Query: The pattern behind the pattern at Roncesvalles?

ORIGINAL QUERY:
Date: Mon, 25 May 2009
From: Niels Bandholm <niels.bandholm (at) gmail.com>

Could one mystery be the answer to another mystery?

Valerie Brewster Willis had a query in the Nexus Network Journal 03 Feb 2006: What is this geometrical symbol in Roncesvalles? (See figure 1)

Fig. 1

I do not have an answer but I see a similarity to a pattern I found in Keith Critchlow's book, Islamic Patterns (1976) on page 39 (see fig. 2). This figure also contains a six-pointed star and it is gyrated an angle of 19.11° from its normal position.

Fig. 2	Fig. 3

The first question: How slanted is the six-pointed star at Roncesvalles?
If the knife at left is vertical then the six-pointed star seems gyrated as in Critchlow's pattern (see fig. 3).

The second question: What is the original reference to Critchlow's pattern?
I have asked Professor Keith Critchlow and in his kind response, he is sorry not to recall the reference as the book was written in 1976.

I am extremely interested in the reference as I have a wonderful elucidation of Critchlow's pattern.

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NNJ READERS' RESPONSES:
From: Dag Nilsen <dag.nilsen@ntnu.no>

How can we know the intended tilting angle? One would suppose that the horizontal planes of the stone were to fit horizontal wall joints, but in the photograph they seem not entirely parallel, and even somewhat curved; that may however be ascribed to lens optics photo angle. The “knife”, or whatever it is to the left, seems not to be perpendicular to any of the wall joints – how would we know that it was intended to be vertical? The present position of the stone may not be exactly the same as when hewn (later settling, or other movement), so I cannot see how it is possible to find the exact tilting angle without meticulously carried out measurements of the stone, and even at that, to deduce anything substantial about some possible meaning associated to that angle.

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From: Mark Reynolds <marart@pacbell.net>

I concur with most of the geometric analyses and commentaries, although I'm not sure why Michael Schneider didn't include the cross in the center as a second drawing, unless he does not agree with Dr. McQuillan's opinion. I'm sure he would know how to do it.

I do not agree with McQuillan's comments about this geometry being done by an apprentice/novice, if my following opinion is true, and also because of the sophistication of the broken circles to create a 6-excircle and a 4-incircle design. The construction joins the hexagonal star and the cross together, thus creating a beautiful Judeo-Christian duality within the cosmic unity of the circle surround. Charlemagne converted to Christianity. Some scholars suggest he may have been Jewish at birth. This would make the geometric symbol even more clear, if it is referencing Charlemagne. I believe it is because the most important event to ever occur at Roncesvalles had to do with him and his good friend and ally, Roland.

In my humble opinion, there are three possibilities regarding the rotation of the star, which is what I believe is the essence of the query from Valerie Willis.

First, it could be a completely aesthetic or creative decision by the geometer to simply have a hexad in movement rather than the standard positioning of the Seal of Solomon. This rotation is a part of the hexagonal grid that can be developed easily (see constructions in responses), albeit more complex and developed. Still, it is not beyond the scope and talent of anyone skilled in geometry. It could be this and nothing more.

Or, secondly, if we are to believe in a intended meaning associated with this number symbolism of 19 degrees in the rotation (I would have to suggest an in situ measurement to ascertain exactly what the angle is in order to prevent "Tons Brunism" in the resulting calculation, as it could be an error created by analyzing the photograph; it is easier to measure and construct a 20 degree rotation than a 19 degree, but certainly not difficult), and if this symbolism were indeed intended by the geometer, it may well reference the tragedy that befell Charlemagne at Roncesvalles.

Charlemagne had to return home to settle an uprising and left his close friend Roland behind to defend his rear guard in the valley there. Roland and his small group of knights were completely overwhelmed by Basque mercenaries, and Roland died. Charlemagne was always associated with the sun. Roland and his knights were defeated under the light of a full moon. But is Roland symbolized by the moon? Well, in the battle, when Roland realized he was in trouble, he used his “olifant horn” to call for help. This horn is made from an elephant’s tusk, a whitish, crescent shaped object! But what is the sun/moon reference and the number 19?

There is difference in time between the solar year and how long it takes the moon to return to the exact place it is in the sky at new moon at the beginning of this lunar cycle. This difference is very nearly 19 years! (See: http://www.bibarch.com/concepts/Calendrics/Index.htm for more on this). In 19 solar years there are 228 solar months (12 x19) which is 7 months short of the 235 lunar months in 19 lunar years 2 + 2 +4 = 12. 12 is the number of months in a solar year and that meaning has already been discussed in relation to the hexad referenced here. This 19 year variance would have been known to any professional sacred geometer working at that time. It was known in 5th century BCE Babylon.

I believe the object on the left is a knife or sword, a blade. Notice how the circles are cut in two, as was the bond between Charlemagne and Roland. The arcs suggest moons, suns cut in two, a broken circle or bond, severed, as Roland had been from Charlemagne.

And thirdly, stand in front of the star geometry, and see what direction it points to in the landscape. Was this battle where Roland die in that direction, 19 degrees from where you stand? Or see what it references in the sky above the construction. This would need to be scientifically analyzed with the help of an astronomer with computer wizardry.

Valerie, we all hope you find your answer.

Respectfully submitted by the NNJ's first Geometer's Angle columnist ,
Mark (Marcus the Marinite) Reynolds

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From Ahmed Ali Gaber <ah012010@yahoo.com>
Ph.D. student, Institut für Gebäudeplanung und Entwerfen, Karlsruhe Universität

I am specialized in studying relations between architecture and Geometry in Islamic architecture (my Ph.D focus), so this let me say that the design of anything in Islamic architecture (from pattern or decoration design to complex building design) not only depends on certain angle (like many of the architects thinking or like many researcher saying), I had found that design in Islamic architecture is a very complex process depending on not only some angles but it consists of three main things and every one of them consists of many steps (you will see the certain angles in one of these steps), the design process is coming under a completed system and a very high and clear geometric methodology.

NIELS BANDHOLM REPLIED:

I know that there is more to the design than certain angles, but this angle leads to a very special ratio between the circumscribed hexagon and the circumscribed slanted six-pointed star. The ratio can be found in astrolabes around 1100 A.D. so I assume it is referring to the Heaven.

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From Antonia Redondo Buitrago<aredondo@sabuco.com>
Department of Mathematics. IES Bachiller Sabuco. Albacete. Spain

After having read the above answers for this query, a few ideas have popped into my head which I thought I would share. The thing which interested me most was why the pattern was tilted 20º counterclockwise (or any other angle near 20º…).

Putting aside the problems of measuring and accuracy, I would like to point out the following fact: The angle of regular hexagon is 120º, and if
we add 20º we obtain exactly 140º; the angle of regular nine-sided polygon. Could we perhaps guess that by turning the hexagon, it is maybe trying to
represent the nine-sided polygon? That is, what cannot be achieved with “ruler or compass”?

Why not? The abbey of Roncesvalles is on the Route of Santiago de Compostela, and we know about the presence and influence of the Knights
Templar. And the number 9=8+1 is an omnipresent factor in the mysticism and symbolism of the Templar Order. In addition, the inner circles remind the Paté cross, one of the crosses of the Templar…

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From Valerie Brewster Willis <vbw@orcon.net.nz>

What a thrill to do a bit of a google search this morning & find that the Roncesvalles geometry has been linked to the growing interest in Islamic geometry. I had wondered about that.

From a Roncesvalles perspective, there are several things I'd like to pass on which may help integrate the use of geometry in architecture and the ideas that inspire design.

Firstly, I am sure that the carving as we see it now, is on a reused stone. The foundations of an earlier building can bee seen in a photograph on Roncesvalles web page, immediately across the path from the wall in which the carving now sits. For this reason, no directional relationship can be inferred from its present physical location.

However, I think the angle of the hexagonal geometry can be safely deduced in relationship to the crossing point of the central figure which takes the form of four arcs suggesting a cross.

At right is a photograph from Kilmartin Scotland, demonstrating what those four arcs in the Roncesvalles geometry may be. In this case the four circles represent the four "airts", the four elements which eventually become the four armpits of the "Celtic cross". For this reason I think that the cardinal points and intermediate directions are meant to be read into the geometry at Roncesvalles.

Detail from a medieval grave slab at Kilmartin Scotland. Below this carved panel the decoration is divided into two panels, the left showing a foliate design, the right showing a sword - a combination I have also seen in islamic art of this period.

This is a detail from a photograph by Max Hirmer found in Thames & Hudson's Early Medieval Art in Spain (London 1967) of Catedral Veija (Seo Antigua) Lerida rebuilt 1203-78.This carving is on a capital of northwest pier of the crossing. I have heard it said that these capitals at Lerida were carved by the same sculptors who carved capitals for the cloister at Pamplona Cathedral including a scene recording women back-packing building materials to the top of a half completed tower. I treasure this carving for joy and pride with which these chaps show off their design knowledge "for those who have eyes to see". It is fun to think that in those days before photo-journalism, there was a sculptor with sufficient interest and respect for the design & build process to include such snapshots in the decoration of medieval buildings.

With regard to the geometry on this capital, if one looks carefully it can be seen that the pentagram, the cross and the 8 loops of the central design are drawn in a continuous thread which reminds me that these men were taught to delineate geometric patterns in the air, in their imagination. I think that the creature peering from the design table lower left is the Vouivre, the salamander like guardian of the precious jewel in Burgundian folk lore, suggesting that these stoneworkers came from that area and took a pride in their "secret" design & build techniques.

I think that the geometry at Roncesvalles provides a very interesting pivot around which discussions examining both the philosophical and practical use of geometry in architecture can swing. My own pet theory (without any real evidence to back it up!) is that there were construction workers in France whose traditional, pre-Christian understanding of cosmic geometry facilitated the flowering of "Gothic" design when employed by patrons inspired by Islamic geometry in the
medieval period.

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From Mike McDermott <Mike.McDermott@htw.com.au>

I thought that I had already answered this by reference to my Star Key site at:
http://www.geocities.com/ResearchTriangle/Forum/5375/
In that site, the volumetric inflation from two dimensions to three is implicit from the cube shape that emerges from joining the six corners of the hexagon through the centre, and the horizontal rotation to a sphere is implicit from the one seventh - 142857 - and six seventh - 857142 spiraling around the spine of nines. The angle in the design -- and Critchlow's -- refers to the vertical rotation. Simple, really. I guess most people who read my site can't get past their knee jerk reactions to such superstitions as astrology, talismans, numerology etc, think I share or am promoting them, and thereby completely fail to see the rational fractals of such beliefs: such is the darkness of our age.
I am certainly not accusing your readers of having such primitive conceptual spaces. The answers given before by James, Valerie (please say hi to Michael Schneider for me - we had an email exchange about a decade ago), Claudia and Maria were all within this same interpretation. Remembering Critchlow's book was about Islamic patterns, it is also interesting to note its Hindu and Buddhist interpretations as well, as only lightly touched upon in my site. For instance, the spine of nines is the sushumna, and the sevenths are the ida and the pingala. Much mathematical knowledge came westwards that way, with the Arab traders picking it up in India, and Fibonacci of Pisa picking it up in North Africa - and much of that was probably concomitant with this. To allege that Fibonacci was the first westerner to pick it up is unsustainable; better to allege he was the first known one, as much of this sort of thing was esoterically confined.
Naturally, the proportions of the vertical rectangle in Critchlow's diagram express the square root of three (which gets back to the Mystery of the Trinity, as explained in my site), but that rectangle also has an emergent figure from the Hindu faith: Shiva's drum - the lines joining its four corners. It is that same drum that appears in the Shiva Natraj and keep the universe ticking. In that cosmology, when the upward and downward triangles part, so ends the universe.
So, I affirm what Dr James McQuillan said before: the full figure "represents a) the Process of Creation (see my section on Genesis in the Star Key), b) the resulting Cosmos, and c) the presence of Christ who will by His Second Coming terminate the Cosmos": Christ being the Lord of the Dance, just like Shiva.
Rather a lot from a few scratches on a rock. But then, so there would be if you scratched e = mc². on a rock. There you go.
By the way, Do not imagine that such thinking is still not alive and well. For instance, check out the website on:
Abstracts of the Contributing Lecturers of the Fourth Miami International Conference on Torah & Science, The Kovens Convention Center, Florida International University, Miami December 18-20, 2001. http://www.borhatorah.org/home/conference/abstractscontr5.html
PS. After sending the message below, I also noted that the square of 19.111310 degrees is the number of days in a calendar year. I'm not sure how this would fit re the range of error possible in a carving of the scale of this one?
By the way, I had considered my Star Key to be an investigation into the history of religious epistemology. Nevertheless, it is interesting that it contains within the stars' projective powers (by successive interior or exterior inversions) towards those areas that mathematicians kicked and screamed against for centuries; zero and infinity.
Perhaps it still has interpretative potencies, as those in the link I gave would clearly believe.

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