Extracted from The Structure of MetrologyThe application of units of length to problems of measurement, design, comparison or calculation., its Classification and Application (2006) by John Neal and notes by Richard Heath for Bibal Group, a member of which, Petur Halldorsson, has taken this idea further with more similar patterns on the landscape, in Europe and beyond. Petur thinks Palsson’s enthusiasm for Pythagorean ideas competed with what was probably done to create this landformThose geometrically connected buildings, natural features or horizon events, necessary for quantifying astronomy, measuring the landscape or, in later times, connecting communities., as he quotes “Every pioneer has a pet theory that needs to be altered through dialogue.” Specifically, he “disputes the Pythagorean triangle in Einar’s theories. I doubt it appeared in the Icelandic C.I. [Cosmic Image] by design.” Caveat Emptor. So below is an example of what metrology might say about the design of this circular landform.
Figure 1 of Palsson’s (1993) Sacred Geometry in Pagan Iceland
In 2006 John Neal wrote,
Interestingly, the degree above the 52nd parallel that lengthens by the factor of 441 to 440 would be close to the Arctic Circle. This is where, in western Iceland, Einar Palsson showed that the founding towns laid out by the first settlers had a distinctly geometric relationship. Not only this, but the foundation circle around which the towns were set out he gave as 216,000 Roman feet (about 64 km) in diameter. Had he used the Standard Canonical variant (Greaves’ Cossutian foot) of .96768ft then the resultant circle would be 209018.88 which is immediately recognisable as the hundredth part of the mean radius of the earth. Palsson did not see this fact, that 1.75 times the diameter is exactly the geographic degree at that latitude. This would be 365783.04 feet or 111490.57 metres, about 66° N.
Figure 2 How the geographical foot varies according to latitude upon the Earth [from Sacred Number and the Lords of Time. 2014. 141. after John Neal’s Mirrors, 2000]
The mean earth has each of its degrees of latitude equal to the actual degree length of 51-52 degrees on Earth (which is called the geographical degree). Neal is taking the mean radius and noting that, according to figure 2, 65-66 degrees (for Iceland) will be 440th part greater than the geographical degree length. See also my extracts on The Ancient Model of the World [new tab] if this topic is unfamiliar .
If Palsson’s diameter is one hundredth of the mean radius, one can say that the sacred image diameter has two relationships;
- Diameter of sacred image is 4/7th of the 65 north-south degree length (7/4 equaling the 1.75 Neal mentions) relevant to Iceland
- Diameter of sacred image is one hundredth of the mean earth radius.
Neal takes (a) as of prime significance and here I consider (b) the interesting fact that the mean radius times 24/25 (roman foot) times 126/125 (standard canonical micro-variation) is one hundred times larger than the sacred image. Perhaps more important though is the fact that the diameter is then a harmonic number, 216,000 roman feet in diameter.
By making the diameter 6^3 x 10^3 = 216,000 SC Roman feet one can see the stade of 600 feet (a Roman stade is 576 English feet [NEAL. ADWM. 2000. 72.]) divides the diameter 360 times. The 360 x 576 (English) foot units of the diameter are also 336 Royal cubits (12/7 feet) which, when multiplied by PIor π: The constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159, in ancient times approximated by rational approximations such as 22/7., change (360 units of 600 Roman feet) into (360 units of 1056 royal cubits) and, all this being standard canonical, there are 360 units of 1056 Std Can Royal cubits of 1.728 feet (the Jerusalem cubit3/2 feet of any sort, such as 12/7 {1.714285}, 1.5 Royal feet of 8/7 feet, but sometimes a double foot, such as the Assyrian {9/10} of 1.8 feet.) on the perimeter.
- In summary, a 216,000 Std Can Roman foot diameter generates 360 rational units on the perimeter of 1056 Std Can Royal Cubits of 1.728 feet.
Therefore, a 216,000 standard canonical roman foot diameter was easily constructed using roman stades of 600. And this diameter has a circumference immediately amenable in 360 segments of a rational nature, having the role of one degree on the horizon. Further, we can see in Neal [2000. 116] that 100 standard royal cubits as diameter give a perimeter of 360 feet. Many of the transformations available in ancient metrology can translate radial rationality into a rational circumference by using different modules and micro-variations of them, these cancelling unwelcome primes in denominators, of whatever rational PI is assumed, usually the prime number seven in 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..
Conclusions
- Palsson’s sacred image clearly hails from a long tradition established thousands of years before the settlement of Iceland, commonly seen in the circular landforms of megalithic Europe.
- The image was easily constructed according to a formula which employs a specific Roman foot easily counted as 360 lengths of 600 feet, a stade, on its diameter.
- These 360 degree divisions were then rational using a Royal cubit (the 1.728 ft Jerusalem cubit) on its circumference.
- Having rational 360 degree divisions around its circumference, degrees are easily counted for cardinal points, exactly as we would use a graduated scale for degrees.
- The same design drawn anywhere in these units images the Mean Earth at a scale of one hundredth, a known symbolism for the spiritual world within sacred space building.
- The image has a dual utility, of the Earth itself enabling the degrees of geodeticUnits of measures and monumental measurements relating to the numerical definition of the shape of the Earth by the late megalithic. latitude, as well as providing local horizon events to be marked. (see Heath [2014. 11, 148, 218.])
- Within this circular image Palsson found a tradition of Pythagorean triangles relevant to Iceland’s myths.
A follow-on article can be found here
Data and Transformations
Feet are English unless named
| Mean Radius of Earth | 7 x 12^6 = 20,901,888 feet |
| SC Roman Foot | 24/25 x 126/125 = 0.96768 feet |
| Palsson’s Diameter | 216,000 x 0.96768 = 209,018.88 feet |
| Stade of SC Roman feet | 600 x 0.96768 = 580.608 feet |
| Construction | 209,018.88 / 580.608 = 360.0 |
| Degrees on Circumference | 580.608 x 22 / 7 = 1,824.768 feet |
| SC Royal cubit | 12 / 7 x 126 / 125 = 1.728 feet |
| Cubits per degree | 1,824.768 / 1.728 = 1,056 cubits |
Bibliography
Heath, Richard. Sacred Number and the Lords of Time. Inner Traditions: Vermont 2014.
Halldorsson, Petur. Pattern of settlements paced from 1 to 9. CreateSpace: Iceland 2013.
Neal, John. All Done With Mirrors. Secret Academy: London 2000.
Neal, John. The Structure of Metrology, its Classification and Application: a paper delivered to Ordo et Mensura IX Oct 20th 2005, Munich. Secret Academy: London 2006.
Palsson, Einar. Sacred Triangle of Pagan Iceland. Mimir 1993.