Astronomy

Session 4.   Number in Time and Space – Astronomy

Notes by Steve Bass    Written Spring 1994    Revised 2024

References

Guides

            Schultz is used here as a guide to the more technical side of astronomy.  While remaining grounded in the facts of observation he takes a  point of view quite sympathetic to the idea of the cycle, and the integration of number and geometry.  He is apparently affiliated with the Steiner movement.      

            Burkhardt has written with deep insight on Islamic civilization and on the comparison of eastern, middle-eastern, and western spiritual traditions.  His translation of the medieval Islamic mystical scholar, Ibn Arabi is used here as a guide to the construction of the zodiac.

            Graves is used as a source for the Greek myths.  He writes in a clear modern style, allowing the symbolic aspects of myth to show through;  although his commentary is somewhat historical and anthropological.

Part I – introduction

Symbolic Astronomy 

            Astronomy as treated here is symbolic astronomy in the sense that it is a median position between Astrology, which is a kind of ‘applied’ symbolism;  and modern technical Astronomy, which deals exclusively with the mechanisms of matter.  It may be called ‘naked eye’ astronomy or even ‘philosophical’ astronomy.  It does not require any hardware, only observation.           

            It is ‘geocentric’ astronomy, but more than merely earth centered, it is observer centered.  It is essentially ‘experiential’ rather than experimental.  The ‘heavenly bodies’, sun, moon, planets and stars, are experienced as moving around the observer, and recorded empirically;  that is, directly as experienced. 

            The value of this may be difficult for a contemporary person to grasp.  We are all required to accept early, the mechanical, Newtonian model of the solar system;  and that useful observation requires hardware, particularly the telescope.  All pre-modern concepts are treated with derision.  But if we are to see astronomy as integrated to other areas of harmonic study we need to suspend, at least temporarily, our allegiance to the mechanical system, and accept, as ancient people did, that, as the saying goes, ‘What you see is what you get.’

The Cycle.

            The key concept of symbolic astronomy linking number, time and space is that of the period, or cycle.  The observation that the movements of the ‘heavenly bodies’ are periodic, can be considered among the oldest of human discoveries.  The most obvious and universally experienced periodic cycle is day and night.  For all people and life, the sun rises, climbs to  a high point, drops back and sets.  As the sun climbs, brightness increases;  as it sets darkness increases.  A period of light is always followed by a period of dark, which is always followed by another period of light.  Metabolic functions of the body, such as waking-sleeping and ingestion-excretion, also follow daily periods.  All life on Earth developed within this ‘diurnal’ cycle

            Animals respond to these light and dark periods too.  The difference in human response is in the awareness of the cyclic pattern of light and dark.  The term ‘man’, meaning humankind, according to Lawlor [SG, p 90] and Critchlow [TSS, p 35], is related etymologically to the Sanskrit word ‘manas’, meaning ‘consciousness capable of reflection upon itself’;  or ‘the balancing consciousness’, in the sense of balancing the higher or more subtle, with the lower or more gross.  If we take balancing or reflecting to be related to the concept of ‘logos’, meaning proportional relationship which facilitates understanding, then to be human means that we are creatures that gain knowledge by recognizing and systematically constructing recurring relationships, such as between periods of light and dark.  For the animal mind a period of light is a period of light, a period of dark is a period of dark;  but to the human, light and dark are consciously related in a repetitive pattern, a day. 

            Once this repetition or cycle is established, time as we understand it, as past, present and future, comes into being.  Prior to this, or on the animal level, there would appear to be only ‘nowness’.  One might try, for example, explaining to a dog or cat that it will be feed tomorrow;  but we would agree that it would have little or no meaning.

               In the Book of Genesis [I.1] we read “In the beginning God created the heavens and the earth.  The earth was without form and void and darkness was upon the face of the deep; and the spirit of God moved upon the face of the waters.  And God said ‘Let there be light’; and there was light.  And God saw that the light was good;  and God separated the light from the darkness.  God called the light Day and the darkness he called Night.  And the evening and the morning were the first day.”   

            In Plato’s Timaeus [47] we are told, “For I reckon that the supreme benefit for which sight is responsible is that not a word of what we have said about the universe could have been said if we had not seen stars, sun and heaven.  As it is, the sight of day and night, the months and returning years, the equinoxes and solstices, has caused the invention of number, given us the notion of time and made us inquire into the nature of the universe;  thence we have derived philosophy, the greatest gift the gods have ever given or will ever give to mortals.”     

            These passages indicate the importance of the idea of the cycle of light and dark in cosmological analysis.                          

Part II – The Heavenly Bodies

The Sun

            The ‘nowness’ of eternity, divided from within itself, into light and dark, may be thought of as being parallel to the timeless One transformed into the alternating Two.  The inevitable third element, providing structural stability to the situation, or the ‘medium’ of communication, is the ‘heavenly body’, the light source, whose movement marks the alternation.  The ’cause’, or marker of the light – dark cycle of the day is the sun.  The sun is both constant and changing.  It shines with constant brightness and is always circular;  but its position in the sky is constantly changing, and there is another half of its path which seems to pass below the earth.

            The sun is not only circular but it moves in a circular path.  Schultz points out [MRS, p 17], “If we follow the sun in the course of its daily movement we find that it describes an arc above and around us in the sky.”  If you point your arm at the place on the horizon where the sun rises, move your arm to follow the sun’s path across the sky and back to the horizon where it sets, you will have traced out a circular arc with yourself at the center,  figure 1.  The circle, as we have seen in previous chapters, may symbolize Monadic unity, wholeness, constancy;  it may also be said to represent the quality of the bounded, the defined. 

            A simple yet fundamentally correct way to measure the changing nature of the sun is by observing a shadow.  One method of controlling the measurement of a shadow is by setting up a shadow stick vertically in flat ground.  The stick may be thought of as a mediating third element in the sun – shadow, or light-dark relationship.  As the sun changes its position in the sky, the shadow changes its position inversely on the ground.  As the sun represents the source of light, the shadow represents the absence of light and its movement is inverse to the source of light.  As the sun moves to the right the shadow moves to the left, as in figure 2a.  

            Observation of the movement of shadows, whether natural or artificial, yields information in pattern form.  An elemental piece of information obtained from the shadow stick is the east – west axis.  This is found by describing a circle with the stick as its center, and marking the position of the shadow on the circumference of the circle, at sunrise, then at sunset, and connecting the points.

            Burckhardt [SAE, p 23] and Critchlow [TSS, p 29], both of whom refer to a Hindu sacred book on temple building called the ‘Manasara Shilpa Shastra’, describe a traditional Indian procedure.  This begins with the shadow stick at the center of the circle.  The shadow is marked when it crosses the circumference of the circle, just after sunrise and again just before sunset.  Connecting the two points on the circumference gives the east – west axis, shown in figure 2b.  The north – south axis, which is marked by the high point of the sun’s movement through the sky, can be found by constructing a perpendicular to the e-w axis, figure 2c.  This is done by using the two points of shadow intersection as centers and the length of the e – w line as a radius.  This generates the Vesica Piscis whose two ‘points’ position the n – s axis.  By repeating the Vesica construction along the e – w axis, the intersection of the four arcs positions a square, figure 02d.

Burckhardt [SAE, p 24] says, “The reader will have noticed that the three phases of this rite correspond to three fundamental geometrical figures:  the circle, image of the solar cycle, the cross formed by the cardinal axes and the square derived from it.  These are the symbols of the Far Eastern Great Triad, Heaven – Man – Earth.  Man appears in this hierarchy as the intermediary between heaven and earth, the active principle and the passive principle, just as the cross of the cardinal axes is the intermediary between the limitless cycle of the heavens and the terrestrial ‘square’.”  

            Another view might be that the second geometric figure to appear after the circle, is the triangle; formed by the initial center and the two shadow points on the circumference, as in figure 2b.  Burchardt’s analogy, we may say, brings into correspondence the ‘ritual sequences’ of:  the first four numbers, the first four geometric forms, and the first four musical consonances, with four basic astronomical observations:

            The theme of the division of the circle is important in the relation of time to astronomy.  As suggested by Burckhardt in the quote above,  segmenting the continuous circumference of the circle is analogous to order being brought out of chaos, or to establishing a moment in eternity.  In modern terms, we say we have become ‘oriented’, when we know where we are.  Orient means east, where the sun rises, so to be oriented implies being aligned with the sunrise and therefore with the patterns of movement of the heavenly bodies.  The point of sunrise is the point of scission and establishes the axis.

            The vertical shadow marker establishes the third directional axis.  This third element, or mean, can be taken to establish the structural relation between heaven and earth.  It is characterized by Critchlow [SSA, p 18] as, “The potency of creation or vertical ray: axis of the lightning flash.  The division of light from darkness.  The ontological axis of being.  Related to (the Greek letter Ø) phi as in phyo, to bring forth, and physis, nature, and phylon, race, sex.  One version of this symbol – the Hittite – is used as the determinative for ‘the gods’.” 

            A good natural shadow marker would be a free standing tree, recalling the symbol of the tree of knowledge.  In many traditions the teacher sits beneath a tree; the Bhudda, for example, receives enlightenment beneath the Bhoddi tree.  A good artificial marker would be a stick, which is a part of a tree.  If, as we will see in a later session, the stick was marked or notched to record observations, it recalls the Biblical symbol of Jacob’s ladder. 

            In ancient Greek times the shadow marker was called a ‘gnomon’; a word related to ‘gnosis’ meaning experienced knowledge.  We encountered the gnomon in the Arithmetic and Geometry chapters associated with proportional transformation through time, and now we see it associated with transformation of light and dark through time.  Its relation to the concept of gnosis indicates that the experience of pattern, or the study of transformation,  is a  pathway to knowledge.

Cycle of the Year. 

            Observation of the daily path of the sun will reveal that the path is slightly different each day.  During the winter the daylight period of the day is shorter than the period of darkness.  The sun rises in the south-east, is low in the sky at noon and sets in the south-west.  Each day the period of light gets a bit longer, the sun rises and sets further to the north, and is higher at noon.  On one particular day the period of dark is equal to the period of light.  This is known as the spring equinox, or the equal point.  When the rising and setting points of the sun are furthest north and noon is at its highest point, it is the summer solstice, or stopping point.  The movements now reverse.  The days get shorter, rising and setting points move south, and the noon  point gets lower.  When the days and nights are equal again, it is the fall equinox.  When rising and setting points are at their furthest south and the noon point is lowest, it is the winter solstice.   The circle of the year is thus marked by two extremes, the solstices, and two medians, the equinoxes.

            Schultz describes two aspects of the sun’s observed movements.  The daily, or diurnal movement and the yearly movement.  Of the diurnal Schultz writes [MRS, p 40], “The rising and sinking of the diurnal arcs takes place in a rhythmic pendulation. like a sine wave.  Figure 03a shows this rising and sinking for twelve equal intervals within the year.  Starting from the middle position, the celestial equator, it swings 23 &1/2 degrees in either direction to the extreme diurnal arcs of the summer solstice on June 21 and the winter solstice on December 22.  On these days the sun attains its highest and lowest arcs, respectively.  When the sun stands near the celestial equator in spring and autumn its declination changes most rapidly. …  Any given diurnal arc of the sun can only be approximated by a circle, although the deviation is very slight.  For the 365 daily arcs pass over, one into the next, in a continuous spiraling movement figure 03b.”

            Daily observation will also reveal that the Sun changes its relation to the background of stars.  Schultz writes [MRS, p 42], “The annual rhythm of the appearance and disappearance of the constellations reflects the progression of the Sun in its course through the fixed stars, which cannot in itself be seen.  The Pleiades, for example, are still visible in April above the point of sunset;  within a few weeks they have disappeared, to emerge again at the beginning of July in the early morning sky.  The Sun has therefore moved from a position to the west (right) of the Pleiades, where it set before the constellation, to a position to the East (left) of it.  Stars visible in the evening sky gradually fade into the twilight to appear again, after a period of invisibility, in the morning sky.  … the Sun wanders through the fixed star sphere in the course of each year, following a path … we call the ecliptic.  As a result of this annual movement, theSun appears to be falling continually behind the 24 hour daily movement of the heavens.  Whereas the latter proceeds from east to west, the annual movement of the Sun through the zodiac takes place in the

opposite direction, from west to east figure 3c.”  Your present author has included  figure 3d to show the relationship of the horizon to the celestial equator and the ecliptic.

            Schultz continues [MRS, p 43], “Let us now bring together the two aspects of the Sun’s movement, which we have thus far regarded separately.  The Sun wanders, in its consecutive positions, once each year through the whole of the fixed star sphere, which is now to be imagined at rest [figure 3d].  It advances along a great circle which crosses the daily circles of movement at an angle of 23 & 1/2 degrees, the obliquity of the ecliptic.  The twelve constellations through which it passes are the zodiacal constellations figure 03e.”

The Moon

            The Moon is the dominant body in the night sky.  Like the sun, it is circular when full, and moves in a circular arc;  it rises in the east, reaches its maximum height in the south and sets in the west.  This common pathway in the sky of the sun, moon, and planets is known as the ‘ecliptic’ band.

            Unlike the sun, however, the moon rarely appears to be fully circular.  Its shape changes on each successive night.  Starting with a full circular shape, seven nights later only the left half is apparent, seven nights later it does not appear at all, seven nights after that, only the right half is visible and on the twenty – eighth night the shape returns to full circular.  So, the Moon marks each part of its 28 day cycle by an incremental change of form.

            During this 28 phase cycle, the sun and moon also go through a cycle of relative position, figure 04.  When the moon is ‘new’, that is, not visible, it rises with the sun at sunrise.  Such an apparent meeting of heavenly bodies is called a ‘conjunction’.  Each day the moon moves eastward along the ecliptic away from the sun by a little less than 13 degrees.  After seven days the moon is at its first quarter and its position forms a right angle with the sun so that it is at its high point when the sun is setting.    The moon at this point can be said to ‘square’ the sun and it appears as a half circle.  After another seven days the moon is full and it rises in the east as the sun sets in the west, the relationship formed is a 180 degree angle, therefore called an ‘opposition’.  From here the waning part of the cycle begins. Seven days later the moon is in its last quarter and again squares to the sun.  But now the moon is at its high point as the sun rises in the east. Finally the moon is new and conjuncts again with the sun.

            The whole cycle takes about 28 days.  We must say ‘about’ because there are [at least] two ways to measure the lunar cycle.  As Schultz points out, [MRS, p 78] “…a sidereal month [a month measured with respect to the stars] lasts an average of 27d 7h 43m 12s.  A lunation, on the other hand [a complete cycle of lunar phases] takes, on average, 29d 12h 44m 3s.  This synodic month [synodos, Greek for ‘meeting’] gives, for example, the span of time from one conjunction of the moon with the sun to the next…  The synodic month is longer than the sidereal because the sun progresses by roughly one constellation for every revolution of the moon.  The following new moon can only take place after about 1 &1/12 sidereal revolutions, or about 2 &1/4 days after the completion of one such revolution.”

            Schultz calls the moon “a mirror of time”,  saying, [MRS, p 83] “For each time of day and of the year the moon has its own particular phase and position, making it possible from an observation of the moon to deduce the momentary cosmic situation.”   For example; if the moon is a narrow crescent low over the eastern horizon it is just before dawn.   If the moon is rising due east and if the angle of the points or ‘horns’ of the crescent is sharper than the angle of the celestial equator, it is autumn;  if shallower, it is spring.  If the angle of the moon is similar to the celestial equator but is rising in the northeast, it is summer, if in the southeast, it is winter; figure 5.  Thus, observation of the moon can reveal the time of day and the season

Arithmetic of the Sun – Moon Relationship.  

            The year is defined by the position of the sun.  One solar year equals 365d 8h;  but 13 sidereal or star based lunar months equals 13 x 27d 7h = 355d 4h and 12 synodic or conjunctional months equals 12 x 29d 12h = 354d 8h.  An approximate resolution of these three periods occurs every 19 years.  19y x 365d 8h = 6939d 14h.  235 synodic months x 29d 12h = 6939d 16h.  254 sidereal months  x 27d 7h = 6939d 16h.  This calculation was initially published by the Greek astronomer Meton [c 430 BC] and is thus called the Metonic cycle. 

            Schultz notes, [MRS, p82] “After the completion of one such Metonic cycle the moon stands in the same phase on the same date. …  The Metonic cycle is a rhythm of higher order between the synodic and tropical month, which results in a whole number of solar years.  (Schultz adds in a footnote) In calculating the date of Easter this 19 year Metonic cycle is used, for on its completion the Easter full moon falls on the same day.  The Golden Number gives the placement of each successive year within this cycle.”  Schultz does not elaborate on this last remark, but we may note here that 19 x .618 (phi) = 11.74 and 19 ÷ .618 = 30.74.  11.74 is slightly greater than the 10.95 days difference between 12 synodic months and one solar year;  and 30.74 is slightly greater than the 30.42 days in 1/12th of a solar year.

The Eclipse Cycle 

            The other important aspect of the sun-moon relationship for our purposes here is the eclipse cycle.  There are two types of eclipses, solar and lunar.  For a solar eclipse the moon must pass directly in front of the sun, in line with the observer;  for a lunar eclipse the moon must pass through the shadow of the earth, so that the observer on Earth is directly between the sun and moon.  Thus for a solar eclipse, the sun and moon must be in conjunction;  for a lunar eclipse they must be in opposition.  Solar eclipses occur only at the new moon;  lunar eclipses only at the full moon. 

            If the sun and moon followed identical paths along the ecliptic there would be two eclipses every month.  But, as Schultz tells us, [MRS, p 85] “… the moon stands sometimes north and sometimes south of the ecliptic, its orbit inclined by 5 degrees to that of the sun figure 06.  On the background of the fixed stars, therefore, the orbits of the sun and moon cross at two diametrically opposed points in the zodiac.  These are known as the lunar nodes.  During the course of each sidereal revolution the Moon crosses the ecliptic once from south to north at the northern or ascending node and some fourteen days later from north to south at the southern or descending node.

            The lunar nodes, however, are not fixed but progress continually along the ecliptic from east to west or clockwise;  or in other words, in the opposite sense to the planetary motions.  …

about 1&1/2 degrees in a month.   The Moon’s course from one node to the same node again must therefore be shorter than the sidereal month:  the ‘nodal month’ [or archaically, the draconitic month] lasts 27d 5h 5m 36s.  In a year the lunar nodes regress by about 19 degrees, or roughly two-thirds of a constellation.  A complete revolution  [of the nodes] requires 18.6 years. … The Moon’s path through the Zodiac is not a closed line returning again to its starting point, but rather an open curve, winding like a ball of wool… 

            [When]  one of the nodes stands at the point of conjunction, the new moon will pass directly before the sun, resulting in a solar eclipse. … Only near the crossing points of the orbits of the sun and moon can the latter, in passing, partly or entirely cover the sun’s disc, thereby eclipsing its light. … If the full moon occurs near a node the sunlight which normally illuminates the moon will be partly or totally obliterated by the earth; the moon enters the earth’s shadow.”

            Schultz continues, [MRS, p 97] “Every year there are two eclipse  periods which occur at intervals of six months when the sun crosses one of the two lunar nodes at the ecliptic.  Each time, a solar eclipse must  occur, so that two such eclipses take place each year: one at the northern node (moon rising), the other at the southern node (moon setting). … As the lunar nodes move around the zodiac over an 18.6  year period the eclipse periods also move through the seasons, occuring about three weeks earlier each year.  However, as eclipses can only occur at full or new moons, they take place earlier from year to year by complex intervals resulting from the interplay between the nodal and phase rhythms. … the syzygies, or full and new moon positions, occur about 10 or 11 days earlier each year.  They therefore move retrograde through the zodiac.  The lunar nodes also move retrograde but at about double the speed, so they slowly overtake and pass the syzygies.  As a result, the eclipses will take place from year to year about 10 or 11 days earlier over a period of 3 to 4 years before leaping to the previous syzygy, in which case they occur about 40 days earlier. … About every 9 or 10 years the solar eclipses fall at midsummer or midwinter, and 4 or 5 years later at the times of equinox  figure 07. … After 18 years the cycle is completed and each eclipse recurs in cyclical sequence. … This cycle appears to have been known in relativly early times to Chinese and astronomers and is designated the Saros cycle. …”

            “The sun passes each node once in a year.  The exact interval between two such meetings, known as the eclipse year, is 346.62 days  which is nearly three weeks shorter than an ordinary year, owing to the annual regression of the nodes.  A Saros contains 19 such intervals.  In the same period 223 synodic months pass (the true length of the Saros) …”   Notice that the number 19 has come up twice in describing long period sun – moon cycles;  and that 12 [a number associated with the sun] x 1.618 [Ø] = 19.4

            The above description gives some idea of the complexity of the moon’s cycle and of the sun – moon relationship.  Schultz concludes [MRS, p94] “The moon, whose surface appears as a dead and hardened cinder, possesses the most complex and varied rhythms of movement of all the luminaries.  It eludes our attempt to grasp its movements by means of rational, numerical calculations.”

The Zodiac

            The  sun and moon appear to move along the ecliptic against a background of fixed stars;  fixed in the sense that their positions relative to one another are experienced as remaining constant.  A band about 30o wide, centered on the ecliptic, is divided into twelve constellations, which are  known as the Zodiac, or circle of animals; figure 08.  Although there does not appear to be any factual – historical, or objective – technical reason for this, we should not assume the division to be arbitrary.  The Zodiac can be considered an ontogenic configuration based on the qualities of 3, and 4.  As we have seen in the sessions on Number and Geometry, 12  can be thought of as 3 x 4.  The Triad represents the cyclic structure of manifestation;  which may be expressed as ‘proceeding, maintaining, and returning’;  or in terms of time, as ‘past, present, and future’.  The Tetrad may be said to represent orientation and direction of that which is manifest [materiality] in space.  The time cycle of 3 multiplied by the space cycle of 4 makes appropriate an astronomical division of 12;  in keeping with the idea of Astronomy as Number in time and space. 

            Each of the twelve constellations has been given a name and a sign.  The signs we are familiar with today are of Mesopotamian decent via Greece.  The images of the signs are related to aspects of the yearly natural cycle.  Warren Kenton [ACM, p 13] sums these up:  “the sign of Aries, the Ram, shows in its sudden rush the initial appearance of the spring corn, while Taurus, the Bull, defines the gathering charge and growth of plants and mating of animals.  Gemini, the Twins, describe the proliferation and interconnection of the ecological pyramid.  With the sun in Cancer, the Crab, nature is full of liquid succulence, each plant and animal charged with the sap of life.  At high summer Leo the Lion’s strength and mane demonstrate the sun’s fiery power.  This is followed by the Virgin, symbol of the harvest and the seed for the next years season.  The sign of Libra, the Scales, marks the autumnal equinox, as summer’s heat becomes milder before the cooling decay of nature turns into the sign of death in Scorpio.  Sagittarius carries the year on to a period of reflection, indicated by the Archer looking back as he gallops towards the winter solstice.  The Fish-Goat sign of Capricorn denotes the transition point from the old to the new as the sun begins to climb again.  The man pouring water on the ground, Aquarius, is the time of the winter rains, and the Fish, Pisces, indicate the living but unseen movements beneath the soaking earth which precede Aries and the first day of spring, beginning the cycle.”  

            This particular cycle of signs is local to its geography and culture;  that of the Archaic Middle Eastern farmer.  Other groups of signs have been used in China, Native America, India and elsewhere, but the use of 12 signs appears to be very widespread;  perhaps because of its cosmic and universal signification of the time periods arising from the solar cycle being sectioned by the moon. 

            Schultz provides this more historical picture of the Zodiac and makes the distinction between the constellations and the signs [MRS, p 47], “Although the majority of constellations in the sky as a whole are Greek, most of the zodiacal constellations seem to have their origin in Babylonian mythology.”

            “The divisions between the single constellations may have varied considerably at different times and in different parts of the classical world.  The divisions described by Ptolemy in his ‘Almagest’ and handed down to modern times, should not therefore be seen as anything final and ultimate.  Indeed, the strikingly different sizes of some of the constellations would seem to point to rural folk- tradition rather than to mystery teachings.  One can hardly avoid having the impression that the divisions were arrived at in a visual, pictorial way, without too much concern for the symmetry of celestial architecture.  These constellations belonged to the lore of peasants and shepherds, who ordered their labors according to a living calendar of the sky.  The seasonal appearances and disappearances of the constellations and their connection to work on the land were described by Hesoid in his epic poem ‘Works and Days’.”

            “This pictorial, folk zodiac of visible constellations is in stark contrast to the zodiac of ‘signs’, which we owe to Hipparchus [c. 150 BC].  In Hipparchus’ system the Sun’s orbit is divided into equal segments, beginning from the vernal equinox.  The segments are designated with the Latin names of the constellations in their proper sequence.  The spring quarter is thus distinguished by the signs Aries, Taurus, Gemini;  from the time of the summer solstice there follow three ‘summer’ signs, Cancer, Leo, Virgo.  Following the autumnal equinox comes the further divisions Libra, Scorpio, Sagittarius, and after the winter solstice the Sun wanders through the ‘winter’ signs Capricornus, Aquarius, Pisces.”

Symbolism of the Zodiac.

            The qualities of the signs form geometrical relationships, based on the Arithmetic properties of 12.  Fourness is represented by the four elements, which form four groups of three signs each.  These signs are arranged in equilateral triangles, called trigons;  for example, the fire trigon of Aries, Leo and Sagittarius.  Threeness is represented by the three parts of the temporal or spiritual cycle;  1) proceeding, called the cardinal, mobile, or active signs;  2) maintaining, called fixed or passive;  and 3) returning, called mutable or synthetic.  These form three squares of four signs each, the ‘active’ square, for example, being Aries, Cancer, Libra, and Capricorn.  The geometry  of the signs form a dynamic yet balanced interplay such that the three fire signs, for example, are a cyclic triad of Aries, active;  Leo, passive;  and Sagittarius, mutable. Each square, such as the active square, in turn, has one member for each element, figure 09.

            The Neo-Platonist philosopher Proclus, writing in the fifth century AD informs us [CFE 167, p132]:  “The Pythagoreans assert that the triangle is the ultimate source of generation ….  Consequently Timaeus says that the ideas of natural science, those used in the construction of the cosmic elements, are triangles.  They are divided into three kinds, bring into unity things that are in every way divided and changeable, are full of the indefiniteness of matter, and set up in advance the dissoluble bonds of material bodies, just as triangles themselves are contained by straight lines and have angles that bring together the plurality of these lines and provide them an imported fellowship and contact with one another.              “Rightly, then, Philolaus dedicates the angle of the triangle the four gods Kronos, Hades, Ares, and Dionysus, since he includes within their province the entire four-fold ordering of the cosmic elements derived from the heavens or from the four segments of the zodiacal circle.  Kronos gives being to all moist and cold essences, Ares engenders every fiery nature, Hades has control of all terrestrial life, and Dionysus supervises moist and warm generation, of which wine, being warm and moist, is a symbol. …  The triangle is the chief agent in the production of sublunary things.  The right angle furnishes them with their essence and bounds the measure of their being. … the acute angle renders nature herself subject to division and the idea of the acute angled triangle prepares the way for the endless distinctions to come.”

            [CFE 173, p136] “The square is the only area whose very nature exhibits an ideal with respect to both its sides and to its angles.  Its sides are equal and each of its angles being a right angle holds the measure of angles, a measure permitting neither of increase or decrease, because it is superior in both respects, then, it has properly received the generic designation. The triangle, even though it has equal angles, has all of them acute, and in the pentagon they are all obtuse.

            “The Pythagoreans thought [the square] more than any other four sided figure carries the image of the Divine nature. … Philolaus, moreover, in another of his reflections calls the angle of the square the angle of Rhea, Demeter, and Hestia.  For since the square if the substance of the earth and the element nearest it, as we learn from Timaeus, and since the earth receives effluences and generative powers from all these goddesses, he rightfully dedicates the angle of the square to these divine life giving forces.  For some call the earth Hestia or Demeter, and they say that it partakes of all that Rhea is, and in her are all the generating causes in earthly fashion. …

            [CFE 173] “We must not omit to observe that Philolaus dedicates the angle of the triangle to four gods and the angle of the square to three, showing their penetration of one another and the communion of all in all, of odd numbers in the even and of even in the odd.  Hence, a tetradic triad and a triadic tetrad that partake of the generative and creative goods maintain the whole order of generated things.  The number twelve, which is their product, ascends toward a single monad, the sovereignty of Zeus.  Philolaus says that the angle of the dodecagon is the angle of Zeus, because Zeus holds together in a single unity the whole duodecimal number.  In Plato likewise Zeus leads ‘the twelve’ and has dominion over all things.” 

            In another difficult but profound passage, Titus Burkhardt, delineates the cosmology of the medieval Islamic philosopher Ibn ‘Arabi [MAI, p 17 – 24]:  “…the limit sphere of the sky is not measurable except by reason of the directions of space … the whole of the directions that radiate from one center virtually contain all the possible spatial determinations.  The indefinite expansion of these directions is the ‘vault of the sky without stars’;  and their center is each living being which is on earth … The indefinity of the directions of the space is in itself undifferentiated … but the qualities of the directions of celestial space are interdependent. … as soon as one direction of the celestial space … is defined, the … other directions become differentiated and polarized with respect to that one. …

            “However, the fixed points of the sky … are above all the respective poles of the diurnal revolution of the  [day] … and of the annual cycle of the sun, and are consequently the points that the divergence of these poles determine on the ecliptic, that is to say the two equinoxes, points of intersection of the solar orbit with the equator, …  and the two solstices, extreme points of the two phases, ascendant and descendant of the solar cycle. … As soon as these four points of the ecliptic are fixed, the other eight zodiacal divisions respond to these by virtue of the ternary  [threeness] and senary  [sixness] partitions which are naturally inherent to the circle, as is expressed in the relationship … of the hexagon inscribed in the circle.  Then it is as though a spontaneous crystallization of spatial relations is produced, each point of the quaternary evokes two other points of a trigon, which in their turn repeat the relation in ‘square’, figure 10 so that the division of the circle by four is thus integrated and compensated by a ‘congenital’ synthesis to the ‘universal’ nature of the cycle, according to the formula 3 x 4 = 4 x 3 = 12.”

            “If the two great circles, that of the celestial equator and that of the solar cycle, coincided, there would be no manifestation of the seasons.  The divergence of the two great celestial cycles evidently expresses therefore the rupture of the equilibrium which engenders a certain order of manifestation, … that of contrasts and complementaries;  and the four cardinal points determined by this divergence are obviously the signs or marks of this contrast.  Ibn ‘Arabi identifies the zodiacal quaternity with that of the qualities of fundamental tendencies of the total or universal Nature which is the root of all the differentiations. …”

            “The universal nature … manifests itself by four qualities or fundamental tendencies which appear in the sensible order as heat and cold, dryness and humidity.  The heat and cold are active qualities opposed one to the other;  they manifest also as expansive and contractive forces;  they determine the pair of passive qualities, dryness and humidity.  Taken to the four cardinal points of the zodiac, cold corresponds to the solstices … heat corresponds to the equinoxes … Because of this fact the cardinal signs succeed each other by contrasts;  but the passive qualities of dryness and humidity tie together two pairs of these. 

            “The four tendencies or qualities of nature are joined two by two in the nature of the four elements or foundation of the sensible world, produced starting with the terrestrial substance:  earth is cold and dry, water is cold and humid, air is hot and humid, fire is hot and dry. …”  figures 09 and 10.

             “The quaternity  [fourness] of the fundamental tendencies of the total nature should be multiplied, according to Muhyiddin Ibn ‘Arabi, by the ternary  [threeness] whose cosmic congenitors are the three movements or principle orientations of the First Intellect or Universal Spirit, or even under another relationship,  the three worlds, that is to say, the present world, the future world and the intermediary state … .  The three movements or orientations of the spirit are:  the descending movement, which obviously recedes from the Principle and which measures the depths of the possible;  the expansive movement which measures its amplitude or width;  the movement of return towards the origin, which is directive in the sense of the exultation or the height. …

            “All points of the zodiac which happen to be in relation to the trigon have the same elementary nature … and all points which happen to be in relation to the square have the same spiritual quality but are differentiated by the elementary contrasts.  From this one can deduce the different characters of the aspects or reciprical positions of the planets on the ecliptic:  the relation in right angles necessarily denotes contrast, in the same way that opposition signifies opposition;  the trigon is the expression of a perfect synthesis;  and the sextile, the relation of 60º, expresses an affinity. …

            “…the cycle is before anything else an image of the development of all the possibilities implied in the amplitude of a degree of manifestation.  In conformity with this, the cardinal signs, critical regions of the  solar cycle, are called ‘mobiles’, … dynamics or expansives.  As for the descendent movements of the spirit, it is translated in the cyclic order by fixation, and it is because of this ‘movement’ that the world subsists as such.  At last, the spiritual movement of return towards the origin is reflected in the … zodiacal cycle by the synthesis of the other two orientations, and the signs coordinated with them are called ‘doubles’ or ‘synthetics’.” 

            In this lengthy and difficult passage Ibn ‘Arabi, via Burckhardt, has shown us the flow of unity into multiplicity.  From the unity of the undifferentiated sky, through the double duality of the four key points of the sun cycle combined with the three phases of the spiritual or temporal cycle, to the twelve signs of the zodiac with their interrelated geometric qualities.

Sun-Zodiac relationship – Precession.

            Since the ecliptic path of the sun runs through the middle of the zodiacal band, the sun will rise each day ‘in’, or superimposed on, a particular constellation.  During the cycle of a year, the sun will rise in each constellation for about one month.  Traditionally, the cycle begins at the spring equinox (March 21) when the sun rises in Aries;   at the summer solstice (June 22), it rises in Cancer;  at the fall equinox (Sept. 23), in Libra;  at the winter solstice (Dec. 22), in Capricorn. 

            But, as Schultz tells us,  the relationship is not that simple.  [MRS, p 69]  “Just as the sun alters its position in the zodiac from day to day, a similar displacement occurs, only on a far slower scale, with respect to its annual positions (equinoxes and solstices).  The sun advances 1o along the ecliptic each day; an equal change in its annual position requires 72 years.  [about 50” per year]  A complete revolution through all the zodiacal constellations takes one year in the former case; while in the latter, it requires about 26,000 years (72 x 360 = 25,920), only moving in the opposite direction.  This period is called a Platonic year.  …

            By emphasizing a single cardinal point within the whole movement of the sun’s annual positions, we can speak of the precession of the spring equinox through the whole zodiac in 26,000 years. …  If, conversely, we regard the spring equinox as a fixed point, and consider the displacement of the constellations relative to this point over a period of 26,000 years, we find that they show the character of a greatly lengthened yearly cycle. … each constellation becomes first a spring constellation, then a summer autumn and winter constellation successively.” 

            The use of the current traditional signs probably began while the sun was in Aries, which it entered at approximately 1900 BC.  The equinox entered Pisces at about 100 BC;  it will enter Aquarius at about 2500 AD.  During the life of the tradition the zodiac has precessed about a constellation and a half so that there is now a large discrepancy between the traditional locations of the signs and the observed locations of the constellations.  Following Schultz’s terminology [MRS, p 50] in this paper, the observed constellations are “designated with the English names, Ram, Bull, Twins, etc.;  while the astrological signs are designated in Latin, Aries, Taurus, Gemini, etc.”  

            We have seen that there are two different ways of measuring the constellations.  The observed sizes vary in angular dimension;  Aries being only 24o along the ecliptic, Pisces being 38o, etc.  On the other hand, equal divisions of 30o can be assigned to each sign.  Including the phenomenon of precession, there are then three zodiacs: 1] a symbolic one of twelve equally divided signs, with the spring equinox in Aries;  2] an observationally based but equally divided one; and 3] the actually observed, unequally divided one;  these are shown in figure 11.  The second type of zodiac is a kind of mediator between the completely symbolic and the completely empirical. 

            Schultz [MRS, p 49] associates the symbolic zodiac with the solar, or tropical year, “As the term ‘tropical’ implies (from the Greek ‘turning’) this rhythm is related solely to the periodic return of the Sun’s ‘turning points’, or solstices, that is, the yearly alternation of its highest and lowest culminations in summer and winter.  No account is taken of its position with respect to the fixed stars.  The tropical year is thus directly connected with the annual breathing rhythm of the Earth, which can be followed outwardly in the dynamic rising and sinking of the sun’s culmination point, and which, as a life rhythm of our planet, is at work in the formation and development of all living creatures, as well as in numerous processes of inorganic nature.”

            Of the empirical zodiac Schultz says [MRS, p 49], “In contrast to the tropical year, the sidereal revolution of the Sun through the constellations of the zodiac can be described as a circulating movement, as the Sun’s journey through the various spatial directions of the cosmos.”

            The median zodiac is described by Schultz [MRS, p 49], “A further possibility of dividing the zodiac is the one prevalent in Babylon from about the seventh century BC onwards.  This was a division into twelve equal segments, but based on the constellations, rather than the tropical points.  In this system the bright star Aldebaran in the Bull was taken as the centre of that constellation, and the starting point of the 30o segments, which thus gave the mid-points of each constellation.  It is especially striking in this system that the two brightest stars in the zodiac, Aldebaran in the Bull and Antares in the Scorpion, stand almost exactly opposite each other in the sky and form the mid points of their respective constellations.  This system strikes a kind of balance between the requirements of the thinker and observer.  Just as the thinker demanded equal and symmetrical divisions of the sky as a sound basis for all mathematical work, the observer wished these divisions to be related to the visible stars.”

The Planets

            Once the zodiacal band is determined, further observation will reveal that certain stars in the band seem to be ‘wandering’;  that is, drifting back and forth between the constellations.  The ancient Greek word for wanderer was ‘planet’.  In addition to the sun and moon, there are five planets whose Roman names are Mercury, Venus, Mars, Jupiter and Saturn.  Greek names respectively are Hermes, Aphrodite, Ares, Zeus and Cronus.   With respect to the cyclic nature of the planets, Schultz reminds us, [MRS, p134] “… a simple period in terms of whole years is never adequate to define the course of a planet’s movement. … their movements never repeat themselves mechanically in all details, but remain in a state of ever changing flux … “;  yet archetypal patterns can be distilled from their movements.

            Each of the planets have symbolic qualities related to their observed behavior. In the sections that follow, some of the mythology that has come to surround each planet is briefly explored with regard to the myth’s relation to number, geometry, harmony, as well as astronomy.  An important aspect of the relevance of myth to the subject of this course is the hope that the reader may become familiar with, and open to, a kind of multi-level perception, in which a planet, or celestial light source, may be identified with a Deity, trace out geometric forms, and have harmonic or musical number relationships with other stars, all simultaneously.   It is this quality of simultaneous awareness of multiple aspects, or we might say the experience of ‘Unity in Multiplicity’ that aids in the work of Platonic remembrance or ‘anamnesis’. 

            Although no attempt can be made within the scope of this paper to seriously comprehend the depths of mythic meaning, we may see at least four levels, or ways to read to myth, the literal, the symbolic, the moral or tropological, and lastly the transcendent.  The chart below shows some correspondences to these categories.

The Planet Mercury

            Mercury is always observed close to the sun.  It is never more than one constellation, or 30o away.  When the planet is to the right of the sun, that is, to the west, it is visible in the morning;  it then moves towards the sun until conjunction, when it is not visible;  the planet reemerges to the left, or eastward of the sun, and is thus visible in the evening.  The movements are then repeated in reverse until the cycle is completed.  One full cycle, or synodic period, takes an average of 116 days.  Three synodic periods equal 348 days, 17 days less than one solar year. 

            Mercury’s observed positions during 1961 are analyzed by Schultz [MRS, p 144], figure 12a.  In this diagram the sun is held still and the monthly position of the planet traces out a six lobed curve.  In 1/61 the planet is moving east through Sagittarius and conjuncts with the sun.  In 2/61, while in Aquarius, Mercury reverses direction, or goes ‘retrograde’.  Now it is moving west in relation to the sun but in the same direction as the yearly movement of the zodiac, so it seems to move slowly west through Aquarius.  In 4/61 Mercury reverses again and now moves east until conjunction with the sun in Aries in 5/61.  Thus one synodic period of Mercury is about four months. 

            This retrograde movement and counter-movement may be thought of as a ‘loop’.  The path of Mercury against the background of the zodiac during one year is shown in figure 12b.  Here, by ‘freezing’ the zodiac and letting the planet move, we can see the three loops and that the loops occur at geometrically significant points;  in this case, a trigon.

            Schultz [MRS, p 141] provides the diagram figure 12c to show the geometry of the Sun – Mercury relationship.  To understand this diagram it is necessary to make use of the mechanical model of the solar system;  specifically the idea of superior conjunction, when the planet passes behind the sun, and inferior conjunction, when the planet passes in front of the sun.  In the diagram, the observer is in the center; the zodiacal band is at the periphery;  and the sun moves in a counter clockwise circle halfway between them.  The planet’s path is shown as a dark line.  Dashed lines indicate conjunctions [alignments] between the Sun, Earth and Mercury.

            Position I, in early January, is a superior  conjunction in the constellation of the Archer.  During January and February the planet is east of the sun, appearing in the evening.  It then loops, and has an inferior conjunction with the sun in late February, in the Waterman, at position 1.  Now it appears west of the sun, in the morning, until inferior conjunction, at position II.  During March and April it is an evening star.  The planet loops again and conjuncts in early May, in the Twins, position 2, becoming a morning star again.  The pattern

continues until position IV, a superior conjunction in mid December, in the Maiden; thus completing the planet’s movement through the zodiac for the year 1961.

            Before continuing with the nature of Mercury, it might be useful to consider a special quality in Schultz’ diagram.  He has taken a modern understanding of celestial mechanics and used it to enhance our perception of the ancient experiential viewpoint.  The path of the planet in the diagram is not the actual observed path, but is abstracted in the context of its mechanical orbit of the sun, to highlight the geometric aspect of its experienced movement through the zodiac.  Schultz calls this diagram the ‘geocentric orbit’ of Mercury.

            The sixfold geometry of the Mercury – Sun – Zodiac relationship for a single year is shown in figure 12d.  Triangle I, II, III are the superior conjunctions;  triangle 1, 2, 3, are the inferior conjunctions.  If we follow the movements into succeeding years, figure 12e, it can be seen that the triangular pattern is open, and rotates or precesses in a counter clockwise, or easterly direction.

            To further follow this experiential pattern we need to shift our focus from conjunctions to loops.  There is one loop in each synodic period of 116 days.  The three loops in any given year equal to 348 days.  The 17 days left over are approximately equal to 1/7th of a synodic period.  Therefore the shortest number of years in which Mercury can complete a whole number of synodic periods is 7.  This is confirmed arithmetically by 365d x 7y = 2555 days.  2555d/116 days per period = 22  periods.  So the relationship between the loops of Mercury and the solar years can be put arithmetically as 22/7.  This, it will be recalled, is an approximation of the value of π.  The 22 loops can be seen in figure 12f.  This diagram is the same as figure 12b, extended in time .  Figure 12g shows the geocentric orbit through a complete cycle of synodic periods, it is an extension of figure 12c.

              The Myth of Hermes.

            Robert Graves, [GM, p55] recounts that Zeus,“… begot Hermes on Maia, daughter of Atlas, who bore him in a cave on Mount Cyllene in Arcadia. …”  After his birth [GM, p 63] Hermes “… grew with astonishing quickness into a little boy…”.  His first adventure is the theft of cattle from Apollo.  He uses gut from the cows, combined with a tortoise shell, to create the lyre.  Apollo discovers the theft, according to Graves, “by observing the suspicious behavior of a long winged bird”  later to be identified as the crane.  Hermes agrees to give back the cattle saying “‘I slaughtered only two, and those I cut up into twelve equal portions as a sacrifice to the twelve gods’.  ‘Twelve gods?’ asked Apollo.  ‘Who is the twelfth?’  ‘Your servant, sir.’ replied Hermes modestly. … this was the first flesh sacrifice ever made.” 

            On the way to retrieve the cattle, Hermes plays on the lyre while singing the praises of Apollo, until Apollo suggests a deal.  “‘A bargain!’ cried Apollo.  ‘You keep the cows, and I take the lyre.’  Hermes agrees and “While the hungry cows were grazing, Hermes cut reeds, made them into a shepherds pipe and played another tune.  Apollo again delighted cried ‘A bargain!  If you give me that pipe I will give you this golden staff with which I herd my cattle;  in future you shall be god of all herdsmen and shepherds.'”  Hermes agrees but adds, “‘…if you teach me augury too, because it seems to be a most useful art.’  ‘I cannot do that,’ Apollo said, ‘but if you go to my old nurses, the Thriae who live on Parnassus, they will teach you how to divine from pebbles.’   

            Zeus, when hearing of the agreements, admonishes Hermes to respect private property and not lie;  while complementing him for intelligence and eloquence. “‘Then make me your herald, father’, Hermes answered, ‘and I will be responsible for the safety of all divine property and never tell lies though I cannot promise to always tell the whole truth.'”   Zeus agrees and lists his duties as “‘…the making of treaties, promotion of commerce, and the maintenance of free rights of way for travelers on any road in the world.’  When Hermes agreed to these conditions Zeus gave him a heralds staff with white ribbons,…a round hat,…and winged golden sandals. … Hades also engaged him as his herald, to summon the dying gently and eloquently, by laying the golden staff upon their eyes. … He then assisted the Three Fates in the composition of the Alphabet, invented astronomy, the musical scale, the arts of boxing and gymnastics, weights and measures (which some attribute to Palamedes), and the cultivation of the olive tree.

            Possibly, due to the speed  of change of the position of the planet, Mercury or Hermes is associated with transformation:  of sound into music;  spoken language into writing;  and even the transformation of consciousness itself.  In the Middle Ages, Hermes, under the title ‘Trismegistus’, the thrice great, was the ruling power of the transformational study called Alchemy. 

            On the relation of Hermes to the alphabet, Critchlow [KW 14] writes, “The 22 intervals or consonances that the Semitic alphabets are invariably based on is a marvel, as well as the most powerful influence on the written languages that have emerged from the Hebrew of the Torah, the Greek of the Christian Gospels and the Arabic of the Holy Qu’ran.  Each inheritance comes from the 22 interval Phoenician alphabet.  The latter two  however expanded to 24 and 28 intervals respectively as they adopted symbols for the vowels.”   

            Critchlow [KW #14] provides figure 12h which shows the 22 Mercury loops and the Phoenician alphabet.  The letters are arranged in the same numerical order as the loops are traced out by the planet.  He then expands this to show the correspondences between these and the sacred alphabets of the old and new testaments.  Critchlow draws our attention to the idea that “…language, whether in number, shape, sound or light, is one of the ladders of convention both necessary and safe for the conveyance of understanding and therefore intelligence for the human family. … Angelic intelligences, as we choose to call them, are generally characterized as mediators between ourselves and God, (or if one wishes to stay outside the tradition of naming the ultimate principle) between ourselves and wholeness.  They are described as ‘guides’ or ‘messengers’ on our return journey to our own wholeness.”   

           Graves also points out that Hermes was said by some to be the father of Eros, [GM, p 58] “His  [Eros’] most famous shrine was at Thespiae, where the Boeotians worshipped him as a simple phallic pillar – the pastoral Hermes, or Priapus, under a different name. … Hermes was a phallic god…”  and [GM, p 102] “Hermes was the power resident in a phallic stone” . 

            Graves [GM, p 184] makes the connection that, “Cranes were sacred to Hermes … and the earliest alphabetic characters were wedge shaped.  [Cranes fly in ‘V’ shaped formations.]  Palamedes [Ancient Intelligence], with his sacred crane … was the Carian counterpart of the Egyptian god Thoth, inventor of letters, with his crane-like ibis;  and Hermes was Thoth’s early Hellenic counterpart.”   Thoth is the god of intelligence, and is pictured as ibis headed.  Cranes and ibis both have long, phallic-like necks.  Graves comments [GM, p 66] that Hermes was related to “stone phalli which were local centers of a pre Hellenic fertility cult – the account of his rapid growth may be Homers playful obscenity …” ;  and to “the Egyptian Thoth, God of Intelligence; [and] Anubis, conductor of souls to the Underworld.”   

            All this may be related to the rapid movement of the planet from night to night;  the quick extension and return of Mercury to the sun.  From another viewpoint, there can be few actions more symbolic of transformation than sexual reproduction.  Standing stones played a role in astronomical siting and served as boundary markers.  Treaties are written agreements, or deals and in ancient times were often written on boundary stones.  Standing stones, or Omphalli may also serve as symbols of transformative or ‘ontological’ movement between earth and heaven. 

            Bulfinch [AF, p37] writes “Hermes … presided over commerce, wrestling and other gymnastic exercises, even over thieving, and every thing, in short, which required skill and dexterity.”   This aspect of the trickster or thief, who hides, or ‘disappears’ things, may be related to the difficulty of observing Mercury.  As Schultz puts it, [MRS, p 132] “the duration of its visibility to the unaided eye in temperate latitudes is, even under the best conditions, only about fifteen to eighteen hours annually. …  The planet usually remains … near the horizon …and is veiled by the atmospheric haze. … however, after attaining its best visibility it disappears quickly into the neighborhood of the sun.”   The prominent role of Apollo in the myth may be more easily understood if we recall that Apollo is identified with the sun.              Hermes dominion over the marketplace may be related to the idea of commerce as transformation of one commodity into another.  Hermes relation to augury, or divination, using stones is quite interesting in that, as we saw in the Arithmetic session, number and geometry were taught with small pebbles.  The word calculation has the same root as calcium, as in stone.  Arithmetic is not only a primary study in philosophy but, pragmatically, is critical in the marketplace.  Also, note that Hermes is taught divination with pebbles by the Thriae, a triad of women;  and that the three fates, also a trio of women, help him invent the alphabet.

            There have been two references in the myth to the staff of Hermes, traditionally called the Caduceus.  The implications of this symbol are too wide and deep to fully explore within the scope of these notes.  Some sense of this depth is given by the comments of cultural historian William Irwin Thompson, [TFBL, p 112] “The staff of the god Mercury , the caduceus [figure 12I], shows two snakes coiling around a central rod surmounted by the two wings of the bird on top.   [In] Tantric yoga … the two snakes symbolize the two nerve channels, the ida and pingala, which spiral around the central passageway, the sushumna, of the spinal column.  The snake symbolizes the cithonic force, the being which crawls along the ground;  the bird symbolizes the higher realms of consciousness, the being which is liberated from earth and can fly off to heaven.  In different cultures around the world this knowledge is rendered in the imagery particular to a place.  In India, the image of a lotus is used … In Mexico, the image is a tree in the jungle … in ancient Egypt, the raising of kundalini was expressed in terms of raising the djed pillars of Osiris. … As the energy rises from the base of the yogi’s spine, his eyes roll up, he becomes absorbed in the visions in the single eye, the third eye, and his whole consciousness becomes polarized.  At the same time that he feels carried up in a vision and out of the body, the base of the spine is filled with energy, the genitals are flooded with vibrations, and the penis becomes erect.”  

            It has been said that a similar set of experiences, including sexual arousal, occur at death.  As we can see, this is getting far afield;  but the passage does serve to illustrate correspondences between otherwise disparate aspects of the myth of Hermes;  as phallic deity, master of transformation, as conductor of souls, and as source of higher intelligence.

            This discussion of Mercury was somewhat extended in order to describe planetary movement, derive Schultz’s diagrams, and to illustrate the relation between an observed heavenly body and symbolic aspects associated with it.  For the remaining planets, descriptions will be more compressed.

The Planet Venus.

            The movements of Venus are similar to Mercury’s in that Venus remains close to the sun, with a maximum separation of a constellation and a half, about 48o.  It also alternates between being an evening and a morning star.  One synodic period of Venus, for example, from one furthest morning, or western elongation to the next, takes an average of 584 days or 1.6 years;  close to the ratio of Ø, 1 :1.618.  Expressed arithmetically, in whole numbers of years and synodic periods, 365d x 8y = 2920 days, 584d/period x 5 periods = 2920 days.  The ratio is 8/5, and this is a whole number approximation of Ø.   The actual cycle is about 2 1/3  days short over 8 years; 584 days is an average. 

            Schultz notes, [MRS, p 117] “Every sixth Venus period is therefore remarkably similar;  the various stages are repeated almost in the same form.  With the eight year period, a kind of Venus calendar is given, in which the total succession of phenomena can easily be surveyed for longer periods of time.”  

            Schultz’s diagrams for the geometry of Venus are shown in figures 13a, 13b, and 13c.  Figure 13a shows two synodic periods, this is similar to figure 12c for Mercury.  Figure 13b shows the five loops of the full eight year cycle;  similar to figure 12f for Mercury.  Figure 13c shows the five fold geometry highlighted by combining the planets observed position and its mechanical distance from us, its geocentric orbit.  Here we see Venus constructing the pentagonal star, the pentagram, by plotting its conjunctions with the sun over an eight year cycle;  similar to figure 12g for Mercury.  Here we see Venus constructing the pentagonal star, the pentagram, by ploting its conjunction with the sun over an eight year cycle.

The Myth of Aphrodite.

            As Graves recounts the story, [GM, p 49] “Aphrodite, Goddess of Desire, rose naked from the foam of the sea and, riding on a scallop shell, stepped ashore first on the island of Cythera … passed on to the Peloponese and eventually … to … Paphos in Cyprus … where, …the Seasons … hastened to cloth and adorn her . … Grass and flowers sprang from the soil wherever she trod, …. all agree she takes the air accompanied by doves and sparrows.  Some hold that she sprang from the foam which gathered about the genitals of Uranus, when Cronus threw them into the sea.”

            Graves continues, [GM, p 67] “Aphrodite could seldom be persuaded to lend the other goddesses her magic girdle which made everyone fall in love with its wearer;  for she was jealous of her position.  Zeus had given her in marriage to Hephestus, the lame smith god;  but the true father of the three children  with whom she presented him – Phobus, Deimus, and Harmonia – was Ares, the straight limbed, impetuous, drunken, and quarrelsome God of War.  Hephestus knew nothing of the deception until, one night, the lovers stayed too long together in bed at Ares’ Thracian palace;  then Helius, as he rose, saw them at their sport and told tales to Hephestus.”

            “Hephestus angrily retired to  his forge and hammered out a bronze hunting net, as fine as gossamer but quite unbreakable…”  he attaches this, invisibly, to the posts of the bed and tells Aphrodite he will be out of town for a few days.  Once he is gone “… Aphrodite … sent hurriedly for Ares, who soon arrived.  The two went merrily to bed, but at dawn found themselves entangled in the net, naked and unable to escape.  Hephestus … surprised them there and summoned all the gods to witness his dishonor.  … Up ran the gods, to watch Aphrodite’s embarrassment. … Apollo, nudging Hermes asked: ‘You would not mind being in Ares position, would you, net and all?’  Hermes swore by his own head that he would not … both gods laughed uproariously. … Zeus was so disgusted that he refused to … interfere in a vulgar dispute between a husband and wife. … “   The lovers are eventually released from the net, and “… Aphrodite went to Paphos where she renewed her virginity in the sea.”

            After this escapade, according to Graves [GM, p 69], come a seemingly endless series of affairs; “Flattered by Hermes frank confession of his love for her, Aphrodite presently spent a night with him, the fruit of which was Hermaphroditus, a double sexed being … Later Aphrodite yielded  to Dionysus and bore him Priapus, an ugly child with enormous genitals …”   The list goes on to include Anchises, their child being Aeneas. 

            Graves now recounts the myth of Adonis [GM, p 69].  In vengeance for a foolish boast, Aphrodite causes a young woman, Smyrna, to fall in love with her father.  She becomes pregnant, and when her father discovers the facts he chases after her with a sword.  “… He overtook her on the brow of a hill, but Aphrodite hurriedly changed Smyrna into a myrrh tree, which the descending sword split in halves.  Out tumbled the infant Adonis.” “

            Out of a sense of responsibility for the situation, “Aphrodite … concealed Adonis in a chest, which she entrusted to Persephone, Queen of the Dead, asking her to stow it away in a dark place.”   Persephone, needless to say, opens the chest, is completely captivated with Adonis, raises him, and they eventually become lovers;  whereupon Aphrodite claims him and appeals to Zeus, who  “… refused to judge so unsavory a dispute;  and transferred it to a lower court presided over by the muse Calliope.  Calliope’s verdict is that Persephone and Aphrodite had equal claims on Adonis … but that he should be allowed a brief annual holiday from the amorous demands of both these insatiable goddesses.  She therefore divided the year into three equal parts, of which he was to spend one with Persephone, one with Aphrodite, and the third by himself.  Aphrodite did not play fair:  by wearing her magic girdle all the time she persuaded Adonis to give her his own share of the year …  Persephone tells Aries who, “…disguised as a wild bore, rushed at Adonis who was out hunting … and gored him to death before Aphrodite’s eyes.  Anemones sprang from his blood, and his soul descended to Tartarus.  Aphrodite went tearfully to Zeus and pleaded that Adonis should not have to spend more than the gloomier half of the year with Persephone, but might be her companion for the summer months.  Zeus magnanimously agreed.”

            Graves concludes the myth of Aphrodite by telling us [GM, p 70]  “The fates assigned to Aphrodite one divine duty only, namely to make love;  but one day, Athena catching her surreptitiously at work on a loom, complained that her own prerogatives had been infringed and threatened to abandon them altogether.  Aphrodite apologized profusely and has never done a hand’s turn of work since.”

            According to Graves, [GM, p 49] “Aphrodite [foam born] is the same wide ruling goddess who rose from chaos  and danced on the sea, and who was worshipped … as Ishtar, or Ashtaroth.” ;  not to mention Innana and Isis.  This deity has long been identified with the planet Venus.  As the movements of the planet literally draw out the pentagram in the sky above our heads, and the geometry of the pentagram reveals, also literally, the Golden Section, or Ø;  so Venus – Aphrodite, is the ruling deity of worldly beauty and reproductive activity.  We may recall that in discussing the geometric root systems Lawlor, [SG, p 31], has told us, “Transformation can be seen to occur by means of three general processes:  the Generative, symbolized by the √2;  the Formative, symbolized by the √3;  and the Regenerative, symbolized by the √5 and its related function of phi Ø, the Golden Mean.”     The geometry of Ø and the pentagram is shown in figure 13d.

            The use of the shell symbol in the myth is quite apt.  As we have seen in earlier chapters, shells as spirals, embody the principle of growth by gnomonic expansion, which can be seen as a physical expression of Ø, figure 13e.  The growth spirals of shells are related to the arithmetic of the Fibbonachi series, whose adjacent terms are whole number approximations of Ø.  That “…grass and flowers sprang from the soil wherever she trod…”  is also quite apt as plants too, embody the Fibbonacci series in the phenomenon of ‘Philotaxis’, which governs branching and distribution of leaves;  and many flowers are five petaled, figure 13f. 

            Cronus, who’s defeat by Zeus initiates Aphrodite’s birth, is better known as ‘Father Time’.  A connection between time and the spiral is made by Lawlor, [SG, p 70] “The deeper purpose for this development of the spiraling of numbers comes from the fact that we have a model for the way an indefinite cause [root] can express itself in a play of definable numbers and forms.  The spiral is still our most profound image for the movement of time and therefore it is central to our vision of evolution.”  Graves charming comment that Aphrodite “…has never done a hands turn of work…” may be a hint that this myth is less concerned with the Generative or Formative principles, than with the Regenerative.

            Aphrodite is not so much the goddess of Love, as she is the goddess of making love.  The main object of her affection is Ares, the planet Mars. The astronomical aspects of this become clearer if we remember that almost the entire cast of characters are planets;  Cronus is Saturn, Zeus is Jupiter.  There is a rather graphic quality about the image of Apollo [the Sun] nudging Hermes [Mercury], asking if he would like to be in the position of Ares [Mars] conjuncting with Aphrodite [Venus].   Mars, as will be shown in the next section,  makes eight loops before completing its cycle of synodic periods (in about 17 years).  This establishes a 5 to 8 relationship between the number of loops each planet makes in a complete cycle.  Since the Mars cycle is about twice as long as the Venus cycle, the two will ‘meet’ regularly in the same part of the zodiac.  Schultz [MRS, p 117] describes the behavior of Venus:  “Upon completion of one of  its  loops, Venus wanders first through all the constellations, and then repeats three – fifths of its journey before the following loop is begun.”;  as shown in figure 13a.  And so it may be, that Aphrodite ‘wanders’ through her affairs.

            The one night affair with Hermes results in the birth of Hermaphroditus.  That is to say, when Hermes, representative of higher intelligence, mates with the representative of sexual reproduction; or when higher intelligence expresses itself sexually, the result is the joining of the male and female polarities.  The relationship with Dionysus, deity of ecstasy, results in Priapus; whose enlarged genitals accentuate gender differences.   As in the discussion of Mercury, this topic takes us too far afield.

            Persephone is the ‘Queen of the Dead’, as Aphrodite is queen of those who are to yet to be born.  The two could be thought of as opposite polarities of the old, neolithic ‘Great Goddess’; and so they struggle for possession of the human Adonis [Adam], archetype of man as ‘manas’ the reasoning animal.  In the myth the struggle manifests in the creation of the seasons, in a similar way as occurs in the myth of Demeter;  but here, we see the older three part year, as decided by  Calliope, become the more recent four part year, as decided by Zeus. 

            Graves comments [GM, p 72], “In Syria, Asia Minor and Greece, the goddess’s sacred year was at one time divided into three parts, ruled by the lion, goat and serpent.  The Goat, emblem of the central part, was the Love goddess Aphrodite’s;  the serpent, emblem of the last part, was the death goddess Persephone’s;  the Lion, emblem of the first part, was sacred to the birth goddess, here named Smyrna, who had no claim on Adonis.  In Greece this calendar gave place to a two season year, bisected either by the equinoxes in the eastern style, as at Sparta and Delphi, or by the solstices in the northern style, as at Athens and Thebes.”  This mytho- poetic use of the numbers 3 and 4 stands in contrast, but not contradiction to the much later, highly intellectual cosmology of Ibn ‘Arabi cited earlier in this session.

The Planet Mars.

            The movements of Mars, Jupiter and Saturn are similar to Mercury and Venus, but these ‘outer’ planets can assume any angular relationship with the sun.  They are not limited 30o or 45o as in the case of Venus and Mercury.  They may ‘ sextile’ the sun, that is be at an angle of 60o with respect to the observer;  ‘ square’ the sun, make an angle of 90o;  ‘trigon’ the sun, at an angle of 120o;  or be in ‘opposition’ to the sun, with an angle of 180o.  A ‘conjunction’ makes an angle of 0o.  See figure 14a. 

            All three planets follow a similar pattern of visibility;  as described by Schultz [MRS, p 157], “At the time of a conjunction with the Sun, Saturn, Jupiter and Mars remain invisible.  The planet, in this position, accompanies the Sun during the course of the day … .  After a number of weeks, the planet becomes visible … in the eastern morning sky [helical rising].  From this time on the planet rises earlier and earlier before the Sun, until it gradually dominates the second half of the night.  At the same time it increases in brightness. …  After some time the planet rises … before midnight, and finally it can be seen near the eastern horizon at sunset;  it then stands in opposition to the Sun. … The planet has now attained its greatest … brightness. … At the time of opposition the planet shines throughout the night, from sunset to sunrise.  In the following weeks and months the period of visibility becomes shorter … [and] increasingly limited to the first half of the night and finally to the … hours shortly after sunset. … [The cycle] ends with the ‘helical setting’, or disappearance of the planet into the evening twilight.”

            The synodic period of Mars is an average of 2 years 50 days, or 780 days.  Schultz  provides figure 14b, showing the observed path of Mars during one synodic period;  and figure 14c, showing the geocentric orbit for a similar period.  Mars makes eight loops before looping again in its initial position in the zodiac.  Figure 14d shows the loops as observed.  Thus both the rhythm of eight and the symmetry of eightness is associated with the archetype of Mars.  Figure 14e shows the geocentric orbit for the same period. 

            The arithmetic of the cycle is 780d x 8 cycles = 6240 days.  365d x 17y = 6205 days, a difference of 35 days over 17 years.  Schultz notes [MRS, p 174] that 7 cycles take 5460 days; 365d x 15y = 5475 days, only 15 days off.  But as seven loops don’t close the figure we may be justified in interpolating, and say that Mars makes 8 loops in an average of 16 years.  Schultz characterizes the behavior of Mars by saying [MRS, p 169], “Of all the outer planets, Mars’ succession of phenomena and rhythms of movement are most difficult to comprehend. … its motions, whether considered spatially or temporally, show irregularities and variations to a degree not found for any other planet.”

            Venus makes 5 loops in 8 years and Mars makes 8 loops in 16 years.  In terms of time the relationship is 1:2;  in terms of the number of loops, the relationship is 5:8, an approximation of Ø.  The conjunctions of Mars and Venus take place on an erratic 13 month cycle, with some periods missed.

 The Myth of Ares.

            Ares is the god of war, some of who’s story has already been told.  Graves writes, [GM, p73] “Thracian Ares loves battle for its own sake, … he never favors one city or party more than another, but fights on this side or that, as inclination prompts him…   Ares has not been consistently victorious. …once, the gigantic sons of Aloeus conquered him and kept him imprisoned in a brazen vessel for thirteen months until, half dead, he was released by Hermes;… [GGH, p 17] Ares had no manners, no learning and the worst of taste; yet Aphrodite thought him wonderful.  His emblems were a wild boar and a bloodstained spear.”  Ares’ erratic nature is stressed in these descriptions and in Schultz’s comments.

              Of Ares’ imprisonment by the Aleoids, whose nature is similar to the Titans, and his release by Hermes, Graves writes, [GM, p 138] “Ares imprisonment for thirteen months is an unrelated mythic fragment of uncertain date, refering to an armistice of one whole year – the Pelasgian year had thirteen months – agreed upon by Thessalo-Boeotians and Thracians, with war-like tokens of both nations entrusted to a brazed vessel…”. 

            Hermes, as we have seen, is responsible for treaties, or armistices.  It might also be suggested here that since Venus and Mercury both remain close to the Sun, Mercury’s period of conjunction with Mars could be about the same thirteen months as it is for Venus.  ‘Imprisonment’ may suggest stationary or retrograde movement;  ‘release’ by Hermes may suggest conjunction.

The Planets Jupiter and Saturn.

            The synodic period for Jupiter is  399 days, about 1y 1m.  The synodic period for Saturn is 378 days, about 1y 2w.  Schultz provides figure 15 a-b, which show Jupiter’s movement during one synodic period.  Schultz writes [MRS, p163], Jupiter “…moves along by roughly 33o, or  one eleventh of the zodiac annually.  A complete revolution contains eleven loops, which are completed in eleven synodic periods, or about twelve years.  …11 synodic periods of Jupiter are 4388 days, whereas 12 years are 4383 days.  The discrepancy is therefore only 5  days.”  and [MRS, p 168] “In the period of 29 years, Saturn completes 28 synodic periods, describing 28 loops. … As the period of 28 synodic Saturn periods is slightly shorter than 29 years [28 synodic Saturn periods = 10,586 &1/2 days, 29 years = 10 592  days], the new 29 year period begins 5 1/2 days earlier than the seasons in the preceding period.”  

            Figure 15c shows the observed path of Jupiter and figure 15d the path of Saturn.  Figure 15e shows the geocentric orbits of both.  The  major feature of the observed relationship of Jupiter and Saturn is the pattern of conjunctions known as the ‘Great Trine’ or ‘Great Conjunction’. 

            As Schultz describes it [MRS, p 207], figure 15f. “Two Saturn revolutions of thirty years each very nearly correspond to five Jupiter revolutions of twelve years each.  This means that in 60 years Jupiter makes 5 revolutions and Saturn 2.  If they begin at a conjunction, Jupiter overtakes Saturn three times (5-2), in other words, every 20 years. … more exactly … 19.86 years.”

            “Moreover, the relative movements of the two planets brings about a displacement from one conjunction to the next of two thirds of the total circumference of the zodiac, that is, by 240o or 8 constellations.  Only after the passage of sixty years [3×20] does a conjunction take place  in the same region as at the beginning. … As the separation between two successive conjunctions is not exactly equal to 240o, but is slightly more [242.7o] the resulting conjunction trigon is an open figure which slowly rotates in forward [anticlockwise] direction through the zodiac.  The conjunctions of Saturn and Jupiter do not, therefore, return every 60 years to exactly the same position in the zodiac, but are displaced by 8o to the east.”   This is true when “…the sidereal revolutions of the planets are used as a basis of calculation.  We can also consider the positions relative to the vernal equinox and thus to the regular signs of the zodiac;  for this the tropical  [equinoctial] periods of the planets are used.”

            “Because of the slow retrograde movement of the equinox through the zodiac, the Saturn-Jupiter conjunctions return to it with a slightly shorter period than to a fixed point in the zodiac.  Relative to the equinox, the conjunctions advance by 9o in 60 years, and by 27o in 180 years.  After 200 years, or ten conjunctions, the trigon has advanced by nearly one complete sign of 30o.  For the next 200 years, therefore, the conjunctions have passed into three new signs, which constitute a new trigon.  After 800 years they have passed through all four trigons in the zodiac.  Forty conjunctions take place during the whole of this period.  Its exact length is 794.4 years.  At its conclusion, a meeting of Saturn and Jupiter will have advanced through all twelve signs of the zodiac and have returned to the vernal equinox. … This point in time was reckoned as the beginning of a new eight hundred year conjunction period.  The last such passage took place in 1593.”

            In analyzing the ‘Great Trine’ Critchlow writes [TSS, p 155],  “Saturn, being the outermost of the planets in the perceived cosmos, is considered the initiator of the  [cycle of] primary conjunctions.  …during this cycle certain archetypal relationships are established in space and time.  These overall patterns have been aptly described by Marcel Hinze as ‘gestalt astronomy’ and when traced through time take the form of certain significant polygons, either frozen as archetypes or in moving time  precessing around the zodiac.  The great trigon was one such pattern.” ;  figure 15g.

            “By taking the conjunction of 1901 in Capricorn as the first corner conjunction to our first trigon, we find that the next time that these two planets are in the same part of the sky is 1921, in Virgo, which makes up the second corner of the trigon.  Finally, 20 years later, the third period of the 60 year cycle, both the major planets are in Taurus, 1941.  When the cycle was viewed in totality, this, the great conjunction, … made a great equilateral triangle within the circle of the heavens.”

            “There are also lesser triangulations which, occurring during the 60 year cycle, create a triplicity of trigons in a most interesting way;   [figure 15h]. …Saturn was in Ares in 1908 while Jupiter was 120o away in Leo, making two corners of a trigon.  In 1928 Saturn was in Sagittarius, 120o away from Jupiter in Ares.  Finally, in 1948 Saturn was in Leo, 120o away from Jupiter who was passing through the position in Sagittarius occupied by Saturn in 1928.  Thus by triangulation in 20  year intervals both Saturn and Jupiter had set up another large equilateral triangle in the sky.  Now, by the same 120o relationships starting in 1915 when Saturn was in Gemini, Jupiter was in Aquarius and by 1934, when Saturn had reached this latter position in the belt, Jupiter had moved 120o away to Libra.  When Saturn reached Libra in 1954 Jupiter was back in Saturn’s first position of 1915, and this gives the third large riangle.  Significantly, when the positions of these conjunctions and triangulations  are put together as features of the same 60 year cycle they describe a nine pointed star.”

            “This enneagon is made up of one grand trigon, … [in our case the Earth trigon], and two others which, described by delayed action as it were, are secondary in effect:  the fire triangle of Aries, Sagittarius and Leo and the air triangle of Aquarius, Libra and Gemini.  None of the water signs would occur in this cycle [Pisces, Scorpio, Cancer]”

            “The three overlapping equilateral triangles making up this version of the nine pointed star are a static and discontinuous version. … each triangle is self contained within its own lines and cannot ‘move’ into another.  There is another version of this star that it is possible to inscribe within nine regularly distributed points, making a continuous line which does not come back to its origin until it has traversed all other eight points.  The particular quality of  figure 15i is not only that it makes a beautifully symmetrical pattern in space but that it follows exactly the sequential pattern of Jupiter throughout our cycle from conjunction point to conjunction point. …” 

            “There is one more way of traversing this 60 year cycle, figure 15j.  This is as a polygonal path through the nine points which represents a stepping stone sequence, whereby one ‘steps over’ each adjacent point to land on the second away each time.  This creates a particular kind of nine pointed star, at the same time giving a significant pattern relating to Saturn’s position in the whole enneagon. …“.

The myth of Zeus and Cronus.

            Graves recounts, [GM, p37] “Uranus fathered the Titans upon Mother Earth, after he had thrown his rebellious sons, the Cyclopes into Tartarus, …  In revenge, Mother Earth persuaded the Titans to attack their father;  and they did so, led by Cronus, the youngest of the seven, whom she armed with a flint sickle.  They surprised Uranus as he slept, and it was with the flint sickle that the merciless Cronus castrated him, grasping his genitals with the left hand [which has ever since been the hand of ill omen] and afterwards throwing them, and the sickle too, into the sea …”

            “Cronus married his sister Rhea …  But it was prophesied by Mother Earth, and by his dying father Uranus, that one of his own sons would dethrone him.  Every year, therefore, he swallowed the children whom Rhea bore him: first Hestia, then Demeter and Hera, then Hades, then Poseidon.”

            “Rhea was enraged.  She bore Zeus, her third son, at dead of night … and … gave him to Mother Earth;  by whom he was carried to … Crete, and hidden in the cave of Dicte… .  Mother Earth left him there to be nursed by the Ash nymph Adrasteia and her sister Io,  both daughters of Melisseus, and by the goat nymph Amaltheia.  His food was honey and he drank Amaltheia’s milk… .  Zeus was grateful to these three nymphs for their kindness and, when he became Lord of the Universe, set Amaltheia’s image among the stars, as Capricorn.  He also borrowed one of her horns, which resembled a cow’s, and gave it to the daughters of Melisseus;  it became the famous Cornucopia, or horn of plenty, …’

            “Around the infant Zeus’s golden cradle … stood the armed Curetes, Rhea’s sons.  They clashed their spears against their shields, and shouted to drown out the noise of his wailing, lest Cronus might hear it from far off.  For Rhea had wrapped a stone in swaddling clothes, which she gave to Cronus …;  he swallowed it, believing that he was swallowing the infant Zeus.  Nevertheless, Cronus got wind of what had happened and pursued Zeus, who transformed himself into a serpent and his nurses into bears:  hence the constellations of the Serpent and the Bears.”

            “Zeus grew to manhood … and sought out Metis the Titaness… .  On her advice he visited his mother Rhea, and asked to be made Cronus’s cup bearer.  Rhea readily assisted him in his task of vengeance;  she provided the emetic potion, which Metis had told  him to mix with Cronus’s honeyed drink.  Cronus, having drunk deep, vomited up first the stone, then Zeus’s elder brothers and sisters.  They sprang out unhurt and, in gratitude, asked him to lead them in a war against the Titans, who chose the gigantic Atlas as their leader;  for Cronus was now past his prime.”

            The war is lengthy and Zeus eventually seeks help from Cronus’s old enemies, the Cyclopes and the Hundred Handed Ones.  Graves continues [GM, p 40], “The Cyclopes … gave Zeus the thunderbolt …, Hades a helmet of darkness, and Poseidon a trident.  … Hades entered unseen into Cronos’s presence, to steal his weapons;  and, while Poseidon threatened him with the trident and thus diverted his attention, Zeus struck him down with the thunderbolt. … Cronus and all the defeated Titans, except Atlas, were banished to a British island in the farthest west…;  they never troubled Hellas again.  Atlas, as their war leader, was awarded exemplary punishment, being ordered to carry the sky on his shoulders… .  Zeus himself set up at Delphi the stone which Cronus had disgorged.  It is still there, constantly anointed with oil, and strands of unwoven wool are offered upon it.”

            Commenting on the nature of Saturn, Critchlow writes, [TSS, p 155] “Saturn or Kronos (chronos), the ‘Father of the blessed gods as well as man you changeful counsel’ as the Orphic hymn puts it,’…strong titan who devours all and begets it anew’, immediately touches on the archetype of ‘moving’ time, the devourer and re-creator of a continuous cycle.  Saturn or Kronos was considered to hold an indestructible bond between heavenly eternity and earthly time:  between changeless principle and acts of change.  Proclus cites another significant Orphic fragment in his  commentary on Plato’s Cratylus:

            ‘The greatest Kronos is giving from above the principles of intelligibility to the Demiurge [Zeus], and he presides over the whole ‘Creation’ [demiourgia].  That is why Zeus calls him ‘Daemon’ according to Orpheus, saying:  ‘Set in motion our genus, excellent Daemon!’  And Kronos seems to have with him the highest cause of junctions and separations … he has become the cause of the continuation of begetting and propagation and the head of the whole genus of Titans from which originates the division of beings and gives him all the measures of the whole creation.’

“On this point of Saturn being granted the ‘measures of the whole of creation’, Macrobius, the late classical commentor … says:

‘Time is a fixed measure derived from the revolutions of the sky.  Time begins there;  and of this is believed to have been born Kronos who is Chronos.’                            

“Again, the phrase ‘derived from the revolutions of the sky’ must not be taken literally but rather as the expression of ‘moving time, or the ‘image of eternity’, as Plato puts it, as it breaks through’ from the archetypal world into our world of generation and cyclic duration.”

            In the above passage, Critchlow is reminding us that Saturn, as the last or outermost of the planets, marks the transition from the perceptible world to the metaphysical;  and that this is the point at which time, as we experience it, begins;  time, in the sense of ‘past, present, future’.  Beyond the realm of Saturn, in the fixed stars and the angelic spheres, there is only ‘nowness’.

            Making the connection of time to geometry Critchlow writes, [TSS p 150], “The circle is the most appropriate form to express undifferentiated space and a totality of time – the full unending cycle.  These two aspects or conditions of existence can be analogously related to properties of the circle in the following way:  firstly ‘qualified’ space can be created by intervals along the circumference of a circle which by joining the straight lines within the perimeter, create polygons;  whereas secondly, sequential time can be considered as the ‘cutting off’ of similar intervals around the circumference (this is related to the image of Father Time [Chronos] whose moon-like sickle cuts off time, a  sectioning which is etymologically related to seconds of time).” 

The Cosmic Picture

            The traditional representation of the cosmos is as a series of concentric, spherical or circular shells with the individual observer at the center, figure 16.  The first set of four shells surrounding the perceiver, are the four elements;  earth, water, air and fire.  These are graded in terms of density, or to put it another way, in the same order as they are experienced;  earth settles to the bottom of water, as air bubbles up through water, and fire, as heat, rises.  This is the material, everyday world, also known as the sub-lunary realm. 

            The next set are the seven planetary spheres;  1, the Moon;  2, Mercury;  3, Venus;  4, the Sun;  5, Mars;  6, Jupiter;  and 7, Saturn.  This arrangement is possibly  related to the speed of change of position of the bodies from night to night in the sky.  The Moon is the fastest of these, making a complete circle of the zodiac in 28 days.  Mercury and Venus move through the zodiac with the sun, but in their night to night movements, Mercury is noticeably faster than Venus,  making three loops [or synodic periods] per solar year;  while Venus makes only 5 loops in 8 years.  The Sun stands in the fourth or central sphere.  The bodies ‘below’ move faster than the sun;  the bodies ‘beyond’ move slower.  The sun has a sidereal or star measured period of 1 year;  Mars about 2 years;  Jupiter, 12 years;  and Saturn, 30 years.  With the exception of the Moon, the deities associated with the planets get older as they get further from the center.  Cronus is the elderly ‘Father Time’;  Zeus is his middle aged son;  Mars, a son of Zeus, is usually pictured as a fighting man in his prime;  Apollo, associated with the Sun, is a young man;  Venus, a young woman;  Hermes is a youth or adolescent.

            The Moon is represented by the goddess Artemis.  She is the twin sister of Apollo.  As the maiden huntress, she carries a silver bow, reminiscent of the crescent moon.  While she remains a virgin, she is the protector of women, and animals, in childbirth;  she is the goddess of midwives.  These attributes point to the relationship of the female cycle and the moon.  Her virginity may be related to the number 7, in the sense that the 28 days of the moon cycle can be factored as 7 x 4.  Four, as we saw  above, is the solar, rational, or male aspect of the zodiacal division of 12;  related to the equinoxes and solstices.  But here, 7 is used rather than 3, to accord with observed movements of the moon;  movements which do not occur with the fixed stars.  Seven, as was discussed in the Arithmetic session, is ‘virginal’ because it does not ‘multiply’ within the decade.  We might say here, that on the seventh night of the cycle, the moon squares, that is, makes a ‘right’, balanced or ‘correct’ angle, with its ‘brother’ the sun.

            The sphere of the moon stands closest to the earthly individual, just as Saturn stands furthest away.  As Burckhardt puts it [MAI, p 30], “…the planets are the intermediaries between the sky of the archetypes and the earth, the distinction is that of a hierarchy  and contains the principles of the ternary [threeness] and quaternity [fourness] according to the gradual order.  As to the number 28 of the houses of the moon, this is obtained by the Pythagorean sum of the numbers from 1 to 7, which signifies that the lunar rhythm develops or exposes, in a successive mode, all the possibilities contained in the archetypes and transmitted, by the hierarchy of the intermediaries, to the sphere which immediately surrounds the terrestrial centre.”

            “The relation between the sun and moon is analogous to that which holds between the Pure Intellect and the human form.  This also finds its most evident expression in the fact that the Moon reflects the radiation of the Sun in the manner of a mirror, and that the cycle of the lunations is like a ‘discursive’ development of this radiation.“

            Beyond the planetary spheres is the sphere of the fixed stars;  the  highest perceptible level;  the level exhibiting to the individual perceiver the least change;  its period of rotation being 26,000 years.  As to what lies beyond this, the commentators disagree on the details, but the major religious traditions maintain that it is the realm of angelic beings who take no physical or directly perceivable form;  as indicated in figure 16.

Astronomy of Timaeus  

            Returning to Plato’s creation myth, the ‘likely story’ of Timaeus, we recall that the Creator had mixed the qualities of the Same, the Different and Being to form the substance of the World Soul.  He then divides this ‘soul substance’ into proportionally related amounts which he reshapes into a ‘fabric’ or ‘strip’.  Timaeus [36] continues, figure 17:  “He then took the whole fabric and cut it down the middle into two strips, which he placed crosswise at their middle points to form a shape like the letter ‘x’ [chi];   he then bent the ends round in a circle and fastened them to each other opposite the point where the strips crossed, to make two circles, one inner and one outer.  And he endowed them with uniform motion in the same place, and named the movement of the outer circle after the nature of the Same,  and of the inner after the nature of the Different. 

            The circle of the Same he caused to revolve from left to right, and the circle of the Different from right to left on an axis inclined to it;   and made the master revolution that of the Same.  For he left the circle of the Same whole and undivided, but slit the inner circle six times to make seven unequal circles, whose intervals were double or triple, three of each;  and he made these circles revolve in contrary senses relative to each other, three of them at similar speed, and four at speeds different from each other and from that of the first three but related proportionately.”

            Taking this one step at a time;  1) The strip of soul fabric, marked out in the Lambda sequence, 1, 2, 3, 4, 8, 9, 27 [all musical numbers, see the Music session], is cut lengthwise into two strips.  2) The strips are placed over one another to form a cross.  3) The ends of each strip are joined so that two circular bands are formed.  4) One of the bands is within the other.  5) The outer band is called the Same, the inner band is called the Different.  The bands or circles can also be thought of as spheres, so that the sphere of the Same carries the fixed stars including the zodiac.  Its ‘uniform motion in the same place’ is rotation.  It is called the ‘Same’ because a) the fixed stars maintain the ‘same’ positional relationship to each other, and  b) the inner sphere carries the seven planets which all move at ‘different’ speeds.  The Same is the ‘master’ movement because the whole of the visible cosmos rotates together, once a day, and unlike the ‘different’, it never moves retrograde.

            The circle or sphere of the Different can also be thought of as the ecliptic.  In figure 17 it is shown as a disk, or section through the sphere.  In this disk six cuts are made, creating seven new bands, one for each planet.  The circles of the different are ‘unequal’ because they must fit, or ‘nest’ inside one another.  The phrase “seven unequal circles, whose intervals were double or triple, three of each”, in Lee’s translation, suggests that the whole of the circle or disk of the Different was cut at harmonically significant points which, in some way, conform to the Lambda sequence.  In this view, it must be noted that Timaeus does not tell us the specific order in which the cuts are made, or the  measure of the whole sphere;  that is, would the total measure add up to 27 or to 54?;  and is the interval of 8, for example, the fifth ring, or some other ring? 

            Thomas Taylor translates the phrase as, “…seven unequal circles, each according to the interval of the double and triple;…”.  This implies something a bit more subtle;  that each of the circles contains all the intervals of the Lambda sequence.  That is to say, each stage, each divinity and by extension, every soul has the complete harmony within it.

            The circles of the Different “revolve in contrary senses relative to each other”, that is, they appear to sometimes move from west to east;  and each moves at a different speed.  The Sun, Mercury and Venus move approximately as a unit;  the Moon, and the three outer planets move independently, but as we have seen above, are proportionately related to each other in terms of their sidereal and synodic periods.

            In the next set of passages, Timaeus discusses the nature of time [Tim. 37d], “The nature of the Living Being  [the pattern on which the cosmos is modeled] was eternal, and it was not possible to bestow this attribute fully on the created universe;  but he determined to make a moving image of eternity, and so when he ordered the heavens he made, in that which we call time, an eternal moving image of the eternity which remains forever at one.  For before the heavens came into being there were no days or nights or months or years, but he devised and brought them into being at the same time that the heavens were put together;  for they are all parts of time, just as past and future are also forms of it, which we wrongly attribute, without thinking, to the Eternal Being.  For we say of it that it ‘was’ and ‘shall be’, but on a true reckoning we should only say ‘is’, reserving ‘was’ and ‘shall be’ for the process of change in time;…”   We are being told here that time as we experience it, came into being along with materiality;  and that in the realm of the non-manifest, there is no past or future, only an eternal ‘now’.

            Timaeus continues [38c], “As a result of this plan and purpose of the Divinity for the birth of time, the sun and moon and five planets as they are called came into being to define and preserve the measures of time.  And when he had made a physical body for each of them, the Divinity set the seven of them in the seven orbits of the circle of the Different.  The Moon he set in the orbit nearest the earth, the sun in the next and the morning star and the one called ‘sacred to Hermes’ in orbits which they complete in the same time as the sun does his, but with a power of motion in a contrary sense to him;  consequently the sun, Hermes and the morning star all alike overtake and are overtaked by each other.  For the rest, if one were to describe in detail where they were set and for what reasons it would involve more attention to this issue than is justified…”  

            The function of the planets, as described here, is to ‘define and preserve time’.  They may be said to do this through their geometric configurations;  in a manner similar to that described by Critchlow as the “cutting off of intervals around the circumference”.  The first sphere is that of the Moon.   The Sun is said to be in the next sphere.  This would seem to be different from the ‘traditional’ sun centered model but, Mercury and Venus are said to move along with it, so there may be some room for ambiguity here.  It may be that the model was modified over time, or that parallel models were in use.

            The timekeeping role of the planetary spheres is linked  by Timaeus to the major perceived cycles [Tim. 39c], “…in the second orbit from the earth the divinity lit a light, which we now call the sun, to provide a clear measure of the relative speeds of the eight revolutions, to shine throughout the whole heaven, and to enable the appropriate living creatures to gain a knowledge of number from the uniform movements of the Same.  In this way and for this reason there came into being night and day, the period of the single most intelligent of revolutions;  the month, complete when the Moon has been round her orbit and caught up with the sun again;  the year, complete when the Sun has been round his orbit.” 

            The phrase ‘single most intelligent of revolutions’, may be taken on two levels;  1) that day and night are easily apparent;  and 2) that perception of the planetary cycles can be thought of as a ‘didactic’ or teaching device, so that those beings who are able to receive it, can obtain knowledge of realms not perceptible with the senses.  Note, also, the critical role played here by light.  As the cycles of the planets can be thought of as the mechanism of cosmic intelligence, so light may be thought of as its medium.  We speak of the gaining of wisdom as ‘enlightenment’ and, even in modern physics, the ‘speed of light’ is set at the extreme limit of the material realm.  Interestingly, in relativity theory, matter moving at this ultimate speed does not experience the movement of time.

            On the nature of the fixed stars, Timaeus says [Tim. 39e], “He decided that  [the world] should have as many forms of life  as intelligence discerns in the perfect Living Creature  [the model of the world].  There are four of these:  the gods in heaven, birds in the air, animals that live in water, and animals that go on dry land.  The divine form he made mostly of fire so that it should be as bright and beautiful to look at as possible;  and he made it spherical like the universe and set it to follow the movement of the highest intelligence, distributing it round the circle of the heaven to be a kind of universal cosmic embroidery. … This is the  origin of the fixed stars, which are living beings divine and eternal…”   

            The sphere of the fixed stars is the furthest, or highest realm;  therefore, its beings are made of fire, the most upward moving of the elements;  and therefore, it follows the movement of the highest intelligence, as it is next to the realm of the imperceptible.  The reference to ’embroidery’ was used previously [Tim. 55;  and Geometry session] to imply the dodecahedron and Critchlow has provided [KW#17] a stimulating diagram [figure 18] showing graphically the relation of the realm of the fixed stars to the dodecahedron.

            At the center of Timaeus’ cosmos is the earth, or sub-lunary realm  [Tim. 40c], “…and the Earth, our nurse, englobed about the axis of the universe, he devised to be the guardian and maker of night and day, the first and oldest of the gods born within the heaven.”  

            Of the realms beyond the intermediary spheres of the stars and planets, Timaeus says [Tim. 41d], “It is beyond our powers to know or tell about the birth of the other gods;  we must rely on those who have told the story before, who claimed to be children of the gods, and presumably  knew about their own ancestors.  We cannot distrust the children of the gods, even if they give no probable or necessary proof of what they say:  we must conform to custom and believe their account of their own family history.”

The Myth of Er and the Harmony of the Spheres

            In the dialogue of ‘The Republic’, Plato has Socrates recount the story of Er, a soldier who has apparently died in battle.  As his body is placed on its funeral pyre, Er suddenly returns to life and tells the story of his twelve days journey in the spirit realm.  After an initial stay in ‘the meadow’ where souls are judged, scene of the ‘chi’ crossing referred to in the Music session, we read [Rep. 616b],  “After seven days spent in the meadow the souls had to set out again on the eighth and came in four days to a place from which they could see a shaft of light stretching from above straight through earth and heaven, like a pillar, closely resembling a rainbow, only brighter and clearer;  this they reached after a further days journey and saw there in the middle of the light stretching from the heaven the ends of the bonds of it;  for this light is the bond of heaven and holds its whole circumference together, like the keel of a trireme.  And from these ends hangs the spindle of Necessity, which causes all the orbs to revolve;  its shaft and its hook are of adamant, and its whorl a mixture of adamant and other substances.  And the whorl is made in the following way.  Its shape is like the ones we know but from the description Er gave we must suppose it to consist of a large whorl hollowed out to hold a third, the third a fourth, and so on up to a total of eight, like a nest of bowls.  For there were in all eight whorls, fitting one inside the other, with their rims showing as circles from above and forming the continuous surface of a single whorl round the shaft, which was driven straight through the middle of the eighth.  The first and outermost whorl had the broadest rim;  next broadest was the sixth, next the fourth, next the eighth, next the seventh, next the fifth, next the third, and last of all the second.  And the rim of the largest and outermost was many colored, that of the seventh was the brightest, the eighth was illuminated by the seventh, from which it takes its color, the second and fifth were similar to each other and yellower than the others, the third was the whitest, the fourth reddish and the sixth second in whiteness.  The whole spindle revolved with a single motion, but within the movement of the whole the seven inner circles revolved  slowly in the opposite direction to that of the whole, and of them the eighth moved fastest, and next fastest the seventh, sixth and fifth, which moved at the same speed;  third in speed was the fourth, moving as it appeared to them with a counter revolution;  fourth was the third, and fifth the second. 

            “And the whole spindle turns in the lap of Necessity.  And on the top of each circle stands a siren which is carried around with it and utters a note of constant pitch, and the eight notes together make up a single scale.  And round about at equal distances sit three other figures, each on a throne, the three Fates, daughters of Necessity, Lachesis, Clotho, and Atropos;  their robes are white and their heads garlanded, and they sing to the Sirens music, Lachesis of things past, Clotho of things present, Atropos of things to come. And Clotho from time to time takes hold of the outermost ring of the spindle and helps to turn it with her right hand, and in the same way Atropos turns the inner rims with her left hand, while Lachesis takes inner and outer rims with left and right hand alternately.” 

            The above is a very profound passage and no analysis within the scope of these notes can hope to do it justice.  It will be persued here only insofar as it connects music and astronomy.  Desmond Lee provides figure 19a in the Penguin translation, which clarifies the analogy of the spindle and shows the relative widths  of the whorls. 

            McLain [(PP, p48] suggests, “A musical parallel to this imagery  [of the whorls] is our view of the tones as they lie along the string of the monochord.  In  figure 19b, the falling Dorian tetrachord is paired with its opposite.  This is the pattern ‘laid up in heaven’, I believe, which Socrates points out to Glaucon and Adeimantus, Plato’s older brothers, at the conclusion of the tyrant’s allegory.  The shaft of Necessity’s spindle at the center corresponds to the point of origin of the string, …  The radaii of the various circles correspond to the string lengths of the various tones, all string lengths for the higher tones being encompassed by the fundamental length which sounds the lowest tone.  This largest circle symbolizes the position of the fixed stars …  The center of the circles is the … Earth.”

             As to the widths of the whorls, it can be seen that the two diagrams, figures 19a-b, do not conform.  Lee’s diagram, which is referenced  ‘after [James] Adam’, seems closer to the text.  Plato gives us the relative widths of the whorls but not specific ratios of each to each, as he did with the apportioning of the World Soul.  The musical analogy is reinforced, however, by the realization that the given description requires that each whorl be a different width;  just as the intervals within an octave are all different linear dimensions.

            One method of identifying the planets is by the colors specified to each whorl.  The 1st and outermost is multicolor, as are the fixed stars;  the 7th is the brightest, the Sun;  the 8th reflects the seventh, as the Moon reflects the light of the sun;  the 4th is red; as is Mars;  the 2nd and 5th are yellow, these are Saturn and Venus;  the 3rd is whitest, Jupiter;  and the 6th is second in whiteness, Mercury.  This is pretty close to the observed color scheme, but there is some discrepancy for the last two planets mentioned;  as they actually also appear slightly yellowish.  A possible connection of ‘whiteness’ to Jupiter and Mercury is provided by Critchlow

 [TSS, p 63], figure 20, as their respective metals are tin for Jupiter and quicksilver for Mercury, both whitish in appearance.

            The apparent speed of the planets, that is, their night to night displacement along the ecliptic, increases as we get closer to Earth as do the inverse specified speeds of the whorls.

            The Fates, by virtue of their described number and position, may be thought of as representing the emergence of time.  The three of them could be thought of as proceeding [Clotho], maintaining [Lachesis] and returning [Atropos].  As Graves describes them [GM, p48], “Zeus, who weighs the lives of men and informs the Fates of his decisions can, it is said, change his mind and intervene to save whom he pleases, when the thread of life, spun on Clotho’s spindle, and measured by the rod of Lachesis, is about to be snipped by Atropos’s shears.”   The trigonal geometry of their positions in the myth of Er and their station, beyond the sphere of Saturn, seem to symbolize the archetypal cycle, before it is ‘cut off along the circumference’, or made quantitative, by the trigonal geometry of Saturn-Jupiter conjunctions.  Clotho, the proceeding turns the circle of the Same, Atropos, the returning, turns the circle of the Different, and Lachesis, the maintaining, turns both.

Cyclic Numbers of the Planets

            The table that follows shows some numbers associated with cycles of the various planets.  It is confined to the smaller integers and some are rounded off.

The Last Word

            It is only fitting that Timaeus, who has been our guide and principle reference in this exploration of the Quadrivium should have the last words.  He reminds us [Tim. 47]  “…that the supreme benefit for which sight is responsible is that not a word of all we have said about the universe could have been said if we had not seen stars and sun and heaven.  As it is, the sight of day and night, the months and returning years, the equinoxes and solstices, has caused the invention of number, given us the notion of time, and made us enquire into the nature of the universe;  thence we have derived philosophy, the greatest gift the gods have ever given or will give to mortals.  This is what I call the greatest good our eyes give us.  There is no need to recite the lesser goods, which anyone who was not a philosopher and had lost his sight might lament in vain;  let us rather say that the cause and purpose of god’s invention and gift to us of sight was that we should see the revolutions of intelligence in the heavens and use their untroubled course to guide the troubled revolutions in our own understanding, which are akin to them, and so, by learning what they are and how to calculate them accurately according to their nature, correct the disorder of our own revolutions by the standard of the invariability of those of the Divinity.  The same again applies to sound and hearing, which were given by the gods for the same end and purpose.  Speech was directed to just this end to which it makes an outstanding contribution;  and all audible musical sound is given us for the sake of harmony, which has motions akin to the orbits in our soul, and which, as anyone who makes intelligent use of the arts knows, is not to be used, as is commonly thought, to give irrational pleasure, but as a heaven sent ally in reducing to order and harmony any disharmony in the revolutions within us.”

End of Astronomy Notes