I suppose it had to happen … in fact I’d guess the only reason it hasn’t happened until now in this post DaVinci Code era we live in is that the oldest Platonic manuscripts are so difficult to obtain and read. This also makes it difficult to discuss – not that this forestalled some immediate expression of academic disdain of the what-more- DaVinci-Code-rubbish sort - despite others supporting this “previously discredited symbolic, rather than literal, way of reading Plato's great works.”
The controversy was unleashed by a press release from Manchester U. in late June announcing the claim one of their profs has cracked "The Plato Code" - the long disputed secret messages hidden in the great philosopher's writings. The fuss even got into the Daily Mail (never one to miss out on a controversy.) A paper explaining the modus operandi of both the prof, Dr Jay Kennedy, and of Plato himself (i.e of the decoding and encoding methods) is being published in an academic journal, Apeiron: A Journal of Ancient Philosophy and Science [U Of Texas], but in fact is already published online by MU as a PDF. Dr Kennedy claims Plato imposed an esoteric framework onto his writings which initiates would understand but those hostile to certain ideas would not be aware of. The covert approach was to protect Plato from being put down as a dangerous heretic: hence the “Plato Code,” as the papers have dubbed it.
What Dr Kennedy, who is not a traditional classicist but a science historian, did was to subject Plato's MSS to a computer analysis to establish its stichometry in each case – basically how the text composition and layout (divisions etc) accorded with the conventions of the time. (It’s implied these formal conventions were respected when the papyrus MSS were copied in post-Classical times, for the oldest Platonic MSS are from centuries later, being early-mediaeval era codexes. Apparently, otherwise unrelated ‘daughter’ MSS done centuries later in different countries have the same breaks.)
He claims this shows a 12-part division which chimes with (I think that’s the best metaphor) the Pythagorean scheme of mathematical harmonies referred to as ‘the music of the spheres.’ The theory as developed was that the musical scale was simply an expression of an underlying cosmic plan which ruled all matter. It could apply to astronomy (cf Bode’s and Kepler’s laws of planetary distances and motion), pure maths (the Fibonacci Sequence, converging on phi), to art (the Golden Ratio /Section rule in Renaissance painting), or (oldest of all) to ‘sacred geometry.’
This is where we come in, with a long-theorised link to our own ‘Celtic’ realm via references to the Druids and their putative megalithic-site-building predecessors.
‘Pythagorean geometry’ or triangulation was theorised by Scots engineer Prof Alexander Thom, after measuring hundreds of British sites, to be behind megalithic constructions which exist from the Mediterranean up the Atlantic seaway to the Orkneys. (He argued the sites’ common ovoid or egg shapes were the result of pegging out Pythagorean triangles and stretching cords around to create a perimeter ellipse, using a standard measure of 2.72 feet, which he called the Megalithic Yard.) Without getting into futile argument whether or not this ‘sacred geometry’ theory is valid (others have published complicated mathematical “proofs” I’m not in a position to argue over), there may well be other links. While nothing is known for sure of the original figure of Pythagoras [6th-C BC] and was not known to commit his ideas to writing, his school, the Pythagorean Brotherhood, is said to have later spread beyond Italy, where its precepts were written down. The Hyperboreans [also 6th-C BC] who lived somewhere in the latitude of the North Sea (Pliny and Diodorus give details from Hecateus’s lost History Of The Hyperboreans) exchanged gifts and visited with the ancient Greeks. It was also said the Druids lived by Pythagorean beliefs. Ammianus Marcellinus’s ‘The Origin of the Gauls’ in his Roman History of c380 AD speaks of “the Druids, men of loftier genius, bound in brotherhoods according to the precepts and example of Pythagoras.” This supports the idea both Druidism and megalithic science were a product of Pythagorean precepts – though we shouldn’t use the latter term as megalithic science predated Pythagoras by perhaps 3,000 years.
Diodorus's account says the Hyperboreans had both a city and a sacred precinct built "after the pattern of the spheres," a phrase that has excited interest. The reference seems to relate to the ancient Greek idea of the cosmos as a nesting set of transparent crystal spheres out from Earth. These were seen as revolving inside one another at different speeds. These totalled ten: Earth, the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn, and the Firmament Of The Heavens holding up the stars, as well as the Crystalline Primum or Mobile Heavens which were also the Abode of the Blessed. Ancient priesthoods taught there was a natural harmony of the universe, in which each planet had a frequency to which it "resonated," and from which comes the inspiration since then for composers to recreate "the music of the spheres" (as in Holst's musical suite "The Planets").
The notion megalithic science had attempted to recreate the 7 nested spheres of the cosmic model seems to have made its debut in print in 1846, when the Rev. E. Duke, who claimed he had found 7 circular "temples" which formed satellite sites around Silbury Hill near Avebury, and that this was evidence such sites were cosmic or planetary models. There were then 7 known i.e. visible planets, but the idea of 7 nested circles exists elsewhere, cf the proverbial “7 circles of hell” (7 vies with 9 as the key magic number for numbers above 3).
‘Numerology’, as it’s known, is not today regarded as a science, but it was before the schism developed between science and religion. Just to give a taste of it, below is a reproduction of a worksheet I designed back in the 90s when I was teaching a related adult-ed course. The scheme involves laws of geometry, astronomy and music, specifically (1) Pythagorean geometry, (2) Kepler's Laws of planetary motion and Bode's Law of planetary distances, and (3) the natural harmonic series of intervals in music. The formula most associated with Pythagorean Geometry (it may well be older) is that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the two other sides, e.g. three squared plus four squared equals five squared. Kepler's First Law said that planetary orbits form an ellipse, which is the shape, Prof Thom determined, of ancient megalithic sites. Bode's Law said that if you take a mathematical series beginning 0, 3 etc and double each successive number, i.e. 0, 3, 6, 12, 24, 48, 96, 192, 384, 768 etc, and then add 4 to each, a rough measure of planetary distances from the sun can be calculated in relation to the Earth-Sun distance (reckoned as one AU or Astronomical Unit) when divided by 10. For example, Earth, by definition one AU from the Sun, would as third planet from the Sun have a Bode number of 6 + 4 = 10 divided by 10 or 1 AU. Below is a partly-completed table you can save (it's a JPEG) and print out to try these ideas out by working out the answers to the blank slots. (You may find some holes in this ancient theory at this point, as I did – the sheet is not designed to prove anything beyond exploring how well the numeric conversions work.)
The modern astronomical calculation of the actual planetary distances show reveals some interesting oddities. One is the Asteroid Belt just beyond Mars has to be included in the series, supporting the idea it is the remains of an exploded planet. Also, the series suggests Neptune's orbit has been drawn in and Pluto's moved into Neptune's "proper" orbit, i.e where it should have been per Bode's Law (and a long-hypothesized "10th planet" in Pluto's "old" orbit) -- suggesting an ancient interplanetary collision akin to a snooker ball shunting others out of their positions. This may also account for a slight difference between the Bode's Law prediction and the actual distance when measured today. For example Mars is officially 1.52 AUs from the Sun, rather than the 1.6 AUs Bode's Law indicates for the 4th planet from the Sun (4th in series 0, 3, 6, 12, plus 4 = 12+4 = 16).
Via the Fibonacci Natural Harmonic Series, the ancient interest in "the music of the spheres" can be taken further by relating these planetary "rules" to the intervals in the musical scale. (The ancient Greek system seems to have been a 12-note scale.) This proposes the progressive series of fractions, diminishing to infinitesimal differences (approaching but never reaching zero) 1:1, 2:1, 3:2, 4:3, 5:4, 6:5, and 9:8, 18:17. In art, if the last number in this sequence is divided by the previous one, it yields an increasingly close approximation of the Golden Mean ratio of 1.6:1 favoured by Renaissance artists. Here it is related to the musical scale (as in minor Thirds, perfect Fourths, Fifths etc). For example, the "basic" or unison frequency, associated with Earth, would be "C" natural [262 Hertz or cycles/second], one octave up being 524 Hz = 2:1 ratio. Multiplying this by the corrected Bode value for Mars (1.52 rather than 1.6) gives 398 Hz, which works out as the pitch nearest "G" which is used in the musical representation of war trumpets -- as in Holst's "Mars The Bringer of War." Holst’s 1914 suite The Planets was inspired by astrology, which of course also ties in the notion of a 12-part zodiac model, which since around 1930 has also been proposed as an explanation for landscape features around Glastonbury etc. which supposedly mirror the constellations; this theory has had little support since some of the proposed shapes have been found by landscape research to be mediaeval, without earlier predecessors. However the “as above, so below” starscape theory has also been applied independently to explain the shapes of megalithic sites having unique configurations and differing number of stones, all around Britain, as per Thom’s sketches.
Anyway, Diodorus' Hyperborean account says that within the sacred precinct, the priesthood sang hymns continually. The most ancient names we have for Stonehenge, the "Chorea Giganticum," implies an assembly involving singing (as in choir) and perhaps dancing or ritual processions as well. The implication here is the Hyperborean hymns celebrated and emulated the natural frequency of the planets, and the pattern of the spheres as the heavens turned in their place, as if held up by an invisible column of power -- generated by this sympathetic choral magic? "My claim," Kennedy says, "is that Plato used that technology of line counting to keep track of where he was in his text and to embed symbolic passages at regular intervals." This "unlocks the gate to the labyrinth of symbolic messages in Plato".
This labyrinth reference brings us to the most famous of Plato’s writings, concerning the dread A-word, Atlantis. Nearly all the details recycled endlessly in popular speculative books on this topic are from two of Plato’s Dialogues, which describe this elusive city-state, capital of a lost maritime empire. Since then, writers have tried to locate the place all over the known world, including in the Celtic sphere. What stichometric manuscript analysis of these two Dialogues can tell us we have to wait and see, but it has always struck me there is something peculiar about Plato’s too-perfect description of the 7 “circles” of alternating land and water forming the Atlantean capital or royal isle, which may have a bearing on the new arguments. His layout plan, which has been sketched out in various books, reminds me of one of those roughly circular mazes carved on rocks here and there around the western fringe of Europe. These rounded maze shapes are different from the rectangular labyrinths of the classical world, and when traced out on the ground as turf maze shapes etc are generically as “Troy Towns”, based on a legendary association with Britain’s supposed founding by Trojan exiles. (See Geoffrey of Monmouth’s 12C Historia Regum Britannorum.) These are different from the “multi-vallate” Celtic hillforts Caesar described as being tribal capitals [oppida], which have perhaps several alternating banks and ditches for defense. However with “ritual” i.e. religious rather than defensive sites (the latter have the ditch on the outside of the first bank), there may be a total of 7 “rings” by counting each up and down separately. Although it’s a composite site built up over different eras, I believe you can do the same with Stonehenge, if you want to, by counting the outer rings. (Anyone wanting to test this out should be aware of the latest archeo-discovery here, of two encircling hedges.
There’s now a 3-D “Virtual Stonehenge” at the Heritage Key website, which requires registration and software download. Just announced [July 2010] is a new 3-year archeo initiative, The Stonehenge Hidden Landscapes Project, to build up a ‘digital chart’ of the landscape, and prove or disprove a theory the surrounding monuments form two large circles or loops around Stonehenge, one with a radius of 0.6-1.2 km away, and the other with a radius of 2-2.4 km away.)
The smaller Troytown mazes seem to be symbolic paths, rather like the ones tiled into cathedral floors to be traced by those whose health or circumstances do not allow them to make a full long-distance pilgrimage and can only make a symbolic observance. (The “Stonehedge” discovery aside, surviving Troytown mazes are ground-level designs only – there are no hedges blocking your view, as in later examples e.g. Hampton Court. You can see your route ahead, though you still have to work out the one correct path to the centre, as convention has it you should not retrace your footsteps at all.) The older, pre-Christian religious symbolism of mazes sadly seems to be lost, the chief modern interpretation trying to link it with goddess worship. The Greek double-headed axe known as the labrys, kept or carved at the centre of the labyrinth – the basis of its ancient name - was used in animal and perhaps human sacrifices to the gods or should we say, goddesses.
I could go on and argue the “Celtic” aspect is more substantial here than previously indicated, but it might be better to leave it at that for now – I think the problem with this topic is already, as they say in text messaging, TMI.
