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The Three Holy Maps

By Adrian Lodge Ph.D.

 

Title

 

Part One

1.1. The first meeting with Greg Rigby

Over the years, I have been fortunate enough to attend a number of the Saunière Society symposia run by John and Joy Millar.  They are organised in order to support the research carried out and inspired by Henry Lincoln into the Rennes-le-Chậteau mystery.  These meetings afford established and up and coming authors and researchers the chance to present their latest studies into the mystery to interested members of the public.  Newbattle Abbey, Scotland is often the setting for the longer symposia, which last three days.  The first evening (Friday) often offers a chance to watch videos related to the mystery, or to meet some of the authors who will be presenting talks over the weekend. 

On one occasion in 2000, when attending the Friday evening’s events with a friend, I overheard that someone called Greg Rigby had discovered pentagonal geometry in Nicolas Poussin’s masterpiece, The Shepherds of Arcadia.  I was rather interested by this because I had been studying the painting on and off for a few years.  Although Greg was not present that evening, I knew that he was scheduled to give a talk on the Sunday afternoon.  However, his presentation was not to be on geometry in the painting.  This meant that the only way to ascertain what he had discovered would be to approach him and ask. Unfortunately, I am of a shy disposition, and anyway as I am wont to do, I then proceeded to forget all about it!

The following afternoon, oblivious to my intentions from the day before, I was sitting amongst a packed audience, waiting for the start of a talk.  The only seat that I could see left available was one directly in front of me.  Just as the speaker was about to begin, the seat suddenly became occupied.  Immediately, I thought that I recognised its occupier – by an amazing coincidence, it was Greg Rigby!  Suddenly reminded of what I had to do, I waited until the talk had finished, and then managing to put my shyness aside, introduced myself.  Greg confirmed that he had indeed found geometry in the painting, and to my surprise, volunteered an impromptu demonstration of his discovery.  He then took a small group, including my friend and myself, to another room where there was less chance of being disturbed.

 

1.2. Demonstration of the geometry

Greg began his demonstration by showing the completed pentagon first.  The construction appeared smaller than the famous pentagon discovered in the 1970’s by the late Professor Cornford of the Royal College of Art (Fig 1).

 

Fig 1. Professor Christopher Cornford’s analysis of the painting The Shepherds of Arcadia by Nicolas Poussin

 

However, like Cornford’s discovery, it too appeared regular [1] in shape, but without checking its internal angles I could not be sure.  He then mentioned how he had always been unconvinced by the Cornford pentagon because it was largely outside the canvas [2]. He was more interested in looking for pentagons whose shape lay entirely within the frame of the painting.  Before Greg described how he constructed the geometry, he stressed that, as he had no plans to publish his findings, he did not mind what anyone did with them.  I then thought it worthwhile remembering the key elements involved in constructing the geometry.  I made no notes but I did attempt to remember the order and position of as many of the alignments that I could. 

According to my memory of events, the first thing that opened Greg up to the possibility of concealed geometry in the painting was his observation of a thick dark mark running almost vertically down the white shepherd’s robe.  He described how he had drawn a line along this particular feature, and to his surprise found that it appeared parallel with the red shepherd’s staff.  A line when drawn along the length of the red shepherd’s staff seemed to confirm this.  Feeling inspired by this discovery, he then looked for other features that would encourage alignments or intersections.

The next thing he noticed was that a number of lines drawn through some of the painting’s features, interacted with these two parallel lines (Fig 2).

 

Fig 2. Lines drawn through some of the key features mentioned in the text

 

One line passed through some point in the region of the white piece of clothing that rested on the top of the left shepherd’s arm.  It then went on to intersect at a point where the red shepherd’s staff, a cloud, and the sky met, before passing through the shepherdess’ eye and then aligning with a branch of a tree (Fig 3).  Further examples included a line through an arrow-shaped point of the shepherdess’ yellow robe, and a separate line through a groove in the central mountain range.  Gradually, with the addition of more and more lines, a pentagon began to take shape.  Once complete, it became apparent that the pentagon had its centre near the blue shepherd’s thumb.  I was certainly impressed, but thought it best not to come to any conclusions about whether the artist actually intended it.  I thought it better to wait until I had the chance to replicate the geometry myself, and then study it over a longer period. 

 

Fig 3. Extension of one line showing its alignment with a branch on a tree

 

1.3. Replication of the geometry

When I returned home from Scotland, I obtained a copy of the painting, in order to set about reconstructing the geometry [3].  I started with the assumption that any pentagonal geometry present in the painting would be of a regular rather than an irregular shape.  I drew support for this from Professor Cornford’s analysis of the painting,which I felt provided excellent evidence for Poussin’s ability to construct regular pentagonal geometry [4].  However, as I reconstructed Greg’s pentagon from memory (Fig 4), it became clear that his proposal had a quite irregular shape. 

Finally, though, after much trial and error, I managed to incorporate a regular pentagon in the painting that I was satisfied with (Fig 5).  This meant replacing or losing some of Greg’s alignments.  For example, the line that ran through, or along the top of, the white piece of cloth (before aligning with a branch of a tree), now passed below this, through a point where the cloth and the arm met.  This meant the line no longer aligned with the branch of the tree furthest to the right. 

 

Fig 4. A rough version of Greg Rigby’s geometry drawn from memory and showing alignments and intersection points [5]

 

Fig 5. My final interpretation of the Rigby pentagon

 

Although I could not recall whether this was part of the original geometry, a further inclusion I made was to circumscribe the pentagon with a circle.  I felt confident in including the circle due to the way it seemed to fit around the curved outline of the central mountain range (Figs 6a and 6b).  Thinking that what I had created was a true reproduction of what Poussin had intended (and Greg Rigby had alluded to), I then proceeded to present it in articles as the ‘Rigby pentagon’ (called as such because Greg had been the inspiration behind its discovery).  

 

Fig 6a.  Close-up of part of the circle circumscribing the geometry

 

Fig 6b.  Close-up showing alignment of the circle with mountain peaks (arrowed)

 

Part Two

2.1. Would the real ‘Rigby pentagon’ please stand up?

Some years went by, and I began writing up my studies in the form of a book.  I decided that a worthwhile part of one chapter would be a discussion on how I began my research into the painting.  Although I felt reasonably confident of the chain of events, I did however start to question the accuracy of my recall of Greg Rigby’s demonstration.  I thought that the best solution would be to contact him via email and ask if he could send me details of the geometry as shown to me back in 2000. 

In an email to Greg dated 16 February 2007, I wrote:  

. . . I would love to know how different your original geometry is compared to that which I have drawn from memory.  It would therefore help me greatly if you are able to send me details (e.g. a photocopy) of the original geometry . . .

I then asked a number of questions, including:

What prompted you into making the discovery, e.g. what key features in the painting alerted you to the possibility of a concealed pentagon?

and, . . .  did a circle circumscribe your original pentagon?

A few days later, I received a reply from Greg.  He stated that he was posting me the papers that he had used for a geometry presentation at one of the Saunière Society meetings some years before.  In answer to my questions he wrote,

The key feature in the painting was the fold in the clothes under the arm of the standing shepherd. 

and, . . . a  circle did not circumscribe the pentagon.

His answer to the first question totally surprised me.  What did he mean that the key feature was the fold in the clothes under the arm of the standing shepherd?  I had been under the impression that it was the thick dark line on that same shepherd’s clothing.  I also found it interesting that he had not circumscribed the pentagon with a circle.  This would explain the slight irregularity of the pentagon constructed.  If he had placed a circle around the pentagon, then not all of its vertices would have touched the encompassing circle.  Only a regular pentagon has this attribute.  Meanwhile, I waited in anticipation for the delivery of the package.  Finally, one week later, the package arrived from the U.S.  To say I was unprepared for what arrived is an understatement. 

On the first page of the document, I noticed a photograph together with notes for a presentation titled, The Poussin Connection (Fig 7).  Greg wrote:

I have always been intrigued by the claim that there is a connection between the ‘Et in Arcadia Ego’ painting [6]by Nicolas Poussin and the mystery of RLC.  At the same time I have been sceptical of the popular representation of a connecting pentagram with three-quarters of itself drawn outside the boundaries of the painting itself.  For these reasons, I examined the painting in an attempt to discern a more obvious and appropriate pentagram. . .

 

Fig 7. Photograph taken from Greg Rigby’s notes titled, The Poussin Connection

 

The initial thing I noticed was there was indeed confirmation of the use of the thick black mark on the shepherd’s white robe, the line through the shepherdess’ eye and the arrow-shaped part of her yellow robe (Figs 8 - 11).  However, there seemed to be more differences than similarities.  The most obvious features were the pentagon’s size (i.e. it was smaller), that it only touched the red shepherd’s staff (instead of being in alignment with it), and that there was a direct interaction with a black mark in the white shepherd’s armpit.  This latter feature was what Greg was referring to as what prompted him into making the discovery of the geometry.  He further wrote,

Observe the shepherd standing on the left of the tomb.  He appears to have the corner of a . . . pentagon . . . tucked under the arm that is leaning on the tomb. 

A further difference I noticed was that the central part of the red staff interacted with the geometry and not its left edge, as I had originally believed. 

 

Fig 8a. Page from Greg Rigby’s notes titled The Poussin Connection

 

Fig 8b. Page from Greg Rigby’s notes titled The Poussin Connection

 

Fig 9. Close-up of the line aligned with the black mark on white shepherd’s robe

 

Fig 10. Close-up of the line intersecting with the red shepherd’s staff and cloud before passing through the shepherdess’ eye

 

Fig 11. Close-up of the line intersecting with an arrow-shaped point on the shepherdess’ robe

 

Although there were similar foundations to both geometric proposals, I found the many differences baffling.  How could Greg’s and my recollection of the demonstration back in 2000 be so different?  How could I rectify the situation?  The only recourse was to try to arrange a meeting with Greg in order to sort out the confusion.  I saw an opportunity for this, because he had mentioned in an earlier email that he was intending to return to the UK in a few weeks. 

Before I sent yet another email to Greg, I looked to see if I might have missed something.  Could there be a connection between the two proposed pentagons?  To find out, I overlaid one geometry over the other.  The first thing that I noticed was a common line that ran along the dark mark on the white shepherd’s clothing.  I then measured the two constructions and to my surprise found that the sides of the larger (R1 – the original ‘Rigby pentagon’) geometry were near identical to the length of the chords of the smaller geometry (R2).  Remembering that the ratio between a pentagon’s chord and its side is equivalent to the divine proportion (or golden ratio, i.e. a ratio of 1.618:1), this meant that the difference in size between the two pentagons was therefore also equal to this ratio.  With this discovery in mind, I then decided to add this detail to the next email that I was writing to Greg.  In addition, I explained my position, detailing the main differences and the few similarities between the two geometries, and asked if we could meet when he returned to the UK. 

I wrote:

Overlaying the 'Poussin Connection' geometry (R2) on the painting (using a half-scale size of the painting) gives a clear interaction with the 'Rigby pentagon' (R1), although R1 has to be corrected slightly and there is an inevitable loss of some of the alignments you noted. However, more importantly, the corner of R2 is still tucked under the arm of the shepherd leaning on the tomb. . .

Another . . .  find is . . . the difference in size between the two pentagons appears equal to the Golden Ratio. This is an appropriate result for a shape such as the pentagon, because its construction infinitely creates the very same ratio!

Below, figure 12 shows the corrected R2 geometry.  It is ‘corrected’ in the sense that the pentagon is now regular (i.e. contains pentagonal angles).

 

Fig 12.  The corrected R2 geometry - with one corner tucked under the arm of the shepherd leaning on the tomb

 

After further correspondence, we then made the final arrangements to meet up when he came to England.  The month would be May, the place Birmingham.

 

2.2. The second meeting with Greg Rigby

After Greg met me at Birmingham New Street train station, we went to the Bella Italia restaurant for lunch.  For most of our time there, our conversation centred on our mutual research interests.  He told me about the books he was in the process of writing, and I filled him in on aspects of my research.  After a thoroughly good meal, we moved on to the foyer of the Burlington Hotel.  It was here that we discussed the main reasons for our meeting – that elusive Rigby pentagon (Fig 13).

We soon found a suitable place to sit and I started the discussion by reiterating my confusion over my memory of his geometry demonstration back in 2000.  I then showed him my interpretation, and asked him what he thought.  He did not seem that surprised with my recall of the events.  He seemed happy to accept that I had in fact described a geometry that he had long since forgotten.  I then let him arrange on the painting my interpretation of the geometry which I had drawn on acetate.  I wanted to observe how he aligned it with the red shepherd’s staff.  I did this because I still had not established which side of the staff he had used – left, right or centre.  Immediately, it was confirmed that he did not use the left hand side of the staff as I had done, preferring instead to align a pentagonal side or chord down its centre (i.e. the line demarcated by the shadow running along its length).  The reason I felt this was important was (besides the obvious need to establish the pentagon’s position) because I felt the actual dimensions of the pentagon were a necessary component to understanding the artist’s intentions.  This was a conclusion I had made based on my many years of examining the painting’s geometry, a factor I feel considered by far too few researchers [7].

 

Fig 13.  Greg contemplates the painting during our meeting at the Burlington Hotel, Birmingham in May 2007

 

Part Three

3.1.  Artistic Intent?

So, the question remains were either of the proposed geometries intended by the artist.  A statistical analysis of the original (R1) pentagon has suggested there were significant grounds to consider it intended by the artist [8].  However, how much faith can we put in the R2 geometry? Can we make an informed opinion on whether Greg Rigby’s geometry (R2 – before ‘correction’) or my attempt at the geometry (i.e. to make it regular) are what the artist intended?  If one considers the number of alignments and intersections, then the answer in both cases is no.  However, is there more evidence available implying artistic intent that we need to consider?  The answer to this is yes. 

 

3.2.  A clue pointing to a new pentagon

“. . . we have hundreds and hundreds of drawings by Poussin – thousands and thousands including his contemporaries – now, not in one of those is there any evidence of a geometrical armature, of angles, of precise proportions being laid down – either at the deeper level or at the top level.  It’s not there.”  Professor Martin Kemp [9]

Is it true, that there is no evidence of a geometrical armature, of angles, of precise proportions in the painting?  In an earlier article, the accuracy of this statement was examined [10].  It showed that Poussin had left on the painting a clear and unambiguous line demarcating the precise position of the white shepherd’s staff.  From this, the importance of such precision became clear when it was used to position further pentagons in the painting. 

That is not all though, because if we magnify the painting in the region around the fold under the white shepherd’s arm, we see two lines that meet at an angle of 108 degrees – a pentagonal angle (Figs 14a - c).   The fact these lines are so close to the mark under the arm gives credence to the validity of further pentagonal geometry in the painting.  Could it be that Poussin included as a clue, the arrow-shaped mark merely as a pointer to this line?

 

Fig 14a.  Enlargement showing the fold under the white shepherd’s arm

 

Fig 14b.  Enlargement of the fold under the white shepherd’s arm showing two lines meeting (arrowed)

 

Fig 14c.  Enlargement showing that the lines meet at an angle of 108 degrees

 

divider

 

Notes:

[1] A regular pentagon contains angles of exactly 18, 36, 54, 72 and 108 degrees.

[2] This is somewhat of a misunderstanding since a pentagon is constructed from an infinite number of smaller pentagons, each reducing in size by the relative proportion of phi2:1. Therefore, although it is true that a substantial part of the Cornford pentagon resides outside of the canvas, the majority of the subsequent daughter pentagons lie within it.

[3] Obtained from Mezzo Mondo Fine Art Ltd, Jersey, California, U.S.A.  It is a little over one-half the size of the actual painting.

[4] The study by Professor Christopher Cornford detected in the work the presence of a regular pentagon.  In order to form a regular pentagon the painting's length and height need to be in the ratio of 1.3764 to 1 (i.e. 1/tan 36 degrees).  This ratio produces what can be termed a pentagonal rectangle; see Lodge, A. Geometry in Poussin's les Bergers d'Arcadie, Journal of the Rennes Alchemist, Vol. 2, Issue 6, June 2004, pp. 15 - 34.

[5] These are mainly arbitrary points that Greg Rigby may or may not have used, and some lines may be a 'better fit'.  Furthermore, a number of the lines interact with key features used in the final interpretation of the Rigby geometry.  For the definitions of 'alignment', 'intersection' 'goodness of fit' and 'key feature', see http://www.andrewgough.com/geometry2.html

[6] Et in Arcadia Ego is another name by which the Shepherds of Arcadia painting is called.

[7] Measurements for the Cornford pentagon and the painting were mentioned in Poussin's Secret (1995, David Wood and Ian Campbell). They suggest that the artist deliberately chose the dimensions of the painting and the pentagon to produce multiples of simple integer values, i.e. 18 and 36 inches - measures that would be easy to produce. Although not agreeing with this aspect of their conclusion, I do think that Poussin intended the painting, Cornford and Rigby pentagons to be of precise measure.  This deduction can be easily proven using clues provided in the painting itself.

[8] See the Journal of the Rennes Alchemist, Vol. 3, Issue 7, October 2004, pp. 9 - 23.  It was subsequently published in Italian as Geometria ed intento artistico nelle opere pittoriche in Indagini su Rennes-le-Château, Guigno 2006, Numero 1, pp. 25 - 36.  An updated English language version (May 2007) can be read at http://www.andrewgough.com/geometry.html.

[9] Quote by Professor Martin Kemp formerly of Oxford University, and was transmitted in the BBC Timewatch programme History of a Mystery (1996).

[10] Lodge, A. Geometry in Poussin's les Bergers d'Arcadie, Journal of the Rennes Alchemist, Vol. 2, Issue 6, June 2004, pp. 15 - 34.

 

Acknowledgements

I would like to thank Greg for giving me access and permission to use his original notes for this article.  Also, thanks are due for agreeing to meet me in Birmingham - I had a thoroughly enjoyable day.  Special mention must go to the tasty Italian meal, and of course his being such excellent company. 

 

About Greg Rigby

Greg Rigby is the author of On Earth as it is in Heaven (published in 1996).  The book discusses the influence of the constellation Ursa Major (The Great Bear) on the builders of the Gothic cathedrals of Northern Europe.  It proposes how a series of Druidic patterns linking these cathedrals provided the foundation for the Grail legends we know today.  Greg connects, for example, Stonehenge, Avebury, and Jerusalem with the position of an ancient Paris meridian.  He also claims an awareness of this Druidic pattern by the first Cistercians, together with a direct link with the village of Rennes-le-Chateau. 

He has given numerous talks at Saunière Society symposia regarding subsequent developments in his research.  He is currently working on a number of further books, for example, applying gematria to decode the Book of Revelation.  He feels he is now at the stage where he can show how an interpretation of the northern stars and the shapes they contrived led to the creation of the Egyptian/Hebrew/Christian pantheon.

 

 

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