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
4. Some native Americans
simply attributed errors of their astronomers to incompetence.
Ray Williamson speaks about the sun-
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.
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
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
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
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
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
"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
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
"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
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.)
61. Such correspondences
fail to be applied mathematics, as mathematicians today understand this term,
because the mathematical structures don't correspond naturally to
anything in the events or things they are purported to apply to.
Gematria, the association of numbers with qualities like justice
or institutions like marriage are examples of what I call appliquéed
mathematics. This is an attempt to attribute a mathematical
62. Edward Strong warns
that the cabalistic and numerological
63. The distinction
between applied and appliquéed
mathematics was made by Kepler (not in these terms) in his controversy with
the physician, Robert Fludd, who was also an alchemist, astrologer and
Hermeticist. This interchange is
described by (among others) Max Caspar in Kepler, 1946, translated from
German by C. Doris Hellman, 1959, p. 290-293; by the Nobel physicist Wolfgang
Pauli, "The Influence of Archetypal Ideas on the Scientific Theories of
Kepler", in Naturerklärung
und Psyche by Carl Jung and Wolfgang Pauli, 1952, English
translation by Priscilla Silz in The Interpretation of Nature and the
Psyche, 1955; by Frances Yates in Giordano Bruno and the Hermetic
Tradition, 1964, p. 440-444; by Robert Westman, "Nature, art, and
psyche", in Occult and Scientific Mentalities in the Renaissance,
1984, p. 177-229; and by
Judith V. Field in Kepler's Geometrical Cosmology, 1988, p. 179-187.
64. It appears to have
been Kepler's harmony theory which led to the controversy with Fludd, who also
had propounded a theory of musical correspondences in his Utriusque Cosmi
... historia (1617-1618).
In Kepler's appendix to his Harmonice mundi (1619 -- sometimes
called Harmonices mundi), Kepler compares his own work with that of
Ptolemy in the 3rd book of Ptolemy's Harmonica, and also with the work
of Fludd. As to Fludd, Kepler
objects that whereas he (Kepler) develops musical theory in considerable
detail and then demonstrates a celestial counterpart, Fludd gives a condensed
version of a textbook for musicians, and then deals with practical matters of
music-making. Kepler says:
"... he differs from me as a
practitioner from a theoretician. For
while he considers
65. Furthermore, Kepler
observes that Fludd derives his harmonies purely from properties of numbers,
whereas he (Kepler) finds his from astronomical measurements.
Indeed, Fludd never makes any reference in his theories to an observed
astronomical quantity. Kepler
remarks that Fludd's Hermetic analogies 'are dragged in by the hair'.
Field says: "The
crucial difference between Kepler and Fludd seems ... to be that Kepler
demanded that his cosmological theories should be in good numerical agreement
with measured properties of the observable Universe." (l.c., p. 187.)
That is, the mathematics should be applied, not appliquéed.
66. In Fludd's opinion
Kepler's science refers only to the "outside of things", whereas he
(Fludd) penetrates to the inner, invisible depths and holiness of things.
Fludd distinguished between formal mathematics (his own kind) and
vulgar mathematics (Kepler's kind). The
mathematics of Fludd was, in fact, largely numerology -- a kind of purely
verbal manipulation of numbers. These
verbal manipulations were, in turn, often extracted from or references to
elaborate engravings which were basic in Fludd's system.
This has been emphasized by Westman who says we must look at Fludd's
engravings "not as illustrations but rather as ways of knowing,
demonstrating, and remembering." (Westman,
ibid., p. 181.) Fludd's pictures,
however, do not function in the way geometrical diagrams do for Kepler.
"It is as though Fludd's pictures," Westman says, which
appear to be about nature, are really pictures of psychic states; they are
visualizations of intuitions and feelings projected onto the world, but
lacking any sufficient criterion of correspondence to an external
reality." (ibid.,
p. 211.)
67. The mathematics of
Kepler (1571-1630) was awakened in him by the cosmos, tested by way of
observations, and found not to be purely a matter of words.
"The divine voice," he says in the Astronomia nova
(1609), "which commands men to learn astronomy, expresses itself in the
world, not in words and syllables, but through things themselves and through
the agreement of the human intellect and senses with the entirety of celestial
bodies and phenomena." (Quoted by Alexandre Koyré, Astronomical Revolutions,
1973, p. 163, translation by R. E. W. Maddison of La révolution
astronomique, 1961).) Kepler's pictures -- geometric diagrams -- were projections
of correspondences between geometrical relations and images in his mind and
geometrical relations realized outside him.
Kepler's view in his Harmonice mundi of the relationship between
the human mind and the Divine Mind -- based on an analogy with the center,
circumference and radii of a circle -- fits in very well, as Pauli observes,
with an interpretation of knowledge as a "matching" of external
impressions with pre-existent inner images. (Pauli, ibid., p. 162.)
68. Kepler says:
"For, to know is to compare that which is externally perceived
with inner ideas and to judge that it agrees with them, a process which
Proclus expressed very beautifully by the word "awakening," as from
sleep. For, as the perceptible
things which appear in the outside world make us remember what we knew before,
so do sensory experiences, when consciously realized, call forth intellectual
notions that were already present inwardly; so that that which formerly was
hidden in the soul, as under the veil of potentiality, now shines therein in
actuality. How, then, did they
[the intellectual notions] find ingress?
I answer: All ideas or formal concepts of the harmonies, as I have just
discussed them, lie in those beings that possess the faculty of rational
cognition, and they are not at all received within by discursive reasoning;
rather they are derived from a natural instinct and are inborn in those beings
as the number (an intellectual thing) of petals in a flower or the number of
seed cells in a fruit is innate in the forms of the plants."
(quoted by Pauli, ibid., p. 162-163.)
69. Kepler's cosmic
harmonies are given by proportions. For
example, Kepler asserted in the Harmonices mundi that the slowest
angular velocity of a planet at aphelion (position on the planet's elliptical
orbit furthest from the sun) is to the largest angular velocity of the planet
at perihelion (position nearest the sun) as one small whole number is to
another. Stated in another way,
the ratio of the angular velocities equals the ratio of two whole numbers.
One of the ratios in this proportion (a proportion is an equality of
ratios) is between two whole numbers, but the other is between two quantities
(the velocities) which can be represented by geometrical magnitudes. Furthermore, Kepler calculated that the ratios of the small
whole numbers were ratios corresponding to consonant musical intervals, such
as a fifth, or a major or minor third, and thus, for example, equal to the
ratios of the lengths of a string (or strings) which would produce the sounds
of these intervals. For example,
for Mars, he found a fifth, and for Earth, a minor semitone. (Alexandre Koyré,
The Astronomical Revolution, 1973, p. 335; translation by R. E. W.
Maddison of La révolution
astronomique, 1961.)
70. When two geometric
magnitudes, or magnitudes which can be represented by geometric magnitudes
(such as velocities or weights) are compared in a ratio, the terms in the
ratio must be in the same units -- for velocities, both feet per second, or
both kilometers per hour, etc. Kepler's
third law of planetary motion maintains that the squares of the periods (times
taken for one revolution around the sun) of two planets are to each other as
the cubes of the semi-major axes of the elliptical orbits on which they move
(approximately) -- provided the the two periods are in the same units, and the
two lengths of the semi-major axes are in the same units.
The periods, or the lengths of the semi-major axes, might be
incommensurable (in the mathematical sense, related to the difference between
rational and irrational numbers) with some unit of measure, but the ratios
could still be equal to a ratio of small whole numbers.
For example, in modern terms, the ratio of 3 times pi to 2 times pi
equals the ratio of 3 to 2.
71. Kepler took geometry
to be fundamental to God's creation, and God's geometrical relationships to be
basic features of the cosmos which can be awakened in us by our sensory
contacts with the world outside us. He
criticized the algebraists of his time for their lack of depth and their
utilitarian attitudes. When it is
a question of the foundations of mathematics, he said, it is necessary to
return to geometry. (cf. Gérard
Simon, Kepler astronome astrologue, 1979, p. 149-153.)
The cosmic harmonies which he derived he considered to be
characteristic of the cosmos by virtue of the fact that they arose from taking
ratios of geometrical magnitudes which appear in nature, and in us.
That the magnitudes which appear in us do indeed correspond to the ones
outside of us can be verified by making measurements outside of us to see if
the proposed ratios of these magnitudes do indeed obtain.
However, he says in the Harmonice mundi that we are born with
archetypal harmonies in our soul which are not images of harmonies, but
the harmonies themselves -- indeed, these harmonies are the soul.
(Simon, ibid., p. 141.) Fludd
also was much concerned with cosmic harmonies, but Kepler complained that
Fludd's ratios did not arise from taking ratios of objective geometrical
magnitudes, but from subjective and arbitrary assignments of numbers to
various pictures which Fludd carried around in his mind.
Fludd's ratios were ratios of small whole numbers not connected with
actual cosmological magnitudes, except in the case of musical intervals.
72. Pauli remarks on
Fludd's aversion to the quantitative, in the sense in which physicists take
this word. In Fludd's system,
there are two polar fundamental principles, form as a principle of
light, coming from above, and matter, a dark principle, dwelling in the
earth. Pauli says:
"Fludd's depreciation of everything quantitative, which in his
opinion belongs, like all division and multiplicity, to the dark principle
(matter, devil), resulted in a further essential difference between Fludd's
and Kepler's views concerning the position of the soul in nature.
The sensitivity of the soul to proportions, so essential according to
Kepler, in in Fludd's opinion only the result of its entanglement in the
(dark) corporeal world, whereas its imaginative faculties, that recognize
unit, spring from its true nature originating in the light principle (forma). While Kepler represents the point of view that the soul is a
part of nature, Fludd even protests against the concept "part" to
the human soul, since the soul, being freed from the laws of the physical
world, that is, in so far as it belongs to the light principle, is inseparable
from the whole world-soul."
73. Pauli says:
"Fludd's attitude, however, seems to us somewhat easier to
understand when it is viewed in the perspective of a more general
differentiation between two types of mind, a differentiation that can be
traced throughout history, the one type considering the quantitative relations
of the parts to be essential, the other the qualitative visibility of
the whole. We already find this contrast, for example, in antiquity in
the two corresponding definitions of beauty: in the one it is the proper
agreement of the parts with each other and with the whole, in the other (going
back to Plotinus) there is no reference to parts but beauty is the eternal
radiance of the "One" shining through the material phenomenon.
An analogous contrast can also be found later in the well-known quarrel
between Goethe and Newton concerning the theory of colours:
Goethe had a similar aversion to "parts" and always
emphasized the disturbing influence of instruments on the 'natural'
phenomena." (Pauli, ibid., p. 205-
74. Kepler's mathematical
images didn't always participate in correspondences in the way Kepler thought
they would to begin with -- as
comparison with nature external to him revealed to him at times -- but in his
view, they were intended to be used to establish correspondences of something
implanted in him with something outside of him.
Furthermore, his mathematics was based on the works of great
mathematicians of antiquity such as Euclid, Apollonius and Archimedes,
augmented by the work of numerous later "vulgar" mathematicians of
the same kind (to use Fludd's pejorative designation), including himself.
Most of this mathematics is as valid today as it ever was, and much of
it is still widely applicable, though often buried in complex mathematical
systems and traditions elaborated since Kepler's time.
75. Kepler was sometimes
extravagant in his correspondences, by today's standards.
For example, there was his proposal in the Mysterium cosmographium
(1st edition, 1597; 2nd edition with extensive added notes, 1621) that the
number and distance of the planets follow a priori from properties of
the five regular solids. However,
he devoted incredible labor to testing this proposition against Tycho Brahe's
observations. In his last major
work, the Harmonices mundi (1619), this proposition had evolved into
Kepler's third law of planetary motion, that the squares of the periods of the
planets are proportional to the to the cubes of the semi-major axes of the
ellipses in which they move. This
law still stands, to a first approximation.
Kepler's theory of the connection of musical harmony with the motions
of the solar system, a quantitative theory of the Pythagorean "music of
the spheres", elaborated in the Harmonices Mundi, hasn't fared as
well as his laws of planetary motion. But
it was not occult
76. Pauli commented on the
difference between people like Kepler, who are concerned with the quantitative
relations between parts of things, and people like Fludd, who are concerned
with qualitative visibility of wholes of things.
There are other contrasts between the viewpoints of Fludd and Kepler.
One lies in the use of language. In
Chapter V of his work De stella nova (On the new star) (1606), Kepler
argues at some length that the names of the signs of the zodiac are arbitrary,
and don't have any occult significance. Gérard
Simon observes that these pages are characteristic of Kepler's attitude, and
show that Kepler grasped the fact that traditional judicial astrology is based
on a lack of distinction between the thing and the symbol, between the symbol
and the name, between the name and the meaning.
"It is a question," Simon says, "of knowing if words
conform to things." (Gérard
Simon, ibid., p. 102.)
77. In the appendix to the
Harmonices mundi, Kepler accuses both Ptolemy and Fludd of concocting
cosmic harmonies which are "pure symbolisms ... poetical and
rhetorical". It's an old
story: the debate about the relation of language to the rest of reality, which
goes back at least to Plato's Cratylus. The
example of the zodiac doesn't reveal the profundity of the question.
It is quite easy to believe that the names of the signs of the zodiac
are named after quite arbitrary shapes assigned to certain constellations, and
that, for example, Libra, the Scales, has
no particular connection with justice or fair-mindedness (although astrologers
believe otherwise). But is all
use of language arbitrary in this way?
78. In the De stella
nova, Kepler ridicules the cabalists for regarding language as a direct
gift of God, and for extracting extravagant hidden meanings from words and
phrases by transposing their characters.
It must be remembered, though, that on the basis of the book of
Genesis, the cabalists believed, as do many others, that God spoke the
world into existence. And, as
Robert Westman brings out, Fludd's major works are of the genre of
commentaries on Genesis, and while "Fludd had a strong interest in the
created world of nature -- perhaps much more so than preceding commentators on
Genesis -- his ultimate concern was still with Genesis itself."
(Robert Westman, "Nature, Art and Psyche" in Occult and
Scientific Mentalities in the Renaissance, 1984, p. 125-229, especially p.
191-200; Westman cites Arnold Williams, The Common Expositor: An Account of
the Commentaries on Genesis, 1527-1633, 1948.)
79. Brian Vickers examines
the distinction between analogy and identity, and between literal and
metaphorical language. He says:
"In the scientific tradition, I hold, a clear distinction is made
between words and things and between literal and metaphorical language.
The occult tradition does not recognize this distinction: Words are
treated as if they are equivalent to things and can be substituted for them.
Manipulate the one and you manipulate the other.
Analogies, instead of being, as they are in the scientific tradition,
explanatory devices subordinate to argument and proof, or heuristic tools to
make models that can be tested, corrected, and abandoned if necessary, are,
instead, modes of conceiving relationships in the universe that reify,
rigidify, and ultimately come to dominate thought.
One no longer uses analogies: One is used by them.
They become the only way in which one can think or experience the
world." (Brian Vickers,
"Analogy versus identity: the rejection of occult symbolism,
1580-1680", in Occult and scientific mentalities in the Renaissance,
1984, p. 95.)
80. Vickers considers such
exemplars of occult attitudes toward language as Boehme, Ficino, Agrippa,
Paracelsus, Comenius and John Webster, and
critics (as least by implication) of such attitudes like Francis Bacon,
Galileo, Seth Ward, John Wilkins, Daniel Sennert, Johann Van Helmont, Robert
Boyle and John Locke. For example, there is Galileo's remark in "The
Assayer" (Il Saggiatore, 1623), addressed to Lothario Sarsi, a
pseudonymn of a Jesuit priest, Horatio Grassi:
"I am not so sure that in order to make a comet a quasi-planet,
and as such to deck it out in the attributes of other planets, it is
sufficient for Sarsi or his teacher to regard it as one and so name it. If their opinions and their voices have the power of calling
into existence the things they name, then I beg them to do me the favor of
naming a lot of old hardware I have about my house, "gold."
(Galileo, "The Assayer" (Il Saggiatore), 1623, in Discoveries
and Opinions of Galileo, 1957, translations and notes by Stillman Drake.)
Later in the same work, we find: "To
excite in us tastes, odors, and sounds I believe that nothing is required in
external bodies except shapes, numbers, and slow or rapid movements.
I think that if ears, tongues, and noses were removed, shapes and
numbers and motions would remain, but not odors or tastes or sounds.
The latter, I believe, are nothing more than names when separated from
living beings, just as tickling and titillation are nothing but names in the
absence of such things as noses and armpits."
(Galileo, ibid., p. 277.)
81. Isaac Newton had
similar views. In a letter to
Richard Bentley of 25 February 1692/1693, he complains about a statement of
Bentley's "representing it as absurd as that there should be positively
an infinite arithmetical summ or number wch is a contradiction in terminis:
but you do not prove it as absurd. Neither
do you prove that what men mean by an infinite summ or number is a
contradiction in nature. For a
contradiction
82. Vickers also refers to
the controversy between Kepler and Fludd.
Kepler's attitude toward analogy is illustrated by a quotation from a
letter of Kepler to Maestlin of 1605: "Every
planetary body must be regarded as being magnetic, or quasi-magnetic; in fact,
I suggest a similarity, and do not declare an identity." (Koyré,
loc. cit., p. 252.) In short,
Kepler understood the limitations of mathematical models.
83. Vickers quotes a 1968
Malinowski lecture of S. J. Tambiah, "The Magical Power of Words",
concerning the effect of "sacred words" which are "thought to
possess a special kind of power not normally associated with ordinary
language", derived from the widespread "ancient belief in the
creative power of the word". Examples
are found in the Vedic hymns of the Hindus, in certain Buddhist doctrines, in
the Iranian Parsi religion, in the religions of the ancient Sumerians,
Egyptians and Semites who believed that the world and its objects were created
by the word of God, and among the Greeks whose doctrine concerning logos
postulated that the essence of things lies in their names.
In the Bible, for example, we find:
"So shall my word be that goeth forth out of my mouth; it shall
not reutrn unto me void, but it shall accomplish that which I please."
(Isaiah 55:11).
84. In fact, the 3rd verse
of the first book of Genesis reads
85. Questions of divinity
aside, language is, of course, a most powerful instrument.
Who would deny the power of command, promise, entreaty, description,
lying, literature, and all the other effective acts of language?
In Plato's Cratylus, Socrates calls Pan the declarer and
mover of all things, and says he is speech, or the brother of speech.
Who can conceive of human society, civilization, culture, not founded
on the motive power of language? But
mover of all things? Of
the sun and planets, and the particles or waves or wavicles that compose them?
86. The limits of language
are under constant review. Suffice
it here to quote two opposed points of view.
"Learning to speak," says Han-Georg Gadamer, "does not
mean to use a preexistent tool for designating a world already somehow
familiar to us; it means acquiring a familiarity and acquaintance with the
world itself and how it confronts us.....
Language is not a delimited realm of the speakable, over against which
other realms that are unspeakable might stand.
Rather, language is all-encompassing.
There is nothing that is fundamentally excluded from being said, to the
extent that our act of meaning intends it."
(Hans-Georg Gadamer, "Man and Language" (1966), in Philosophical
Hermeneutics, 1976, p. 63, 67, translated by David Linge from Gadamer's Kleine
87. Contrarily, Alfred
North Whitehead says: "Language was developed in response to the excitements
of practical actions. It is
concerned with the prominent facts..... But
the prominent facts are the superficial facts.....
There are other elements in our experience, on the fringe of
consciousness, and yet massively qualifying our experience.....
Language is incomplete and fragmentary, and merely registers a stage in
the average advance beyond ape-mentality.
But all men enjoy flashes of insight beyond meanings already stabilized
in etymology and grammar. Hence the rôle of literature, the rôle
of the special sciences, and the rôle
of philosophy: -- in their various ways engaged in finding expressions for
meanings as yet unexpressed." (Alfred
North Whitehead, Adventures in Ideas, 1933, p. 166-167, p. 227-228.)
88. Kepler made the point
that naming a sign of the zodiac Scorpio after a tenuous resemblance of a
constellation to a scorpion does not give the sign, or planets in the sign,
any capacity to instill in humans any of the characteristics of scorpions.
This is a false conclusion based on an invalid analogy.
But Kepler didn't reject the usefulness of analogy in general.
Alexandre Koyré observes that in Kepler's Astronomia nova, when Kepler was
concerned with the nature of the force which causes the planets to revolve
around the sun, he says we can only proceed by analogy with other more usual,
better known emanations, notably light and magnetic force.
Kepler commented that if we proceed in this way, our knowledge of the
motive force of the sun will be vague and incomplete.
But it gives some idea of the kind of reality we are dealing
with. (Koyré, ibid, p. 199.)
89. Kepler's attitude
toward analogy resembles to a degree (is analogous to!) Galileo's attitude
toward idealization, about which Koyré‚ wrote so eloquently in his Études galiléennes.
Galileo conceived of bodies falling in vacuums, frictionless surfaces,
undisturbed objects moving forever with constant
velocities equal to their initial velocities (in circles, to be sure), the
orbits of cannonballs being perfect parabolas (just as the ancients had
conceived of the paths of the stars as being perfect circles -- but the
cannonballs are sublunary), simple pendulums being isochronous (a little off,
but nearly right for small oscillations).
As we would say today, Galileo produced mathematical models for
various physical states or processes, and such models capture only certain
quantitative aspects of phenomena. Kepler
was also much given to making geometric models, and he was especially fond of
his exotic model of the solar system based on the regular and star-shaped
polyhedra.
90. Neither Kepler's nor
Galileo's models agreed exactly or completely with reality.
Mathematical models seldom do. They
are idealizations or abstractions, and, in the case of quantities conceived of
as continuous, inevitably introduce some degree of approximation.
Galileo's treatise in which he founds the science of strength of
materials contains drawings of unidealized wooden beams, with knots in the
wood visible, and showing plants growing out of crevices in the stone wall in
which the beam is anchored. (Galileo Galilei, Discorsi e dimostrazioni
matematiche intorno … due nuove
scienze, 1638; the drawings are on p. 116 and 119 of the translation into
English by Henry Crew and Alfonso de Salvio, Dialogues concerning Two New
Sciences, 1914.) Galileo's
geometrical idealizations and abstractions obviously don't capture all
the properties of such objects, but only certain essential properties
-- essential for Galileo's purpose.
91. As for Kepler, he
realized in the long run that his lovely model with inscriptions and
circumscriptions of the regular solids in the planetary spheres didn't match
reality, and that not even the introduction of the star-shaped semi-regular
polyhedra would give an exact model. But
the model served to guide him to the discovery of his three planetary laws,
which have endured. They too,
however, apply only to idealized systems, such as the pair consisting of one
planet and the sun, with the sun fixed, in which the effects of other planets
and objects are ignored. And even
here one often considers the planet and the sun as mere points, rather than
extended bodies. Thus the laws
yield only good approximations to certain behavior of planets.
It isn't too easy to give a precise meaning to the "good" in
"good approximations", but it is clear to many who compare the
predictions of the laws with actual measurements that the approximations given
by the laws are not subjective assignments of numbers to the phenomena: the
laws can be used to estimate something which is happening outside their
users.
92. We have seen something
of the gulf between number mysticism and applied mathematics.
Johannisson's assertion that the Hermetic tradition stressed
"rationality in a mathematical sense" must not be taken as support
for the contention that natural philosophers were led by Hermeticists to
realize the place or importance of mathematics in such sciences as astronomy
and physics. People applying
mathematics to nature on the whole have had to struggle against the influence
of Hermeticists. This judgement
is not a new one. For example,
Robert Westman concludes in a study of the supposed contributions of
Hermeticism to the Scientific Revolution:
"Kepler and Galileo provide specific criteria for allowing us to
weight one theory above another in terms of their mathematical intelligibility
and their empirical adequacy. This
the Hermeticists failed to do because they either separated mathematics from
natural philosophy or could not see how they were connected or totally
subordinated mathematical statements to physical ones.....
What significant physical and mathematical insights Bruno and other
alleged Hermeticists arrived at came from their individual, creative
intuitions, often under the influence of doctrines first formulated in
medieval natural philosophy, and in spite of their adherence to
Hermetic doctrines." (Robert
Westman, "Magical Reform and Astronomical Reform: The Yates Thesis
Reconsidered", in Hermeticism and the Scientific Revolution, 1977,
p. 71, his italics.)
93. Johannisson also
discusses the role of Freemasonry and Rosicrucianism in early modern science.
"The Rosicrucians," she says, "-- whether existing as an
actual society or not -- integrated in their program an open view of the world
and a rejection of the Church's authority together with a passionate belief in
science as the way to progress." (ibid.)
Their science was based on Hermeticism and Paracelsianism, and
comprised chiefly magic, cabala and alchemy.
To these, Johannisson adds "mathematics, physics, cosmology, and a
medicine that stressed humanitarian ends."
However, the mathematics and physics were more in the manner of Fludd
than of Kepler, and show little trace of the tradition of Euclid, Apollonius,
Archimedes or the quantitative natural philosophers of the Middle Ages who
studied the motions of physical objects.
94. A number of the theses
of Frances Yates, especially those having to do with Rosicrucianism have been
toned done by most of her followers -- Johannisson, it seems, is one of the
more faithful. In 1979, Brian Vickers went so far as to argue at length that
in her book The Rosicrucian Enlightenment, "Yate's proposed
rewriting of Renaissance history is an edifice built not on sand but on
air." ("Frances Yates
and the Writing of History", Journal of Modern History, v. 51, no.
2, 1979, p. 287-316.) Still,
Merkel and Debus say in 1988 that "there are few who would now dispute
that, taken in context, the Rosicrucian tracts were of great concern to
seventeenth-century scientists and physicians representing many schools of
thought." (ibid.,
"Introduction", p. 9.)
95. Newton wrote a few
comments on a Hermetic tract, described by Betty Jo Teeter Dobbs
("Newton's Commentary on the Emerald Tablet of Hermes
Trismegistus: Its Scientific and Theological Significance", 1988, 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. 182-191.) Newton
carried out extensive alchemical studies, which Dobbs treated in her book The
Foundations of
96. The psychologist and
psychoanalyst Carl Jung argued at length that much of the symbolism of such
studies, especially of alchemy, arose from projections of changes of the
personality of the investigators onto their material.
The older alchemy, according to Jung, never had as its central aim the
investigation of the nature of matter and its combinations.
Such maneuvers as it undertook that we would be willing to today to
admit as bona fide chemistry were secondary to the work of
psychological transformation which was performed by way of alchemical
operations. In this view, only
during the course of the 17th century did a kind of rationalistic and
materialistic alchemy precipitate out of the older alchemy, by way of
corpuscular and mechanical theories of matter, in which matter was conceived
to be made of tiny particles moving according to regular patterns.
97. It should be kept in
mind that in our concentration on the heavens, on astral religion and
astrology, and later, on mathematical cosmology and the inititiation of
celestial mechanics, we must guard against a distortion of the attitudes of
the people who have pursued these subjects.
Although of course there were individual differences, such people were
often also very interested in the transformations of matter on earth, and
didn't always try to live with their heads above the lunar sphere.
Whatever the merit of Jung's theories about the psychological burden of
alchemy, many natural philosophers were concerned with what we would call
chemical reactions, although to be sure until the 17th century these were
usually presented in a context of some four or five element theory (fire, air,
earth, water, and "fifth essence" (quintessence or aether)
inherited from antiquity.
98. During the late 16th
and early 17th century in Europe there was a kind of flowering of alchemy,
analogous to the flowering of astrology in that period.
Dobbs says: "In their
rejection of the pagan accounts of natural phenomena offered by Aristotle and
Galen, Renaissance Hermeticists had come to emphasize anew the importance of
the first chapter of the book of Genesis.
In Genesis was a divine account of the creation of the world, one which
could not be disputed, and one which could lend itself to interpretation as a
divine chemical separation. If
the act of creation itself was to be understood chemically, then all of nature
was to be understood similarly. In
short, chemistry was the key to all nature, the key to all the
macrocosmic-microcosmic relationships sought by Robert Fludd and others.
A study of chemistry was a study of God as He had Himself written out
His word in the Book of Nature. Such
a study could only lead one closer to God and was conceived as having moral
value as well as contributing to the better grasp of the workings of nature
and to the providing of better medicines for the relief of man's
99. In the 17th century,
it was a common assumption of the "corpuscularians" -- of whom
Robert Boyle (1627-1691) is perhaps the most famous -- that everything natural
is made of elementary corpuscles or particles, all made of the same kind of
matter. Dobbs says:
"The primitive particles might differ in figure and magnitude, as
did the letters of the alphabet; larger units, like words, were formed by the
combinations of the primitive particles in different orders, groups, and
positions. The alphabet analogy
was quite commonly drawn upon to explain chemical changes.
Yet however the particles might differ in size, shape, and arrangement,
they were all made from the same basic substance."
(Dobbs, ibid., p. 46.) Thus
we are tempted to make a link between Jewish kabbalism and the alphabetical
notation of our own
100. Newton spent
considerable time and effort on alchemy, but it remains difficult to say
exactly how alchemy and Hermeticism influenced his work in mechanics.
J. E. McGuire has argued that "Newton's intellectual orientation
embodies a framework of concepts that largely emerge from the Neoplatonism
developed by his Cambridge contemporaries" and that "traditions of
magic and alchemy did not play a significant role in shaping Newton's
conception of nature." Hermeticism
played a limited role in Cambridge natural philosophy, he says, because the
Cambridge Platonists sought a restoration of Neoplatonism, which they tried to
legitimize by relating their writings to Christian Hermeticism.
"For a short time in the early 1690s," McGuire says,
"Newton explicitly accepted this ideology, but, like his Cambridge
contemporaries, he did not accept any specific Hermetic doctrines." (J.
E. McGuire, "Neoplatonism and Active Principles: Newton and the Corpus Hermeticum", in Hermeticism
and the Scientific Revolution, 1977, p. 131-133.)
101. On the other hand,
Richard Westfall argues: "I am seeking the source of the Newtonian concept of
forces of attraction and repulsion between particles of matter, the concept
that fundamentally altered the prevailing philosophy of nature and ushered in
the intellectual world of modern science,
I am offering the argument that alchemy, Newton's involvement in which
a vast corpus of papers establishes, offered him a stimulus to consider
concepts beyond the bare ontology of the mechanical philosophy.
It appears to me that the Newtonian concept of force embodies the
enduring influence of alchemy upon his scientific thought."
(Richard Westfall, "Newton and alchemy", p. 330, in Occult
and scientific mentalities in the Renaissance, 1984, p. 315-335.)
Westfall says he sees no necessary opposition between his views and
McGuire's. He takes McGuire to
have shown that the Platonism of Newton's teachers at Cambridge, in which one
finds a concept of "active principles", influenced Newton's
conception of force. Westfall
agrees, and says that alchemy influenced Newton's conception of force, too. He observes that: "... for every page in Newton's papers
of direct reference to [the Cambridge Platonists] More and Cudworth there are
well over a hundred on alchemy. I
cannot make those papers disappear."
(Westfall, ibid., p. 331.)
102. Dobbs, Westfall and
others, have said that Newton's concept of force, one of the central
and more mysterious concepts in Newton's mechanics (his theory of how pieces
of matter behave), descended at least partly from his alchemical ideas.
There has been an enormous debate over the ontological status of
Newton's forces. Newton himself
indicates at the beginning of his Principia that there are three kinds
of forces: resistive force, or inertia; impressed force,
which tends to change the state of a body from rest or uniform (constant
velocity) motion, and of which he mentions the three kinds, from percussion,
from pressure and centripetal; and attracting force, such as gravity (repelling
force is not mentioned here, although presumably a centripetal force might be
interpreted as repelling -- Newton does speak of repelling forces elsewhere in
the Principia.) (Isaac
Newton, Philosophiae naturalis principia mathematica (MathematicalPrinciples
of Natural Philosophy), familiarly known as the Principia, 1687,
Motte's translation revised by Cajori, 1934, p. 2.)
Procedures for quantitatively measuring forces are provided by Newton's
three laws of motion (ibid., p. 13; see Appendix to this chapter), especially the second law which, in our
terms, asserts that a force on body is to be measured by the rate of change in
momentum of the body it produces, where the momentum of a body is to be found
by measuring the mass and velocity of the body, and multiplying these together
(Newton's definition, ibid., p. 1). Thus,
in the case of a mass constant in time, a quantity of force acting on a body
is proportional to the acceleration of the body, the rate at which its
velocity changes.
103. The question has
often been asked, do Newton's definitions and axioms constitute a definition
of force? Is "force"
just a word we use for rates of changes of momentum, or is there something in
addition to this which constitutes the force, a "power" or
"cause" or "activity"?
(See, for example, Ernst Nagel, The Structure of Science, 1961,
Chapter 7, esp. p. 186-192.) A
number of physicists and philosophers have taken the attitude that Newton's
statements should be interpreted as defining the word
"force", and felt that to postulate any additional underlying
properties would be to introduce non-existent or useless or nonsensical
"metaphysical" principles. The only way we know a force to be present, in this view, is
to make physical measurements, and interpret them according to Newton's laws.
For a fixed mass, if an acceleration is found by measurement, then a
force has acted, and not otherwise.
104. In the earlier years
of the debate, beginning in Newton's own lifetime, the word "occult"
rather than "metaphysical" was often used.
Many natural philosophers, especially Descartes and his followers,
wished to eliminate "occult properties" from physical science.
This indeed was one of the most revolutionary aspects of the Cartesian
philosophy, and one which goes a long way toward explaining its enormous
success in connection with physics, even though Descartes's detailed physical
theories were often faulty, and also the considerable opposition it provoked
among theologians, despite Descartes' care to avoid controversy with
ecclesiatical authorities. Descartes
argued for a sharp separation between matter and spirit, and to a large extent
reduced matter to mere extension, something amenable to mathematical
description. In the astrological,
alchemical and theological contexts of the time, this must have seemed to some
like an infusion of pure oxygen, and to others like an intrusion of poison
gas. In either case, it was not
something philosophers could take lightly.
105. Descartes's views
were not wholly agreeable to Newton and some of his teachers and followers for
a number of both physical and theological reasons, and a considerable debate
grew up around this question. One
of the reasons Newton wrote the Principia was to make a contribution to
the overthrow of certain aspects of the Cartesian philosophy, as Euclid's
motive in the Elements may have been to introduce people to the theory
of regular polyhedra -- both works turned out to be monumentally more
applicable. Part of the
continuing debate hinged on whether or not there are spiritual
components of forces. Questions
like these were asked: are the planets held in their courses by continual
divine action, or were they set in motion by divine action and left to run on
their own, or were they set in motion by purely physical actions, or have they
simply been running forever?
106. The arguments of
later philosophers, especially a host of positivists from Comte to the
present, over whether or not Newtonian forces can only be recognized by making
physical measurements and seeing whether or not they satisfy Newton's laws
leave out the way Newton arrived at the concept of force.
Some positivists have said about this, roughly speaking, that they are
only interested in reconstructing mechanics on a sound logical basis, and not
in how the discoveries were made. A
few years ago, there was much reference to the "context of
discovery" versus the "context of verification".
It is certainly true that physicists have paid little serious attention
to the astrological and alchemical background of classical mechanics, and seem
in many ways to have been the better for it.
Still, we may enquire whether or not a knowledge of the background
might lead to the re-introduction, suitable refined and modified, of some of
the older notions which are excluded by a positivistic point of view. Indeed, we may go further and ask whether or not many
physicists still harbor and frequently make use of thoughts about forces and
energy which go beyond measurements interpreted according to mathematical
equations. For one thing, with
the advent of quantum mechanics, observers have catapulted back into a
prominence which they formerly had. If
Carl Jung and his followers are right, one of the great differences between
alchemy and chemistry as we know understand lies in the amount to which the
minds and emotions of observers is present within the practice of alchemy
itself, and absent from our practice of chemistry -- at least officially.
107. The physicist Paul
Davies starts his book The Forces of Nature, 1986:
"In daily life we see the activity of forces all around us.
The force of gravity guides the planets in their motion and raises the
ocean tides. Electrical forces
display themselves in thunderstorms. Mechanical
forces drive our machines and our own bodies.
Everywhere we look, matter is subjected to forces of some sort, arising
from a multitude of agencies ..... The world is full of objects -- people,
planets, clouds, atoms, flowers -- and full of motion.
Things happen when moving objects act collectively.
How do objects know about each other?
How do they respond to the presence and activities of other objects?
..... Although uniform motion is natural and needs no explanation, changes
in motion require the action of some external agency.
Because the state of uniform motion is regarded as natural, we say that
when a body is disturbed from this state it is being forced. The agencies which produce forced motion are called forces.
It is the action of forces which enriches the activity of our universe,
and which enables different parts of the world to be aware of each other's
existence. Without forces,
nothing could act on or influence anything else, and all the matter in the
universe would disintegrate into its elementary constituents, each subatomic
particle moving independently of all the others."
(Paul Davies, The Forces of Nature, 2nd edition, 1986, p. 1-2.)
108. Just so: agencies,
actions, influences. Davies goes on: "The
effect of a force on a material body is to bring about an acceleration.
This is described by Newton's second law.....
To determine how a body responds to a given force F, which may be
varying from time to time and place to place in both magnitude and direction,
it is necessary to solve [ F = ma ] for the position of the body."
(ibid., p. 3.) The force
is there before the acceleration, and before the equation, and it takes a
brave philosopher to maintain this is only manner of speaking.
109. The physicist James
Trefil remarks that the Nobel laureate physicist Richard Feynman once said, in
the witty way he had, that in pre-Newtonian theories of planetary motion,
"you have to have angels following the planets along, flapping their
wings to move them." He
added that in Newton's explanation, "the angels flapped their wings to
push each planet toward the sun, rather than along its orbit."
(James Trefil, Reading the Mind of God, 1989, p. 8.) I don't know if this was a pure joke, or if Feynman was
revealing a knowledge of how theories of planetary motion actually developed.
We will see later that the theory that angels control the planets was a
popular one in the middle ages. For
example, St. Thomas Aquinas held a version of it.
110. At one stage in his
work, up through the 1670's, Newton postulated a kind of "universal
subtle matter" or "aether", which could be used to explain the
attractive force of gravity and other forces.
It was, so to speak, a kind of "unified field theory", or GTE
(Grand Theory of Everything). Newton
never could quite make this theory work, but he didn't abandon the idea of a
universal aether entirely. In
what appear to have been his last ruminations about the mechanism of the
world, in the Queries at the end of his Opticks (4th edition, 1730), he
speculates on a very thin, exceedingly "elastick and active"
aetherial medium -- definitely not a fluid -- which conveys light and
heat, and "pervades all Bodies", and is "(by its elastick
force) expanded through all the Heavens", and can also be used to account
for the mechanism of vision. (Newton,
Opticks, 1730, Dover edition, 1952, p. 339-406.)
111. Newton goes so far as
to ask: "Are not gross
Bodies and Light convertible into one another, and may not Bodies receive much
of their Activity from the Particles of Light which enter their
Composition?" (ibid., p. 374.) There is considerable speculation in the Queries on the
nature of chemical interactions, based on a corpuscular theory of matter.
And in the very last sentence of the Opticks, he takes a swipe
at astral religion: "And no
doubt, if the Worship of false Gods had not blinded the Heathen, their moral
philosophy would have gone farther than to the four Cardinal Virtues; and
instead of teaching the Transmigration of Souls and to worship the Sun and
Moon, and dead Heroes, they would have taught us to worship our true Author
and Benefactor, as their Ancestors did under the Government of Noah and
his Sons before they corrupted themselves." (ibid., p. 406.)
112. While Newton failed
to make his unified aether theory work in general, he certainly made his
theory of forces work in the domains to which he applied them.
In Dobb's words: "The
universe lived again as Newton's thoughts swung on toward the Principia
in the 1680's, for forces and active principles were everywhere.
Not only was there the attractive force of gravity binding the planets
into a vibrant whole, there was also activity in the sub-structure of matter.
Gone, in Newton's mind, were the inert particles of Cartesian matter
resting quiescently together between impacts. In
their place were structured corpuscles of increasing complexity, held together
upon occasion by attractive forces of their own, but also capable upon other
occasions of repelling each other. Change
was the order of the day in the little world and matter matured and decayed
and was constantly replenished by active principles."
(Dobbs, ibid., p. 212.) Newton's
universe did not run like a clock. An
untellable number of writers have referred to Newton's system of the world as
a clockwork or machine-like universe, but as far as Newton himself is
concerned -- aside from various of his followers -- the accusation is not
just. It might be better
attributed to Descartes or even Leibniz, with whom Newton was frequently at
odds.
113. In his Introduction
to the Principia, Newton defines rational mechanics (as distinguished
from practical mechanics) to be "the science of motions resulting from
any forces whatever, and of the forces required to produce any motions,
accurately proposed and demonstrated."
He offers his work as "the mathematical principles of
philosophy", and says that this philosophy consists in this -- "from
the phenomena of motions to investigate the forces of nature, and then from
these forces to demonstrate the other phenomena; and to this end the general
propositions in the first and second Books are directed."
Newton continues: "In the third book I give an example of this in the
explication of the System of the World; for by the propositions mathematically
demonstrated in the former Books, in the third I derive from celestial
phenomena the forces of gravity with which bodies tend to the sun and several
planets. Then from these forces,
by other propositions which are also mathematical, I deduce the motions of the
planets, the comets, the moon, and the sea.
I wish we could derive the rest of the phenomena of Nature by the same
kind of reasoning from mechanical principles, for I am induced by many reasons
to suspect that they may all depend upon certain forces by which the particles
of bodies, by some causes hitherto unknown, are either mutually impelled
towards one another, and cohere in regular figures, or are repelled and recede
from one another. These forces
being unknown, philosophers have hitherto attempted the seach of Nature in
vain; but I hope the principles here laid down will afford some light either
to this or some truer method of philosophy."
(Newton, ibid., p. xvii-xviii.) It
appears from this that he had even greater goals in mind than those he
achieved in the Principia, and that the Queries in the Opticks
are as close as he came to reaching them.
Do you suppose Newton thought he had failed in what he wanted to do?
114. Paul Davies wrote a
second version of his The Forces of Nature, he says, to take account of
new theories that there is a single "superforce" in which all forces
have their origin. (Davies,
ibid., p. vii.) There has been
great hope among certain physicists that a GUT (Grand Unified Theory) of this
kind will be generally accepted in the near future.
But even if this doesn't come to pass, the success that Newton had with
his forces remains, suitably altered to meet the demands of relativity and
quantum
theory.
115. James Trefil begins
his book Reading the Mind of God "This
book is about an idea, one of the most astonishing and least appreciated ideas
in modern science. I call it the
principle of universality. It
says that the laws of nature we discover here and now in our laboratories are
true everywhere in the universe and have been in force for all time."
(James Trefil, Reading the Mind of God, 1989, p. 1.)
Trefil goes on to say that has found in lecturing to a wide variety of
audiences that those not made up of university scientists give evidence of not
knowing about this kind of universality.
His explanation is: "The
principle of universality is so important that it is never explicitly taught.
We [scientists] learn about it almost by osmosis.
It pervades our work, particularly in fields like astronomy, but is
seldom explicitly stated." (ibid.,
p. 2.) If Trefil is right, many people even today assume unless
taught otherwise that celestial objects play according to different rules than
material things on earth.
116. This doesn't, though,
in itself exclude theories in which angels control planets, unless angelic
control is confined to a kind of perfect celestial matter, different in kind
from terrestrial matter. One need only extend angelic control to everything
that moves. Furthermore, Newton's
idea of universality had precedents. Some
of the Stoics, for example, believed that the universe, the Divine Mind and
ordinary matter everywhere, is made of one kind of stuff, such as Chrysippus's
pneuma, and they had the idea that Fate rules the world with the orderliness
of the heavens, akin to the idea that there are natural laws which are the
same throughout the physical world. Some
of the pre-Socratic philosophers of Greece had ideas of the same genre,
concerning elements or atoms, and logos or cosmos.
A number of them had systems in which there was more than one kind of
stuff, but most of these postulated the same several kinds of stuff
everywhere. There were also the
long-lived theories, popular among astrologers and poets, of man, a microcosm,
correlated with the universe, the macrocosm.
All of these are kinds of physical universality.
117. What was different
about Newton's kind of universality? Newton
had a concept of momentum, which can be very simply measured by
multiplying inertial mass times velocity, and a concept of force as a
rate at which momentum is changed. And
he had a mathematical technique, the calculus, which could be used, in some
important cases, to find mathematical expressions for determining the motion
of a body when mathematical expressions for the forces acting on the body are
known. His law of gravity gave an
expression for one force, the inverse square expression for gravity. That there is something reasonable about the way matter moves
was not a novel idea in the time of Newton, nor was the idea that there are
quantitative expressions describing such motions, nor was the idea that matter
is made of the same kind of stuff everywhere.
But who would have thought, until Newton, that a program for deriving
mathematical expressions giving the successive of moving objects could be laid
down with three such simple laws, stateable in three sentences?
Such a simple program! Alas,
finding expressions for all the relevant forces acting on an object is seldom
easy and probably sometimes impossible, and even when such expressions have
been found, carrying out the program has turned out in many important cases to
be mathematically very difficult, and most likely sometimes impossible in any
deterministic or at least determinable (or, as some say, computable) way. But when Newton's method works, it works like magic!
Appendix to Chapter 2 (Newton's Laws)