Metaphysical Geometry and the Golden Ratio

All the ancient cultures patiently arranged a correspondence between the heavens - especially the sun's orbit and the zodiac, with the settled land - and especially with the holy buildings and important cities, and with people - especially the religious and governmental elite.

Various researchers present enormous astrological diagrams in the Mediterranean basin. The zodiac stretched across the land and the sea, and passed through many centers of pilgrimage in ancient times. The architects of these huge earthly zodiac signs turned their country into a living image of the sky.

Other sacred geographies have a whole base that comes from geodesy, the branch of mathematics and applied geometry, which deals with measurements and distances on Earth, and the location of points on the surface. These special measurements evolved into geometric paintings over vast expanses of triangles, squares, and circles, and more complicated geometric forms and connections. Ancient builders erected temples in the landscape, which were placed exactly according to the knowledge of sacred geometry.

The ancient Egyptians ruled this science. The main line of ancient Egypt was determined to cross the country in half. Cities and ceremonial centers were deliberately built at distances measured precisely from this sacred longitude. Even in ancient Greece, religious centers were all separated from each other by precise distances.

We find evidence of ancient landscape geometries in France, Germany and England. Researchers have found extensive evidence in these countries for a linear arrangement of ancient sacred sites over long distances. Their source is a huge system of merchant routes that were built in the Neolithic period. Archaeological findings have since confirmed the Neolithic origin, but the idea that the lines were used for transport purposes should be ruled out. The lines form a straight arrow on the ground, making them impractical for useful transportation. These are energy lines, and in fact there is a sense of energy or power flowing along them, felt by people with sensitivities to earth energies.

This category belongs also to straight lines created on the landscape by archaic cultures in the Western Hemisphere. Examples include the Nasca lines in Peru, similar lines across Bolivia's deserts, and many linear signs left by Indians in the Chaco Canyon area of New Mexico. These lines are also integrated into giant drawing of animals and humans in adjacent geometric shapes. These are spiritual lines - a symbol created on Earth to represent the spiritual journeys, magical flights and experiences outside the body of ancient shamans.

The Nasca lines in Peru are the most important example of huge shaped lines on the landscape. The lines were discovered in the 1920s when regular commercial flights began over the desert. The lines can be identified as meaningful shapes on when viewed from the air.

The Nasca Desert is a high, arid plateau that stretches 85 kilometers off the coast of the Pacific Ocean some 400 kilometers south of Lima, the capital of Peru. The creators of the lines belonged to the Nasca culture, which existed between 200 BC and 600 AD. The lines form hundreds of shapes, whose complexity varies from simple and straight lines of up to 20 kilometers, to triangles and trapezes, to complex and stylish forms of animals such as birds, spiders, monkeys, lizards, whales, and even human figures. The lines were formed by digging the dark gravel that covered the desert and removing it to the side, so the lighter surface was revealed. The color of the lines is yellow and beige, and their depth is no more than a few centimeters. The total area of the lines is nearly 500 square kilometers and the length of the greatest characters reaches 270 meters. The lines are preserved due to the stable weather, which is windless and very arid.

The conventional archaeological theory is that the Nasca people created the lines with meticulous planning and simple technologies, and in a relatively short period of time. The lines are the remains of 'walking temples', in which a large group of believers walked along a predetermined pattern, which was dedicated to a unique sacred entity, similar to the custom of walking through a maze. They asked the gods to ensure that the water will continue to flow to them from the Andes through the extensive underground water channels they have constructed.

In Christian and Islamic Europe, in the Middle Ages and the Renaissance, painters were known to define the initial design of their paintings according to different geometrical formulas, imitating and perfecting ancient knowledge. According to this approach, the placement of elements within the painting is as important as the theme itself. This geometry was integrated into the worldview, and in the planning and construction of temples, public buildings, and entire cities.

Particularly prominent in metaphysical geometry formulas is the 'Golden Ratio'. This is ostensibly a simple mathematical series of numbers, but it is also referred to as the 'divine proportion'.

The golden ratio is the series of numbers in which each bigger number is the sum of the two numbers before it:

Let's take the number 1 and add it to 1. To the result 2 we shall add the previous number 1 and the result is 3. To 3 we shall add the previous number 2 and the result is 5.

Here are the first numbers in the series:

1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584

In this series of numbers there are many interesting mathematical phenomena. The most important is that the ratio between two consecutive numbers in a series, for example between 5 and 8 or between 21 and 34, is always about ... 1: 1.618. 

This ratio is never an integer. 

The 'Golden Section' is the name of the geometric form of the arithmetic golden ratio. The basic geometric form is that of a line divided into two according to the golden ratio: the length of the smaller part of each line relative to the larger part is like the length of the largest part relative to the entire length of the line.

When you take two consecutive lines in this sequence and form a rectangle, you get a rectangle of elegant dimensions known as the Golden Rectangle. 

This rectangle can be divided into sub-squares, smaller and smaller. If you draw an arch between two opposite edges in each inner square and connect all the arches created, you get a spectacular shape, called the Golden Spiral.

The golden section was discovered through practical experience thousands of years ago, and was used by the ancient architect, who debated what is the best point in dividing one line into two parts. The most beautiful dividing point is when the two parts of the line have the golden ratio between them.

The dimensions of the Great Pyramid in Egypt, the Parthenon in Athens and the Pantheon in Rome were designed according to the golden section. The ratio was the central visual concept and the focus of religious attraction in these temples. The ratio appears in various places in the buildings, from the general appearance to the rooms. The golden ratio is considered, since then, the most perfect form in art. The great Renaissance artists made sure to use it. It is found in Mozart's symphonies. It is also common in modern art and is used by architects, musicians, poets and designers.

The golden ratio and the golden section are also of great importance in the natural sciences because they appear in innumerable and very different natural phenomena. The organs of the human body are shaped according to the golden ratio. This fact was one of the principles of classical sculpture in the ancient world. The relationships in the human body produce the deepest effects on the human mind. The DNA form is also of two integrated gold spirals.

It is therefore possible to say that the reality in which we live is built to a large extent according to the principles of this ratio. The golden ratio has been used by builders of temples already in antiquity, whereas modern scientists have found that it is one of the basic mathematical frameworks of the universe. Its effects help shape a harmonious personal world, because it is used in nature, science, and art. This is the perfect standard. Preoccupation with it created entire worldviews, in past and present. Historians attribute great importance to the golden ratio in shaping human history and knowledge.

A 100-meter-long bird drawn across the Nasca plain in Peru

golden section

The golden ratio in a graph of rising and falling

The golden ratio in a pentagram, the most known star shape

The golden ratio in the Great Pyramid of Egypt

The golden ratio in the Parthenon of Athens

Human dimensions according to the pentagram

The golden ratio in nature

golden ratio in the human body

The golden ratio in the fingers

A golden rectangle and the golden spiral inside

A golden spiral shaped conch

The golden ratio in the DNA

The UN building is a golden rectangle

A golden rectangle in Renaissance painting

golden spiral in Botticelli's Venus painting

The golden ratio as an infinite wave

Mandala and Feng Shui

Another example of Sacred Geography, which stems from the symbolic realm, can be found in Mandala. The mandalas are circular paintings, geometrical arrangements gradually evolving from center to periphery, and various abstract symbols appear in them. Over the centuries, the use of mandalas in China has evolved in everyday life as a way of channeling spiritual energy in a positive and individual way through Feng Shui.

Chi

The Chinese view nature as a living and breathing organism. They see the universe as a chain of life that is joined together, like a living body. This spirit of life is called Chi, and it can be expressed in three forms: one that moves in the atmosphere, one in the earth, and another that moves through the human body.

The Chinese have been conducting topographic surveys since 2000 BC, interpreting land forms according to their beliefs in mythology and Taoist astrology. All of China was organized into a huge sacred geography. Mountain areas were vigorous Chi, while flat ground was slow Chi.

Chinese medicine deals with Chi in the body, Tai Chi is the development of physical Chi through harmonious exercises, while Feng Shui deals with the research and use of earthy Chi for the purposes of human environment design: room, house, street, and city.

Yin and Yang

Yin and yang are the basic concepts of plus and minus. In the Chinese world, the comparison is analogous to the full moon and the missing moon. In a world of full moon people become more Yang, meaning they tend to have more activity. The opposite is true in the days of the New Moon. So people tend to Yin, they are peaceful and spiritual, relaxed and self-absorbed.

Every view, rural or urban, has its own Yin or Yang quality. A peaceful landscape, such as a forest or green meadow, has a female influence on chi energy. Large cities have a Yang - masculine quality. Places exposed to the sun are also of Yang quality, and shady places are of Yin quality.

Four Elements

The Yin and Yang are divided into four elements: air, water, earth, fire. Every element affects the other in a constructive or destructive relationship. For example, the element of the earth: plenty of sun - fire, in the fall season will bring good crop, but with too much sun the crop will be destroyed.

There are those who add a fifth element - tree. It is common and basic in ancient cultures as the source of life, which incorporates all four elements: it sucks water and is rich in moisture, its top moves in the wind, its fruits are like fire and its place of planting is in the ground.

Mandela

The four elements are also the four winds of the sky, and in this way the spatial mandala pattern is created.

The mandala is a circular metaphysical geometric illustration of the cosmos, containing various symbols, each of which is an archetypal symbol, in an inside to outside direction from the center. It express man's desire for self-unity with the universe.

Mendalas usually describe spiritual, intellectual, and emotional processes. 
There are also ancient mandalas that are cognitive maps of geographical regions. These landscape mandalas created a sacred geography. They include mountains and rivers, and other holy sites, such as tombs of saints. Monks and pilgrims made pilgrimages to them according to a certain route painted on the mandala. The holy places were seen as steps in the world of enlightenment.

Feng Shui

A useful sacred geography that developed from the world of mandala, and is very common nowadays, is called Feng Shui. The literal meaning of the concept is "wind and water," and it expresses harmony between the Chi of the earth and the Chi of mankind for the benefit of both.

Feng Shui is a collection of many archaic symbols from different fields designed to express the harmonious connection between nature and man. In Feng Shui, the basic concept that has evolved is that the original Chi can be channeled through a system of elaborate metaphysical geometry to each person and place, to the level of the individual organ. In this way, a complex and integrated system of law and practice evolved, encompassing all aspects of human life.

Bhagua

The most common tool for practical use in Feng Shui is the Bhagua, which is actually a mandala. The Bhaguan mandala is shaped like a compass, in which symbols of Fang Shui appear instead of the directions of the compass.

In addition to the four elements, the four seasons will appear in accordance with each direction, the main landscape bodies such as the sea, the sky, the mountain and the plain, the various family members such as father and mother, brother and sister, and many other archetypal symbols, abstracts of the world in which we live. Each direction features are well detailed in tables. The complex traditional Chinese calendar, which has a dozen animals, is also based on a similar principle.

The use of the Bhagua is done by placing it in the center of the space or the desired time, with its head toward the source of spiritual energy. From then on, the characterization of all parts of space and time is made.

Landscape painting inspired by idyllic Chi energy

The symbol of Yin and Yang, of two opposite Chi energies in the universe

The five elements arranged in the shape of a star

The mandala is a symbolic circular illustration of the universe

A meditating Tibetan monk draws mandala with colorful sand

Bhagua is an eight-sided mandala used by Feng Shui

The Humanized and Sacred Space

Gaston Bachelard wrote, in his book "The Poetry of Space", that metaphysics is rooted in geometry. Whether we like it or not, there is a basic spatial quality in thought. Man exists in space much more than he exists in time. We define ourselves in the expressions of our space, much more than in any other way. The combination of the concepts ''outside'' and ''inside'' created a dialectic of division. This is a clear geometry that blinds us once we bring it into action in reality. It is very similar to the dialectic of "yes" and "no", which decide everything. If one is not careful, it becomes the basis for images that control all positive and negative thoughts. Contrary to this, these concepts, because of their proximity, are also in intimate relations. They are always willing to change direction and convert their hostility. As a result, in the images of space we are in an area where exaggeration and reduction are easy and common. We live through reducing and exaggerating them. We strive to define existence and by doing so, elevate all situations to create a super-situation. The dialectic of ''here'' and ''there'' has thus been elevated to an absolute level, whereby these two unfortunate adverbs are adorned with the uncontrolled powers of a determined being.

In his book "Air and Dreams," Bachelard wrote that the landscape is a process of witty changes, in which the imaginary is present in the reality. It lead and amplify the powers of the soul. The real journey on earth is a journey to the imaginary land. In real psychology, imagination is primarily a form of spiritual mobility, of the best, most vivid and exciting kind. There is nothing more correct than to grant the land, which mobilizes all our forces, to be employed in it, an imagination that will elevate it from the level of materialism and give it a life of its own. We experience the face of the earth through the ability to renew our hearts and minds. Imaginary life with real laws controls its images, and they create an invitation for a journey, which we feel within us as feelings of liberation and relief. Imagination is not a condition; it is the embodiment of human experience.

Rocks that resemble the human figure, whether wholly or partially, are one of the most common phenomena in nature and are some of the best attractions for humankind. Around the world there are many sites where such forms appear, and there are many that are concentrated in one place, such as canyons. One of the most famous places in the world of human forms carved in the rock is the Red Rock Canyon of Petra.

For the Chinese there is even more significance to the forms of mankind in the rocks, since according to ancient Chinese religion the origin of the gods is in the mountains cliffs. In the heart of the Imperial Palace in the Forbidden City of Beijing are gardens with a number of large natural limestone rocks, pierced by many natural holes in a variety of shapes, whose purpose is to evoke the human imagination of the connection between the human figure and the landscapes of nature.

Martin Gray writes that throughout the ages, many cultures have described the geographical space in which they existed, and expressed this in a variety of ways. One expression of these concepts was the establishment of holy places.

Perhaps the oldest form of sacred geography is that of the Aborigines of Australia.

According to their ancient legends, in the mythological period of the beginning of the world, known as the 'dream', different creatures in the form of totem animals and humans emerged from the surface of the earth and began to roam the earth. They wandered across the earth, forming features of the landscape through everyday activities such as birth, play, singing, fishing, hunting, marriage and death. At the end of each dream these characteristics became clear as stones, and the bodies of their forefathers became hills, rocks, caves, lakes and other landscapes.

Prominent places, such as Ayers Rock, have become holy places. The Aborigines followed the paths of their fathers' dreams. The paths that the totem fathers passed through the landscape were called dream trails, or songs, and they connected the holy places with special powers. The mythological births of these ancestors gave the Aborigines a sacred geography, a tradition of pilgrimage, and a nomadic way of life for more than forty thousand years, making their culture the most lasting in the world.

The ''elephant and fish'' rock in Petra, the world's number one tourist site, all of which are natural anthropomorphic forms carved in the canyon's walls, alongside which the Nabataean curved monuments.

The cafe on the shore of the lake is an illustration of a dialectic between 'inside' and 'outside'

  

A rock garden in the heart of the Imperial Palace in the Forbidden City of Beijing

  

The Ouluru is a large, isolated desert rock. It is about 330 meters high and the base diameter is about 9 kilometers. It's the world's largest monolith. It is located almost exactly in the geographical center of Australia. It is sacred to the Aboriginal population.

The book Anthropomorphic Maps

Modern technological revolutions did not make the location less significant. On the contrary, they have increased its importance, because humans have become more aware of themselves. There is no more natural in our time than to combine the spectacular views of the earth's surface and outer space with new images.

Anthropomorphism, which is the provision of human qualities and appearance to inanimate objects and animals, is very common in world cultures as a means of expression. Within the framework of all known religious beliefs, this principle is used on a daily basis, but modern technologies also require the use of it in order to improve the connection between the machine and the person.

The great popularity of Anthropomorphism rests on the fact that the human body is the focal point of attention to cultivation, nutrition and health. The human body is a miniature world in which the outside world is reflected. Therefore, there is a historical collaboration between medical professionals and artists for the purpose of illustrating the anatomy by the most graphic and artistic methods, even at the expense of pure scientific description.

In the book "Anthropomorphic Maps" are described, in the first part - ''anthropomorphism", the origins of anthropomorphism.

The second part, "The Anthropomorphic Map," describes the sources of these maps, in which the surface is described as a human figure.

The third section, "Historical Anthropomorphic Maps," covers the development of these maps from the dawn of history to the present.

In the fourth section, "Other Anthropomorphic Maps", original maps of different regions of the world, from continents, through states to islands, are presented.

The fifth part - "Map of the Human Figure of the Holy Land" - deals with the original work of the author of this book, which sheds light on the origins and meaning of Jewish faith.

The sixth part - "The Anthropomorphic City" - deals with the city. The city is a whole expression of Anthropomorphism in space.

The seventh part - "Earth and Outer Space" - is devoted to the Anthropomorphic landscapes that are revealed in outer space.

The eighth part - "Means of Transport" - deals with the car, the ship, and the airplane, through which mankind travels from place to place, and in the way gives them humanized qualities.