THE RESEARCH OF BERNHARD IOAN SIEGEL

THE RESEARCH

BERNHARD IOAN SIEGEL

( unpublished )

The basis of BIS discoveries were laid in about 40 years of studies. It was Pythagoreism, the science related to sound,

also called HARMONIK, that inspired the artist and composer in his invention a new type of instrument, the HARMONIC MEGA HARP.

BIS spent many years in Asia, and thus was able to investigate-amongst other subjects- eastern music-systems, also of the sacred variety. BIS discovered previously little known harmonical and astronomical aspects inherent in Buddhist sacred architecture. It took BIS about 10 years to bring his findings to paper.

BIS research is divided into two main categories of articles: One concerns the evident influences of Pythagoreism on eastern and western sacred architecture, and the second category concerns mainly the sacred sites of Buddhism, that have a special significance for western practitioners. In the `Astronomy at the root of Tibetan sacred architecture ´ the various cultural influences on Buddhist sacred architecture are shown.

The article- form allows BIS to keep the texts as short as possible. Therefore the diagrams form the main bulk of the argument. The articles are mainly concerned with findings that show, that ( a ) heliocentricity was known to ancient astronomers; that ( b ) several types of geometrical morphologies of the solar-system were known, that allow ( c ) to compute from geocentric planetary periods to the heliocentric periods and ( d ) further to the correct distances of the planets from the sun. This knowledge was obviously kept secret. It allowed the architects in both east and west -until the Italian Renaissance to develop almost infinite interpretations of the universe, which they transformed in sacred shrines.

The essence of the Pythagorean tradition was ( e ) therefore transmitted via sacred architecture, and not via books. BIS also shows ( f ), that much of the astonishing astronomical knowledge of ` the ancients ´ was transmitted via sacred tone-scales as it was via sacred architecture. A relevant sacred tone scale BIS detected in Tibet, through its ritual oboe Gyaling.

BIS goes on to show, that the musical -and therefore qualitative -aspect was very important to the ancients, because it allowed communication with the universe. It becomes clear, that ´ the ancients ´ studied also the qualities of our solar-system.. The basic quality seems to have been, the possibility- via sound- to establish a communicative link with the cosmos. This aspect may explain the importance ancient Greek philosopher placed on the mysterious Harmony of the Spheres. It seems, that `Harmony of the Spheres ´ also was part of a spiritual concept.

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THE ARTICLES RELATED TO

SACRED ART AND ARCHITECTURE , AS VEHICLES OF ASTRONOMICAL DATA

( Except article nr. 1)

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1 The symbols of prehistoric art at Lascaux in the light of Buddhism

The Enigma in Prehistoric Art: ( a ) The high tech in the art of the Neanderthal and the symbolism
The bone of the Ishango, a 19 000 year old `computer ´
Orpheos and his deeds, that surprising parallels with the great Tibetan sage Shenrab Miwoche
Pythagoras of Samos: His time and his influence on Indian culture
A tone-scale of the Tibetan ritual oboe Gyaling, that can be transformed into planetary distances
The `House Of the Creator ´; a pre-Inca site at Tiahuanacu, Bolivia, and the inherent astronomical data
The Holy Tetraktys : A Pythagorean symbol: The basis for a astronomically precise morphology of our solar-system.
Egypt: The Great Pyramide of Giseh, seen in the light of the tone scale of the Gyaling, and the possible astronomy
Babylon: The Babylonian Ziggurat and its inherent astronomy , synodic and sideric
The Athena temple at Paestum : The inherent arithmetic, geometry, harmonik and astronomy
A contribution to questions related to the `Lay-Line-System´ of the city of Rome.
The ancient star-form of the city of Rome and its astronomical import
The Pythagorean Underground-Basilica in Rome
The Roman Pantheon, as it mirrors astronomical data in its geometry and harmonik
Charlemagnes Dome at Aquisgrana : The harmonical, geometrical and astronomical implications of the Octogon
The Gothic cathedral at Chartres as a mirror of a astronomical harmonies.
Leonardo´s famous design: The Vitruvian Man
A detailed investigation into the complex geometrical, arithmetical, harmonical and astronomical implications of

Raffael Santi´s `School of Athens´

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The second set of articles investigates the connection between Buddhist sacred art and

Mesopotamian and Greek influences

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1 On prehistoric art: A investigation of certain configurations found at Lascaux seen from the point of view of a

meditating Buddhist

2 A preliminary comparison between eastern and western origin myths: The Tibetan Bön-tradition and Orphism

3 The Great Buddhist Stupa at Sanci and Egyptian-Mesopotamian influences.

4 The geometry of a Buddhist Symbol found at Sanci and the astronomical implications

5 The image of the Buddha and the Babylonian Ziggurat

6 A contribution to questions concerning the Lay -Line system of the Kathmandu Valley

7 A small `prototype ´ of the Tibetan Chörten and the Babylonian Ziggurat

8 The Great Stupa at Bouhdanath, Nepal and the astronomical implications.

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9 Astronomy at the root of Tibetan sacred architecture concludes the investigation.

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THE SYMBOLISM IN PREHISTORIC ART

LASCAUX

SEEN IN THE LIGHT OF BUDDHISM

60 pages 22 plates

List of plates:

A section of the cave -paintings at Lascaux, France
The bison and the shaman . Detail from Lascaux

The so called sorcerer a symbol of the non dual nature of man and animal. Cave Trois Freres, Ariege Fr.
A Neolithic symbol of the non dual view: A sculpture most probably showing Pan. Tuscany, Italy.
Another Neolithic symbol of the non dual view: A rock incision showing Pan. Photos by the author.
A Neanderthal design . The straight lines might reflect, what on grand scale today are called Ley line´s

Another design most probably executed by the Neanderthal

A possible self-portrait by the Neanderthal

A Ley-line design dating from the Neolithic period.
The non- dual ( man and animal ) as seen in the Paleolithic period
The non dual ( male -female ) as a enigma; Paleolithic period
The archetype of a compassionate mother. Paleolithic period

Neanderthal idols?
Another archetypical form: The compassionate mother

A Paleolithic tripod of bear sculls.
A detail from the axis gallery at Lascaux

The constellations around the polar star
Drop-like abstract symbols
Two antelopes and a Paleolithic symbol of quarternity

The deer flanking the Buddhist symbol Dharmacakra

A Assyrian tree of life , flanked by two deer
Raffael Santi: The Pythagorean Holy Tetraktys

Table of content:

I Dedication / II Foreword :

The various motivations to inquire into the prehistoric spiritual roots of man / How to overcome the limitations of contemporary art and science, that impede a comprehension of the patrimony if the Paleolithic period / The spiritual roots of science in Pythagoreism / The practitioner-artist- scientist / The results of the fusion of eastern thought and meditation; and western art and science can bring./ What the form of age-old and unchanged symbols can tell about the content of symbols/ The spiritual roots of art/ The opposed motivations of the contemporary artist versus the artist of prehistory.

Perception of time/ Is the human perception of time subject to a illusory distortion as is visual perception? / Could there be a `central perspective ´ that distorts the perception of time?/ Herbert Kühns discovery: The parallels in the alternating styles in art: Abstract art and realism are also detectable in prehistoric periods/ The curious time-spans of the four Indian Yuga´s / the decline in length and in quality.
The basic differences in `life-styles ´ between Paleolithic- and modern man./ The approach to darkness./ The light and the darkness in the life of a modern artist./ The visible light within us./
The animal: Animals our great benefactors once were regarded as possessing wisdom /Paleolithic spirituality may not have been concerned with asking gods for favors , but based on a balanced `give and take ´ between man and animal. / Are modern artists, scientists, and spiritually inclined persons on the giving side`? /
Ancestors? How many ancestral parents do we count? / Were the painters of the caves of Chauvet and of Lascaux our ancestors? / There are both, genetic and spiritual reasons to inquire about the motivations of the Paleolithic artists.
Reincarnation: Was reincarnation assumed in Paleolithic periods?/Is the bison-shaman scene at Lascaux depicting the help a spiritual human can provide for the animal? / Is the ´ see through ´ figure a psychopompos?

The other human : The Neanderthal . / The slow re-evaluation of the talents the Neanderthal possessed on behalf of the Paleontologists/ His physical powers: eyes that see at night, and his sense of hearing excels that of the Homo sapiens. / Why was Lascaux painted? / What does Darwins `survival of the fittest ´ imply for the spirituality of mankind?/ Does Darwinism indicate, that man-in previous ages was more noble? /
Prehistoric art versus contemporary art: The differing motivations./ The bard-artist as a leader of the clan.
The begin and end of a cultural exchange: The Paleolithic revolution the result of the contact between Neanderthal and Cro Magnon.

What can science tell us about prehistoric art? The scientific terminology : Animalism, Therio-animalism, magic has

no practical significance./ the symbolic language and the symbols found at Lascaux reappear in the Neolithic period as well as in historic times in Asia

Why engage Buddhism in our research? The cave paintings of the Paleolithic period show, that deism was absent then./ The factors that point towards the possibility, that man saw himself not a singular creature, and therefore non-dual with the rest of creation./ The subsequent sense of responsibility for all life-forms. /Cave paintings as an act of compassion, expressed in ritual./ The natural whish for a fortunate rebirth of animals /Prehistory can be understood with the help of the keys that Buddhism provides.
The parallels between prehistoric and historic art styles./ The alternating realistic and abstract styles./ A vortex of

time?

The measured earth:/ The symbols of union: Sacred locations, places of power and Ley -lines./ The symbols of union

in Paleolithic art./ The lost union/ The scope of art: To reconcile the individual/ The symbols of compassion./

The small stone: The earth, a living organism reflects the proportions that rule everywhere else in the solar system./

science sees the earth as something dead. How come, that human intelligence has difficulty to fully understand the workings of a dead nature? The prehistoric `landscape architects ´/ The desired and the undesired results./ the great amount of small stones.

Who were the artists? Were the painters of the cave-art in the Paleolithic period enlightened, realized beings? /Were

extreme practices of self-sacrifice practiced amongst the elders of the Homo sapiens sapiens? What were the means

to obtain unlimited compassion?

Some scientific views: The terminological inventions of Paleoanthropology/ Why was the animal denied to have a anima-by the church?/ Why god was denied by science./ The polarity between mysticism and Gnosis and the written words of gods. / Lama Norlha´s explanation of the sense experiences in the god-realm. / The possible spiritual competition between the two human species./ Why did Homo sapiens adopt the cult of the bear?/ Was the slow degeneration of the Neanderthal the result of too much killing?
The situation today: The limited interest of contemporary man in animals./ Animals as objects for sacrifice,

experiments and excessive `animal-food- production ´. Did the ancients knew of a possible transmigration between

the animal-realm and the human realm? / Is transmigration also a cause contributing to the growing human

insensibility?

Who is man? Were the Origin Myths with man since the beginning? / Without Origin Myth no ritual./ What were

the reasons Homo sapiens pushed out of Africa, where a balanced vegetable diet was possible? / Is the excessive

carnivorous diet the cause of a slow degeneration of man?

Purification: Is purification a Paleolitic concept? / Are the various methods of purification the only means to re-

pristine consciousness?

Reincarnation II : Paleolithic Cro-Magnon thought non-dual ./ Therefore he must have understood the effects of what Buddhist call karmic retribution. / Sacred animals./ Was the cult of the Great Mother also a cult of the grand mother? / Was she the compassionate female, who invited the life-force of all noble beings into her womb and into the womb of her `daughters ´?/ Is she therefore the queen of all animals? /
The small stone II: Offerings for mother nature./ The vast depository fields./ the possible dangers concerning

excavation/ The function of the worked-stone-depositary as a history book/ The frightening Neanderthal features

portrayed in stones/ The madonna figurines and the Homo Sapiens. / Attitudes, that both man and animal have in

common.

Reality: Possible differences in the perception of reality /Lama Kyab Dje Kalu Rinpoche on reality.
The three tantric categories: The peaceful, the wrathful, and the peaceful/ wrathful. /What Tantra can do for practitioner-artists working with scientific methods. / Tantra, and the complexio oppositorum / the changeing needs of society. / The end of art and the begin of ecology. / To satisfy mind is to satisfy inborn compassion. / The translation of inborn compassion into symbols and pictures.
The wrathful: Was the early Homo sapiens fond of carnivorous animals? / The cave of Chauvet was painted about

17 000 years earlier then Lascaux. Does it provide us with the evidence, that early man showed a greater concern

towards the meat -eaters? / What are the gifts of the carnivorous animals?

The peaceful-wrathful: The bear and his gifts/Medicine/The Neanderthal-bear symbiosis.

The peaceful: A detail of the cave paintings found at Lascaux/ Lascaux celebrates the giving nature./ Cows and horses/ A dance -ceremony in which the animals dance round in the sky/ The astronomical implications/ Ekstatic dancers look through-animals and the rocks -right into the sky: To aid the giving animals depicted./ to be on the `giving side ´ means, having the possibility for a favorable transmigration.
The abstract symbols at Lascaux: The ´ geometrical ´ symbols painted at Lascaux. / Symbols of salvation? Did there

exist a taboo to depict geometrical perfection?

Continuity: All symbols and symbol-conglomerates painted at Lascaux reappear more then 10 000 years later all over

the world: The so called `animal-trap ´ flanked by two long horned antilopes reappear as the symbol of a tree of life

In Assyria. In the 2^nd millenniumBC/ The Buddhist symbol of the Dharmacakra is flanked by tow deer / The `animal

trap ´ is actually a fore-runner of the Pythagorean symbol of the Holy Tetraktys, as depicted by Raffael Santi /The

drop-like triple-triad reappears in Tibet as the symbol called ter.dzar / In ancient Greece, that symbol is also used to

represent the most profound proto-mathematical insight into the nature of the overtone-and undertone-ranges. /

Today it is the symbol for percentage.

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THE ENIGMA IN PREHISTORIC ART

Prehistory has seen several human species. Homo sapiens sapiens,our ancestors, also called Cro-Magnon, and the Neanderthal are the two species best known to us. It is said that the Neanderthal survived until some 27 000 years in the Balcans.

We looked carefully at the artistic remains of the Cro-Magnon and we found, that a mere scientific starting point cannot

deliver the evidence, that early man was a spiritual being. Therefore we applied the non-deistic standards of Buddhism, that are based on the inborn qualities of man. We also found, that the moment we allow our ancestors to be spiritual beings, the art of the Cro-Magnon turns into a spiritual teaching, with a highly developed sense for symbolism.

When it comes to interpret the remains of the other famous species, the Neanderthal we run into several difficulties that originate in the eye of the beholders: We have become accustomed to assume that the Neanderthal was a brutish and primitive creature, who left us nothing but some roughly hewn stone-tools. But this creature did not only leave us worn out tools. The remains of the Neanderthal are no prehistoric junkyard. Such a view can only be forwarded by researchers who have little understanding of art. We find re-shaped huge boulders and smaller stones, that may not correspond to tastes preferring classical art, but they certainly correspond and even excel that what we find in our museums on modern art. That is, if we attribute the remains we find at Neanderthal centers -in France, Spain, and Italy really to this species.

Here the design of the smaller stones corresponds -on scale with the huge reshaped boulders found in the Amiata region of lower Tuscany in Italy. The technique of the stone-cutting methods invariably excel that of modern art, as does the artistic concept.

But we may ask, if that is so, that the Neanderthal was -compared with the sculpture modern art produces- the superior artist, how come nobody so far has discovered this fact? The answer to this question lies partly in the general disinterest of scientists in art, and partly in the psychological difference between us and the Neanderthal.

In fact, that what we initially recognize to be features of man and animal, are often terrifying and distorted features. And definite stereometrical features are absent. That means, that a slight change of position of the beholder may produce a totally different picture.

If we are willing to accept most of the smaller reshaped stones to be pieces of art, we look into a horrible concept of art. Therefore it may not be art all, that we see, but interpretations of existence. Only a handful of the most realistic western artists are willing to depict their -for others- terrifying outlook on life. If we apply also the Buddhist point of view, then the Neanderthal art may be a interpretation of life in general, and/or of the conditions of certain unseen sentient beings in particular.

BIS studies the remains of the artistic output of the Neanderthal in the Amiata -region in Tuscany, Italy and he concludes,

if the remains there are really stemming from the Neanderthal, then this species possessed far more developed stone-cutting methods then the Cro-Magnon, together with contemporary man.

In this article, the author puts forward a series of photographs that show the refined character and technique seen on certain large rocks and smaller stones. But, as is the case with the remains of the Homo sapiens sapiens, the spiritual level of a species cannot be measured applying scientific levels.

It might seem hazardous to venture into a interpretation of the spiritual level of the Neanderthal. But without it, we will never allow ourselves to see, and understand, that innumerable rocky locations of great beauty, that we find all over the globe are in reality the outcome of a very careful landscape design.

Therefore BIS chooses as a basis for his hypothesis the ancient Indian concept of the `Spontaneously Arisen ´ , also called

`not -man -made ´, or swayambhu, a concept certainly age old, and not necessarly limited to Indian traditions. Buddhism adopted this concept, applying it as also to natural laws, but also features in the landscape. Also in the Tibetan tradition, special features in landscapes as rocks were and are regarded as enlivened by divine presence.

Since the `art style ´ of what we believe to be of Neanderthal origin can be found all over the word, the possibility exists, that long ago, in pre-history, a world culture may have existed, in which man enhanced certain features in the landscape, that nevertheless remained seen as `Non-Man- Made ´.

The features that grace sacred landscapes are also reflected in a multitude of smaller stones, that may have been-long ago- deposited at sacred locations as votive-offerings. On those stones, we rarely find only one sole precisely defined feature, as contemporary art is fond of. But we find invariably a multitude of enigmatic features can be seen on one singe object. The design and cut shows, that in pre-history, man possessed a technology - unknown today - that allowed the most minute treatment and the shaping of ` miniatures ´.

These `miniatures ´, the author believes, depict mostly sacred landscapes on a small scale. The author discusses the question, ( a ) how ancient man could enhance natural features with his `design ´ without harming the ´ spontaneously arisen ´ natural form, and ( b ), why almost invariably the images seen in big rocks and in small stones have a terrifying aspect.

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ORPHEOS

HIS LAND; HIS TIME; HIS REAL LIFE; HIS MYTH

Here BIS takes a close look at the many parallels between Orphism and Pythagoreism on one side and Bön and Buddhism on the other.

TABLE OF CONTENT

Introduction.

A possible heritage: A recent discovery. The Mesolithic culture in eastern Europe that produced the earliest known form of writing: The Vinca culture.
The cultural changes: The end of the Matriarchal society, the Indo-German invasions/ Orpheos interprets the Origin Myths
The proto-chemical and metallurgical aspects: The Orphic Origin Myths seen from the point of view of metallurgy and Alchemy
The Dionysian confusion
The Menades.
The multitude of divinities. The 90 Orphic divinities / Deified elements/ The planetary gods/ The nine muses

The Orphic literature: Compilations by Diels, Capelle : Anaxagoras, Aristophanes/Kirk Raven and Schofield: Plato, A Orphic fragment found in a grave/ Aristophanes : Frogs
The writings for the dead: The golden plate found in the grave of Petelia, Crotone, Italy
The Orphic theogony: Damaskios Principles/ The various Orphic Origin Myths / The Orphic cosmogony

differentiates between ( the cosmos as spatial development; the medicinal aspect; and the inner energies of man

A Tibetan Origin Myth: The Origin Myths in the Bön tradition/ The meaning of the Mang and the rites of human

Generations/ the Mang: the proclamation of truth/ The perfect convergence with prevalent scientific views on the origins of the cosmos/ the Myth of the cosmic egg.

The first science in the western hemisphere : Etymology: The original Etymology is a philosophical discipline
Orphic mysticism: The historical roots of mysticism and Orpheo´s role.
The Orphic mysteries.: the concept of purification as a basic necessity to participate in the Orphic initiation
The symbols shown at orphic initiations: The ball, the mirror, the dice/ Plato´s warning, that the non initiate faces dangers in the underworld.
Oracles
Orpheos and Homer: The Argonautes, Orpheos, Odysseus, Heracles, Jason.
Orpheos, the legend
Are there traces of Dionysian music?

A PRELIMINARY COMPARISON

BETWEEN

( a ) TIBETAN BÖN/ BUDDHISM , (b ) THE MEMORIES OF THE NATIVE AMERICAN HOPI;

AND

( c ) GREEK ORPHISM AND PYTHAGOREISM

ca 25 pages

-In this treatise BIS investigates similarities in the above mentioned traditions. He detects ( a ) a curious absence of dependency on deism in those spiritual traditions, ( b ) similarities between the Tibetan bards Shenrab Miwoche and Orpheos of Thrakia.

BIS bases a part of this investigation on Chögial Namkhai Norbu´s Drung, Deu and Bön. Without this work the world would know next to nothing of the origins of the Bön tradition in Shang Shung, a prehistoric kingdom in the Mt Kailash region, that existed before the formation of Tibet, nor of the great Bön master Shenrab Miwoche

In the same way, Europe has forgotten the real accomplishments of Orpheos. This bard was the highly realized founder of a religious movement that shows features that parallel Shenrab Miwoche`s achievements- and it predates those of Sakyamuni Buddha.

B.I.S. compares the lives and work of the two spiritual reformers living at the end of the Neolithic period, who both attempted to abolish animal sacrifice, and who left a lasting impact on ( a ) the Tibetan Bön tradition, and on Greek Orphism, that later was reformed by Pythagoras.

Table of content:

-The various spiritual traditions. that reveal previously unknown concordances.

-The Ionian Greeks and Alexander the Great. The `Harmony Of The Spheres ´: A superior type of astronomy

-Bön, Buddhism, Dzogchen . Chögial Namkhai Norbu

-Possible links between the Native American Nations and Tibet?

-The keys provided by the protagonists of Orphism and Pythagoreism allow the rediscovery of the` Harmony Of The

Spheres ´. But they also are useful, to elucidate similar questions concerning Tibet and the South American cultures.

-The history of the Hopi according to Hopi White Bear, as written down by :J.F.Blumrich

-The implication of the Hopi memories.

-The parallels between the historical founders of Bön and of Orphism; Shenrab Miwoche and Orpheos

-Origin myths seen as a chain of transformations. Their equivalencies in

( a ) proto-chemistry and in ( b ) proto- mathematics, and in the Indian geometrical system connected with Yantra .

-The Cosmic Egg.

-The origin of the origin myths

-The Bön and the Orphic efforts to abolish animal sacrifices

-Atheism? The realistic Bön, Buddhist and Hopi view on the ` gods ´.

-Art, symbolism and numbers . The origin myths also providing proto-mathematics

-Non-dualism

-Another possibly connected ancient tradition: Alchemy

-Perception of time-The symbolism of a Orphic funeral vessel. J.J.Bachofen revisited

PYTHAGORAS

Here B.I.S. treats the impact Greek Pythagorean teachings had on Buddhist builders in India. These teachings were of two kinds, spiritual and worldly. Pythagoras reformed the spiritual Orphic school, that showed astonishing parallels with to the Tibetan Bön traditions and with Buddhism. A part of Pythagoras teachings, collected by the master in Egypt and Babylon, became the root of western scientific thought. About three hundred years later, Pythagorean teachings were again brought to the east. As many Ionian Greeks became Buddhists, Pythgoreism became part of Buddhist sacred architecture, possibly also including the famous `Harmony of the Spheres ´, a religious-astronomic system.

B.I.S. also traces parts of the Pythagorean teachings to Tibet, and he discusses three possibilities: ( a ) Tibet inherited its proto-mathematical knowledge from a previous world culture- as postulated by Hopi elder White Bear, ( b) that between Tibet and Persia and Tibet and Babylon existed contacts, which would explain the astronomic, astrologic and architectural similarities between the two cultures, and ( c ) the third possibility, that the `Harmony of the Spheres ´ was introduced by Pythagorean philosophers accompanying Alexander the Great to Asia.

BIS believes, that today there would be no knowledge of the famous `Harmony of the Spheres ´, if we did not possessed the Indo/ Tibetan keys. Also the following investigations rests on two legs: The harmonic aspect related to Tibetan sacred music, and Tibetan sacred architecture.

The highlights:

- The difficulty to reconstruct Pythagoras´s teachings / The continuity of Orphic thought.

The Pythagorean teachings on sound / The Tantric teachings on sound/ Astronomy in Tantra and in sacred architecture
The difficulty of western musicologists to interpret eastern sacred tone-scales/ Music-therapy/ Pythagoras teachings
On music / The `cycle of fourths ´ and the `cycle of fifths ´ only recently applied in the Pythagorean sense
The teachings on the non -dual view / The human voice, the vocals and the overtone and undertone-ranges
The heritage of megalithic-times/ The Pythagorean heliocentric astronomy : Aristarch of Samos
The Harmony Of The Spheres
The various types of secrecy / The Buddhist Kalacakra Tantra
A.v. Thimus / H. Kayser / The Monochord / Harmonik /Tabula Pythagorica / Vitruvius Pollio
The contemporaries of Pythagoras : Sakyamuni Buddha , Lao Tse , Konfuzius, Zoroaster, Ezekiel
Pythagoreism found in all cultures , including in South America / What serves a morphology of the planetary system?
The Italian Renaissance genius Raffael Santi
Bön Origin Myths / The tone-scale of the Gyaling / The double impact of the Pythagorean teachings on sacred Muslim architecture
Pythagorean literary fragments / Empedocle / Ion of Chios / Timaios of Tauromenion /Apollonious of Tyana Porphyrios / Iamblichos / Plato / C.G.. Jung / The mysteries / The oracles / The Pythagorerism-Buddhism parallel
The Muses- Dakini parallel /
-Copericus , Kepler
Pythagoras according to the legend.

THE HARMONY OF THE SPHERES IN TIBET

NEW LIGHT ON A TONE SCALE OF THE TIBETAN RITUAL OBOE GYALING

INTRODUCTION

- The number 12

A ritual tone-scale on the Monochord.
Subsequent transformations
The possibility to deduct a proportionate model of our heliocentric solar system

LIST OF PLATES

- The patterns the potential harmonics or overtones form on any tight chord

A Tibetan symbol: The knot of eternity

- The Pythagorean Lambdoma

The harmonic -Canon
The Gyaling tones on a short monochord of 120 cm length of string

can be transformed into a sequence in the overtone-range on a string measuring 12 times 120 cm

The Gyaling tones and the Tibetan long neck lute Damien

- The Pythagorean `Holy Tetraktys ´

The Egyptian way of extracting out of a circle-square relationship the harmonic proportion 8:9
Leonardo´s unification of the square and the circle
How to arrive at the ' squaring of the circle ´ in relation to the circumference
Keplers initial model for a `cosmography´.
A proto-mathematical transformation of numbers mentioned in a Tibetan Origin Myth into the proportions of the

tone-scale of the Tibetan ritual oboe Gyaling

Several ` cosmogone ´ diagrams :

-The `Alpha´diagram and the numbers of the Pythagorean Tetraktys

-The `Alpha´diagram containing the proportions of the Gyaling tones

-The `Alpha´diagram and the time-spans of planetary revolution

-The `Alpha´diagram and the mean distance of the planets from the sun

-The transformation of a square into a triangle and the Vesica Piscis

-Six successive transformations of a square into a triangle

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THE HOUSE OF THE CREATOR

A PRE -INCA SITE

AT

TIAHUANACU IN BOLIVIA

Introduction

The `Living Quarters ´ of the creator

The central building, the Akapana

The proportions

The arithmetic

The geometry

Angles and fractions

The division into 13 and 20 equal parts

The astronomical implications

The harmonik

Proto-mathematical transformations

The proportions of the sacred tone-scale of the Tibetan ritual oboe Gyaling in the proportions of the Akapana

The lowest tone of the Gyaling

The second lowest tone

The third-lowest Gyaling -tone

The fourth Gyaling -tone

The fifth Gyaling- tone

The sixth Gyaling-tone

The calendaric possibilities

The sideric periods of revolution

The key that unites synodic and sideric appearances

The structure of the keys: the Proto-harmony, Geometry and arithmetic.

The orb of Mercur

The orb of Venus

The orb of Mars

The orb of Jupiter

The orb of Saturn and the equivalence in the ground-plan of the Akapana

The transformation of circles into squares and vice versa: The three squarings

The affinities with the ground-plan of Stonehenge

The ground-plan of the Akapana 3 times octave reduced and the superimposed model of the heliocentric planetary system

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THE BONE OF THE ISHANGO

Introduction:

Page 1 What are modern mans greatest suppositions?/ The term `primitive ´ in science/ A straight time-track

Page 2 Ancient mathematical calculation versus modern calculation obfuscating the original numbers/ Can a number

be really known? / Numbers as symbols

Page 3 Transformations/ Was the overtone-scale known in ancient times?

Page 4 Proto-mathematics not only a intellectual affair/ The Neandertal -beginnings

Page 5 Archaeological excavations at Sungit near Moscow/ The number of pearls on in bone-ornament. The

rhythmical context, facilitating to keep count of astronomical cyclic recurrences / Time , space and weight

Page 6 Bone pearls on a mantle from a grave at Sungit/ Why were astronomical correspondences regarded to be

sacred?

Page 7 The most ancient Raga and Tala systems of the East/ Why are certain modes no longer appreciated?

Page 8 A musical multiplication

Page 9 Reciprocity in mathematical fractions/ Overtone-sounds in nature: Cracked Bamboo-poles/ The humans

interred at Sungit had no problem with numbers above 1 000/ The decimal system versus doubling and halving

The disregard of commas in proto-mathematical symbolism/ Ornaments as counters/ The various numbered-

Mala rosaries of India/ The Eastern medicine systems making use of astrological time-circles / The ritual

proclamation and instruction on truth based on origin myths/ ransom payments and offering of effigies

Page 10 The knowledge of time cycles / The psychology of the ritual

Page 11 The number 60 in pre-history / Heinzelin´s excavation of the about 9 000 year old bone in Africa

Page 12 Conclusion

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THE HARMONY OF THE SPHERES IN THE ANCIENT EGYPTIAN HERITAGE

Introduction : The principles determining ancient Egyptian sacred art /What are the reasons to use a rigid Canon? No texts on art surviving /What the Pythagorean keys can do/The Canon/The psychology of an artist practicing `Objective Art ´/What was the initial spin to canonize art?/Ritual is based on myth.

-The ancient Egyptian symbols of the `non-dual ´ view : The triad man, god, animal

-The ancient Egyptian Canon of proportion

-The arithmetic means of transformation:

-The symbolic geometry

-The Pythagorean Tetraktys -numbers

-The proportions found in the Tibetan tone-scale of the Gyaling are also proportions in the ancient Egyptian Canon

-The pyramid build by Imhotep

-The pyramid of Cheops buildt by Hem On

-The proportions determining the `Harmony of the Spheres ´ in the Great Pyramid

List of plates:

1 The wooden plate depicting Hesire , a high official living about 2500BC

2 The `Eye of Re ´

3 A unfinished detail in a tomb showing a practical application of the Canon

A Hermetic interpretation : Two squares fuse through their transformation into circles
The arrangement of squares and their diameters that lead to the Pythagorean Tetraktys-numbers
The geometrical interpretation of the proportions in the figure of Hesire

7 The five-star in the figure of Hesire, indicating the presence of the `Golden Section ´.

8 The proportions corresponding with the Gyaling tones in the figure

9, 10, 11, 12, 13, and 14 : The Gyaling tones in the figure

The Gyaling-tones as degrees.
The Gyaling-tones as degrees in the figure of Hesire
The superimposition of a geometrical possibility to construct a diagram that shows the identity of both, the Egyptian Canon of proportions of gods and men as of the inner and outer shape of the Great Pyramid

One of the several possibilities to superimpose proportionally the inner chambers of the Great Pyramid over the figure of Hesire.
A contemporary drawing of the inner sections of the Great Pyramid

The possible arithmetical construction of the G.P. with the help of the numbers 11 and 14 by Bindel
A possible geometrical construction of the G.P. out of the five-star by Bindel

A possible geometrical construction of the G.P. through circle and square by Michell
A geometrical way of construction with the help of the Vesica Piscis by Michell

A mode found in Indian Buddhist sacred architecture corresponding to the proportions found in the G.P.
Piazzi-Smyths findings: A peculiar `inner square´ in the G.P. based on the level of the sea.

The possibility to find the harmonic proportions equaling the tone-scale of the Gyaling : The Mercur-tone.
The Gyaling tone that can be transformed into the AU of the planet Venus.

The Gyaling-tone that can be transformed into the AU of the Earth.
The Gyaling-tone that can be transformed into the AU of the planet Mars.

The Gyaling-tone that can be transformed into the AU of the planet Jupiter
The Gyaling-tone that can be transformed into the AU of the planet Saturn
Two pyramids superimposed.
The pyramid that holds the planetary distances in AU
A geometrical way to arrive at both ( a ) the proportions of the Gyaling tones

( b ) the planetary distances in AU.

35 The AU based orb of the planets Mercur, Venus and Earth in circles that can be inscribed into the side-view of the

G.P

36 The orb of all the six in antiquity known planets ( including the earth ) that can be drawn into five pyramids each

double the size of the previous.

THE ZIGGURAT; OR THE TOWER OF BABYLON

List of plates:

A Koldaway´s map of Babylon

B The Arithmetic of the sacred area

C The geometry of the site

D The number 1728 and the diameter of the sun/ and the concept of the Indian Yuga´s / the list of mythical kings

THE ASTRONOMY

E The tropical year

F The Lunar year

G The dimensions of the Ziggurat

H The synodic period of Mercur

I The synodic period of Venus

J The synodic period of Mars

K The synodic period of Jupiter

L The synodic period of Saturn

M The synodic periods in triangles

THE POSSIBLE HELIOCENTRICITY

N The sideric periods

O The radii of the circles providing sideric periods

P The mean distances of six planets from the sun, as proportions found in the Ziggurat

THE ZIGGURAT

A graphical reconstruction of the famous tower, including the stairways

THE ARITHMETIC

The numbers of the `Plate of Esaglia´, and the graphical reconstruction
A transformation
A hidden triangle, that thousands of years later became the Arabian- and the Gothic arch

THE GEOMETRY

The geometry
The successive square-triangle -transformations
Another geometrical possibility to construct the Ziggurat
A hidden `circle of the square ´
Another possibility
The `circling of the square ´ related to circumference
The synodic periods of planetary revolution as circumferences of circles
The sideric periods of planetary revolution as contents of circles
How the content-related circle fits into the side view of the Ziggurat
How the radius of the circumference -related circle fits into the ground-plan and side view of the Z.
A surprise, the exact angle of the Great Pyramid of Egypt found in the Z.
How the Z. helps to elucidate the positions of the inner chambers of the Great Pyramid

THE HARMONIK

The geometrical construction of the ground-plan of the Z. that equals Monochord-lengths of string
Another possibility to find the proportions of the Gyaling-tones

THE CALENDARIC POSSIBILITIES

The superimposition of the division of the year according to the Mayan tradition
Two more possibilities
The time-aspect, that could have played a role in the Egyptian view on time, related to the passage through death
Another possibility

THE SIDERIC PERIODS OF PLANETARY REVOLUTION IN THE ZIGGURAT

The sideric periods of the in antiquity known planets Mercur and Venus
The sideric periods of the planets Mars Jupiter and Saturn

THE MEAN DISTANCES OF THE CELESTIAL BODIES FROM THE SUN

IN AU

THE MEAN DISTANCES DEDUCTED DIRECTLY FROM THE GROUND-PLAN OF THE ZIGGURAT

Six successive transformations of a square into a triangle

The arithmetical proportions of the Ziggurat

The ground-plan and side-view of the Babylonian Ziggurat , the Gyaling tone-proportions

A schematic frontal view of the Ziggurat with the circles that have radius that correspond proportionately to the medium distances of the planets Mercur, Venus, Earth and Mars

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ANNOTATIONS TO THE LAY- LINE - SYSTEM OF THE CITY OF ROME

Foreword
The main axis of Rome, and 9 equal distances within the city, marked by important sites
The main axis of Rome , the equal distances and various sites outside the city of Rome

THE STELLAR FORM OF THE FIRST WALLS OF THE CITY OF ROME

This chapter is based on Prof. Lugli´s findings

The geometrical key of the stellar form. By Lugli
A Indian parallel: A irregular octogon, formed out of three intersecting triangles
The stellar form superimposed over the map of the city of Rome
The possible coordinates within the irregular octogon corresponding to the proportions of the tone-scale of the Gyaling on a Monochord with 120 cm length of string
Also the doubled diameter of the circle holding the irregular octogon gives precise proportions
The circle, the stellar-form and a mysterious harmony within the harmony of the spheres:

If we place the circle corresponding with the AU of Mercur on the four cardinal points , the these circles give the

dimension of a circle that corresponds with the medium distance of the planet Mars from the sun. The circle

corresponding to the AU of Venus is obtained through the two radii involved. That concerns also the AU of Jupiter.

This clarifies the many allusions mentioned by Lugli, that the stellar form has to do with the sun. It is much more. It

concerns the time - space relationship of the planets!

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THE PANTHEON OF ROME

A older representation of the `Rotonda´.
The Alpha-diagram in the groundplan of the Pantheon
The Alpha-diagramin the side view of the Pantheon

THE GYALING TONES AS PROPORTIONS

If the front part of the ground-plan of the Pantheon is given 120 (cm) Monochord-string lengths, the all the other five tones- corresponding to the tones of the Tibetan ritual oboe Gyaling -can be obtained through the architecture of the Pantheon: The Mercur- tone 8/15B , or 64 cm ( here mm) can be obtained through the octogon. The tone of Venus 4/7 Bbb, or 68,57 and the tone of Mars 3/4 F 90, give us two circles that in the ground-plan of the Pantheon correspond with the width of the columns in the altar niches. The tone of the Earth, 2/3 G 80 , as a radius of a circle indicates the thickness of the walls of the Pantheon. The Jupiter tone 6/7 Ebb 102,85 is given by the distance between the center of the round part of the site and the position of the columns outside it.
A side sectioned view of the Pantheon. A limited selection of Gyaling tone-proportions, seen as colored lines

Show, that the geometry of the Pantheon is such, that it is thoroughly structured according to the `Harmony of the Spheres ´.

THE ARITHMETIC

Here we apply a Canon of the Buddhist tradition. It shows, that a rhythmical and arithmetical proportioning of the

side view is -not only possible- but it clarifies the proportions of the portico. The height up to the roof can be

taken as having 34 units compared with the length of the axis of the Pantheon as having 100, and the opening ,

the eye measures 12 units

Here we apply the Buddhist Canon with the small side on the baseline. Also her we can see that we arrive at

important proportions

THE GEOMETRY

The Alpha- diagram seems to be good for infinite surprises:

This diagram shows, that if we divide its wider expansion by five, and then draw circles, both, radii and intersections provides us with proportional keys , helping us to understand the multiplicity of proto-mathematical interconnections.
Here can be seen, that the Alpha diagram -if divided by 3 - allows us to draw triangles that correspond with

With the proportions of the Cheops Pyramid! ( the pyramid has a proportional ground-line of 440 and a height of 280( Therefore we divide the 120mm of the small side of the Alpha -diagram by 440 = 0,2727 and then multiply by 280 = 76,36 times 3 = 229,08.A good enough approximation.) Above we saw the ground-plan of the Pantheon as determined by the Alpha diagram, now we detect, that the side-view of the portico of the Pantheon was determined by the trisection of the Alpha-diagram, that gibes us the proportions of the Cheops Pyramid

If we place the trisected standing Alpha diagram over the side view of the central part of the Pantheon, then we

detect that certain proportions are determined by it. But most interesting is, that the width of the opening, the

`eye´ of the Pantheon is determined by it.

THE PROPORTIONS OR MORPHOLOGY OF HELIOCENTRIC ASTRONOMY IN THE ROMAN PANTHEON

We detected a Mandala -like structure in the ancient star-form of Rome, where each circle corresponds proportionally with the mean distances of the in antiquity known planets from the sun -in AU . Each circle is determined by the circumference or the radii of all other circles. Similar figures can be inscribed into the ground-plan of the Pantheon. This type of geometrical development is detectable in several sacred sites in Europe, with the best example found in Chartres Cathedral in France. By no means, these `chains of circles´ do only have ornamental character. There are more ´ harmonies ´ hidden, then science cares about. It is recommended, to study the astronomer Thomas Michael Schmidt´s findings in this context.

Here we detect that if we draw a circle around the entire ground-plan of the Pantheon, we can take this circle for 1/8 of the mean distance of Saturn from the sun. The 1/2 AU of Jupiter runs right through the columns inside the round, The AU of Mars seems to determine the thickness of the wall.

Also the orb of Venus, and Mercur can be drawn such, that they fit geometrically. We notice two vesica´s :

One can be formed by the (orange) Jupiter AU and the ( blue ) circles of Venus proportion the width and the breath of the portico. The AU of the Earth here is transformed into a rectangle formed by two squares. It includes all columns and proportions also the inner depths of the site. The five `Mercur´ cycles do form a chain that marks the inner extension of the Pantheon. .All of those circles have a definite ´hold´ in the proportions

A section of the side view of the Pantheon , over which are drawn the small red circle-chain of the Mercur AU;

the blue Venus AU, and the red Mars AU.

THE PYTHAGOREAN UNDERGROUND BASILICA NEAR PORTA MAGGIORE IN ROME

This site, build in the style of a Greek forensic Basilica was most probably cut into the ground by members of the

Pythagorean brotherhood in the 1th. cent BC. It seems having been closed by emperor Claudius, and subsequently was

forgotten. But it must have been known amongst Roman architects also in later centuries, because it is the only site in

Rome that could have provided Christianity with a model of the Roman Christian church: The elongated three naves,

the rounded Apsis a prototype of the Christian church.

PLATE 1: A view of the central Apsis of the underground Basilica .

PLATE 2 : A section of the stucco relief ´s that decorate walls and ceiling in the Basilica. We notice a very strict delineation and a Mandala-like arrangement of the main motifs. The delineation seems proportionally identical to the one decorating Piazza San Marco in Venice. The themes of the motifs are distributed in a highly symbolic -arithmetical arrangement. We find a precise number of faces of Medusa. Here she is shown in her peaceful form, smiling. ( Medusa seems to have been a protectoress of the Pythagoreans. Interesting to note is, that she has two distinct aspects: One peaceful and another is wrathful, baring her fangs. Therefore it is not impossible, that Medusa was seen as a personification of the inspiring principle, not unlike the Muses. Medusa parallels the Dakini-principle of Tantric Buddhism.) Numbered are also the masks of Ammon, a form of Zeus together with the `decorative´palms. Most archaeologists therefore attribute this temple to mystic Pythagoreism

The interpretation of the motives depend therefore if we apply a exoteric or a esoteric point of view. For instance, the central motif, the apotheosis of Ganymede certainly can be seen is a symbol of a pure person´s affinity with the divine realms. The motif is known as the `Rhaptus of Ganymede ´. Strangely enough, rhaptus is often translated by German scholars as `Raub´ meaning theft, while Anglo Saxon scholars translate it with `rape´. Both interpretations are rather absurd, but they reflect the worldly spirit of the times very well. That the artists had something else in mind then abduction can be deducted from another presentations: The so called `rape´ of Leukippide. If we have a close look at the motif, we detect a humorous aspect, together with the application of mathematical degrees hidden in the placement of the arms of the supposedly abducted lady.

THE ARITHMETIC

PLATES 3, 4 and 5 show the ground-plan and the side-view of the site, together with the arithmetical probabilities.

THE GEOMETRY

PLATE S 6 and 7 show the geometrical plan of the ceiling decorations.

PLATE 8 : The Alpha diagram superimposed over the ground-plan of the site. The meaning the Alpha diagram cannot

be overvalued, because the proportions

120 : 230 give us a circumference that equals 700 ; and 12/23 of 700 = 365,21

this equals fairly precise the number of days in a year.

PLATE 9 shows a Alpha diagram, in which three triangles can be inscribed, that mirror with proportions of the

Cheops-pyramid; and we saw it also to be determent for important proportions on the Roman Pantheon.

PLATE 10 shows how the division of the Alpha diagram by four intersecting circles helps also to find important

proportions in the site.

PLATE 11 shows a Canon of proportions of Indian Buddhist provenience, that Tibetan painters of sacred scrolls use to this day, superimposed over the ground-plan of the Underground Basilica. We can see, that the most distant ancient cultures -in space and in time-used the same proto-mathematical tools: The Buddhist Canon fits perfectly into the Pythagorean site. This Canon has very interesting properties: It measures 120 times 210, and thus has a circumference of 660. We will have look at the details in the chapter on Buddhist sacred architecture.

PLATE 12 shows, that the apside of the basilica fits into a enlarged Canon. Also the pillars.

PLATE 13 : The side view of the Underground Basilica.

PLATE 14 shows, that if we draw a circle around the ground-plan and take this circle as the AU of Saturn, then the dimensions of the site allow to draw further circles that have a affinity to the largest circle: They are proportioned as the six in antiquity known planetary bodies

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THE HIDDEN ASTRONOMY

IN

THE ATHENA TEMPLE AT PAESTUM

Foreword
The literature
The practical aspect
The course of investigation

PART I

The geometry of the ground-plan
The arithmetic of the ground-plan
The geometry of the side-view
The arithmetic of the side view
The third step : The Tetraktys-numbers determining the entire site
The `Three Tables ´ of Chartres Cathedral applied at the Athena temple
The circle and the rounded rectangle determining the Athena-temple
Another possible combination applying Charpentiers `Modul ´
The circle and the `Modul ´
The harmonikal proportions of the 6 Gyaling tones as geometrical keys
The side-view of the temple
The successive application of transforming a square into a triangle, applied to the frontal view
The Venus-tone 4/7 Bbb taken 7 1/2 times

PART II

The synodic time-cycles of the planets as circles
The synodic time-cycles as circles transformed into squares
The Schmidt-equations I
The Schmidt -equations II
The synodic planetary cycles as rectangles
The synodic planetary cycles as triangles
The synodic planetary cycles as triangles -superimposed over the ground-plan of the temple

PART III

The diagrams relevant in the transformation of the synodic planetary cycles into sideric periods

and into AU -related distances.

The circles and the squares
The square and the circle + the squaring of the circle
The phenomenal geometry that allows the transformation of the synodic periods of revolution of all the in antiquity known celestial bodies into sideric periods and into Astronomical Units (AU)
The transformation of the synodic period of Mercur into sideric periods
The radius of the the sideric cycle of Mercur as proportions in the structure of the Athena temple

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_________________________________________________________________________________________________________________________________________________________________________________

CHARLEMAGNES DOME IN AQUISGRANA

Introduction

A previous investigation by H.Weisweiler

The Alpha-diagram in the side-view determining the inner space
The Alpha-diagram placed sideways over the side-view determining inner space
The Alpha- diagram determining the static , or the center of the walls
Another application of the Alpha diagram
A geometrical reconstruction of the ground-plan of the Octogon

6 The proportions of the Gyaling tones can be inscribed as chains into the side view of the dome.

7 What was the measure? A picture out of a Carolingan script, showing the way the dome was measured

8 The ground-plan of the Octogon together with the adjacent Gothic extension: Also here the Gyaling-tones are

proportionally present.

9 One amongst several possibilities to `extract the proportions of the Gyaling-tones from the ground-plan

The highest Gyaling tone ( that can be transformed into the AU of the planet Mercur )can be inscribed in the

ground-plan forming beautiful patterns.

The second highest Gyaling tone ( that can be transformed into the AU of the planet Venus) forming patterns
The third Gyaling tone ( that can be transformed into the AU of the Earth) and the possibility of forming

patterns.

The fourth Gyaling tone ( that can be transformed into the AU of Mars ) and the possible patterns

14 The fifth Gyaling tone ( that can be transformed into the AU of Jupiter ) and possible patterns.

15 The basic Gyaling tone( that can be transformed into the AU of Saturn) and possible patterns.

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CHARTRES CATHEDRAL

THE DIAGRAMS

The irregularities in the ground-plan
The arithmetic of the ground-plan , centered inside the walls
The arithmetic of the ground-plan outside the walls
The arithmetic of the ground-plan inside the walls
The affinities between the ground-plan of the Athena-Temple at Paestum and Chartres Cathedral
The Apsis
The Canon of Polyclet

PART II

The synodic periods of the planetary revolution reflected in circle and square
The transformation of the synodic planetary cycles into rectangles
The transformation of the synodic planetary cycles into triangles
The planetary cycles superimposed over the ground-plan of Chartres Cathedral
The cyclic periods of Jupiter, Saturn, the Earth and the Moon as intersecting triangles
The synodic periods of the above planets transformed into tringles superimposed over the ground-plan
The reconstruction of Charpentiers `Three Tables ´
A very unusual tone-scale
The `Three Tables ´ at Chartres providing the necessary proportions for the Gyaling-tones
The `Three Tables ´ forming a chain
The Gyaling tones proportioning the Cathedral
The proportional equivalents between Chartres Cathedral and Raffael´s `School of Athens´

PART III

The medium heliocentric distances in the geometry of the `Three Tables ´ at Chartres
The proportional application of the mediumplanetary orbs in Chartres Cathedral
The orb of Mercur
The orb of Venus
The orb of the Earth
The orb of Mars
The orb of Jupiter
The orb of Saturn?
Patterns in the ground-plan

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THE GREAT BUDDHIST STUPA AT SANCI

Introduction
The site
The main Stupa
Does a spiral determine the apparent excentricities in the Great Stupa?
The very ancient concept of the `cosmic egg ´.
The square in the side view
Is the composition of the side view related to the Alpha-diagram?
The Alpha-diagram the other way around
The ubiquitous Alpha-diagram and its many applications
Four Alpha-Diagrams in the ground-plan
The circle-square progression in the Great Stupa
The circle -square progression in the side-view
The circle-square development and its numbers
The proportions of the circle-square development found in the Great Stupa
The Harmonik Canon superimposed
The tones of the Gyaling in the proportions of the sacred site
The tones of the Gyaling providing angles
The polygons of the 8^th, 9^th, 10^th, 11^th, 12^th, 13^th, 14^th, 15^th, and 18-point stars
The arithmetical implications
The mean distances of the six in antiquity known planets, based on a Gyaling-derived tone-scale
The archaeological comparison between the Great Stupa of Sanchi and the Babylonian Ziggurat
The proportional comparison between the ground-plan of the G.S. and Stonehenge
The schematic ground-plan of the prehistoric site Stonehenge
The proportional comparison between the ground-plan of the G.S. and Stonehenge
The proportions of the ground-plan of temple A at Sanci
The proportions of temple B at Sanci
The superimposition of a wall-design from Nimrud , New- Assyrian -period, about 850 BC
The superimposition of a wall-design from Nimrud over the ground-plan of temple II at Sanci
The arithmetic of the symbols in the wall-design(1)
The arithmetic of the proportions in the wall-design (2)
The Triratna -symbol from Sanci
The Triratna -symbol as a spoke of a wheel
The Triratna -symbol and the Alpha diagram (a)
The Triratna -symbol and the Alpha-diagram upside -down
The Triratna-symbol and two Alpha Diagrams superimposed
The step-pyramid proportionally superimposed over the G.S.
The proportions of the step pyramid, elevation -plan
The polygons in the step pyramid (a)
The polygons in the step pyramid (b)
The number 365 in the step-pyramid
The arithmetic of the ground-plan of the step-pyramid (a)
The geometry in the ground-plan of the step-pyramid (b)
The geometrical solution of the ground-plan ( c )
The Gyaling-tones in the step-pyramid
The perfect heliocentric model of our planetary system in the step-pyramid
The Cheops-type pyramid `behind ´ heliocentricity
The arithmetic of the entire symbol
The Gyaling-tone-proportions in the entire symbol
The medium planetary distances from the sun , mirrored in the Triratna -symbol
The riddle of the geometrical center (i)
The riddle of the geometrical center (ii)
The riddle of the geometrical center (iii)
Speculative geometry with the mean planetary distances as circles

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THE GREAT STUPA JAHRUNGKAHSOR AT BOUDHANATH NEPAL

AND THE

HIDDEN GEOMETRICAL, ARITHEMTICAL, HARMONICAL AND ASTRONOMICAL TREASURES

PART I

Proto-mathematics and the transformation of geometry into arithmetical-, harmonical and geodetical values

Introduction
The immaterial treasures
Forerunners: The Great Stupa ast Sanci in central India
The geometrical development of the Great Stupa at Sanci
The portion symbolizing the element earth in the Great Stupa Jahrungkhasor
The geometry of the ground-plan of Jharungkhasor
The ancient enigma of `squaring the circle´
The whole-numbers in the earth-element of the Great Stupa
A possible ancient `Tala´ (rhythm) cycle-system in the earth element
Harmonical patterns inherent in the earth -element
The patterns that harmonics form on a tight chord
Some important pure-notes and musical tones used in a sacred context
A geometrical way to divide a plot harmonically
The circle, the square and the triangle
Ground-plan and elevation
The successive doubling of the Great Stupa
The arithmetic of the Rathas of the great Stupa derived from the division of the circle into 24 equal parts
The arithmetic of the three times doubled dimensions of the earth -element of the Great Stupa

PART II

THE GREAT STUPA AS A ASTRONOMICAL SITE; REFLECTING CALENDARIC; OR GEOCENTRIC VIEWS

The orb of the planets as seen from the earth
Mercur, Venus, Mars, Jupiter, Saturn and the Moon
The Rathas and their angles
The composition of the Rathas and their angles
The possible geometry reflecting geocentric appearances
Looking for other principles leading to the methods of constructing the Great Stupa
The regular polygons in the Earth-element of the great Stupa
The possible calculation of the synodic movements of the planets via the regular polygons
The coordinates seen as strings on a Monochord
Musical rhythms in the geocentrical revolution of the planets

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ASTRONOMY AT THE ROOT OF TIBETAN SACRED ARCHITECTURE

This work concentrates all elements related to astronomy in Buddhist sacred architecture. It discusses a possible geodetic knowledge of the ancients, together with what we call coincidental

Geodetic know-how
The shadow of the sun
The sphere in the Buddhist Stupa
The Om-Omega parallel
The most significant oboe of the world: The Gyaling
The transformation of a tone-scale of the Gyaling
The Gyaling - tones on the Tibetan Long-Neck-Lute Damien
The possibility to ` extract ´ the Gyaling - tones from the famous `intersecting triangles ´.
The Gyaling-tones, geometrically derived
The small Tibetan Chörten
The music system hidden in the Chörten
The six Gyaling tones in the Chörten
Geometrical secretes hidden in the Chörten
The Gyaling-tones in the Great Stupa Jharungkhasor at Boudhanath in Nepal
The influences of the Babylonian Ziggurat
The Ziggurat and the Chörten
The Ziggurat and the diagram that give us the possibility to arrive at the proportions of the Gyaling tones
The Gyaling tone-proportions in the Ziggurat
The Great Stupa Jharungkhasor and its hidden squares
Jharungkhasor and the Gyaling tones II
The Ziggurat and the hidden pyramid
The Gyaling tones as components of the Great Pyramid of Gizeh
The great Stupa at Sanci and the Ziggurat seen diametrical
The Great Pyramid and the Great Stupa at Sanci
The ground-plan of the Stupa at Sanci and the ground-plan of Stonehenge
A hidden geometric principle underlying the ground-plan of Stonehenge
The `squared circle´ that connects the synodic period of Venus with the sideric revolution around the sun.
The transformation of the gyalingtones into Astronomical Units (AU)
The astronomical data hidden in the Tibetan Chorten
The Shrivatsa-symbol at Sanci
The proportions of the Gyaling-tones in the step-tower of the the Srivatsa-symbol
The AU in the coordinates in the step-tower of the Srivatsa symbol
The Grat Stupa Jahrrungkhasor and the heliocentric view
The Great Stupa three times doubled
The heliocentric view in several ancient sacred sites in Europe
The Great Pyramid of Gizeh as a carrier of precise heliocentical data.
Five successively doubled pyramids provide coordinates that proportuionally `accomodate´ the solar system
A short history of the influences Buddhist sacred architecture exerted after the destruction of Buddhism in India
The form of a Mahayana Stupa in a Christian context in Ethiopia
The union of sun and moon in a pre-Muslim stele in Ethiopia
The influences on Muslim sacred architecture.
Europe
Chartres
Raffaels `School of Athens ´
A six-star, whose coordinates provide us with the Gyaling -tones, that can be transformed into AU
Raffael´s star -figure turned 45° turns into a Buddhist Canon
The figure of the Buddha and planetary orbs
Circles and squares, together with the squaring of the circle that provides us with a morphology of the universe

LEONARDO´S `VITRUVIAN MAN´

The diagrams:

1 A Egyptian view: The harmonical difference between a circle and a square is the whole tone step C-D, or F-G =8/9.

2 Leonardo´s square is basically divided into 16 squares

3 The proportions 1/10, 1/12, 1/40, 1/15.

4 The navel of the Vitruvian man is the center of the square

5 The angles

The transformation of the square into a circle with same content
Leonardo´s harmonical way finding a circle that corresponds with the circumference of the basic square
Another way
How we obtain circles that in content equal he square in Leonardos Vitruvian Man
Harmonical divisions of the square
Another variation
Another variation

RAFFAEL SANTI S `SCHOOL OF ATHENS `

THE PROTO MATHEMATICAL AND ASTRONOMICAL PRINCIPLES

IN THE STRUCTURE OF THE SCHOOL OF ATHENS

Table of contents:

Foreword Introduction

The proportions in the `School of Athens ´

Plate 1

THE TEXT FOR THE DIAGRAMS

The structure of the fresco including the arch and the lower part of the wall

Plate 2 The `squaring of the circle ´

Plate 3 Raffaels methods of ´squaring the circle ´.

Plate 4 The architecture and the placement of the depicted personalities in connection with the coordinates derived from

`squaring the circle ´

Plate 5 The half-square that gives the width of the painted arch, and the width of the central nave

Plate 6 The transformation of the proportion derived from the square-circle operation into harmonical proportions

Plate 7 The half-square derived from the halve circle of the arch in a vertical application together with circles and

coordinates

TEXT WITHOUT DIAGRAMS: THE SYMBOLS IN ` THE SCHOOL `

Plate 8 The `Holy Tetraktys ´

Plate 10 The geometry of the Tetraktys determining proportions in the fresco

Plate 11 The elaboration of the geometrical possibilities sugested by the arches in Raffal´s Tetraktys

Plate 12 The vertical application of the Tetraktys-numbers in circles

Plate 13 A method to arrive at PI

TEXT WITHOUT DIAGRAMS

Raffael s view on how to arrive geometrically at the proportions that give us the base for a astronomical `Harmony of the spheres ´, meaning a correct heliocentric view on our planetary system.

The geometrical possibility to `extract ´ the harmonical proportions of the six Gyaling -tones out of a circle
The proportions of the tones of the Gyaling applied as geometrical layers over the fresco
The seven spheres?
The geometrical construction of the harmonical progression 1/2, 2/3, 3/4, 4/5……24/25
A more complicated way arriving at Astronomical Units ( AU )
The six-star on the black-board in the painting
The application of a combination of a six -sided polygon and a six point star , and the proportions of the Gyaling-tones

21 The six star and additional coordinates

( b ) The six star transformed

( c ) One of the many possibilities to ´ distort ´ a regular six- star and transform it into the figure Raffael drew on the

blackboard in the picture.

( d ) Another possibility Raffael ´ distorted ´ the six star.

( e ) The AU of the six in antiquity known planets and the ´ distorted ´ six-star

( f ) The coordinates of the distorted six star ( fig 21 e ) taken as horizontals and verticals in Raffale´s`School´

( g ) The opening of the central nave in the ` School ´ without the parts drawn in `central perspective ´

( h ) A error turns into a boon: Lauenstein´s model of the ground-plan of the `School ´

( i ) A `inter-cultural ´ Canon

( j ) The ` basic square, and the great Stupa of Boudhanath in Nepal

( k ) The ´ basic square ´ and the geometric outline of the Kalacakra Mandala

( l ) The potential ground-plan Raffael did not apply : A cosmogone diagram

The real dimensions of the nave and the expansion of the ground-plan, including the outside arch via a successive 6/7

enlargement

( n ) A Carlolingan connection? The `Cross of Lothar´ at Aachen is identical to the ground-plan of the `School ´? If this

holds true, then the `School ´ is a painting that holds then unknown astronomical data, data that was, at the time of

Raffael kept secret.

(o ) The ground-plan of the `School of Athens ´ and the ´Cross of Lothar´ in proportion

( p ) H. Weisweilers discovery : The Vitruvian Analemma and the ´Cross of Lothar´

(qu) The Analemma drawn for the geographical position of the city of Rome

( r ) The Vitruvian Analemma drawn over the `School of Athens ´

( s ) The Vitruvian Analemma and the the circles indicated by the ´basic square´

( t ) The basic square, the Analemma, and the AU based orbs of four planets

( u ) The Vitruvian Analemma and the `Triphos´ indicating the centre of the orb of Mercur and Venus

22 The Particulars on the `Alpha Diagram´.

The Alpha Diagram
The Alpha Diagram ´ upside down ´
Four Alpha Diagrams with circles placed ´ upside down ´
Another arrangement of the four Alpha Diagrams
All possible ways to place the Alpha Diagram

PART II

RAFFAEL S METHOD OF PROPORTIONING THE AFFRESCO WITHOUT THE PAINTED PILLARS

AND THE

PAINTED ARCH ABOVE

The coordinates
The question of the `central perspective ´ in the architecture of the `School ´.
The square transformed into a triangle , also a Indian method

PART III

THE CALENDARIC SYSTEM IN THE PAINTED ARCH

The secrets of the Meander
The `Eierstab´ motif
The secrets of the pillars
Further details of the pillars

35 Parallels to the outlay of Stonehenge : Prof Hawkins

35b Raffaels division of the arch and the ground-plan of Stonehenge

36 Parallels to the Great Stupa at Sanci in India

Parallels to the Great Stupa Jharungkhasor at Boudhanath Nepal
Parallels to the outer graphic form of the Kalacakra Mandala
The five-, and the ten-point -star drawn over the fresco -without the painted arch
The five-, and the ten-point-star drawn over the entire fresco
The five-, and the ten-point-star drawn upside-down over the fresco without the painted arch
The five-, and the ten-point-star drawn side-ways over the entire fresco
A summary of the horizontal and vertical lines, taken from the coordinates of multiple stars, inclusive
A summary of the horizontal and vertical lines taken from the coordinates of multiple stars, exclusive

44b The 14 -point -star drawn over the entire fresco

44c The 14- point -star drawn without the arch

44d The 18-point-star inclusive

44e The 18-point-star exclusive

44f The 22-point-star inclusive

44g The 22-point-star exclusive

44h The 26-point-star inclusive

44i the 26-point-star exclusive

Points 44a until 44i are so rich in `interconnections ´ that there is no need to comment them in the text.

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