THE PENTAGRAM AND THE ELEMENTS John Opsopaus November 1993 INTRODUCTION In many contemporary Wiccan Traditions, as well as the Golden Dawn and other schools of ceremonial magic, the elements are associated with the points of the Pentagram in the following way: Spirit Air Water Earth Fire I have reason to doubt it, at least from the perspective of the apparent Babylonian origins of the Pentagram as well as Babylonian, Egyptian and Greek astrology, and, more recently, in Alchemy. The GD/Wiccan pattern seems to be traceable back to Levi but no further. While I agree with the philosophy, "If it works for you, use it," I think that structures of ideas tend to work better to the extent that they have a high degree of internal coherence -- thus the importance of understanding the "inner logic" of the Pentagram/Element connection. While the GD/Wiccan system has its logic, I suspect it's a comparatively recent invention, and some of the older systems seem more comprehensive, to my mind, anyway. I cannot offer a definite alternative at this time, but I can show some of the pieces I'm trying to fit together. If anyone can help, I would certainly appreciate it. THE PLANETS THE ELEMENTS AND THE DIRECTIONS There are (at least) three interrelated systems (evidence cited later) connected with the Pentagram: (1) The Five Planets, (2) the Four Elements + Quintessence, and (3) the Four Directions. Henceforth, Four Directions: NESW Four Elements: EAFW + Q Five Planets: (K = Saturnus [Kronos], J = Juppiter, M = Mars, H = Mercurius [Hermes], V = Venus), plus S = Sol, L = Luna. A further complication is that we can go around the pentagram two ways: (1) circularly, around the outside, and (2) linearly, tracing the "three interlaced triangles." If we number the points in a circular circuit 12345, then the linear circuit (in the same direction) visits them 13524; this is important when the p.g. represents the stages of a process. Working backward in time: An alchemical image of "Man as Microcosm" gives one of the only direct associations of elements with the pentagram: Q A F W E It is reproduced in Godwin (Alchemical Mandala, 11), but I don't know its original source. Another alchemical diagram (Godwin, 20; original source unknown) gives the following: F A Q E W There is ancient support (see below) for the center of the square being equivalent to the apex of the pentagram, so this would correspond to: Q F A E W which is a logical arrangement (given the square of opposition of the elements), but not the usual GD/Wiccan one; it's also the mirror image of the first p.g. given above. Other alchemical sources (e.g. Jamsthaler 1625) arrange the planets pentagonally, typically to represent stages in the alchemical procedure: S L H M J V K The Moon (L) indicates the passive ascending process and the Sun (S) indicates the active descending process (Burckhardt, Alch. 193). The five lesser planets (HMJVK) form the pentagram, with Mercury (H) at the apex; a position which has much ancient support (see below). Some alchemists (e.g. Valentine, 1659) invert both processes: H V K M J Burckhardt shows that another arrangement (Boehme 1628, Stolcius 1624), which brings Venus and Jupiter together, aligns corresponding steps of the ascent and descent: S L H M V K J The latter arrangement also agrees with the standard association of the planets with the hand known from palmistry (the p.g. being 1=J, 2=K, 4=H, palm=M, thumb=V), though it unfortunately reverses S (3) and L (heel). Despite the confusion, all seem to agree in attaching special significance to Mercury and in putting Jupiter/Saturn on one side and Venus/Mars on the other. The pentagrams in Agrippa (De occulta phil., 1533) are associated with the planets; these are what we find (Lib. II): M L S V V S J J (the latter not really a p.g., but easily L M connected with it via the human figure) H K H K He also shows the planetary assignment of palmistry, which seems unrelated to these others, but matches better some alchemical associations (see above). The planetary associations can be converted to elementary associations by means the the Scala Quinarii (also in Lib. II), which gives K/W, J/A, M/F, V/E, H/M (mixtum), and hence for the first pentagram: F E A M W However, I don't have great confidence in his planet/element associations (though if F and M were switched I'd buy it). In Lib. III we find the HUGIEIA (Soundness) Pentagram of the Pythagoreans, with U/G/I/EI/A clockwise from the top over an inverted pentagram. However, this doesn't help us with elemental associations, though it falls in a tradition of writing magic words around pentagrams (e.g. te/tra/gram/ma/ton) and other pentacles, which dates back to at least the 4th or 5th cent. BCE (Jewish jar handles from Palestine). (The pentagram itself goes back to Mesopotamia -- early 3rd mill. BCE; see below.) This is what I've found so far on the Babylonian, Egyptian and Greek evidence on the relation of the Pentagram and the Elements. It should be considered work in progress, and any suggestions or other help would be greatly appreciated. BABYLONIA: The Pentagram appears as a sign (UB) in the earliest form of Sumerian pictographic writing (c. 3000 BCE). Although such pictographs do not have a unique meaning, the general sense seems to be "heavenly body." By the cuneiform period (say, after 2600 BCE) the pentagram means "region," "heavenly quarter" or "direction" (Forward Backward Left Right) and is generally used with the number 4. It is conjectured that early Babylonians added a fifth direction (Up) because they believed Heaven ruled the Four Quarters; de Vogel makes an analogy with the Jewish Prayer of the Night in which Schekina rules over the Four Archangels (Michael, Raphael, Gabriel, Uriel). In Babylon the Four Directions were ruled, according to de Vogel, by the planets Jupiter, Mercury, Mars and Saturn, but he doesn't say which ruled which; Venus, the fifth planet, corresponded to the Queen of Heaven (Ishtar). (De Vogel, Pyth., App. A) Although I've been unable to find any evidence for a Babylonian theory of the Elements, there are suggestive indications. For example in the Babylonian Creation Myth "Enuma Elish" (before 1000 BCE) and elsewhere Marduk assigns The Four Worlds as follows: Luminous Heaven: Anu, Sky: Enlil (Lord Storm), Earth: Marduk, Watery Abyss: Ea. Thus we have rather clear elemental associations, Anu: fire, Enlil: Air, Marduk: Earth, Ea: Water. Unfortunately only one of these is a planet: Marduk = Jupiter. (King, Enuma Elish, xlix, lxxxiv; Kramer, Sum. Myth., 41; Perry, Lord Four Quart., 75-80) In anticipation of considering the Greek system I'll observe that there may be a basic incompatibility between the Babylonian and Greek conceptions of the elements. In Babylonia the typical arrangement is (from top down): Fire, Air, Earth, Water, since the Abyss is under the Earth. In Greece (at least as early as Heraclitus, c.500 BCE) the order (from top down) is: Fire, Air, Water, Earth, since this is the order of increasing density which forms the basis of Plato's Cycle, which is fundamental to alchemy. In both systems, Spirit (Aether etc.) is above the Four Mundane Elements, but the arrangement of the latter may ultimately depend on whether you prefer the Babylonian or Greek scheme. The preceding gives one correlation between Elements and Planets but, unfortunately, I've been unable to establish a credible relationship between the other Planets and Directions in Babylonia. The Seven Planets correspond to Gods: Sin/Moon, Shamash/Sun, Marduk/Jupiter, Ishtar/Venus, Ninurta/Saturn, Nergal/Mars, Nebo/Mercury (in their canonical order; yes, the Moon originally had priority over the Sun). Further, the division of Heaven and Earth into Four Quarters was a central part of Babylonian cosmology. Interestingly, when they assigned things (such as months or days) to the Directions, they did so in the order SEWN, which is reminiscent of the Cabalistic Tree of Life. If we take the Gods Ruling the Four Elemental Worlds and assign them to the directions in their usual order (Anu, Enlil, Ea, Marduk), then we get: N: earth/Marduk W: water/Ea E: air/Enlil S: fire/Anu This is certainly a reasonable and familiar arrangement for the Elements, but since it involves only one Planet, its connection with the Pentagram is tenuous. Unfortunately, I've been unable to find other direct associations between the Planets and the Directions, and indirect assignments (via lists of Gods, or the Months and their Gods) have produced dubious results; that is, none associates one Planet with each Direction. If we assign the planets in their constant Babylonian order (L/Luna, S/Sol, J/Jupiter, V/Venus, K/Saturn, M/Mars, H/Mercury) to the directions SEWN, omitting Venus (which is Up), then we get the following Directional arrangement for the Planets: K J H M which is reasonable, but has little to support it (and disagrees in its placement of Jupiter/Marduk, though here He is in the context of a different rank of Gods). (see Jastrow, Rel. Bab. Asyr., Ch. 22) Although the Babylonian system, with the special significance it attaches to Venus, does not agree with the Egyptian or Greek systems, which distinguish Mercury, we can perhaps take as a general principal that the distinguished planet corresponds to Up or Center, and the remaining four to the Quarters. EGYPTIAN: I have found no evidence of a specific theory of Four Elements in Egypt, although, as is common in many cultures, there is informal recognition of parts of the Cosmos that correspond, more or less, to the elements. On the other hand, Egyptian cosmology is based on a system of Four Directions, so there is some hope of making the connection between the Four Planets and the Directions. However, I've not yet been able to do so. What I've found is the following: In Manetho's "Epitome of Physical Doctrine" (fr. 83) we have a system of correspondences that explicitly associates the Five Elements with Five Gods: Spirit: Zeus [= Amon?] Fire: Hephaestus [= Phah?] Air: Athena [= Neith?] Water: Ocean (Nile) [= Nile] Earth: Demeter [= Geb?] In addition, Moon and Sun are associated with Isis and Osiris. Unfortunately, there is no connection given between the Directions and either the Gods or Elements. Also suggestive is the Ogdoad of Hermopolis, which comprises four male-female couples. Two of the four are clearly associated with Elements, but I know of no directional associations: Nun & Naunet: Abyss (water) Huh & Hauket: Expansiveness (fire?) Kuk & Kauket: Darkness (earth?) Amun & Amaunet: Hidden (air) These Eight are considered the Souls of Thoth = Hermes = Mercury, which is one instance of the Egyptians, like the Greeks, making Mercury the distinguished planet/God (rather than Venus, like the Babylonians). The various Enneads (Heliopolis, Greater, Lesser) are also suggestive (1 + 4 pairs), but I've been unable to find clear elemental or directional associations. Though I haven't been able to find a conclusive association between the Pentagram and the Elements in any Ancient Tradition, there is quite a lot of suggestive material, and I can do a reasonable (re)construction. After summarizing the conclusions from the Babylonian and Egyptian material, I'll turn to the Greek. SUMMARY: The Pentagram originated as a five pointed star in the earliest pictographic writing in Babylonia, with a meaning something like "a quarter of the heavens." Scholars have conjectured that the five points correspond to Four Directions (originally Front/Back/Right/Left) and Up; they further conjecture that Up was associated with Ishtar/Venus, the Queen of Heaven, and that the other Four Directions were associated with the other four Minor Planets (Mercury, Mars, Jupiter, Saturn). I conjecture that this basic 4+1 pattern was imported into Egypt and Greece (the latter via Pythagoras), but that they both made Thoth/Hermes/Mercury the distinguished planet (rather than Venus). So then, the problem reduces to associating these Planets or Gods with the Directions, associating the Directions with the Pentagram, and associating the Elements with the Planets or Gods. GREEK EVIDENCE: First I'll deal with the Four Elements, and then consider the Pentagram and the Five Elements. Some of the preliminaries will be very familiar to everyone on this list. My major source is Ptolemy's Tetrabiblos (I.4-8, 10, 17, II.3) which gives a explanation of the associations. However, I think Aristotle's discussion (e.g. De caelo 268b11-296a32; De gen. & corr. 329a24-331a6) of the Four Elements and Four Qualities is much more profound, and is really necessary for seeing the significance of this analysis. See also Plato (Tim. 53c-64a). Ptolemy's (like Aristotle's) is based more on the Four Qualities than the Four Elements. The Four Qualities comprise two Dualities: Hot/Cold (active) and Dry/Wet (passive), usually displayed in a Square of Opposition, thus: C W D H (NB: This does NOT produce the familiar Wiccan/Golden Dawn (for lack of a better name) arrangement of the Elements, but more on that later.) The Four Qualities also fall into a Natural Order, which might be called the Organic Order: Wet, Hot, Dry, Cold (the preceding circle counterclockwise). I won't repeat Ptolemy's explanations, but here are some of the correspondences he derives: Quality Age Season Moon Winds --------------------------------------- Wet Child Spring 1st Q. W Hot Youth Summer 2nd Q. S Dry Middleage Autumn 3rd Q. E Cold Old/death Winter 4th Q. N Note that this makes the Cold/Wet transition of the Cycle a key Transition Point: (1) it represents the Dark of the Moon, (2) the traditional start of the year (Vernal Eq.), and (3) reincarnation (the passage from death back into birth). Note that the Directional associations are made via the Winds (although there are other Directional assignments based on Government of the Trines). I've worried about the Directions, since they are crucial, but have finally come to accept Ptolemy's assignment. It's also important to keep in mind another Order, which I'll call the Physical Order and goes in increasing or decreasing Density (or Subtlety): Earth, Water, Air, Fire; thus Earth and Fire are the Extremes (Absolute Heavy/Light) and Water and Air are the Means (Relative Heavy/Light). The corresponding order for the Qualities is: Dry/Cold/Wet/Hot/Dry. The Physical Order is also a Physical Cycle, for example in the Circulation of the Elements in Alchemy. Thus, in addition to the Organic Transition Point between Cold/Wet = Water (Vernal Eq.), there is also a Physical Transition Point at Dry (Samhain). (In most Greek philosophy -- certainly Aristotle's -- the Physical Order is also the Cosmological Order: the arrangement of the Levels (Spheres or Planes) of the World; note however, that the Cosmological order in Babylonia and many other places is Water, Earth, Air, Fire, since the Watery Abyss lies under the Earth. This is the important arrangement for Shamanic Traveling, and is expressed more accurately as Abyssal Water, Earth, Air, Celestial Fire.) Ptolemy's assignment of qualities to the Five Minor Planets is more complex, but when all is said and done, it works out fairly naturally. Planet Qualities Element Dominant Element -------------------------------------------------------- Mercury Dry/Wet alternating * * Venus Wet(Hot) ~Air Water Mars Dry, Hot Fire Fire Jupiter Hot(Wet) ~Air Air Saturn Cold(Dry) ~Earth Earth Note that Mercury, unique among the Planets, is Duplex in displaying an alternation of opposed Qualities. The "Element" column shows the Element corresponding to the pair of listed Qualities, which does not work well. Therefore, in the "Dominant Element" column, I've associated the Element based on a direct Element/Quality association (Water/Wet, Fire/Dry, Air/Hot, Earth/Cold). Aristotle does something similar, though he takes the other Quality out of each pair associated with an Element (Water/Cold, Fire/Hot, Air/Wet, Earth/Dry). The issue is simply whether the Element is represented by its clockwise or counterclockwise neighbor in the Square of Opposition: Water Earth Cold Wet Dry Hot Air Fire (NB: It's traditional to place the Elements at the corners of the Square of Opposition and the Qualities on the edges. However, this is not the best arrangement for, as Aristotle says, the Qualities are absolute and primary, whereas the Elements are always relative mixtures and secondary. Therefore the Qualities should be placed at the corners; then the edges can represent various proportions of the Qualities constituting an Element, e.g., Earth that is more Dry or more Cold.) The associations I've taken seem to work better overall, but the point is arguable. Also it's important to keep in mind that in associating an Element with a single Quality we are making an approximation; the Elements actually belong *between* the Qualities, and thus *between* the Directional Quarters, Seasons, Moon Phases, etc. Be that as it may, when these Elemental associations are combined with the Qualities, we get: Quality Age Season Moon Dir. Element Planet/God ---------------------------------------------------------------------- Wet Child Spring 1st Q. W Water Venus (Born of Seafoam) Hot Youth Summer 2nd Q. S Air Jupiter (Sky God) Dry Middleage Autumn 3rd Q. E Fire Mars (Burning Red) Cold Old Winter 4th Q. N Earth Saturn (Earth/Vege. God) -- Death -- -- Up Spirit Mercury (Guide of Souls) The relation of the Five Elements and Four Qualities is neatly displayed by the Wheel of Heaven: Draw an equal-armed cross in a circle. The cross arms represent the Four Qualities (or the Four Elements). The center of the Cross and Circle represents the featureless Substratum, the Prima Materia, wherein all qualitative difference, all duality disappears (it is, if you like, the "zeroth" substance). The bounding Circle represents the Quintessence, the Aither, the "Sphere of the All" (Aetius), which Plato associated with the Dodecahedron (a mystic figure, made of Pentagons, and like the Pentagram, used as a symbol of recognition by the Pythagoreans). As Plato says, "The God made the Dodecahedron the Image of the Universe, as being the nearest to the Sphere." It is the Spirit governing the Four Mundane Elements. According to the Timaeus, the Four Elements are the offspring of Concrete Matter (the Center) and Abstract Form (the Circle). Now that we have the cyclic arrangement of the Four Elements, we can consider how they are assigned to the Pentagram. * * * I've previously shown the correspondences between Elements, Qualities, Directions, Seasons, Ages and Planets that results from Ptolemy's analysis. Further, I'm operating on the hypothesis that the five points of the Pentagram correspond to the Four Directions and Up. Therefore, think of a five-rayed star as a perspective picture, with the lower cross representing the Four Directions and the vertical ray representing Up. Depending on the direction we're facing, there are four possible arrangements: * * * * N E E S S W W N W S N W E N S E I will argue that the first arrangement is the correct one. To this end, I'll use the Directional Correspondences to label the Pentagram with Elements, Planets, etc. For improved readability I'll use: E=Earth, W=Water, A=Air, F=Fire, S=Spirit H=Mercury, V=Venus, M=Mars, J=Jupiter, S=Saturn Elements Planets S H E F S M W A V J To see what's going on more clearly, you might want to draw a Pentagram with a circumscribed Pentagon. It will be helpful later if you draw the Pentagram and Pentagon in contrasting colors. The the lower trapezoid of the figure is then a (distorted) Square of Opposition representing the Four Elements EWAF, Directions NWSE, and Planets SVJM. First observe that this Pentagram embodies the Physical Order of the Elements; if we stay on the Mundane level we have EWAF, and we can make it a cycle counterclockwise (as in the Alchemical Circulation) by returning from F to E across the horizontal beam of the Pentagram. Likewise, the Pentagram includes the Extended Physical Order (the Metaphysical Order), which includes the ascent to Spirit: EWAFS by a counterclockwise circuit. Of course we get the descent SFAWE by going clockwise. Also, the Organic Order WAFE = spring/summer/fall/winter is still embodied in the lower trapezoid, though the Organic Transition Point (Water) is the left leg of the Pentagram, an undistinguished position. Notice, too, how Spirit, with its four descending lines, surrounds the Cross of Opposition with its Form. (In my previous post I described how the Four Elements etc. are circumferentially bounded by Form or Spirit.) According to Ptolemy the two lower planets VJ are "beneficial" and the two upper SM are "maleficient." Also, the two left planets SV are nocturnal and the two right MJ are diurnal. Thus as is commonly done, we can draw the Moon (C) on the left side of the Pentagram, and the Sun (O) on the right: C O H S M V J Mercury/Hermes, as usual, stands apart from these distinctions. However, as Psychopomp (Guide of Souls), Hermes shows us the Two Shamanic Paths represented in the diagram: C O H E F W A The Left-hand Path, the Path of Darkness (C), takes the Way of Earth (E) down into the Watery Abyss (W). The Right-hand Path, or Path of Light (O), takes the Way of Air (A) up into the Celestial Fire (F). (There is, however, no implication here that one Way is Good and the other Evil.) Hermes (H) stands as the Master of the all. Now let's label the corners of the Pentagram with the first letters of Greek words for the Elements: U: `Udor = Water G: Gaia = Earth I: Idea = Form/Idea Th: Therma = Heat or EI: `EIle = Sun's Warmth A: Aer = Air Depending on which abbreviation you like for Fire, you get the following Pentagrams: I I G Th G EI U A U A If you read the letters in order, starting at the Organic Transition Point, you get UGIThA or UGIEIA, the Pythagoreans' mystical name for the Pentagram. Readers of my Olympic Banishing Ritual may recall that there are two labelings, either UGIEIA = hugieia = Soundness, or the somewhat inexplicable UGIThA, with Theta replacing Epsilon-Iota, which appears at least as early as Agrippa. Though the Theta may be explained as a joined Epsilon and Iota, we see here an alternative explanation, for either is an abbreviation for the Fiery Element. Notice how the pattern of the letters, UG/I/EIA or UG/I/ThA, matches the arch structure of the Pentagram; interestingly the Greek word has a high-tone accent on the Iota (correponding to Spirit), which seems appropriate. By the way, if you think that there are probably enough Greek words for the Elements to get UGIEIA from many Pentagram arrangements... take my word for it; there aren't. If you don't believe me, then get yourself the big Liddell & Scott and have fun. But as far as I've been able to discover, this is the *only* arrangement that generates UGIEIA or UGIThA (let alone both) from plausible Element names (though another comes close; see below). Also I should note that the above Element names are the usual ones that appear, for example, in Aristotle, except Fire, where Pur is usual; however Empedocles (who came up with the Four Elements) uses Eelios = Sun, which is described as Thermos, for Fire (DK 31B 21; see also Kirk, Raven & Schofield 292-3). Also, though Aristotle uses Aither for the Fifth Element, Plato clearly associates it with the World of Forms (Ideai). This brings us to an interesting property of our Pentacle (the Pentagram with Circumscribed Pentagon). In mathematical terminology the Pentagram is dual to the Pentagon (one is like the other turned inside-out). To see this draw a black Pentagram in a red Pentagon, and a red Pentagram in a black Pentagon; each Pentacle is the dual of the other. For example, if we number the first Pentagram clockwise, and transfer the numbers counterclockwise to the second Pentagram, then our Pentacles will be: 1 1 5 2 4 3 4 3 2 5 The second Pentacle has the Even Numbers, which according to Pythagorean theory are Feminine, on the left, and the Masculine Numbers on the right; since according to the Pythagorean 1 is Androgynous (cf. Hermes Duplex), it is appropriate that it is in the middle. Now label the first Pentacle with the Elements and Planets as described above; I will call this the Elemental Pentacle. Next trace the Elemental Pentagram in Counterclockwise Order (HVMSJ = SWFEA) and lay out these elements in Clockwise Order around the second Pentacle; they will be arranged as follows (the Sun/O and Moon/C are left in position): C O H/S J/A V/W S/E M/F The resulting Dual Pentacle is interesting for a number of reasons. First observe that the Elements are arranged in the familiar Wiccan/Golden Dawn format, so henceforth I will call this the W/GD Pentacle. Because this is the dual of the Elemental Pentacle, tracing the W/GD Pentagram in Invoking Order, SFAWE, corresponds to circumscribing the Elemental Pentagon in (descending) Physical order, SFAWE. The W/GD Pentacle also displays the steps of the Alchemical Process in order; on the left we have the Lesser Work, Saturn to Jupiter and culminating in the Moon (C); on the right we have the Greater Work, Venus to Mars and culminating in the Sun (O). The entire process is governed by Mercury (Burckhardt, Alch. XV). Recall also that the Planets in the Solar side (V, M) have a Circle in their astrological symbols, while those on the Lunar side (J, S) have a Crescent; Mercury (H), of course, has both. As is well known, Plato associates the Five Elements with the Five Platonic Solids (Tim. 55c-65c), and Kepler made a similar association between the Planets and the Platonic Solids. So let's lay out the Platonic Solids around the W/GD Pentacle; I'll abbreviate the Solids by their number of faces: 4=Tetrahedron, 6=Cube, 8=Octahedron, 12=Dodecahedron, 20=Icosahedron. This is the result: 12 8 20 6 4 Notice that the Platonic Solids fall around the circumference in increasing order of number of faces. Since the Elemental Pentagram is its dual, we know that it can also produce the series 4, 6, 8, 12, 20 (by tracing the Pentagram). So the W/GD Pentacle also has some interesting Correspondences, though it loses the Directional and Organic Cycles and especially the Square of Opposition, which I think is fundamental and essential. That's all I have to say, for now, about the Elemental and W/GD Pentacles. Needless to say, they can be profound Mandalas for meditation if fully labeled with color-coded Correspondences. * * * I would like to point out a couple interesting properties of another Pentacle, which preserves the Square of Opposition, Directions and Organic Cycle, but loses the Metaphysical Cycle. This is the one we get if we take the view toward the Southeast (as might have been the norm among the Etruscans): Directions Elements Planets * S H E S F A M J N W E W S V If we trace this Pentagram, starting at the top (Mercury/Spirit) and proceeding to the Organic Transition (Venus/Water), then we will trace the Planets in the order HVMJS (Mercury, Venus, Mars, Jupiter, Saturn) -- the so-called Chaldean Order for the Planetary Spheres, which was commonly used in ancient Greece (and is of course the modern order for the Five Minor Planets). On the other hand, if we trace them counterclockwise around the Pentagon, then we get HMSVJ, which -- astonishingly -- is the standard Babylonian order for the Planets (Jastrow, Rel. Bab. Ass. 461n2): Merc. (Nabu), Mars (Nergal), Sat. (Ninurta), Venus (Ishtar), Jup. (Marduk). (Actually, the Babylonians would normally reverse this order, but that's just going around the Pentagon in the opposite direction. This also gives 5 days of the week: M/Tues, H/Wed, J/Thur, V/Fri, S/Sat) In other words, the Chaldean and Babylonian Orders are duals of each other. Therefore, I call this the Planetary Pentacle. Finally, I'll briefly consider whether the Planetary Pentacle could generate the Pythagorean UGIEIA/UGIThA. Taking UGA as fixed we get the Pentagrams: Th EI ? A ? A G U G U That is: U: `Udor = Water G: Gaia = Earth I: ? = Fire Th: Thumos = Spirit or EI = EIdos = Idea = Form A: Aer = Air Unfortunately there is not, so far as I know, any Greek word meaning Fire (or Heat or Sun, etc.) that begins with Iota. (BTW, Ignis is, of course, Latin, and I'm sure Pythogoras wouldn't have stooped to put a Latin Word in his formula.) Another problem with this arrangement is that, although Thumos = Spirit is reasonable enough in a psychological context, it doesn't work well in Plato's or Aristotle's metaphysical context. Finally, we lose the high-tone accentuation of Spirit in the middle of the arch structure. So the Planetary Pentacle is interesting, but ultimately packs less meaning than the Elemental Pentacle. APPENDIX: DRAWING PENTAGRAMS AND PENTAGONS I've paraphrased the following from Charles W. Benfield, "Constructing a Pentacle" (_Nematon_, Vol. I, No. 3; Beltane 1974, pp. 12, 14-16): Procedure I 1. Draw a horizontal line, which will be the diameter of the bounding circle. 2. Bisect the line to get its center, and draw a perpendicular through this center. 3. Draw a circle around the center with the given diameter. 4. Bisect the horizontal three more times to get its sixteenth part. 5. Mark on the horizontal the point 13/16 from its left end (5/8 of the right-hand radius). 6. Use the compass to measure the distance from this point to the intersection of the vertical and the circle; this is the pentagon's side. 7. With the compass set as described, set off five points around the circle's circumference. 8. Connect these points to make the pentagram. Procedure II 1. Construct as before the circle ABCD with vertical diameter AOC and horizontal diameter DOB. 2. Bisect OD at E. 3. Set the compass to measure EA. 4. With E as the center, drop an arc AF which intersects OB at F. 5. Set the compass to measure AF; this is the side of the pentagon. 6. Step off the five points and draw the pentagram as before. * finis *