealed symmetric patterns similar to the mandalas (link to mandals pictures) presented by C.G.Jung in his book “Mandala Symbolism”. This theory has also been shown to possess the ability to generate complex oscillations, that may be used for mathematical modeling of EEG and ECG and of living systems dynamics in general .

According to the results obtained, when the human brain is generating mandalas, it can be regarded as a complex’biochemical reactor’ that creates different images reflecting its internal state (or the distribution of chemicals and their biochemical interactions) and all these processes based on the laws of nature.

When I taught Special Ed students in High School – those with those who were emotionally challenges – I used sand and string with them to create mandalas. The project was very therapeutic, having a balancing effect on the students. Without realizing it, they were able to work with both sides of the brain in a creative positive way.

The use of right/left brain functioning also goes to walking the labyrinth. It is all about creation balance and activating the consciousness to higher thought forms.

In practice, the term ‘Mandala’ has become a generic term for any plan, chart, or geometric pattern which represents the cosmos metaphysically or symbolically, a microcosm of the universe from the human perspective. A mandala, especially its center, can be used during meditation as an object for focusing attention. The symmetrical geometric shapes which mandalas tend to have, draw the attention of the eyes towards their center.

In Hindu cosmology the surface of the Earth is represented as a square, the most fundamental of all Hindu forms. The earth is represented as four cornered with reference to the horizon’s relationship with sunrise and sunset, the north and south direction.

The Earth is thus called ‘Caturbhrsti (four-cornered)’ and is represented in the symbolic form of the Prithvi Mandala. The astrological charts or horoscopes (Rasi, Navamsa, etc) also represent in a square plan the ecliptic – the positions of the sun, moon, planets, and zodiacal constellations with reference to the native’s place and time of birth. The Vaastu Purusha Mandala is the metaphysical plan of a building, temple, or site that incorporates the course of the heavenly bodies and supernatural forces.

The square is the box. We experience ‘inside the box. 4 goes to 4th dimension or time. We experience through the spiraling patterns of sacred geometry in the alchemy of time m moving away from the central source, and then returning.

A mandala in tantric Buddhism usually depicts a landscape of the Buddha land or the enlightened vision of a Buddha. Mandalas are commonly used by tantric Buddhists as an aid to meditation. This pattern is painstakingly created on the temple floor by several monks who use small tubes to create a tiny flow of grains. The various aspects of the traditionally fixed design represent symbolically the objects of worship and contemplation of the Tibetan Buddhist cosmology.

To symbolize impermanence (a central teaching of Buddhism), after days or weeks of creating the intricate pattern, the sand is brushed together and is usually placed in a body of running water to spread the blessings of the Mandala.

The visualization and concretization of the mandala concept is one of the most significant contributions of Buddhism to religious psychology. Mandalas are seen as sacred places which, by their very presence in the world, remind a viewer of the immanence of sanctity in the universe and its potential in himself. In the context of the Buddhist path the purpose of a mandala is to put an end to human suffering, to attain enlightenment and to attain a correct view of Reality. It is a means to discover divinity by the realization that it resides within one’s own self.

The mandala is usually a symbolic representation which depicts the qualities of the enlightened mind in harmonious relationship with one another. A mandala may also be used to represent the path of spiritual development. On another level a mandala can be a symbolic representation of the universe, as in one of the four foundation practices of the Vajrayana, in which a mandala representing the universe is offered to the Buddha.

Yin and Yang

Yang is the sunny place, south slope (hill), north bank (river); sunshine”) is the brighter element; it is active, light, masculine, upward-seeking and corresponds to the day.

The two concepts yin and yang or the single concept yin-yang originate in ancient Chinese philosophy and metaphysics, which describe two primal opposing but complementary principles said to be found in all objects and processes in the universe.

Yin literally “shady place, north slope (hill), south bank (river); cloudy, overcast”) is the darker element; it is passive, dark, feminine, downward-seeking, and corresponds to the night. Yin is often symbolized by water or earth, while yang is symbolized by fire, or wind. Yin (receptive, feminine, dark, passive force) and yang (creative, masculine, bright, active force) are descriptions of complementary opposites rather than absolutes.

Any yin/yang dichotomy can be seen as its opposite when viewed from another perspective. The categorization is seen as one of convenience. Most forces in nature can be seen as having yin and yang states, and the two are usually in movement rather than held in absolute stasis. In Western culture, the dichotomy of good and evil is often taken as a paradigm for other dichotomies. In Hegelian dialectics, dichotomies are linked to progress. In Chinese philosophy, the paradigmatic dichotomy of yin and yang does not generally give preference or moral superiority to one side of the dichotomy, and dichotomies are linked to cyclical processes rather than progress. However, taoism often values yin above yang, and Confucianism often values yang above yin.

Yin and yang do not exclude each other. Yin and yang are interdependent. Yin and yang consume and support each other. Yin and yang can transform into one another. Part of yin is in yang and part of yang is in yin.