In diagrammatic form with the thirds alone, the following graphical representation emphasizes the astronomical significance of the Pheidian planorbidae and their relationship to the four major planets. Here it now becomes apparent that Spira Solaris occupies a key position between the two most massive planets in the Solar System, Jupiter and Saturn--a situation further complicated by the elliptical nature of the respective orbits of the latter pair, their known resonances and further complexities concerning their inverse velocities with respect to the mean velocity of Mars as discussed in Sections II and III (see also below):  

  Fig. 19.  The Phedian Planorbidae in Astronomical Context

Fig. 19b.  The Phedian Planorbidae in Astronomical Context
In Figure 19b the numbers to the left of the planetary and intermediate synodic positions represent the corresponding exponents that generate the mean periods of the Phi-series exponential planetary framework. Thus the mean sidereal period of Jupiter is Phi raised to the fifth power ( Phi 5 = 11.090169944 years), Saturn: Phi raised to the seventh power ( Phi 7 = 29.034441854 years) and Uranus Phi raised to the ninth ( Phi 9= 76.013155618 years). For the inverse velocities, a.k.a the Pheidian growth factors, these may be obtained by applying the cube root to the periods, or in a single step from the division of each period exponent by three. Thus for Jupiter (PENTAD) k = Vi Phi 5/3; for Saturn (HEBDOMAD) k = Vi Phi 7/3; for Uranus (ENNEAD) k = Vi Phi 9/3, and for good measure (between the first pair) Spira Solaris: k = Vi = Phi 6/3 = Phi 2.
    In passing, it is not out of place to note here that the occurrence of the Pheidian spiral k = Phi 2/3 among Conidae may be back-tracked with respect to the double spiral and larger growth factors, i.e., k = Phi 2/3 raised to the fourth power is in turn k = Phi 8/3 now associated with the Saturn-Uranus synodic cycle, i.e., the eighth "third", with the other major synodic cycle (Spira Solaris) the sixth. Thus there is a continuous integer range from 5 though 9 with the odd-number planetary assignments (PENTAD, HEBDOMAD and ENNEAD) predominating. Although these are archaic terms, their inclusion here arises from a difficult passage in Proclus that in addition to incorporating the decad ("since the decad is the number of the world", i.e., Base-10) and "the quadripartite divisions of all things" makes cryptic references to all three. Readers may judge for themselves whether this includes the present topic or not; see: Pentad, Hebdomad, Ennead.
  Lastly, included in Figure 19 are two photographs of Minoan rhytons.42, 43 Perhaps unexpected or even unacceptable to some, based on their shapes and their markings alone, to the open minded they must surely represent complex objects rendered all the more complex by their great antiquity. To what extent they can be classified as specific examples of man-made conidae may be difficult to assess with certainty, but sufficient examples of the assignment k = Phi 2/3 for Conidae (in addition to width versus height considerations) nevertheless permit the application of this particular primary spiral directly to the rhyton in question. As the assignment shows, the spiral not only becomes critically aligned with respect to the common "stellar" center; at the top the outermost whorl also follows the slight curvature of the rim. The same assignment and fit also applies to the second rhyton, which is perhaps even more complex, at least in terms of its artistic and informative markings, including pheidian rectangles, horned-goats (though not ramshorns) and multiple spiral patterns.
    Although this aspect will not be pursued further here, it seems possible that similar (if not related) threads may also have survived the passage of time, i.e., reflected in the shapes of certain Greek vases and amphorae as pursued in detail in Jay Hambidge's little known and even less understood Dynamic Symmetry (1920).36

Having introduced rhytons, amphorae and bowls at this juncture it is necessary to point out that a considerable amount of complexity attends the matter, especially in the case of the rhytons in view of their greater antiquity. Even so, information concerning the symbolism associated with bowls and amphorae is certainly available in later Greek commentaries. Moreover, although the extant works may be obscure at times, the subject under discussion is nevertheless clear enough, e.g., as expounded in the works of the Neo-Platonist Porphyry.
    Readers may skip the following or judge for themselves the degree of complexity involved and relevance to the present discussion. The excerpts provided below are from The Selected Works of Porphyry, specifically, the latter's commentary on The Homeric Cave of the Nymphs in the Thirteenth Book of the Odyssey. Here, after introducing the topic with the question: "What does Homer obscurely signify by the cave in Ithaca"  Porphyry proceeds to unveil the associated symbolism in detail, i.e., he states:67
 . . .   it is evident, not only to the wise but also to the vulgar, that the poet, under the veil of allegory, conceals some mysterious signification; thus compelling others to explore what the gate of men is, and also what is the gate of the Gods: what he means by asserting that this cave of the Nymphs has two gates; and why it is both pleasant and obscure, since darkness by no means delightful, but is rather productive of aversion and horror. Likewise, what is the reason why it is not simply said to be the cave of the Nymphs, but it is accurately added, of the Nymphs which are called Naiades ? Why, also, is the cave represented as containing bowls and amphorae, when no mention is made of their receiving any liquor, but bees are said to deposit their honey in these vessels as in hives ? Then, again, why are oblong beams adapted to weaving placed here for the Nymphs; and these not formed from wood, or any other pliable matter, but from stone, as well as the amphorae and bowls? Which last circumstance is, indeed, less obscure; but that, on these stony beams, the Nymphs should weave purple garments, is not only wonderful to the sight, but also to the auditory sense. For who would believe that Goddesses weave garments in a cave involved in darkness, and on stony beams; especially while he hears the poet asserting, that the purple webs of the Goddesses were visible. In addition to these things likewise, this is admirable, that the cave should have a twofold entrance; one made for the descent of men, but the other for the ascent of Gods. [p.172]

 . . .  The ancients, indeed, very properly consecrated a cave to the worId, whether assumed collectively, according to the whole of itself, or separately, according to its parts. Hence they considered earth as a symbol of that matter of which the world consists; on which account some thought that matter and earth are the same; through the cave indicating the world, which was generated from matter. For caves are, for the most part, spontaneous productions, and connascent with the earth, being comprehended by one uniform mass of stone; the interior parts of which are concave, but the exterior parts are extended over an indefinite portion of land. And the world being spontaneously produced, [ i.e., being produced by no external, but from an internal cause,] and being also self-adherent, is allied to matter; which, according to a secret signification, is denominated a stone and a rock on account of its sluggish and repercussive nature with respect to form: the ancients, at the same time, asserting that matter is infinite through its privation of form. Since, however, it is continually flowing, and is of itself destitute of the supervening investments of form, through which it participates of morphe 1 and becomes visible, the flowing waters, darkness, or, as the poet says, obscurity of the cavern, were considered by the ancients as apt symbols of what the world contains, on account of the matter with which it is connected. Through matter therefore, the world is obscure and dark; but through the connecting power, and orderly distribution of form, from which also it is called world, it is beautiful and delightful. Hence it may very properly be denominated a cave; as being lovely, indeed, to him who first enters into it, through its participation of forms, but obscure to him who surveys its foundation, and examines it with an intellectual eye. So that its exterior and superficial parts, indeed, are pleasant, but its interior and profound parts are obscure, [and its very bottom is darkness itself].
   Thus also the Persians, mystically signifying the descent of the soul into the sublunary regions, and its regression from it, initiate the mystic [or him who is admitted to the arcane sacred rites] in a place which they denominate a cavern. For, as Eubulus says, Zoroaster was the first who consecrated, in the neighbouring mountains of Persia, a spontaneously produced cave, florid, and having fountains, in honour of Mithra, the maker and father of all things; a cave, according to Zoroaster, bearing a resemblance of the world, which was fabricated by Mithra. But the things contained in the cavern being arranged according to commensurate intervals, were symbols of the mundane elements and climates.
     3. After this Zoroaster likewise, it was usual with others to perform the rites pertaining to the mysteries in caverns and dens, whether spontaneously produced, or made by the hands.  For, as they established temples, groves, and altars, to the celestial Gods, but to the terrestrial Gods, and to heroes, altars alone, and to the subterranean divinities pits and cells; so to the world they dedicated caves and dens; as likewise to Nymphs,2 on account of the water which trickles, or is diffused in caverns, over which the Naiades, as we shall shortly observe, preside. [p.175]
As for the "Nymphs" themselves, Porphyry explains that because they:
. . . .  preside over waters, a cavern, in which there are perpetually flowing streams, is adapted. Let, therefore, this present cavern be consecrated to souls, and, among the more partial powers, to nymphs, that preside over streams and fountains, and who, on this account, are called fontal and Naiades. What, therefore, are the different symbols, some of which are adapted to souls, but others to the aquatic powers, in order that we may apprehend that this cavern is consecrated in common to both? Let the stony bowls, then, and the amphorae be symbols of the aquatic Nymphs. For these are, indeed, the symbols of Bacchus, but their composition is fictile, i.e., consists of baked earth; and these are; friendly to the vine, the gift of the God; since the fruit of the vine is brought to a proper maturity by the celestial fire of the sun. But the stony bowls and amphorae, are in the most eminent degree adapted to the Nymphs who preside over the water that flows from rocks. [p.179-180]
 ( Selected Works of Porphyry, commentary on The Homeric Cave of the Nymphs in the Thirteenth Book of the Odyssey) translated by Thomas Taylor, Thomas Rod, London 1823:171-180; emphases supplied)
Whereas Thomas Taylor [1758 - 1835 ] -- the generator of more than nine thousand  "necessary emendations" to the Commentary of Proclus on the Timaeus of Plato  -- elaborates further in the present context with footnotes of his own:

    1 But morphe, as we are informed by Simplicius, pertains to the colour, figure, and magnitude of superficies.
    2Nymphs,” says Hermias, in his Scholia on the Phaedrus of Plato, “are Goddesses who preside over regeneration, and are ministrant to Bacchus, the offspring of Semele. Hence they dwell near water, that is, they are conversant with generation. But this Bacchus supplies the regeneration of the whole sensible world.”

36. Hambidge, Jay. Dynamic Symmetry, Yale University Press, New Haven 1920.
Marine decorated rhyton from Zakros (Crete). Wondrous Realms of the Aegean, selected by the editors, Lost Civilizations Series, Time-Life Books, Virginia 1993:110.
43. Embossed, carved 12-inch rhyton from Zakros (Crete). Wondrous Realms of the Aegean, selected by the editors, Lost Civilizations Series, Time-Life Books, Virginia 1993:99.

Copyright © 2003. John N. Harris, M.A.(CMNS). Last updated on July 10, 2004. Links checked April 2, 2009.

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