Einar Palsson [1, at end] saw that the myths of foundation for Iceland’s settlement in 930 had Pythagorean roots. Since then Petur Halldorsson has identified patterns that could not have been influenced by Pythagoras (c. 600 BC) and Pythagoras was known to have adapted the existing number sciences found (according to his myth) from Egypt to China.
Such patterns, called Cosmic Images by Halldorsson [3], seek to establish a geometric connection between places on the landscape and on the horizon, here in the south-western region near Reykjavik, the only Icelandic city. The spirit of a region or island was integrated through organising space in this way, according to centers (Things) of circles and their radius and diameter as numbers of paces, circles punctuated with places and alignmentsIn general, to the sun and moon on the horizon, rising in the east or setting in the west.
Also, a name special to Carnac's groups of parallel rows of stones, called Le Menec, Kermario, Kerlescan, and Erdevan. to other places, horizon events or cardinal directions. John Michell provided a guide to some of the techniques in his books [2, at end].
Figure 1 The Cosmic Image east of Reykjavik proposed by Palsson
Palsson had noticed a number symbolism within Iceland’s foundation epic, involving geographical features. This resembles the situation where Ernest G. McClain interpreted Biblical, Vedic, and Babylonian mythic texts as involving harmonic invariance [4, at end]. Palsson intuited Pythagorean influences, where the 3:4:5 triangle could form a numerical myth of origin in Iceland, of a race of giants from the element Fire. This source of creation is seen in the bottom right of figure 1 where the “Primeval Hill” is located within such patterns. New creations arise from Fire and must surely return there, to formlessness; a myth conguent with the alignment of midsummer sunrise (top left) and midwinter sunset (bottom right).
The Primeval Hill, Fire, and the Number 27
If one accepts that the Primeval Hill in Iceland was based on the number 27, several otherwise unintelligible bits of information fall into place….
The Primeval Hill was based on Fire; the Earth was created through Fire and it is going to vanish in Fire. The pivotal event of Njals Saga is the destruction of the abode of Niall through fire. Its allegorical meaning is that of the fabulous phoenix bird, destroyed every 500 years after two periods or life-cycles. In the year 1000 Christianity was formally accepted as the state religion of Iceland. The seven ages of paganism vanished; Time, personified by Kari in the Saga, escapes from the flames and flies northeast to the land of the sunrise… the abode of the apostle of Christianity, Hjalti Skeggjason. Kari flies a precisely measured distance, 216 M (M = 1000 and 216 / 27 = 8), that of the diameter of the world as understood in those days.
The number 27 stands for Fire at the Primeval Hill. It also stands for kingship. It stands for the beginning and the end of time…
The number 27 is, of course, the number 3 multiplied three times with itself (3x3x3=27). The importance of the number 27 is typical for learning attributed to the Greek thinker Pythagoras. For Plato the soul of the world is divided according to a particular numerical series, which is thought to derive from the earlier Greek thinker. (It is called the Lambda-formula, so called because of its resemblance to the Greek letter, consists of two “arms “. One is 1-2-4-8 and the other 1-3-9-27.1 Multiplied together the 8 and the 27 make 216 – the basic number of the created world in pagan Iceland. Pythagoras and his followers are said to have believed that they would be reincarnated every 216 years.[2]
The Sacred Triangle in Iceland, page 26-27
Figure 2 The Pythagorean diagram called the Lambda in which powers of 2 (female) and 3 (male) increase, creating all of their factorised Children between them, here not shown, for example, between 2 and 3 is 2 x 3 = 6.
John Neal discovered that the 216-nature of Palsson’s cosmogram (as per figure 1 and previous posting) was calibrated in Roman feet (24/25 = 0.96 feet) of a slightly increased (by 126/125) length of 24/25 x 126/125 = 0.9677 feet so that 216,000 feet are exactly 1/100 the mean earth radius of 7 x 12^6 = 20,901,888 / 100 = 209,018.88 English feet. By using the foot the Icelandic geometers had demonstrated two things:
- That they saw the need to integrate the third powers of two and three to make 216 units of 1000 roman feet.
- And to have their geometrical circle model the mean earth as a spiritual norm for temple building.
This Roman foot enabled a fractional and non-regular number (209,018.88 feet) to be made regular as 60^3 = 216,000 feet. These two numbers are proximate and so the 126/125 ratio makes the size required a simple integer, made up of only factors 2 and 3 in its head number 216.
This type of Roman foot also has special properties as a diameter, illustrated most clearly by having a single foot diameter. As a fraction this foot is 3048/3125 feet long and this, times 22/7The simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods., leaves 3024/3125 x 22/7 = 3.0413 x 12 = 36.4956 inches. This looks like 36 inches and dividing by 36: 36.4956/36 = 1.01376 inches – the so-called geographical inch of the English/Greek module. The formula for 1.1376 feet is 3168/3125, the 3168 was symbolic as an ancient world norm for the perimeter of a sacred space emanating from the spiritual form of the Earth, its mean size.
To recapitulate: One Roman foot of this type on the diameter gives 36 (geographical) inches on the circumference. Multiplying 36 by 6 gives 216 on the circumference, a diameter of 6^2 gives (36^2) 1296 on the circumference and 6^3 (216) gives 36 x 216 = 6^5 = 7,776 (geographical) inches on the circumference .
The same is true with powers of 60, so that the diameter of Palsson’s cosmogram of 60^3 = 216,000 Roman feet gives 60^5 = 777,600,000 geographical inches around its perimeter. In terms of numerical symbolism, Ernest McClainAmerican Cryptologist and Pythagorean Musicologist who decoded Plato's cryptic numerical ciphers in The Pythagorean Plato. The Myth of Invariance showed limiting numbers had been an ancient way of defining the onset of key musical tuning realities, then coded into many religious texts. Wikipedia. found 60^5 = 777,600,000 is associated with the god YHWH (6.5.10.5 as 60^5 = 777,600,000) in the Bible, whilst that number of geographical inches corresponds the meridian length of the mean earth since 12^6 feet x 22 x 12 = 788,299,776 /1.01376 = 777600000 Greek geographical inches.
Figure 3 Palsson linked two cosmic images with a Thing place called Pingvellir. Since then Halldorsson doubts the reality of the second image but something is profoundly true about the 432,000 length he found.
In Palsson’s figure 3 above, this property of the Roman foot appears to be employed to make a diameter two times the circles, of 432,000 to present an exact 1/100th scale model of the mean earth meridian, where the central Thing is the centre of the mean Earth, and the two subsidiary Things form a north and south pole, within the limitations of the landscape.
I first noticed that the meridian was 777,600,000 geographical inches in Sacred Number and the Lords of Time (LINK), page 194. But I had not guessed that there was such a smart diameter to circumference relationship involving a type of Roman foot and maintaining a pure-powers-of-60 relationship between the two. This illustrates how such relationships are inexplicably present within ancient monuments. One probably cannot know when such knowledge arose, or from whence it came but the monumental record and intuitions of later interpreters bring us to recover them: which is an important and objective outcome.
Whilst the Thing or primal centre, in Celtic, Nordic and other Ritualised Landscapes [2] is often found at the centre of a region or island, the interior of Iceland was and is inhospitable and so therefore the central place for the national assembly to meet is the center of a 432,000 foot length.
Ulfljotur’s, who had studied Norse traditions, formed a law involving 36 godar or law courts at 36 thing-places and his foster brother Grimur “Goatsfeet” was commissioned to locate the national Al-thing and subsidiary thing-places, after a year-long survey of the island. The resulting geometry of figure 3 emerges as multiplying 432,000 x 18 = 7,776,000. The miracle behind this is bound up with metrologyThe application of units of length to problems of measurement, design, comparison or calculation. but the outer symbolism is that 18 of 36 godar are transforming the mean diameter into the image of the meridian.
Figure 4 The Image of the Earth’s Meridian or distance from north to south poles, based upon the circular mean earth model.
The actual geometries, according the Palsson’s protégé, Petur Halldorsson [3], are somewhat variable and Iceland might be a swan song for the tradition.
References
1 Palsson, Einar. The Sacred Triangle in Iceland. Mimar:Reykjavik 1993.
2. Michell, John. At the centre of the World. Thames & Hudson: London 1994. and also Twelve-Tribe Nations(both reprinted as The Sacred Center and Twelve-Tribe Nations by Inner Traditions.)
3. Halldorsson, Petur. Pattern of Settlements paced from 1 to 9. CreateSpace 2013. and The Measure of the Cosmos, 2007.
4. McClain, Ernest G.. The Myth of Invariance. Hays/Shambhala: 1976.