Andrew Gough's Arcadia

By Adrian Lodge Ph.D.

General Introduction

Rennes-le-Château dedicated Internet forums have frequently discussed the Grail Star geometry by Brian Ettinger. Looking through the forums of recent years reveals the geometry has met with almost complete rejection. Brian Ettinger persistently counters these rebuttals but never seems to convince the detractors. Correspondences have frequently degenerated into misunderstanding and name-calling. While such discussions may be entertaining for the neutral observer, this approach does not bring us any closer to solving the Rennes-le-Château mystery. When reviewing the Grail Star geometry, one could quite easily end up falling into the trap of subjective interpretation that this topic seems to encourage. Therefore, this article attempts to find a more objective method of determining artistic intent.

The article is divided into two sections:

The Grail Star geometry proposed by Brian Ettinger. This is in response to an official request by the editor of the Journal of the Rennes Alchemist and Mr Ettinger to review his discovery of a novel geometric figure in certain 17th century paintings and on a formation of islands and points of land in Nova Scotia.
A discussion on geometry and artistic intent that includes a scientific comparison of a number of geometric constructions.

Section 1

The Grail Star geometry by Brian Ettinger

1.1. Introduction

According to Brian Ettinger a number of Renaissance and Baroque paintings contain a geometric composition that hold the key to finding the lost treasure of Rennes-le-Château. Examples of these paintings include les Bergers d’Arcadie (Shepherds of Arcadia) by Nicolas Poussin (circa. 1640) and Saint Antony and Saint Paul in the Desert by David Teniers the Younger (circa. 1657). He proposes that the geometry hidden in these paintings conforms very well to a formation of islands and points of land in the Mahone Bay area of Nova Scotia, Canada. . . [1] Furthermore, when applied to an accurate map of that area will also perfectly co-ordinate with the infamous Oak Island treasure site which is located in the same bay. [2]

Mr Ettinger considers the most significant part of the geometry is a figure consisting of two circles, each enclosing an irregular pentagon. Both constructions are, other than their size and orientation, identical. The larger pentagon is tilted at 18 degrees anti-clockwise while the smaller is tilted at 21 degrees. Certain features found in les Bergers d’Arcadie (Louvre version) and Saint Antony and Saint Paul in the Desert supposedly define this arrangement (Figs 1 and 2). When superimposed upon the islands, the extended central axes of the geometry converge at the location of the Oak Island money pit (Figs 3 and 4). According to Mr Ettinger, the convergence angle is precisely 3 degrees.

Fig 1. The Grail Star geometry on les Bergers d’Arcadie

Fig 2. The Grail Star geometry on Saint Antony and Saint Paul in the Desert

Fig 3. The Grail Star geometry on a satellite image of the islands of Mahone Bay

Fig 4. The Grail Star geometry on a map of Mahone Bay

So why is Brian Ettinger so sure that the geometry he proposes is correct? A number of inferences may explain the basis for Mr Ettinger’s belief in his Grail Star geometry and, for example, its relationship with Poussin’s les Bergers d’Arcadie.

Oak Island, Nova Scotia supposedly has treasure buried there.
Mr Ettinger believes Arcadia was the original name for Oak Island, Nova Scotia. [3]
It is thought the Knights Templar buried a treasure hoard.
The Knights Templar are associated with the Rennes le Château mystery.
There is a connection between Poussin’s les Bergers d’Arcadie and the Rennes le Château mystery.
There is apparently hidden geometry in les Bergers d’Arcadie.
les Bergers d’Arcadie includes a reference to Arcadia.

Therefore, geometry on a map of the proposed site (i.e. Arcadia) pinpoints the site of the Knights Templar treasure hoard.

In addition, Brian Ettinger states he can use the Grail Star geometry to pinpoint the location of a ‘treasure’ in or around Rennes-le-Château. [4] However, he has not published proof of this on his websites (e.g. http://grailstar.4t.com) or on any public forums. The only reference is that the ‘treasure’ lies south of the village. [5]

1.2. A study of the Grail Star geometry on Mahone Bay

At first glance there is nothing in the arrangement of the islands that tells the observer to draw a precise irregular pentagon. Any number or size of irregular geometric constructions may be drawn.
The Rennes-le-Château environs (and Bornholm) have chateaux and/or churches with ‘lines of sight’ that at least suggest how the geometry may have been pinpointed. Where in Mahone Bay are there such structures? If such structures are present, do they correspond with key aspects of the geometry? Mr Ettinger does mention the presence of two stone glyphs that he believes pinpoint the position of the geometry. [6] However, if he is to convince others of the reality of the geometry, he will need to find a greater number of ground-based structures that directly correlate with the Grail Star figure. Since the geometry is not intuitive (i.e. it is not regular and therefore predictive), a greater number of ground-based structures would need to be found in order to reflect its complexity.
Without any structures to fix the geometry it can be moved a certain distance up or down, left or right and still cover the islands in question. Doing this means the lines will no longer converge on the money pit.
How can we be sure the convergence lines (see Fig 4) specifically point to the location of the Oak Island money pit? It is not enough to just point to it using a satellite photograph or a low-resolution map. At the scales used, the lines are probably equivalent to being over 100 feet thick. Furthermore, Oak Island is only a few millimetres across on both the photograph and the map.
To obtain the precise convergence angle, Mr Ettinger would have to know the distance between the Oak Island money pit and the specific points where the geometry and the islands correlate. How can a satellite image and a low-resolution map provide such accuracy? Furthermore, Mr Ettinger does not show how he derives the precise angles he quotes.

Mr Ettinger’s thesis is dependent upon the small chance of finding the Grail Star geometry not only in Mahone Bay but also in two seventeenth-century paintings. He is saying the appearance of one reinforces the presence of the other, but the strength of this argument diminishes greatly if there is no evidence for the Grail Star geometry in the paintings.

1.3. A study of the Grail Star geometry on les Bergers d’Arcadie

The first impression of the Grail Star geometry is that it appears to be an irregular arrangement of lines where any alignments with the features on both paintings are a) imposed by Mr Ettinger or b) purely coincidental. Here are a few examples for les Bergers d’Arcadie.

The top left vertex of the large pentagon is outside the painting.
A majority of the geometric lines do not coincide with any features in the painting.
The axis of larger pentagon only runs along the top few inches of the white shepherd’s staff. The line is completely misaligned with the main length of the staff. If Poussin intended this, then why did he not paint the staff so the line would fit?
Not all vertices of the pentagons touch the circumference of their respective circles. Bearing this in mind, what is the point of ‘circumscribing’ the geometry?

Mr Ettinger has anticipated some of the problems listed above with the comment: you won’t see all the parts of the geometry being pinpointed by features in the images either, this would make it far to easy to solve. [7] He also states the reason parts of the geometry are beyond the canvas is a simple ploy to make the solution more difficult. [8] Why would Poussin purposely make solving the geometry more difficult when it is already so incredibly hard to discover? What is the point of deliberately misaligning an already irregular geometry? Surely, on the balance of probability, it is more likely that a non-alignment is merely evidence that the proposed geometry does not exist.

Other problems include the immense complexity of the geometry that Mr Ettinger proposes. There are at least three additional complex geometric designs that he suggests were used to position the Grail Star geometry correctly. On presenting the complete les Bergers d’Arcadie solution he states that although it appears to be so complex as to be impossible. . . once broken down into its constituent figures. . . it is clear that they are all amply confirmed by the painting’s features. [9] However, he does not explain how he obtains these complex regular geometrical constructions. Indeed, it is hard to understand how the mathematical precision of regular and complex geometry perfectly creates his irregular Grail Star geometry.

A further consideration is whether the vertices of the geometry drawn on the islands correlate with key features in the painting. For example, the top left vertex of the larger pentagon points to an island, but on the painting, it rests outside the canvas. The bottom right vertex of the smaller pentagon touches the red shepherd’s staff, yet on the map it lays in the sea. Surely if any artist intended the Grail Star geometry, key features in the painting would reflect the position of each island.

Mr Ettinger has stated that the Grail Star geometry explains pretty much every major feature of the painting and that it is going to be very difficult to produce an alternate solution which will account for as many features. [10] So how does the Grail Star geometry compare with another proposed design?

1.4. A comparison of the Grail Star geometry with the Rigby pentagon

A previously published article has demonstrated that the length: height (aspect) ratio of the image-bearing part of les Bergers d’Arcadie is a close fit with that expected for a pentagonal rectangle. [11] So why would Poussin use a regular pentagon to construct the painting and then include an irregular and mismatched geometry? Is it not more likely that contained within the painting is another regular pentagon? The previous article discussed how Greg Rigby may have discovered just such a construction (Fig 5). [12] A cursory examination of the Rigby pentagon on les Bergers d’Arcadie shows:

All vertices lie within the frame of the painting.
All vertices touch the circumference of the circle enclosing the pentagon.
The circumference of the circle enclosing the pentagon aligns with some of the painting’s features.
The pentagon’s five sides, axes and chords intersect or align with a number of features in the painting.

Of course, much of the above analysis is subjective. What is required is a more scientific approach that will help us to determine the validity of the Grail Star and the Rigby pentagons.

Fig 5. The Rigby pentagon on les Bergers d’Arcadie (Louvre version)