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     Chapter 2.  From Astral Beliefs to Kepler, Fludd and Newton                       

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        1.  In the Chinese Commentary on the Chuang Tzu by Kuo Hsiang  (4th century A.D.) we find:  "The principles of things are from the very start correct.  None can escape from them.  Therefore a person is never born by mistake, and what he is born with is never an error.  Although heaven and earth are vast and the myriad things are many, the fact that I happen to be here is not something that spiritual beings of heaven and earth, sages and worthies of the land, and people of supreme strength or perfect knowledge can violate.....  Therefore if we realize that our nature and destiny are what they should be, we will have no anxiety and will be at ease with ourselves in the face of life or death, prominence or obscurity, or an infinite amount of changes and variations, and will be in accord with principle.”  (A Source Book in Chinese Philosophy, 1963, translated and compiled by Wing-Tsit Chan, p. 332.)

        2.  In a charming although perhaps not authoritative book, Peter Lum says:  "The Chinese believed that the world of stars was exactly similar to that of men.  It was perforce a happier land, without flood or famine, but it was subject to the same laws as China, and its immortal inhabitants were very similar to the Chinese.  The familiar world known to mankind, with its obvious imperfections, was rather like a reflection in troubled waters of that ideal world which existed above.  And the Chinese believed that as long as life on earth followed the pattern of the star world in every detail, there would be peace and happiness.  It was only when, owing either to insufficient knowledge or else to lack of skill in carrying out their instructions, the earth got out of step with the sky world that discontent and war and suffering followed.  If there was a famine, or rebellion, or civil war, it must be because the astronomers were held responsible.  It was a theory which certainly led to a rapid development of astronomical knowledge, especially when the unfortunate astronomers discovered that if they made a mistake, or even failed to predict and eclipese, they might lose not only their jobs but their heads as well."  (Peter Lum,The Stars in our Heaven, Myths and Fables, 1948, p. 16-17.)

        3.  Another version is given by Evan Hadingham, based on the  annals of the Formal Han Dynasty (202 B.C. - 8 A.D.).  The Chinese Emperor's rule was sanctioned, Hadingham says, by a blending of  earthly and cosmic forces.  The King was said to have Heaven for father and Earth for mother.  The main task of the state astronomers was to detect imbalances in this relationship by watching for portents such as eclipses, meteors, comets and other unusual celestial phenomena.  This responsibility placed them in a position of immense power in the Han bureaucracy.  An examination of the annals shows that the scribes edited them, making additions, deletions, and alterations.  Certain omens, such as eclipses, were reported on dates which were astronomically impossible, which suggests that the importance of obtaining a sign overrode the Han astronomers' concern for facts.  (Evan Hadingham, Early Man and the Cosmos (1984), p. 247; Hadingham cites W. Eberhard, "The Political Function of Astronomy and Astronomers in Han China" in Chinese Thought and Institutions, 1957, p. 38.) 

        4.  Some native Americans simply attributed errors of their astronomers to incompetence.  Ray Williamson speaks about the sun- watchers, or sun priests, functionaries of the Pueblo Indians, the Hopi and Zuni, who maintained a kind of solar horizon calendar by monitoring positions of the sun from day to day, and correlated them with various ceremonies, e.g., at the solstices.  He reports a journal entry for April 18, 1921, made by Crow Wing, a Hopi Indian:  "We think the Sun-Watcher is not a very good man.  He missed some places, he was wrong last year.  All the people think that is why we had so much cold this winter and no snow."  (Ray Williamson, Living the Sky, The Cosmos of the American Indian, 1984, chapter on sun-watchers and p. 111.)

         5.  We see why star-watchers, who were often also weather-watchers, were in demand.  We have a flourishing weather prediction industry today, also not as reliable as we would like.  We announce in our daily newspapers summer and winter solstices and equinoxes, eclipses, comets, meteor showers, and so on.  Supernovae are reported, and are especially valued by our cosmologist/astronomers, who use them to make predictions about the future and past of the whole universe.  Just as people have done for thousands of years, we teach our young how to read and use calendars, what solstices and equinoxes are, and how such things are related to predicting future changes in daily sunlight and weather.  We teach them current theories of how eclipses work, and what meteors and comets are thought to be.  We also find in our newspapers predictions about the affairs of individuals, in daily horoscopes written (one supposes) by astrologers.  And we hear of officials who consult astrologers about propitious times for taking actions.

        6.  Edward Schafer says of the role of astronomy and astrology in China during the T'ang dynasty (618-907 A.D.) that astronomical and calendrical affairs were a monopoly of the court.  This was because astronomical activities had a ritualistic and religious component which involved the sovereign, the Son of Heaven, who was the link between celestial energy flowing from above and terrestrial responsibility flowing from below.  Only the Son of Heaven could possess true knowledge of the stars.  Prying into such affairs could be treasonable.  To understand the workings and readings of the armillary sphere and star chart was to approach dangerously close to state secrets.  Thus ordinary citizens of the T'ang empire were forbidden to dabble in such matters.  Officials maintained that this taboo was intended prevent inexpert interpreters and charlatans from misleading and defrauding the ignorant masses.  There were stringent penalties for the possession and use of most implements and books which could be used to obtain exact astrological of what the T'ang code called "our occult counterparts in the sky".  (Edward Schafer, Pacing the Void, T'ang Approaches to the Stars, 1977, p. 11-12.)

         7.  "The 'star gods' of ancient China were not mere ensouled stars," says Schafer, "except, perhaps, to the vulgar.  They were inconceivable beings whose masks and costumes were always hanging in the Vestry or Green Room of the sky, ready for occasional use when the formless powers who owned them chose to show themselves more closely to advanced students of the Highest Clarity than they ever did to mortals whose vision was more clouded by the obsessive fogs of ordinary careers and mundane preoccupations.....  The beginnings of official Chinese worship and propitiation of these remote and sublime intelligences are lost in the roots of Chinese history.  In Han times [25-220 A.D.], however, when we begin to have some clear idea of official cult practices and beliefs, star-worship was already firmly established.  A prominent place was given to it in the state rituals connected with the worship of heaven carried out in the capital city.  An example, under the date of A.D. 26, was the great imperial sacrifice to Heaven, with offerings of oxen to the sky-gods, inaugurated in the southern suburb of Lo-yang.  The rite was conducted on a central round "altar" (i.e., ceremonial platform) and external altars to the five paramount gods of the directions.  The place of sacrifice was furnished with representations of the purple palace of the pole and with blazons representing the positions of the sun in the east, the moon in the west, and of the Northern Dipper.  There were also lesser altars for the planets.  These celestial deities were always paramount in the state cult, since they had a special relationship with the imperial house, the earthly nexus of the power that radiated from them."  (Schafer, ibid., p. 222-225.)

         8.  Schafer goes on to say that state ceremonies conducted by the Son of Heaven himself, or by his surrogates, were momentous and complex affairs in which numerous potent spirits were invoked.  At the winter solstice, in the most honorable position on a great round platform -- the northern one, facing south -- the imperial court worshipped the ritual presence of the "Supreme Theocrat of the Heaven of Primal Light".  This epithet refers to "the white radiance of the eternal breath which pervades the cosmos".  Schafer emphasizes that we should not regard Taoist star worship merely as worship of the stars.  If we do so, we misunderstand their faith as much as if we regarded the adoration of St. Michael and St. Gabriel as bird worship because these creatures of pure spirit are often represented with wings.  To the Taoists, the stars were not gods but tokens and guises of cosmic beings, who might assume other guises and reveal themselves in other symbols.  "They were deities whose location was nowhere, who existed simultaneously in the brain and in outer space, and could exhibit their numinous presence in any manner or place that seemed desirable."  Taoist priests and initiates wore special costumes which symbolized their spiritual advancement and embodied mana which was revealed outwardly by magical diagrams and talismans.  Their divinites were often described as wearing costumes just like those of their earthly hierophants.  Most prominent of these vestments was the "star hat", referred to very often in T'ang poetry.  A westerner might imagine this as the conical hat of an Arabian Nights' sorcerer, or white-bearded Merlin, or a fairy godmother, or a wicked witch.  However, it appears that no graphic representation of a Taoist star-hat has survived from T'ang times.  (Schafer, ibid.)

         9.  According to the Book of T'ang astrology was unnecessary in the golden ages of China's remotest past:  "In the Grand Tranquillity of antiquity, the sun was not eroded and the stars did not explode."  Is this a reference to sun spots, comets and meteors?  to supernovae?  In any case, after the rule of godlike supermen in the earliest times came to an end, Schafer says, "the skies over the Middle Kingdom were soon flashing with warnings from the All Highest."  Interpretation was needed.  The earliest Chinese astrology, like the earliest Mesopotamian astrology, was an omen or portent astrology, whose function was to predict on behalf of the monarch and nation.  The fate of individuals was only of interest as far as it bore on the fate of the empire.  Astrologers were officers of the kingdom, "devoted to the interpretation of strange lights and movements in the heavens, and the timely anticipation of disasters".

         10.  Apparently not long before the beginning of the Han dynasty, the body of lore associated with such startling phenomena acquired a theoretical framework, chiefly the cosmic dualism of  yin and yang, along with the doctrine of the Five Activities, which could be made to correspond with the five visible planets.  Along with these, there was a fundamental "theory of correspondences".  Schafer says:  "Celestial events are the "counterparts" or "simulacra" of terrestrial events, sky things have doppelgangers below, with which they are closely attuned.....  The germinal essences of the Myriad Creatures in every case have counterparts up in the sky."  They form shapes or contours under the sky.  "Correspondence" has been defined as the relation between the cosmic and political realms, and between the natural and human worlds, between macrocosm and microcosm.  The emperor, the Son of Heaven, is a critical nexus between them all, "dedicated to maintaining the exactness of the correspondences by means of ritual observances".  As a consequence, the early Chinese philosophers pondered relationships rather than substance, a matter which preoccupied the Eleatics.  However, Schafer observes, there were always skeptics.  (Schafer, ibid., p. 55-57.)

         11.  Among the earliest of the Chinese philosophical skeptics was Wang Chhung [27-97 A.D.], said by Joseph Needham and Wang Ling to have been "one of the greatest men of his nation in any age  ..."  They say: "[He] made a frontal attack upon the Chinese State 'religion' by an uncompromising resistance to anthropocentrism of any kind.  Again and again he returns to the charge that man lives on the earth's surface like lice in the folds of a garment.  At the same time, he admits that among the 300 (or 360) naked creatures, man is the noblest and most intelligent.  But if fleas, he said, desirous of learning man's opinions, emitted sounds close to his ear, he would not even hear them; how absurd then it is to imagine that Heaven and Earth could understand the words of Man or acquaint themselves with his wishes.  This position once gained, the whole weight of Wang Chhung's attack on superstition was deployed.  Heaven, being incorporeal, and Earth inert, can on no account be said to speak or act; they cannot be affected by anything man does; they do not listen to prayers; they do not reply to questions."  (Joseph Needham and Wang Ling, Science andCivilisation in China, v. 2, "History of Scientific Thought, 1969, p. 368, 374-375.)

         12.  Still, paradoxically, Wang Chhung favored individual or horoscopic astrology, and may even have introduced it into China.  He believed "that among the most important of all influences acting upon men during the formative period of their lives were those of the stars.....  The paradox lies in the probability that it was precisely Wang Chhung's scientific naturalism which pushed him into this theory. as a means of escaping from the arbitrary endowments of local gods and spirits and other 'supernatural' agencies.  The stars were at least regular in their motions." (Needham and Ling, ibid, p. 384.) 

         13.  The Chinese astral religion did not contain horoscopic astrology until relatively late.  This shows, on the one hand, how astral religion in general may be separate from astrology and in particular from horoscopic astrology, and on the other hand, how astral religion may be an important ingredient in a religion as a whole.  Charles Dupuis (1742-1809) went so far as to claim that all religions have grown out of astral religions.  Dupuis was a scholar who became a member of the revolutionary government in France in 1792, and also served briefly in Napoleon's government.  However, he soon retired from politics, and devoted the rest of his life to his studies.  In 1795 he published an extensive work called Origine de tous les cultes, ou la religion universelle in which he propounded his theory of the astral origin of all religions, and futhermore that the place where all organized religion originated was northern Egypt.  The work stirred up considerable controversy, and is said to have led to the expedition organized by Napoleon for the exploration of Egypt, an invasion which had enormous political and archeological consequences.

         14.  Few believe at present that all religion originated in Upper Egypt, or that all religion grew out of worship of celestial objects.  However, that astrolatry had a considerable influence on the development of many religions is undeniable, as shown by Dupuis's own impressive scholarship which covers a multitude of times and places and peoples.  He begins by asserting that in the beginning all religion was pantheistic.  Of the early idea of God, he says:  "When man began to reason upon the causes of his existence and preservation, also upon those of the multiplied effects, which are born and die around him, where else but in this vast and admirable Whole could he have placed at first that sovereignly powerful cause, which brings forth everything, and in the bosom of which all reenters, in order to issue again by a succession of new generations and under different forms.  This power being that of the World itself, it was therefore the World, which was considered as God, or as the supreme and universal cause of all the effects produced by it, of which mankind forms a part.  This is that great God, the first or rather the only God, who has manifested himself to man through the veil of the matter which he animates and which forms the immensity of the Deity."  (Charles Dupuis, The Origin of all Religious Worship, 1871, p. 15-16, anonymous translation of material from Dupuis' work.  It is difficult to trace the exact provenance of the material.  Dupuis's work of 1795 was revised by P. R. Auguis and published in 1822, 10th edition, 1835-1836.  An abridgement by Count M. de Tracy was published in 1804.  While the content, roughly speaking, of the anonymous translation into English can be found in the edition of 1835-1836, the semantically equivalent passages are quite different linguistically.)      

         15.  Dupuis goes on:  "Although this God was everywhere and was all, which bears a character of grandeur and perpetuity in this eternal World, yet did man prefer to look for him in those elevated regions, where that mighty and radiant luminary seems to travel through space, overflowing the Universe with the waves of its light, and through which the most beautiful as well as the most beneficent action of the Deity is enacted on Earth.  It would seem as if the Almighty had established his throne above that splendid azure vault, sown with brilliant lights, that from the summit of the heavens he held the reins of the World, that he directed the movements of its vast body, and contemplated himself in forms as varied as they are admirable, wherein he modifies himself incessantly."  Dupuis quotes Pliny the Elder (Natural History, II.1):  "The World, says Pliny, or what we otherwise call Heaven, which comprises in its immensity the whole creation, is an eternal, an infinite God, which has never been created, and which shall never come to an end.  To look for something else beyond it, is useless labor for man, and out of his reach.  Behold that truly sacred Being, eternal and immense, which includes within itself everything; it is All in All, or rather itself is All.  It is the work of Nature, and itself is Nature."  (Dupuis, ibid., p. 16.)

         16.  Later, Dupuis says:  "It would be a mistaken idea to believe, that [the Ancients] considered the World merely as a machine, without life and intelligence, moved by a blind and necessary force.....  As the World seemed animated by a principle of life, which circulates in all tis parts, holding it in eternal activity, it was believed that the Universe lived as man did and the other animals, or rather that these lived only because the Universe, being essentially animated, communicated them for a few instants an infinitesimal portion of its immortal life, which it infused into the coarse and inert matter of sublunary bodies.  Was it restored back to itself?  Man and beast died and the Universe alone, always alive, circulated around the remains of their bodies by its perpetual motion, and organized new beings,  The active Fire or the subtle substance, which animated it, by incorporating itself in its immense mass, was the universal soul of it.  This is the doctrine, which is embodied in the system of the Chinese, on Yang and Yin, one of which is the celestial matter, moveable and luminous, and the other the terrestrial one, inert and gloomy, of  which all bodies are composed."  (Dupuis, ibid., p. 49-50.)

         17.  "This is the dogma of Pythagoras," Dupuis continues, "contained in those beautiful verses in the sixth book of the Aeneid [of Virgil], where Anchises reveals to his son [Aeneas] the origin of the souls and their fate after death.  'You must know, my son, he said, that Heaven and Earth, the Sea, the luminous globe of the Moon and all the Stars, are moved by a principle of eternal life, which perpetuates their existence; that there is a great intelligent Spirit extended in all the parts of the vast body of the Universe, which, while mixing itself in All, is agitating it by an eternal motion.  It is this soul, which is the source of life of man, of the beasts, of the birds and all the monsters living within the bosom of the Ocean.  The vital force, which animates them, emanates from that eternal Fire, which shines in the Heavens, and which while it is held captive in the raw material of the bodies, is only developed as much, as the various mortal organizations permit it, which subdue its power and activity.  At the death of each creature, these germs of a particular life, these portions of an universal breath, return to their principle and to their source of life, which cirulates in the starred sphere.'"  (Dupuis, ibid., p. 50.)  

         18.  Matching lives of men with lives of stars is nearly universal.  In Africa, according to Harold Courlander, the following cosmogony is told among the Yoruba people of Nigeria.  "In ancient days, at the beginning of time, there was no solid land here where people now dwell.  There was only outer space and the sky, and, far below, an endless stretch of water and wild marshes.  Supreme in the domain of the sky was the orisha, or god, called Olorun, also known as Olodumare and designated by many praise names.  Also living in that place were numerous other orishas, each having attributes of his own, but none of whom had knowledge or powers equal to those of Olorun.  Among them was Orunmila, also called Ifa, the eldest son of Olorun.  To this orisha Olorun had given the power to read the future, to understand the secret of existence and to divine the processes of fate.  There was the orisha Obatala, King of the White Cloth, whom Olorun trusted as though he also were a son.  There was the orisha Eshu, whose character was neither good nor bad.  He was compounded out of the elements of chance and accident, and his nature was unpredictability.  He understood the principles of speech and language, and because of this gift he was Olorun's linguist ....."

         19.  "Down below, it was the female deity Olokun who ruled over the vast expanses of water and wild marshes, a grey region with no living things in it ....."  The two worlds were separate, and the orishas of the sky took no notice of what went on below, except for Obatala, King of the White Cloth.  In order to overcome the monotony of what lay below, he went to Orunmila to ask how land could be introduced below.  By casting palm nuts in his divining tray, Orunmila determined that Obatala should make a golden chain with which to descend to the water with sand, to make land with.  This Obatala did.  He planted a palm nut, and there was vegetation in the land, but no people, so Obatala decided to make people out of clay.  After making a number, he got thirsty and began to drink palm wine.  He drank so much that he got drunk, and some of the people he made after that were misshapen.  A city called Ife was founded.  Olokun, the orisha of the sea, angry that water had been covered with land, flooded it, and many people were drowned.  After a while, Orunmila, the deity of divination, whose name means "The Sky Knows Who Will Prosper", came down from the sky and turned back the sea.  He also taught certain orishas who had come to live below on the land, and certain men, the arts of controlling unseen forces, and others the art of divining the future, "which is to say the knowledge of how to ascertain the wishes and intentions of the Sky God.....  Earthly order -- the understanding of relationships between people and the physical world, and between people and the orishas was beginning to take shape."  (A Treasury of African Folklore, edited by Harold Courlander, 1975, p. 189-193; this story is from his own Tales of Yoruba Gods and Heroes, 1973.)

         20.  Lum relates that in the myths of Britain, the  constellation of the Great Bear (Ursa Major, the Big Dipper) is interwoven with the story of King Arthur and the Round Table. His name was alleged to have come from the words "Arth" and "Uthyr", meaning "bear" and "wonderful".  Some of his followers are said to have claimed that he was an incarnation of the spirit of the Great Bear.  The Round Table may have referred to the circle made by the swinging of the Great Bear's tail each night when it swept the northern sky.  "Fiona Macleod tells an old story," Lum says, "of how Arthur once fell asleep on the seashore, long before he had any thought of being king, and in his sleep a spirit came to him and guided him far up to the north where the stars of the Great Bear were bright.  There he found the knights of heaven seated at a great circular table, resplendent as the shining stars, and they spoke to him and gave him wise counsel.  They told him that his name should be Arthur, that he would be king, and that he must pattern his life and the rule of his kingdom on that of the kingdom of heaven."  (Lum, ibid., p. 38-39.)

         21.  Gene Weltfish tells how some Native Americans who lived along the Missouri River saw the connection of the heavens with the affairs of men:  "The Pawnees had many tasks to accomplish in the early spring before the time of planting.  Some of them were practical and some ceremonial, but to the Pawnees who believed that nothing on earth could move without the heavens, no practical task could be undertaken unless the appropriate ceremony had preceded it..... The round of spring renewal ceremonies was heralded by the appearance of two small twinkling stars known as the Swimming Ducks in the northeastern horizon near the Milky Way.  They notified the animals that they must awaken from their winter sleep, break through the ice, and come out into the world again." (Gene Weltfish, The Lost Universe: Pawnee Life and Culture, 1965,  p. 79.)  And Ray Williamson relates that according to Pawnee stories, they received from of their ritual direction from the stars.  They claimed that at one time they organized their villages according to patterns of the stars, and each village possessed a sacred bundle given to it by one of the stars.  When the different villages assembled for a communal ceremony, they arranged themselves in a way which reflected the celestial positions of the stars whose bundles they possessed.  There were 18 Skidi Pawnee villages, each associated with a different star." (Ray Williamson, Living the Sky, 1984, p. 229.)     

         22.  The Oglala Dakota, a branch of the Sioux Indians, were among those who defeated Custer at the battle of Little Bighorn in 1876.  (Cf. Evan S. Connell, Son of the Morning Star, 1984)  Their chief god, great spirit, creator and chief executive was (is?) Wakan Tanka, who is sixteen individuals in one, each of the four categories containing four individuals.  As great spirit, he is sky.  Paul Radin says of this religion:  "The sky is an immaterial god whose substance is never visible.  His titles given by the people are taku skan-skan and nagi tanka or the great spirit, and those given by the priests are skan and to, blue.  The concept expressed by the term taka-skan-skan is that which gives motion to anything that moves.  That expressed by the shamans by the word skan is a vague concept of force or energy and by the word to is the immaterial blue of the sky, which symbolizes the presence of the great spirit.  His domain is all above the world, beginning at the ground.  He is the source of all power and motion and is the patron of directions and trails and of encampment.  He imparts to each of mankind at birth a spirit, a ghost, and a sicun [an invisible god] and at the death of each of mankind he hears the testimony of the ghost and adjudges the spirit.  His word is unalterable except by himself.  He alone can undo that which is done.  His people are the stars and the feminine is his daughter."  (Paul Radin, Primitive Man as Philosopher, English translation 1927, p. 329-332, quoting James Walker, "The Sun Dance of the Oglala Divison of the Dakota," Anthropological Papers of the American Museum of Natural History, XVI, Part II, p. 72-92.)     

         23.  Plato speaks in many places of the workings of the stars.  For example, there is the myth of Er in the 10th book of Plato's meditation on the nature of justice,  the Republic.  Er, the son of Armenius, is killed in battle, but comes to life again just before he is to be burnt on a funeral pyre.  He describes what he has seen in the other world.  This includes a vision of the structure of the universe, described like this by Francis Cornford in his translation of the Republic:  "What the souls actually see in their vision is not the universe itself, but a model, a primitive orrery in a form roughly resembling a spindle, with its shaft round which at the lower end is fastened a solid hemispherical whorl.  In the orrery the shaft represents the axis of the universe and the whorl consists of 8 hollow concentric hemispheres, fitted into one another 'like a nest of bowls,' and capable of moving separately.  It is as if the upper halves of 8 concentric spheres had been cut away so that the internal 'works' might be seen.  The rims of the bowls appear as forming a continuous flat surface; they represent the equator of the sphere of fixed stars and, inside that, the orbits of the 7 planets.  The souls see the Spindle resting on the knees of Necessity.  The whole mechanism is turned by the Fates, Clotho (the Spinner), Lachesis (She who allots), and Atropos (the Inflexible).  Sirens sing eight notes on consonant intervals forming the structure of a scale (harmonia) which represents the Pythagorean 'music of the spheres.'"  (Republic, translated by Francis Cornford, 1941, p. 350.)

         24.  "All this imagery," Cornford concludes, "is, of course, mythical and symbolic.  The underlying doctrine is that in human life there is an element of necessity or chance, but also an element of free choice, which makes us, and not Heaven, responsible for the good and evil in our lives."  In the myth, after the souls have completed their journey to the Spindle resting on the knees of Necessity (probably the Milky Way) Lachesis, daughter of Necessity, distributor of human fates, says:  "Souls of a day, here shall begin a new round of earthly life, to end in death.  No guardian spirit will cast lots for you, but you shall choose your own destiny." (Cornford's translation, p. 355).  The dead souls are shown a large number of sample lives to choose from.  The man who had drawn the first lot chose, in thoughtless greed, to be reborn as a tyrant.  He did not see the many evils this life contained, and that he was fated to devour his own children.  Plato attributes his choice to innocence and ignorance:  "He was once of those," Plato says, "who had come down from heaven, having spent his former life in a well-ordered commonwealth and become virtuous from habit without pursuing wisdom.  It might indeed be said that not the least part of those who were caught in this way were of the company which had come from heaven, because they were not disciplined by suffering; whereas most of those who had come up out of earth, having  suffered themselves and seen others suffer, were not hasty in making their choice." (ibid., p. 357).  Cornford draws attention to Plato's intention that such stories be taken as myth.  By this means Plato synthesizes older speculative interpretations in the manner of Pythagoreans with newer ideas of rational philosophy.

         25.  Plato's visions still exerted great cultural force near the close of the 16th century, just before the advent of new cosmologies based on the works of such people as Copernicus, Kepler, Galileo and Descartes, unified by Newton in his system of the world.  At Florence, in 1589, an elaborate theatrical production known as the intermezzi was presented at the Medici court in honor of the marriage of the Grand Duke of Tuscany.  Here is the opening scene, as described by Roy Strong:  "On May 2nd 1589 the front curtain on the Teatro Mediceo parted to reveal a Doric temple and above it a cloud, surrounded by rays of light, which slowly descended to the ground.  On this rode the Doric Harmony, singing of her descent to mortals.....  The initial statement of the Doric Harmony was carried to fruition in the first intermezzo which took the form of a representation of the Harmony of the Spheres according to Plato's cosmology, and in particular as described in the tenth book of Plato's Republic.  The prospettiva [a view of the city of Pisa in perspective] was suddenly covered with star-spangled clouds.  Eight Platonic sirens plus two more of the ninth and tenth sphere sat on clouds telling how they had forsaken the heavens to sing the praises of the bride.  On a central cloud sat Necessity on a throne with a diamond spindle of the cosmos between her knees.  She was attended by the three Parcae or Fates and they in turn were flanked by clouds bearing the seven planets and Astraea, whose advent on earth signalled the return of the Golden Age.....  Above were twelve heroes and heroines, each pair embodying virtues attributed to the onlooking couple [the Duke and his bride].  Both the sirens and the planets joined in a dialogue describing the joy of the cosmos at so auspicious an alliance and as the clouds arose from the lower part of the stage sunlight streamed in, while above night approached.  A concluding madrigal expressed hopes of  'glorious heroes' as a result of the match.  As the cloud vision faded the stage was filled with sunlight, revealing the prospettiva of the city of Pisa....."  (Roy Strong, Arts and Festivals, Renaissance Festivals 1450-1650, 1973 (1984); p. 137 and 23-24.)

         26.  The Renaissance court festival, says Roy Strong, "unlike its medieval forebearers, stemmed from a philosophy which believed that truth could be apprehended in images.....  Our guide to it is a vast tract of literature, books of emblems and imprese and mythological manuals.  These compilations were an extension and elaboration, under the impact of Florentine Neoplatonism, of the inherited tradition of hidden meanings .....  Although these texts were known to the middle ages, they were studied with renewed fervour during the renaissance, when scholars examined them to recover a lost history or secret wisdom, pre-dating the Christian revelation, that was passed down through Moses and the Egyptian priests by way of Hermes Trismegistus to the Greeks.....  The acceptance of a pagan theology that descended from Zoroaster through Hermes Trismegistus to Orpheus, Pythagoras and Plato enabled Renaissance man to assimilate the whole heritage of classical mythology and history."  (Roy Strong, ibid.; we will talk about Hermes Trismegistus in a moment.)

         27.  In a relatively recent European account of the relation of astronomy to destiny, Goethe (1749-1832) writes:

        "Wie an dem Tag, der dich der Welt verliehen, 
        Die Sonne stand zum Grusse der Planeten, 
        Bist alsobald und fort und fort gediehen 
        Nach dem Gesetz, wonach du angetreten. 
        So musst du sein, dir kannst du nicht entfliehen, 
        So sagten schon Sibyllen, so Propheten; 
        Und keine Zeit und keine Macht zerstückelt 
        Geprägte Form, die lebend sich entwickelt..... 
        Das Liebste wird vom Herzen weggescholten, 
        Dem harten Muss bequemt sich Will und Grille. 
        So sind wir scheinfrei denn, nach manchen Jahren 
        Nur enger dran, als wir am Anfang waren." 

        ("The way the sun stood at the planets' greeting, 
        The way it stood the day the world endowed you, 
        You were from that time on developed 
        According to the law by which you entered. 
        Thus must you be, and you can't escape, 
        The sybils and the seers have said it; 
        No time nor force can disassemble 
        Imprinted form that grows itself in living..... 
        What's loved is kept away from hearts that want it, 
        Will and whim are shaped to a Must unyielding. 
        We only seem free, and after many years, 
        We're more bound than when we started.")

(From "Urworte, Orphisch", German text taken from German Poetry from 1750-1900, 1984, edited by Robert Browning, p. 66, 68, my translation.)  

        28.  We have said that Stoics were devoted to astrology in the Hellenistic era.  There were others in that era who embraced astrology.  There were, for example, the Hermeticists.  The works called Hermetica, or the Corpus Hermeticum, are Greek and Latin writings of uncertain origin, evidently composed from about 200 to 500 A.D., which contain religious or philosophic teachings ascribed to Hermes Trismegistus, the "three-great" Hermes, perhaps a mythical person or god.  Some say this Hermes is not the Greek Hermes, but the Egyptian god Thoth, perhaps identified with Hermes by Alexandrian Greeks; however this is also uncertain.  William Grese says that "the predominant view is that the Hermetica are a Hellenistic development of Greek (especially Platonic and Stoic)  philosophy, and the leading exponent of this position has been André-Jean Festugière."  (William Grese, "Magic in Hellenistic Hermeticism, in Hermeticism and the Renaissance, Intellectual History and the Occult in Early Modern Europe, edited by Ingred Merkel and Allen Debus, 1988, p. 45.)  However, as Grese observes, in addition to the religious and philosophic elements in the Hermetica, there are also magical and astrological elements.  These writings are to this day an important part of the so-called occult tradition.

        29.  A definition of occult, in this sense, is given by Edward A. Tiryakian:  "I understand intentional practices, techniques, or procedures which: a) draw upon hidden or concealed forces in nature or the cosmos that cannot be measured or recognized by the instruments of modern science, and b) which have as their desired or intended consequences empirical results, such as either obtaining knowledge of the empirical course of events or altering them from what they would have been without this intervention ..... To go on further, in so far as the subject of occult activity is not just any actor, but one who has acquired specialized knowledge and skills nevessary for the practices in question, and insofar as these skills are learned and transmitted in socially (but not publicly available) organized, routinized, and ritualized fashion, we can speak of these practices as occult sciences or occult arts." (Edward A.Tiryakian, "Toward the Sociology of Esoteric Culture", American Journal of Sociology 78, 1972, p. 491-512; quoted by Mircea Eliade, Occultism, Witchcraft and Cultural Fashions, 1976, p. 48.)  The word esoteric is also used in this connection, and Tiryakian says "esoteric" systems are the "religio-philosophic belief systems  which underlie occult techniques and practices; that is, it [the word "esoteric"] refers to the more comprehensive cognitive mappings of nature and the cosmos, the epistemological and ontological reflections of ultimate reality, which mappings constitute a stock of knowledge that provides the ground for occult procedures." (quoted by Eliade, l.c., p. 48).  

        30.  F. L. Peters observes that Hermeticism was an extremely complex phenomenon.  The theoretical and speculative works of the Corpus Hermeticum were accompanied by an immense variety of tracts on practical Hermeticism, which is to say, on the manipulation of natural substances.  Hermeticism had a considerable influence on Muslim culture.  With the assistance, it seems, of Iranian astrologers, Hermes Trismegistus was incorporated into Islamic learning a generation before Plato or Aristotle found a firm base there.  Many Muslims believed in the influence of stars on individuals.  One of the greatest of the early Muslim scientists was al-Biruni (11th century a.D.).  Among his many works was an Instruction on the Elements of Astrology, which became a standard work on the subject.  Peters says:  "Once again, even in Biruni, one can see the two faces of Islamic science; the secular tradition of trigonometric functions, astronomical tables and schemes of world chronology was accompanied and contaminated by a parallel tradition of horoscopes, astral influences and elaborate theories of the descent of occult wisdom from the hoary past into the bosom of Islam ...  Each discipline had authentic credentials that established it as a science; and if astrology was somewhat less exact in its predictions, as Ptolemy willingly conceded, it was not more so than ethics, for example, with respect to geometry."  (F. L. Peters, Allah's Commonwealth, A History of Islam in the Near East 600-1100 A.D., 1973, p. 270, 274, 351.)

         31.  The Hermeticist Joannes Stobaeus (c. 500 A.D.), says:  "For the stars are the instrument of destiny; in acccordance with this they bring to pass all things for nature and for men."  (in Hermetica, edited by Walter Scott, 1924, v. 1, p. 434).  Scott translates a passage from the Latin Hermetic work known as the Asclepius as follows:

        "Asclepius:  But tell me, Trismegistus, what part of the government of the universe is administered by Destiny?."

        "Trismegistus:  That which we name Destiny, Asclepius, is the force by which all events are brought to pass; for all events are bound together in a never-broken chain by the bonds of necessity.  Destiny then is either God himself, or else it is the force which ranks next after God; it is the power which, in conjunction with Necessity, orders all things in heaven and earth according to God's law.   Thus Destiny and Necessity are inseparably linked together and cemented to each other.  Destiny generates the beginnings of things; Necessity compels the results to follow.  And in the train of Destiny and Necessity goes Order, that is, the interweaving of events, and their arrangement in temporal succession.  There is nothing that is not arranged in order; it is by order above all else that the Kosmos itself is borne upon its course; nay, the Kosmos consists wholly of order.  Of these three, the first is Destiny, which sows the seed, as it were, and thereby gives rise to all that is to issue from the seed thereafter; the second is Necessity, by which all results are inevitably compelled to follow; and the third is Order, which maintains the interconnexion of the events which Destiny and Necessity determine.  But Destiny, Necessity, and Order, all three together, are wrought by the decree of God, who governs the Kosmos by this law and by his holy ordinance.  Hence all will to do or not to do is by God's ruling wholly alien from them.  They are neither disturbed by anger nor swayed by favour; they obey the compulsion of God's eternal ordinance, which is inflexible, immutable, indissoluble.  Yet chance or contingency also exists in the Kosmos, being intermingled with all material things....."  (Hermetica, v. 1, p. 362-364.)

        32.  In the Lord's Prayer of the Christian New Testament we have:                   

                  "Our Father who art in heaven, 
                    Hallowed be thy name. 
                    Thy kingdom come, 
                    Thy will be done, 
                    On earth as it is in heaven." 
  

(Mark, 6.7-12 (Revised Standard Version, 1952, revision of American Standard Version, 1881-1885, 1901, in turn a revision of King James Version, 1611)      

         33.  The influence of Hermeticism in the European Renaissance, and on the origins of modern science has been much debated.  There can be no doubt that its influence was considerable in some ways.  A translation and publication of the Corpus hermeticum was completed in 1471 by Marsilio Ficino, and this and subsequent translations and related works were in considerable demand.  An ancient pedigree was sought for Hermes Trismegistus.  The pedigree according to Ficino runs from Plato (who, Ficino claims, couldn't have thought up all his wisdom by himself) to Philolaus, then to Pythagoras (said to have obtained his wisdom in Egypt), and so on, back to Hermes.  What about Hermes' source?  "Here," says Wayne Shumaker, "we pass out of the world altogether.  Mercury 'puts aside the fogs of sense and of fancy, bringing himself thus to an approach to mind; and presently Pimander, that is, the divine mind, flows into him, whereupon he contemplates the order of all things.'  The pedigree of the pimander [divine intelligence] terminates in God Himself, whose word must perforce be accepted."  (Wayne Shumaker, Occult Sciences in the Renaissance, A Study in Intellectual Patterns, 1972, p. 204.)  What emerges, says Shumaker, is una priscae theologiae ubique sibi consona secta, "a system of aboriginal theology everywhere harmonious with itself".  That is, a certain group of Renaissance scholars and their followers sought in the Hermetic writings a pattern which would allow the reconciliation of any pagan system with Christianity.  It was a kind of structuralism.  Shumaker remarks that a vestige of it is found in George Eliot's Middlemarch, in which Mr. Casaubon is attempting to work out a "Key to All the Mythologies."  The aim of Renaissance syncretists like Ficino (who was an enthusiastic astrologer) was not to contrast mythologies, nor to criticize them, but to unite them in a harmonious concordance.

         34.  In her Giordano Bruno and the Hermetic Tradition (1964) and subsequent works, Frances Yates tried to show that Hermeticism was a major influence on the development of modern science.  "The Renaissance magus," she says, "was the immediate ancestor of the seventeenth century scientist." (Frances Yates, "The Hermetic Tradition in Renaissance Science", in Art, Science and History in the Renaissance, 1968, edited by C. S. Singleton, p. 258.)  Karin Johannisson summarizes this point of view.  The Hermetic tradition in the Renaissance, she says, started in the 15th century with the translation of Neoplatonic writings by Marsilio Ficino and his circle in Florence, Italy.  This included the Corpus Hermeticum.  "Here," says Johannisson, "the proud notion of a pristine knowledge was depicted, a gift from God to Adam and an exhortation to Man to complete the work of creation by unlocking it and decoding its underlying structure ... Nature has its own language, and the means of interpreting it was a secret alphabet, derived from Greek number mysticism and the cabala, accessible only to the chosen."  This Hermetic tradition was carried further by Paracelsus and his followers, and such people as Cornelius Agrippa (1486-1535), John Dee (1527-1608) and Robert Fludd (1574-1637).  These traditions, according to Johannisson, were transformed into a concrete program in two renowned Rosicrucian manifestos, the Fama fraternitas (1614) and the  Confessio fraternitas (1615).  Johannisson takes these to have made a positive contribution to the development of early modern science.

         35.  "They maintained," Johannisson says, "the idea that knowledge cannot be limited by given methods, and that against rationality, objectivity, and critical doubt as the cardinal virtues of science must be polace proud hope that the boundaries of science can always be transcended, the dream of a perfectible science in the service of mankind."  Johannisson takes the story to the end of the 18th century, when during the years around the French Revolution, "the concepts of magic and science once again seem to merge in the intense mystical activity of the orders, and when the scientific academy and the secret society fulfill similar functions as platforms for scientific activity and propaganda."  (Karin Johannisson, "Magic, Science, and Institutionalization in the Seventeenth and Eighteenth Centuries", in Hermeticism and the Renaissance, Intellectual History and the Occult in Early Modern Europe, 1988, based on a 1982 meeting, edited by Ingrid Merkel and Allen G. Debus, p. 251-261.)

         36.  Johannisson asserts that a 16th and 17th magus considered himself to be a natural philosopher in the same way, say, as Kepler, Galileo and Newton were natural philosophers.  (The terms "scientist" and "physicist" were not yet in common use.)  "The magus," she says, "understands nature as an animate and active network of ultimately spiritual forces, the scientists sees it as a "machine," a manifestation of the universal laws of nature."  Thus Johannisson regards laws of nature as antithetical to spirituality, rather than as rules complementary to spirituality, or perhaps rules which even spirits must obey.  "The magus believes that because nature is animate -- not completed and finished -- he can enter into it, operate on it, and manipulate it."

         37.  But a magus is himself a part of nature, and had no choice about entering it.  And to say that nature is not complete is not to say that it doesn't obey natural laws, be they only laws of probability.  Johannisson says:  "The scientist on the other hand would not attempt to exceed nature; his task is to understand and to describe it, to come as close as possible to its unassailable mechanism; for him the laws of nature are inexorable and unbreakable, absolute criteria for what is natural and supernatural.  For the magus, the supernatural simply coincides with the unusual, the marvelous, the artificial; the laws of nature are not regarded as absolute and can be exceeded by art.....  Magic and science work with different methods.  Whereas science is based on the conviction that experience and reason are valid instruments of knowledge, magic is based on the conviction that such values cannot be fixed, and the aim is continually set far beyond the boundaries of what is empirically and rationally verifiable.  The theories of science are dictated by logic, those of magic by analogy.  In opposition to rationality and understanding (episteme) stand irrational hope and use (techne).  At its most general, then, magic can be characterized as the utilization of art in order to attain specific desired ends, not in order to attain knowledge and understanding.....  Magic strove to transcend the laws of nature, science to decode them, but also to accept subordination to them."  (Johannisson, ibid.)

         38.  But there isn't, and never has been, a clear demarcation between science as knowledge and understanding, and technology as use of science and other practical arts.  Scientists, on the whole, must use and create or rely indirectly on technology in their pursuit of understanding, and technicians must use and create scientific understanding in realizing their goals.  There is, however, a clear demarcation between technology as use limited by natural laws, and magic as use not limited by natural laws. 

         39.  "To summarize," Johannisson says, "magic as a scientific activity builds on a defined conception of knowledge -- derived from the Hermetic tradition -- stressing experiments and rationality in a mathematical sense, together with a visionary utopianism aiming at practical results."  The Hermetic tradition, however, shows few signs of appreciating what applied mathematics is like, as understood by such people as Archimedes, Newton, and mathematicians today.  On the contrary, Hermeticists are prone to engage in numerology, number mysticism and number magic, which are not applied mathematics in the same sense.

         40.  Number mysticism and numerology go back to ancient times.  The Hellenistic era, the period of the Hermeticists, the Gnostics, the Stoics, the Epicureans, the Academics, and early Christianity, was also the period of the Neoplatonists, who looked back not only to Plato but to the Pythagoreans, some of whom have customarily been taken to have been among the great mathematicians of ancient Greece, and some of whom (not necessarily the best mathematicians) were devoted to a kind of numerology.  How much of classical Greek mathematics was due to Pythagoras or his immediate followers, and how much to other pre-Socratic or later Greeks has been for a long time a difficult and debated question.

         41.  Pythagoras himself appears to have been a kind of shaman, "the wisest of men", a miracle-worker who founded a secret society in which he taught metempsychosis (the reincarnation or migration of souls), the music or harmony of the heavens or spheres, immortality of souls among the stars, and various magical rituals and practices.  Walter Burkert has been a relatively recent participant in the long debate about the relation of Pythagoras and Pythagoreans to the science of mathematics.  He holds that the general belief in  the Pythagorean origin of mathematics (mathematics, say, as Aristotle and Euclid understood it) stems from no earlier than the Neoplatonic and neo-Pythagorean scholastic traditions of late antiquity, many hundreds of years after the introduction of mathematical science in the 6th and 5th centuries B.C.

         42.  It is questionable that Greek mathematics originated in the revelation of a guru, within a secret society founded to do mathematics, since it arose in close connection with the development of Greek naturalistic views of the world by Pythagoreans and non-Pythagoreans alike.  Geometry was an important component of astronomy among the classical Greeks, and some of the geometers were not Pythagoreans.  Earlier than in other fields, geometry and astronomy became the domain of specialists because their increasing complexity required special talent, and the existence of such talent is independent of membership in any particular school.  The Sophists, who were not mathematically inclined, were detached from the natural philosophers, and the exactness of the mathematical parts of natural philosophy contrasted more and more with the uncertainty of other kinds of philosophy.  By Plato's time, mathematics was already the model science.  Individual Pythagoreans had some part in this development, but the mathematics of the classical Greeks was Greek, not merely Pythagorean.  (Walter Burkert, Lore and Science in Ancient Pythagoreanism, translation with authorized revisions by Edwin L. Minar, Jr., 1972, of Weisheit and Wissenschaft: Studien zu Pythagoras, Philolaus und Platon, 1962, p. 406, 426-427.) 

         43.  Some early Pythagoreans, perhaps including Pythagoras himself, were devoted to numerology, which Burkert takes to be of  pre-historic origin.  Indeed, number dominates the Pythagoreans' general view of the world.  But devotion to number in the form of number mysticism and number symbolism is quite different from devotion to mathematics as a science.  Burkert gives this as another reason that Greek mathematics in the manner of Euclid or Archimedes didn't arise from the Pythagoreans.  He says:  "It has long been known that conscious and unconscious, rational and irrational impulses, logic and mysticism, interpenetrate in a complicated and nearly inextricable fashion.  As Kepler discovered his second planetary law in 'Pythagorean' manipulation of regular polyhedra, so one might find it obvious that precisely the pre-philosophical lore of Pythagoras provided the stimulus for Pythagorean science.  But not only does the cosmic significance of number [as in numerology] come from pre-logical number symbolism, but, even in that which Aristotle presents as the philosophy of the Pythagoreans, there emerges again and again a spirit and method directly opposite to that of exact mathematics, so that the latter cannot have arisen from the activities of the Pythagoreans.  It is not an unbroken unit of science and religious-ethical teaching that we find in the Pythagorean tradition, but a groping attempt to mediate between two levels, to transpose an ancient interpretation of the world into the language of the recently founded philosophia."  (Burkert, ibid., p. 466, 479-480).

         44.  It appears, then, that the contrast of numerology with mathematics related to experience is found already among the pre-Socratic Greeks.  In the early 17th century, in the work of people like Johannes Kepler and Robert Fludd, heirs of a neo-Pythagorean revival in the European Renaissance of a neo-Pythagorean upsurge in Hellenistic times in North Africa, we find a mixture of the two, with mathematics and its relation to experience having mostly the upper hand in Kepler, and numerology and magic having mostly the upper hand in Fludd.  (I will give details about the contrast and clash between Kepler and Fludd later.)

         45.  Burkert concludes that the Pythagorean philosophy synthesized scientifically valid mathematics with scientifically invalid numerology.  He regards this synthesis as largely the the work of Philolaus, following some prodomal attempts by Hippasus.  He says:  "The tradition of Pythagoras as a philosopher and scientist is, from the historical point of view, a mistake.  But the fascination that surrounded, and still surrounds, the name of Pythagoras does not come, basically, from specific scientific connotations, or from the rational method of mathematics, and certainly not from the success of mathematical physics.  More important is the feeling that there is a kind of knowing which penetrates to the very core of the universe, which offers truth as something at once beatific and comforting, and presents the human being as cradled in a universal harmony.  In the figure of Pythagoras an element of pre-scientific cosmic unity lives on into an age in which the Greeks were beginning, with their newly acquired method of rational thought, to make themselves masters of their world, to call tradition into question, and to abandon long-cherished beliefs.  The price of the new knowledge and frreedom was a loss in inner security; the paths of rational thought lead further and further in different directions, and into the Boundless.  There the figure of the ancient Sage, who seemed still to possess the secret of unity, seemed more and more refulgent.  Thus after all, there lived on, in the image of Pythagoras, the great Wizard whom even an advanced age, though it be unwilling to admit the fact, cannot entirely dismiss." (Burkert, ibid., p. 480, 482.)46.  Nicomachus and Iamblichus and other neo-Pythagoreans of the 2nd through 4th centuries A.D. (part of the Hellenistic era, in the extended sense) associated numbers with ethical and social entities, taking themselves to be following a tradition established long before by the Pythagoreans themselves.  To take one case, justice was associated with square numbers, perhaps because there are two "balanced" factors in a square (4 = 2·2, 9 = 3·3 etc.).  One of Aristotle's commentators, Alexander of Aphrodisias, reports that some took the number 4 to represent justice, or even to be justice, since it is the least square of a whole number (not counting 1).  Others took 9 to represent justice, perhaps because (as a guess) it is the square of the "balanced" number 3 which has a beginning, middle and end.  The number 2 might be considered as balanced, but some Pythagoreans took odd numbers to be "limited" and even numbers to be "unlimited", and perhaps 3, as the least of the limited numbers, was considered more appropriate for justice.  Or maybe this wasn't the way it happened at all. W.K.C. Guthrie observes, thus complicating matters, that some late commentators took 3, 5 or 8 for justice.  (W.K.C. Guthrie, History of Greek Philosophy, 1967, v. 1, p. 303-304.)

         47.  To take another example, marriage is associated with 5, or is 5, because it is the union of male, associated with odd numbers (in particular 3), and female, associated with even numbers (in particular 2), and, of course, 3  + 2 = 5.  Again, opportunity, or "fit and proper" time was identified with 7 "because in nature the times of fulfilment with respect to birth and maturity go in sevens."  A man, for example, can be born after 7 months, cut teeth after another 7, reach puberty after the second period of 7 years, grow a beard after the third period of 7 years, etc.  As inaccurate as this sounds, the reckoning of human lives in multiples of 7 is said by Guthrie to have been a commonplace of Greek thought.     

         48.  Aristotle severely criticized theories of this kind in his Metaphysics.  Nevertheless, some of the followers of Pythagoras were some of those who initially developed the classical Greek mathematics which culminated with the works of such mathematicians and astronomers as Eudoxus, Euclid, Eratosthenes, Apollonius and Archimedes.  Many of these works are theoretically sound and of practical value to this day.  Mathematics, especially, has the peculiar property, among sciences, that while there continue to be new developments in it, often the old developments remain useful, or even essential.  On the whole, good mathematics may be forgotten, ignored, re-invented, re-formed or  reformed, extended, placed in more general contexts, placed on new foundations, and so on -- but not shown to be mistaken.

         49.  Edward Strong argues against such authors as E. A. Burtt (The Metaphysical Foundations of Modern Science, 1925) that the triumphs of mathematical philosophy in the work of people like Galileo, Descartes and Newton did not descend from the mathematical philosophy of the neo-Platonists and neo-Pythagoreans which had been elaborated by a number of Italian philosophers in the 15th and 16th centuries.  "The Florentine Platonism of the fifteenth century and the Pythagorean-Platonic metamathematics of the sixteenth century are not historically eligible for the honor of having instructed men to turn from classification to measurement."  (Edward W. Strong, Procedures and Metaphysics, A Study in the Philosophy of Mathematical-Physical Science in the Sixteenth and Seventeenth Century, 1936, p. 10.)

         50.  The "classification" which Strong refers to is a kind of numerology, and the measurement a kind of applied mathematics.  In Platonic philosophy, numbers, as such, have an intermediate existence between what can be sensed and the eternal ideas of which they are instances.  Among the neo-Platonists, this led to a kind of theological mathematics, as Strong calls it.  This is found in such neo-Platonists as Nicomachus and Theon.  "Neither one," Strong says, "attempts to deduce mathematical or 'scientific' truths from the mystery of numbers; rather we see them treating number as possessing properties which they insist is other than that of their arithmetical work.  Both recognize that arithmetic is a self-contained science, but they also consider it as the way of initiation into realities which lie beyond the limited procedures of the mathematicians."  (Edward Strong, ibid., p. 28.)

         51.  In theological arithmetic, properties of the soul, society, ethics, the elements, and so on, are identified with numbers by a succession of analogies.  "Numbers provide a symbolism and method of classification -- a symbolism of unity and multiplicity in explaining creation, and a classification of hierarchical relationships and essential virtues by means of triadity and triangularity, and so forth.  Number as a kind of  'universal and exemplary plan' in the mind of God has its fundamental meaning not so much in the notion of law as in the notion of efficacy or power .....  Efficacy and creation rather than law and quantitative relations, divinity rather than demonstration, divine numbers as transcending the physical and mathematical rather than a vision of mathematical order 'saving' appearances: these contrasts emphasize the transformation which mathematics undergoes in its elevation to the status of divine arithmetic."  (Edward Strong, ibid., p. 33.) 

         52.  In ancient Hebrew, Greek and Arabic, numerals are letters of the alphabet, though perhaps specially marked in some way.  It appears to have been this that gave rise to the view that hidden meanings and correspondences of written words can be found by adding together the numerical values of their letters.  Among the Jewish cabalists, this was known as gematria, among the Greeks isopsephia, among the Muslims, hisab al-jumal.  (Cf. George Ifrah, From One to Zero, A Universal History of Numbers. 1985, translation by Lowell Bair of Histoire Universelle de Chiffres, 1981, Part IV, Ch. 16-21.)  Various Christian writers also use the technique.  Such techniques are still practiced today, here and there.  Idries Shah gives a number of examples in one of his works on the Sufi mysticism of the Muslims, which began to spread with the advent of Islam in the 7th century of the Christian calendar, and which still lives today.  Shah regards the Sufis to have means of contacting the underlying wisdom of humanity, and to "correspond to the inner reality of Islam, as with the equivalent aspect of every other religion and genuine tradition."  (Idries Shah, The Sufis, 1964, p. 28)

         53.  Unfortunately, this wisdom seems to exist largely in cryptic or secret form, and illogicality is said by Shah to be a key feature of Sufism.  In any case, in Arabic, most words can be assigned roots consisting of 3 consonants.  Many words will then have the same root.  Furthermore, there is a standard way of associating letters of the Arabic alphabet with numbers (given on p. 174 of The Sufis).  The Hisab el-Jamal (different transliteration of the hisab al-jumal of Ifrah?) is said to be the "standard rearrangement of letters and numbers". (Shah, p.110.)  With these things in mind, Shah says, in a comment on the significance of "dots" to Sufis:  "Among the Sufis, NQT -- "dot," "point," sometimes "abbreviation" -- has an important value in conveying teachings.  In one aspect this is connected with the mathematical part of Sufism.  The Arabic word for "geometrician" or "architect" is muhandis.  It is composed of the letters M, H, N, D, S, which are equivalent to the numbers 40, 5, 50, 4, 60.  These total 159.  These numbers, resplit conventionally into tens, hundreds and units, yield 100 = Q, 50 = N, 9 = T.  These three consonants, combined in the order 2,1,3, provide the root NQT.  This root means "dot," "point."  In certain ceremonial usages, therefore, the word "point" is used to convey the concealed word which is its parent -- the word muhandis, the Prime Builder." (Shah, ibid., p. 372.)

         54.  Gershom Scholem describes a short Jewish work called the Sefer Yesirah or Book of Creation which seems to date from the 2nd or 3rd century A.D.  It circulated widely in many lands during the European Middle Ages, and is found today even outside of academies, especially among occultists.  Scholem considers that it probably originated from neo-Pythagorean sources such as the writings of Nichomachus of Gerasa (c. 140 A.D.), together with the idea of "letters by means of which heaven and earth were created" which may have come from within Judaism. 55.  The basic thesis of the work, accoording to Scholem, is that:  "All reality is consituted in the three levels of the cosmos -- the world, time, and the human body, which are the fundamental realm of all being -- and comes into existence through the combination of the twenty-two consonants [of the Hebrew alphabet], and especially by way of the '231' gates, that is, the combinations of the letters into groups of two (the author apparently held the view that the root of Hebrew were based not on three but on two consonants)."  The 22 consonants are divided into 3 groups according to a peculiar phonetic system.  The groups contain 3, 7 and 12 letters.  The group of three consists of "matrices" (sometimes translated "mothers"), corresponding to ether (or spirit), water and fire.  From these everything else came into being, and correspond also to the 3 seasons of the year (3 rather than 4 was an ancient Greek partitioning), and the 3 parts of the body: head, torso and stomach.  The letters in the group of 7 correspond especially to the 7 planets, 7 heavens, t days of the week and 7 orifices of the body.  They also represent 7 fundamental opposites: life and death, peace and disaster, wisdom and folly, wealth and poverty, charm (or beauty) and ugliness, sowing (or fruitfulness) and devastation, domination and servitude.  And they correspond to the six directions of heaven: above (or height), below (or depth), east, west, north and south [presumably the 7th is earth, or an observer?]  The 12 remaining consonants correspond to the 12 principal activities of man, the 12 signs of the zodiac, the 12 months of the years, and the 12 chief limbs of the human body.  Scholem observers that the scheme of the Sefer Yesirah betrays its relationship with astrology, although it is based on language mysticism.  From such ideas, says Scholem, "direct paths lead to the magical conception of the creative power of letters and words"  (Gershom Scholem, p. 24-35 of origins of the Kabbalah, 1987, translation of ursprung und Anfänge der Kabbala, 1962; there is an English translation of the Sefer Yesirah by Knut Stenring under the title The Book of Formation or Sepher Yetzirah, 1923, and another in The Qabala Trilogy, unattributed, called the "The Sepher Yetsira", from the French translation by Carlo Suarès, 1968.  (Gershom Scholem, p. 24-35 of origins of the Kabbalah, 1987, translation of Ursprung und Anfänge der Kabbala, 1962; and another in The Qabala Trilogy, 1985, unattributed, called "The Sepher Yetsira" based on the French translation by Carlo Suarès, 1968.

        56.  There have been numerous other species of number magic and mysticism.  Examples are beliefs in special values of certain numbers, such as a belief that 7 must be especially significant since in Genesis God is said to have created the universe in 7 days, and there are many other places in the Bible where the number 7 appears.  The connection with the Bible is stressed in an unusually elaborate and worked out treatment of the religious significance of small integers in two volumes by the Christian writer Paul Lacuria (Les Harmonies de l'être, exprimée par les nombres, 1899. The number 7 is especially considered in Chapters XV-XVIII. Sample: the 7 divine attributes Life, Liberty, Light, Holiness, Wisdom-Justice (linked) and Eternity correspond (in these orders) to the colors red, orange, yellow, green, blue-indigo and violet, to the musical notes do, re, mi, fa, sol-la (linked), ti (v. 1, p. 196-197), and the integers 1 through 7.    Of course there are also 7 days in a week, according to the ancients 7 "planets" (Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn), etc.

        57.  Henry Corbin describes the "science of the balance" ('ilm al-Mîzân) associated with the Muslim writer Jâbir ibn Hayyân, as described by the Muslim Shî-ite writer Haydar Amli (8th century A.D., 14th century A.H.), and said by him to have been originated by Pythagoras.  Haydar Amôli explains that 1 is the cause of number, 2 is the number of the First Intelligence as second existence; 3 is the number of the universal Soul; 4 is the number of nature; 5 of "prime matter"; 6 of space ("corporeal volume"); 7 of the celestial Sphere; 8 of the Elements; 9 of the 3 natural kingdoms, mineral corresponding to 10's, vegetable corresponding to 100's, animal corresponding to 1000's.  "Each number carries by itself an esoteric secret which is not found in any other number."

        58.  There are "balances" of 7 and 12, "correspondences between the astronomy of the visible [exterior] Heaven and the astronomy of the spiritual [interior] Heaven, between the esoteric hierarchy and its cosmic correspondences."  The 7 divine attributes as given here are Life, Knowledge, Power, Will, Word, Hearing and Sight, to which correspond 7 names called the "Imams of the divine Names".  In the spiritual world, there are 7 prophets who are manifestations of the 7 "ecstatic Angels of love": Adam, Noah, Abraham, Moses, David, Jesus and Mohammad.  There are 7 planets, 7 climates corresponding to them, 7 Earths and 7 peoples who inhabit them, and 7 degrees of hell.  One has the 12 primordially created angels, the 12 Imams who are the 12 friends of God, and the 12 signs of the zodiac.

          59.  There is also a "balance" of 19, which is of greatest importance, "for the system of the world is ordered according to the number 19."  This is because "the whole universe is in the image of God."  There are 7 planets and 12 signs of the zodiac: total 19.  There are the Intelligence and Soul of the universe, 9 celestial spheres, 4 elements, 3 natural kingdoms, and Man:  total 19.  There are 7 great prophets and 12 Imams belonging to them: total 19.  The 28 letters of the Arabic alphabet are reduced to 19 "degrees" of letters by a rather complicated process.  And so on.  There is a balance of 28, and other balances.  Corbin ends his treatment of this numerological system with a description, derived from  Ibn 'Arabî of the "knights of the invisible", the Sages who, it is said in the Koran, understand the true meaning of certain parables:  "it is thanks to them that we can have in this world a 'science of correspondences'."  (Henry Corbin, Temple et Contemplation, Essais sur l'Islam Iranien, 1980, "La science de la balance et les correspondences entre les mondes en gnose islamique, p. 67-141.)     

          60.  Another familiar kind of numerology is a belief in magical properties of square matrices of numbers, "magic squares", in which the entries are the integers from 1 to n2 for some n, and the sums are the same in rows, columns and main diagonals.  For example, if the 4 rows 1-15-14-4, 12-6-7-9, 8-10-11-5, 13-3-2-16 are arranged into a square in this order, the sums are all 34.  This particular example appears in a work called Oedipus Aegyptiacus (1652) by Athanasius Kircher, a noted 17th century Jesuit "Hermetic pseudo-Egyptologist" (so characterized by Frances Yates, The Rosicrucian Enlightenment, 1972, p. 230; the square is given by Hans Biedermann, Handlexikon der magischen Künste, 2nd edition, 1973, p. 316.)