A Geometric Language (Yanträ)
THE visual language of symbols makes use of elementary geometric forms, corresponding to the phonemes of the spoken language and to the numerical intervals of the musical language. Through their mathematical connections, the Yanträ(s) reflect the fundamental structures of matter and the principles of life in a more obvious way than does spoken language.
"Einstein and some of his successors, such as Wheeler, when they constructed the theory of general relativity, have put forward the idea that everything is geometric at base" (D'Espagnat: La Recherche du réel, p. 81).
Yanträ(s) allow the representation of particular states of being. There is a Yanträ and a Manträ for each god; they are an expression of his nature and enable us to summon him.
Yanträ(s) thus play an essential role in ritual. The anthropomorphic images are proportioned according to canons based on Yanträ(s) and are accompanied by accessories that call to mind the role and the individual characteristics of each god. The Yanträ(s) are essential to all magical accomplishment; they are also the basis of the plans of temples and the proportions of all sculpture. The artist first of all draws the Yantra of a god and then, within the limits thus established, he brings out of the stone the anthropomorphic image that was concealed within it.
The human body is formed according to particular proportions and harmonies, which are the secret of its beauty. By means of yogic introspection we can perceive geometric diagrams in the subtle centers, connected to the sound symbols which define the body's role and actions. The Yanträ(s) are the expression of the constants that are to be found at the base of all the structures of the world, of atoms as well as of galaxies, of the genetic components of life and the mechanisms of thought. They are also a key to the mechanisms of our emotions.
In musical intervals we can analyze the psychophysiological action of purely numerical relationships that cause emotive reactions in listeners. This suggests the possibility of a mathematical definition of our reactions and feelings.
THE POINT
In the language of the Yanträ(s), the point (bindu) represents the transition from nonmanifest to manifest. All manifestation must start from one point. It corresponds in Manträ(s) to Anusvarä, the nasalization of syllables.
THE SPIRAL
The symbol of ether, the principle of the development of space and time, and of the expansion of the universe, is the spiral, which, starting from the initial point, develops indefinitely with circular movements like the universe itself. It corresponds to hearing (hence the labyrinthine shape of its organ, .the ear). The corresponding Manträ is Han, the guttural semivowel, stemming from A. The spiral is perceived in the experience of Yogä in the center of purity, situated in the throat.
THE CIRCLE
The symbol of the gaseous element of air is the circle, or occasionally the hexagon. It corresponds to nondirectional movement perceptible by touch.
It is from the gaseous state that the other elements are born through orbitation or condensation. It is thus the first manifestation of the energetic principle represented by the Manträ Ya, the semivowel Y, stemming from I (energy, shakti). The corresponding color is blue-black. The principle of the gaseous element is achieved in Yogä in the center of spontaneous sound (Anâhatä Chakrä) close to the heart.
THE TRIANGLE
The symbol of the liquid state is the triangle, resting on its point, which is also the symbol of feminity. A simple horizontal line can also represent the liquid state, for water always tends toward a leveling. Its corresponding sense is that of taste. Its Manträ is Va, deriving from U. In Yogä it is perceived in the center of the Svâdhishthanä, at the base of the sexual organs. Its corresponding color is blue-green. The symbol of the fiery state is a triangle with its point at the top (the masculine symbol), or simply a vertical line: fire tends to rise. The corresponding sense is that of sight; its Manträ is Ra, derived from Ë (ri). It is perceived in Yogä in the center of the navel (Nabhi Padmä). Its corresponding color is red.
The triangle, symbol of femininity, illustrates the numerical relationship 2 (base) above 3 (triangle) corresponding to (2/3), that is, C–F (Do–Fa), or a fourth in music, a gentle, feminine interval.
The masculine principle shows the relationship of 3/2. In music this is the frequency ratio of the fifth, C–G (Do–Sol), a sparkling, masculine interval. The six-pointed star represents the union of principles, the erect phallus in the vulva.
The cross too is a symbol of the union of water and fire: the union of opposites, which is the origin of the perceptible world.
THE SQUARE
The square is the symbol of the solid element or earth. It corresponds to the sense of smell, to the color yellow, and to the syllable La (deriving from Ü). It is also the symbol of the god Brahma, the shaper of the world, riding on the elephant Airavatä.
THE PENTAGON
The number 5 (Shivä's number) is the symbol of life and of consciousness. At the base of all living conscious structures is to be found the factor 5 (five senses, five fingers, five places of articulation, etc.). The crescent moon, used as a symbol, has the shape of the moon on its fifth night and thus stands for the number 5.
In music the perceptible and emotive intervals are those which include the factor five (harmonic third 5/4, minor third 6/5, harmonic sixth 5/3, minor seventh 9/5, etc. (See Alain Daniélou, Sémantique musicale.) Various aspects of the living being reflect symbolic features: such are the hand (with its five fingers), the erect phallus (the axis or column, symbol of the continuity of species), the eye (the sun), and the ear (a labyrinth).
The Swastika
THE swastika is the symbol of the irrational. It reminds us that the principle which is at the origin of the world, and the universe itself are twisted (vakrä). Any explanation that seems to be simple and logical is inevitably wrong. Starting from the nonspatial point (bindu), the universe develops in a spatial form; this is represented by a cross, image of the union between Purushä and Prakriti, the masculine and feminine principles. But this space is twisted: one becomes lost in space if either the inner or the outer branches of the swastika are followed. One never reaches the center. It is necessary at a given point to change direction and reject apparent logic. This is why in mathematics the irrational numbers are closest to reality. The prime numbers, which defy simple logic, are the only important ones.
The geometry which we know as Euclidian is merely approximative and has very narrow limits. In music the cycle of fifths, which seems to be a rational base, is exact only until the fifth fifth. Social theories, the relationships between human beings and the rites or relationships with the subtle beings, are never simple. All slogans are by their very nature wrong. For this reason the swastika is a beneficial sign: inscribed on the door of a temple or a house, it reminds us that there is no logical solution to any problem and that all simplification leads to absurdity.
Any science or technology or philosophy or religion that claims to be in possession of the truth is illusory and dangerous.
The god Ganeshä, who is both man and elephant, is the iconographical equivalent of the Svastikä. He evokes the identity between the macrocosm, the immense being, and the microcosm, the human being. He defies logic. One cannot be at the same time small and large, immortal and mortal, god and man, but nonetheless there exists a fundamental identity between irreconcilables. The divine principle is that in which opposites coexist, and so it is likewise in the divine work, in all the aspects of the created world.
Appendix II
Chronology of the Kali Yugä
The First Millennium (3100–2100 B.C.)
THE SHAIVA REVELATION
3313 Beginning of the Maya calendar in America
3100 Prithu, the first (legendary) king of India, develops agriculture.
3100 Founding of the First Egyptian Dynasty
3000 Fo Hi, first emperor of China
The first writing: Indus Valley, Sumer, and Egypt Development of cities in
the Indus Valley and in Mesopotamia
2800 First Minoan civilization in Crete
2750 Founding of Troy
2675 Gilgamesh
2100 Megalithic monuments in Europe (The oldest of the megalithic monuments are prior to the Kali Yugä, dating back to the middle of the fourth millennium B.C.)
The Second Millennium (2100–1100 B.C.
THE DESTRUCTIVE POWERS
2000 Invasion of Sumer by the Amorites and the Elamites
1900 Arrival of the Achaeans in Greece
1800 Destruction of the cities of the Indus by the Aryans
Birth of Abraham at Ur
The Aryans import the horse.
1400 Invasion of Knossos by the Achaeans
1300 Babylon taken by the Assyrians
1250 Trojan War
The Third Millennium (1100–100 B.C.)
THE RETURN OF ARIHAT
1100 The Dorian Invasion
1050 The Aryans occupy the Ganges Valley.
1016 David becomes king.
900 First Phoenician alphabet
The Védä(s) and the Homeric tales transmitted orally
The gamä(s) and Purânä(s) in occult tradition
817–778 Pârshvä, the 23rd Jaïna prophet
705 Hesiod
700 Beginning of the Greek alphabet
600 Midpoint of the Kali Yugä
Kharoshti (Phoenician) writing appears in India.
630–553 Zoroaster
603–531 Lao Tse
560–484 Makkhali Gosâlä
551–479 Confucius
550–483 Gautamä Buddhä
547–467 Mahâvîrä
540 Xenophanes
530 Pythagoras
520 The Indus region annexed by Darius
Introduction of Brahmi (Aramaic) writing into India
500 Rome becomes a republic.
The grammarian Panini
469–399 Socrates
384–322 Aristotle
356–323 Alexander
274–237 Ashokä
The Fourth Millennium (100 B.C.–A.D. 900)
THE SHAIVA RENAISSANCE
100 Lakulishä
78 Manes, first Scythian king of India
50 Beginning of Mithraism in Rome
50 House of the Mysteries in Pompeii
25 B.C.–A.D. 27 John the Baptist
22 Ambassador of Augustus visits King Pandion of South India.
Simon the Magician
Growth of the Pashupati cult
19 Herod restores the Temple of Jerusalem and favors the Essenes.
4 B.C.–A.D. 30 Jesus
The Gnostics
100 The Gospels are written.
100 Indian ambassador visits Trajan.
117 Basilides, Gnostic Christian at Alexandria
325 Constantine convenes the Council of Nicea.
379 Buddhism becomes the official religion of China.
600–1200 Construction of the great Indian temples
632 Death of Muhammad
788–820 Sankarâchâryä
The Fifth Millennium (900–1900)
THE DECLINE
1055–1113 Râmânujä founds Vaishnavism
1095 Building of Cathedral of San Marco, Venice
1139 Lateran Council (the Inquisition)
1167–1227 Gengis Khan
1192 Muslim conquest of North India
1202 Destruction of Benares by the Muslims
1244 Massacre of the Cathars (Montsegur)
1266–1274 Saint Thomas Aquinas
1307 Massacre of the Templars
1321 Death of Dante
1380 Mâdhavä, founder of the Vaishnava sect
1387 Sâyanä, editor of the Védä(s)
1483–1546 Martin Luther
1556–1605 Reign of Akbar
1818–1883 Karl Marx
1876 Victoria, Empress of India
1939 Beginning of the twilight of the Kali Yugä Discovery of atomic fission
Endnotes
Part One: THE HUMAN ADVENTURE
Chapter 1. Origins
1. See Alain Daniélou, Histoire de l'Inde, pp. 32-33.
2. Thomas McEvilly, An Archeology of Yoga, I, p. 46.
3. See Alain Daniélou, Shiva and Dionysus (New York: Inner Traditions, 1984).
4. Ibid.
5. Jean Bernard, Le Sang et L'histoire, pp. 118, 120.
6. McEvilly, An Archeology of Yoga, p. 45.
7. See Alain Danielou, HLa sagesse assassinée," Historia, no. 440, pp. 37-40.
Chapter 2. The Religions of the Kali Yugä
1. A. L. Basham, History and Doctrines of the jîvikäs, pp. 131, 134.
2. These dates, which are approximations, are deduced from data given in the Bhagavatî Sutra. See Basham, History and Doctrines ofthe jîvikäs, pp. 74–78.
3. Basham, p. 285.
4. Ibid., p. 51.
5. Dîghä Nikâyä 1.53 (Buddhist text in Pali).
6. McEvilley, An Archeology of Yoga, I, p. 57.
7. Basham, History and Doctrines of the jîvikäs, p. 6.
8. J. Van Duk, Introduction to the Lugal-ud.
9. D. L. Lorenzen, The Kapalikas and Kalamukhas, p. 108.
Chapter 3. Rediscovered Tradition
1. See M. R. Sakhare, History and Philosophy of Lingayat Religion, p. 192.
2. For these similarities, see ibid., pp. 159-165.
3. Ibid., p. 172.
4. Ibid., pp. 172, 192,231.
5. Ibid., pp. 136-138.
6. See Karl-Heinz Golzio, Der Tempel in alten Mesopotamien und seine Parallelen in lndien, Brill, LeiJen, 1983.
7. See Stella Kramrish, The Presence of Shiva, p. 43.
8. Lorenzen, The Kâpâlikäs and Kâlâmukhäs, p. 39.
9. Ibid., p. 39 n.
Part Two: SHAIVA PHILOSOPHY
Chapter 2. Vaïsheshikä and Nyâyä
1. The Manimekhalaï has only partially been translated. I am striving to indicate the Sanskrit equivalents of certain terms by using information given by S. Krishnaswami Aiyangar in his incomplete English translation of the text.
Chapter 3. The Sâmkhyä: The Study of the Macrocosm
1. Number now appears to be the only entity in physics that is sufficiently stable to really be taken seriously by science. Bernard d'Espagnat, La Recherche du réel, p. 12.
2. The relationship between the numerical factors of frequencies in musical intervals and the psychophysiological effect of music is a fundamental element of the theory of the râgä(s), or musical modes. It is on this basis that I have attempted to establish a general theory of aesthetics and of the expression of music in my Sémantique musicale.
3. The conception of the earth as a whole system, an organism in itself, has only recently appeared in the field of scientific research ... (Jonathan Schell). For the mathematician Freeman Dyson of Princeton, "Somewhere the universe knew that man was going to come. It was programmed to lead to a complex and intelligent molecular being" (Disturbing the Universe).
4. In terms of modern industry, we could call these two aspects software and hardware. We can sell the plans of a machine to Japan, this is the software, while the machine itself is the hardware. As far as the universe is concerned, we can either consider the software as a point of departure, the plan prior to matter, to the reality of the object, or the realization of the plan in the substance of which the world is made.
5. In Chinese translations of the texts of the Sâmkhyä, Svâbhavä and Prakriti are represented by the same character. We also find this ambiguity in Western vocabulary.
6. We find a simple illustration of the three principles in a car battery: the positive terminal (Tamas) and the negative terminal (Sattvä) create the magnetic or energetic field (Rajas), which provides power for the headlights and makes the starter-motor work.
7. The human body is made up of an immense number of cells, each having an independent self. Each cell, each organ of the body, has its own identity, which means that a transpl
anted organ can be integrated into another collective self, a different individuality.
8. One of the problems with the return of spacecraft is that the gaseous atmosphere of Earth, when penetrated at a certain speed, behaves like a liquid or even a solid.
Chapter 4. The Exploration of Man's Inner Universe
1. The triad of the Sâmkhyä—consciousness, internal organ, physical body—corresponds to the gnostic triad spiritus-anima-corpus, which the Council of Constantinople (869) reduced to the Catholic dualism of soul and body.
Chapter 5. The Being of Knowledge
1. I discussed this question with René Guénon in the course of translating certain sections of his works into Hindi. He fully recognized this difficulty. Cf. Alain Daniélou, René Guénon et la tradition hindoue, Dossier H, 1984.
Part Three: THE MÎMNS: THE RELIGIOUS, RITUALISTIC, AND MYSTICAL APPROACH
Chapter 1. The Two Mîmânsâ
1. See J. Muir, Journal of the Royal Asiatic Society 5.
2. See M. R. Sakhare, History and Philosophy of Lingayat Religion, pp. 147–150.
Chapter 2. The Doctrine of the Pâshupatä
1. See M. R. Sakhare, The History and Philosophy of Lingayat Religion, pp. 212–214.
2. Chittadvârenä tmeshvarä sambandhäheturyogah.
Chapter 3. Communities and Monastic Orders
1. See McEvilley, An Archeology of Yogä, I, p. 69.
2. See M. R. Sakhare, History and Philosophy of Lingayat Religion. p. 223.
Part Four: SOCIAL MAN
Chapter 1. The Individual and the Species
1. According to Mendel: "The genes are at the root of it all. It is they that determine completely what we are. They reproduce in identical form from generation to generation without the environment having the slightest influence on them. Occasionally, however, it happens that one of these genes mutates spontaneously; this mutation is perpetuated just as is the normal gene."
2. According to a report by the FAO of November 1983, in recent years high-yield food plants have been developed through hybridization; research has led to the development of plants that are all genetically similar. Should disease strike them, the contagion might destroy the entire species if the original variety of species no longer survives. Such "genetic erosion" is spreading around the world as quickly as fire on a prairie. There remain no more than 80 vegetal species in Peru out of more than 1,500 before the Incas. Things are no different for the animal species, including mankind.
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