About

Marina Graham

I was born in 1960 in England.  I studied French and German at Newnham College Cambridge before doing a BA Hons in Sculpture and printmaking at Bath Academy of Art. For 15 years I worked as a freelance artist, doing portrait sculpture, bronze figures and restoration work.  I spent some time living in Germany, France and Italy during the eighties and nineties but my home has mainly been Wiltshire in England.  Both my parents came from Longtown near the Scottish border where my wider family is still based.

I will eventually add pages showing my sculptures, which I have now also recommenced, although for the time being I am mainly occupied with this geometry.

 

The Geometry

Geometry is a natural extension of the work of a sculptor and since 2010 I have been engaged in a thorough investigation of the geometry of Avebury Henge, which is just a few miles from where I live.  To begin with I worked with a ruler, a compass and a pencil on A2 sized drawings on a Google Earth view of Avebury.

I soon realised I could never test my hypotheses about the geometry accurately enough to reduce potential ambiguities in its significance without the help of a very detailed aerial view of Avebury.  Fortunately I was given one.  It was incorporated into a piece of graphics software with layers showing the positions of the surviving stones, Alexander Keiller’s concrete markers, the missing stones and various other features.

A2-Book-Page-10a---Geometric-Patterns without text bottom

 

The Basis of the Research

My detailed graphics document was originally created by the writer Steve Marshall to assist him with his own research into the landscape of Avebury.   His book Exploring Avebury; The Essential Guide comes out in May 2016.  It contains many beautiful photographs and aerial views and a wealth of information on all the features in the landscape within a five mile radius of Avebury Henge.

He gave me a copy of his aerial view of the Henge with all the stone positions several years ago for me to use as a basis for my geometrical experiments.  All my research since then has been based on his original document.  Its northing matches the one on Alexander Thom’s Survey, which it was possible to insert as an overlay for comparison;  they correspond extremely well.   I have created hundreds of layers of geometrical drawings on top of it and these are the main body of my research.

The image of the aerial view of Avebury is very large.  In addition to this the graphics software measures the azimuth from due East of every line drawn on it to within one tenth of a degree.  It also allows for layers to be made transparent to different degrees and switched on and off.  This means that I can experiment with many different geometrical constructions, all based on the actual layout of the stones and earthworks, which can be made to show through from underneath or switched off, and I can compare the resulting patterns with one another and discover where and how they synchronise.

I compiled a table based on data from NASA.  It givies the lengths of planetary orbits of the sun and other cosmic cycles in days and various calculations based on them.  I then set about matching the geometrical patterns formed by the ratios between these cycles with the patterns I had drawn on the aerial view of Avebury by cycling its lines of stones around its geometrical centre.  This may sound arcane but it is in fact entirely logical, if a bit laborious.

Probably, one of the reasons no one has ever tried this before is that we are used to thinking of our stone circles as circles, even though we all know they are not round, and this has prevented people from recognising that the outer ‘circle’ at Avebury in fact contains many straight Lines.  Alexander Thom, despite the accuracy of his survey, still perceived these straight lines as very shallow curves.

The other reason it hasn’t been done before is probably just that it required a lot of maths as well as a lot of imagination, although there is actually no good reason why mathematics and imagination should not co-exist!

If the theory I put forward in my book is recognised to be correct, as I believe it gradually will be, then it is a discovery of major importance about a significant aspect of the purpose of Avebury.  It may have potential implications for other stone circles as well (although perhaps Avebury is unique) so it will also be important to recognise all the steps up to this point and all the people whose earlier hard work has made it possible to get here.

 

Previous Researchers and protectors of Avebury

If my theory is correct then it should shed light on the findings of archaeologists about the way the site was used by people during the Neolithic era.  If geometry is outside the usual domain of evidence any archaeologist would be expected to consider this need not be seen as a criticism of archaeologists;  I doubt that I would have got very far without them.  Nor however should it trivialise the importance of geometry.  I am confident that the bigger picture will eventually be visible and make sense to more researchers.

Because specific detail as to the purpose of the henges and stone circles in the British Isles has long remained unknown they have attracted a whole range of speculative ideas. Archaeologists established their true age as going back three millennia BC and therefore that they could not have been built by the druids of the iron age who the Roman invaders described.  Modern archaeologists are nevertheless indebted to the antiquarians John Aubrey and William Stukeley for their detailed records drawn and written before so many of the stones were destroyed, even though Stukeley also considered himself an archdruid and had mystical imaginings which archaeologists cannot accept as truth.

Archaeologists have had good reason to be sceptical of many things.  They remain sceptical of astronomy being suggested as a primary purpose for Avebury and Stonehenge. They do however see them as ritual spaces which appear to have been exclusively accessed by elites.

Alexander Thom’s survey of Avebury is still regarded as the most accurate one there is, even though his theories about the Megalithic Yard appear to have been dismissed as wishful thinking by a number of leading archaeologists.

Without Alexander Keiller who bought Avebury to save it from further destruction or Alexander Thom’s recognition of the element of engineering in the layout of Neolithic stone monuments I very much doubt that I would ever have done this study and made the discoveries I have made.  Without having seen the books of John North, John Michell and John Martineau I probably would not have had the inspiration and had it not been for the geometer Joan Moore telling me how she always followed the geometry wherever it led her I may never have completed it.

Actually I’m still working on it;  every time I think I’ve finished I discover more, although I have now filled in all the missing pieces in the jigsaw of Avebury’s lines and angles and the cycles they all reflect.

I am making some big claims here and fully expect these to be met with healthy scepticism from more critical and discerning thinkers.  Geometry is however mathematics, which can be demonstrated to work, and my full set of geometrical proofs will appear clearly in my book.   My work came to a near standstill  for several years while I looked after my mother during her battle with Alzheimer’s.    Now that I am back into this project with a critical eye, and having tested my hypotheses many times over, I feel confident that they amount to a coherent theory.

The fact that I am a sculptor and not an archaeologist or a scientist should not rule out the possiblity of my theory being logically coherent;  consider after all that if I make a dancing figure in bronze that stands on one toe then it must not fall on people and kill them, and that this must work in practice and not just in theory.  Consider also that sculpture is an ancient art that depends greatly on ancient science for its successful execution.

Lost wax casting of complex shapes in bronze is as subtle and as old a technique as is designing temples and maintaining calendars based on observation of the skies.  All of these things came originally from the minds of sculptors and architects, artists who observed their world and recreated its forms in temples whose highest priest was also the king.  Pythagoras learned everything he knew about geometry in Egypt, a nation of sculptors and architects.  No sculpture or architecture that stands up at all, let alone for millenia, exists independently of mathematics and logic.

It is however to the modern mathematicians who researched the Antikythera Mechanism that I owe my breakthough in understanding the geometry of Avebury, hence the name of my book.

The Antikythera Mechanism was made in bronze in about 200BC and was found in 1900 on a shipwreck near the Greek island of Antikythera on a ship thought to have been on its way to Italy.  Although the bronze was corroded so that it looked like one large lump it was discovered to actually consist of a number of gearwheels with hand cut teeth.

The Greek archaeologist who discovered the gearwheels believed it to be an astronomical clock but this was considered too complex for its time and so investigations into this idea were dropped until the British science historian Derek de Solla Price took an interest in it in 1951.  He published extensive findings on it in 1974.   In 2006 the Antikythera Research Project succeeded in clearing up a number of outstanding puzzles.   They were also able to produce clearer images enabling the greek text on the gearwheels to be read as never before, thereby providing written evidence for the precise numbers of teeth and the purpose of some of the wheels.

The BBC documentary about their research provided me with the solution to the biggest mystery that was bugging me about the persistent recurrence of certain types of numbers in the geometry of Avebury.

For this reason I have called my book ‘The Avebury Mechanism’ although in the case of Avebury the ‘mechanism’ is a theoretical one whose gearwheels reside in the geometrical patterns for which the stones in the outer circle form baselines.

The geometry of Avebury, though theoretical, is nonetheless real and precise, so I expect it to be at least mostly recognisable to the mathematicians familiar with the numbers and ratios of the Antikythera Mechanism, both of these things being based after all on the same cosmos.

I feel I can reasonably describe the Avebury Mechanism as an instrument that plays the music of the spheres, even though the music is in this instance not heard in the way the Pythagoreans claimed to be able to hear it but seen in the synchronisation of the geometrical patterns.

 

Two books have been written recently which are pertinent to my subject.

One is Anthony Johnson’s Solving Stonehenge, which came out in 2008, and which I have only just read because I knew he was dealing with the geometry and wanted to follow my own methods to their conclusion about Avebury before comparing this to his evidence and conclusions about Stonehenge.  His book addresses in depth the roles of both archaeology and geometry in understanding the architecture of Stonehenge.

The other important book is Nicholas Mann’s Avebury Cosmos, which builds on the work of John North before him in the sense that it puts forward a strong argument in favour of an important role having been played at Avebury by the rising and setting of certain stars and constellations.  This is a valuable book, which I also put off reading until my research was at an advanced stage.

I believe that my discoveries make sense in the context of these two books but since I have concentrated exclusively on geometry they go far beyond anything that either of these two authors would ever have expected to find.  The fact that I have concentrated exclusively on the geometry in my study should not be taken to mean that I consider other elements in the choice of location for the henge, such as the availability of water or the suitability of the landscape for farming to be unimportant, just that they are not part of a geometrical study.

Had I studied Stonehenge instead of Avebury, I think I may have stayed with two of the conclusions Anthony Johnson came to;

  1. that the builders of Stonehenge were using a type of Pythagorean geometry 2,000 years before Pythagoras.
  2. that they were engaging in the practice of geometry purely for its own sake.

I am very grateful to Anthony Johnson for having written his book and established within the academic world a theory that Pythagorean type geometry  is present in a British henge so that I am not the only person saying this is so!

I had concluded by 2011 that 1. was definitely true of Avebury, but without having read Anthony Johnson’s book.  I still think that Britain could possibly have been the original roots of the Pythagorean geometry.

For a long time I believed 2. to be true of Avebury.  It seemed bizarre but  an enormous effort and great numbers of people had clearly been involved in the pursuit of these geometrical patterns over very long periods of time.  Not only this but I could not escape the impression that they had found the peculiar numbers it kept generating highly amusing, if not absolutely hilarious.  For a long time it really did seem to me that this obsessive practice of geometry was a big game they played purely for entertainment.  It may have required a lot of people to hold hands and form lines, circles and patterns or they may have used sighting tools and marked points and fractions of circles out with sticks.  Sighting tools and sticks may have been an easier method than ropes on a site as huge as Avebury.  They had no television of course, and so I began to think that maybe the geometry was a form of regular sport.

But there is in fact a lot more information and complexity in the geometry of Avebury than in that of Stonehenge and so eventually it took me beyond these conclusions.

At the beginning I thought that by far the oddest thing about Avebury was the way it was absolutely infested with multiples of ten ninths.  It got to the point where I imagined people falling on their backs and laughing all around me every time I divided an angle into 360 or a length into a radius and got 1.11111’1′, 2.22222’2′, 3.33333’3′, or 6.66666’6′.   I began to regard these imaginary laughing people, and these numbers, as ‘the henge demons’.

The most puzzling question really though was this;  why set it in stone when it would have been so much easier to continue this pursuit with conveniently sized sticks?

 

The Big Breakthrough

Finally the thing that enabled me to make the most crucial breakthrough in understanding the patterns I had drawn and the seemingly Kabbalistic or even demonic numbers they generated was the BBC’s documentary on the Antikythera Mechanism.

I have called my book The Avebury Mechanism because of the similarity of my patterns and the way they synchronise with one another to the gearwheels of the Antikythera Mechanism with their hand-made bronze teeth.

 

The Reason

I am not an archaeologist or a historian. I am a sculptor who likes music and has an aptitude for learning languages.  Perhaps few people will expect that I will really be able to back up my claims with proof – but geometry, however it may relate to art and music, is ultimately a branch of mathematics, and there is no such thing as ‘maths fiction’, as I intend to demonstrate.

 

 ‘Mad Mathesis alone was unconfined,
Too mad for mere material chains to bind ;
Now to pure space lifts her ecstatic stare ;
Now running round the circle finds it square :

 

 

These lines from the Dunciad by Alexander Pope appear to speak of insanity but they also remind me of an experience I had in the late eighties while visiting Egypt.  The outlines of the pyramids are all indisputably straight triangles from a distance but they  transform themselves when approached into huge curved edges due to the effects of perspective when something of such size is seen by the human eye from close up.

While walking around the Great Pyramid about two yards from its sides an idea suddenly occurred to me – and I went and stood at the middle of one of the huge sides and looked up.  I howled with laughter;  what I saw was just as I had suspected;  a huge semicircle.

 

It was still square when I ran round it though!

Hahahahaha!

Rather like this, the geometry of Avebury is a language.  When read starting in the East, it takes on a startling narrative ability of its own and after millennia of silence it speaks again its many deep volumes of mathematical truth.

The Geometry of Avebury

The Avebury Mechanism; front cover design

 

.

The Book Itself

The proof copy of The Avebury Mechanism, which I am editing and printing at the moment, is A2 sized and contains over a hundred precise and detailed geometrical drawings with annotations and explanatory text.  There is a comprehensive index to these.

There is an introduction to the basics of the geometry, how I established the working centre, my methods of experimentation leading to the discovery of the patterns, their eventual decipherment and my discovery from these patterns of specific events in time, giving rise to the concept of the Avebury Calendar.

There are chapters explaining why I believe the Neolithic people went to such trouble to build Avebury at all when they could just have carried on using wooden sticks in the ground.

There is some speculation about the types of beliefs they may have based on their perceptions.  This has to remain open speculation since it is very difficult to cross the large void from ancient geometry to the oral tradition of the British Isles in the form it survives in, tantalising though it is to try.  Both Anthony Johnson and Nicholas Mann venture into this territory to some degree in their books and made some suggestions I either agree with or at least find plausible.  It is hard to resist adding some further thoughts on the subject, even though I am aware that we may possibly all run into errors which come from the particular perspective of our own time.

The main body of my book however will be ‘The Circumnambulation’.

This starts with the line of stones on the easternmost side of the outer circle and moves sunwise around it, examining by means of annotated drawings and explanations every angle the lines of stones make in the centre by crossing three significant circles and every angle between the radii to these lines.  All angles are considered in the light of the patterns they create when cycled around the circles and the cosmic cycles these reflect.

It will be seen that this process reveals a remarkable complex of endlessly interrelated proportions that is stunningly beautiful in itself.  These willin fact show themselves to be a complete account of the planetary and luni-solar cycles as perceived by the ancient Britons.  Whether this was still the astronomy of the druids at the time of the Emperor Hadrian I do not know but it would certainly have been something they would have wished to knew.

Once deciphered it is shocking, both in its simplicity and in its sophistication.  Nothing is left out;  the series of angles covers all the cycles, and after you have been round the circle once you can go round again and look into it in greater depth in relation to other circles.

A series of angles between the various radii covers ratios between the orbits of all the visible planets and adds up to 360º.

There will be sections in the book on the various axes running through the monument and on the orientation of other sites in the wider landscape with respect to its centre. One of these axes is very similar to the axis described by Nicholas Mann with reference to the stars of the Southern Cross, except that in the terms of this geometry it does not relate to stars.  (It would be interesting at some point to discuss this with Nicholas Mann because I think that at some point there was a shift in emphasis from stars to planets and I also think I know why this happened.)

There will be some analysis of the geometrical layout of other sites in the Avebury landscape as well as Avebury Henge itself.

The earliest origins of the geometry can be traced back to certain places.  One of the inescapable conclusions of my research is that a profound understanding of spherical geometry is evident from a very early stage in the Avebury complex of monuments and may have been a mature tradition even before they were built.

As well as hundreds of geometrical drawings the book will include photographs showing the planets and the sun and moon taken from within and interacting with the Avebury landscape.

 

Gramus Hyperboricus Publications © Marina Graham 2016   All rights reserved.

2 thoughts on “About

  1. Marina – You have clearly been working hard on this and I fully understand the fascination it has presented. I walked through along the Avon – Stonehenge to Avebury in May (then along the Ridgeway – Icknield Way) and with a bit of reflection and reading was soon upon the solar – lunar significance of it all

    To add into your investigations I feel there may well be a significance in the third portion of the solar year – 21 April and 24th August relative to the Winter Solstice particularly as Avebury appears to be aligned to a sunrise on these days (being the same alignment)

    http://suncalc.net/#/51.4285,-1.8545,15/2016.04.21/13:11

    In relation to this and the rolling sun on Silbury Hill I think the 21 April alignment works again when viewing the setting sun from along the Kennet – a correlation with the Croagh Patrick rolling sun phenomenon on the same dates helps this prediction

    Anecdotally there is mention to Silbury Hill Palm Sunday gatherings – the Sunday before Easter which is a movable feast of course but perhaps joins things up

    I wish you well with the publication

    Hope to hear from you

    Ian

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    • Thank you Ian.

      Sorry to take so long to reply! I am just getting back to the geometry since the equinox as it is a winter activity for me; something I do at night when the fire is lit!

      Your point about Avebury being aligned to dates which enclose a third of the solar year has set me thinking today for a good few hours…

      That diagram in your link is helpful and you have raised a very interesting point.

      The geometrical patterns I drew did eventually include patterns based on Avebury’s roads. The North and South roads produced a seventeen-pointed and an eight-pointed star respectively when cycled around a circle based on the top of the SE bank.
      The East and West Roads are not straight and so, although I imagined they were likely to have originally involved lunar and solar alignments I put off trying to base any patterns on them because, although Green Street is known to be at least medieval, it seemed likely that the roads would have moved a bit from any original direction. Green street also has elbows, one or two depending on which side of it you try to place a line.

      Eventually I did all the patterns anyway, on every possible direction, expecting a lot of work to produce meaningless results. Instead I got five cycles, all lunar.
      I left it there though and hadn’t yet attempted to consider Green Street from the point of view of the azimuth of sunrise indicated by its overall direction. Having just measured the direction of the main bit of it again (after the elbow) it gives an azimuth of 27° or 28° on the North side, and these produce lunar patterns when divided into 360°. However, if you subtract 28° from 90° it leaves 62° which is the maximum elevation of the Summer Solstice sun when it crosses the meridian at midday at our latitude of 51.4°, so here is at least one solar significance as well.

      To find the day when the azimuth of sunrise is 62° I have just used Stellarium again and this would be 6th to 8th May depending on whether you switch the refraction effect on or off (6th with refraction). However, if you take the azimuth from my geometrical centre to the North side of Green Street where it crosses the circle based on the SE bank it passes by the side of the huge recumbent Stone 73 at just over 70°and the dates with this sunrise azimuth are 21st and 22nd April, the same as you get from taking the general direction of the whole of Green Street, disregarding the elbow, as you seem to have done.

      So, it seems you are right. Avebury has an alignment to the 21st April (and 20th or 21st August).

      Why might this be? Leaving aside the sunroll for the moment, there is a simple mathematical reason, one which is also a very good example of Avebury’s inherent spherical geometry:

      I have just said that the elevation of the Summer Solstice sun on the meridian is 62° at latitude 51.4°.
      It is also true that on 22nd April (and 20th August) the maximum elevation of the sun crossing the meridian at midday is 51°.

      So it seems the reason for the alignment you mention is that the overall direction of Green Street from the centre of the circle indicates the azimuth of sunrise on the day when the max height in the sky of the midday sun is equal to our latitude at Avebury.

      Wheehee!! The whole thing is full of numerical reversals like that. They loved them! As an added bonus in this instance it also divides the year into three with the Winter Solstice being one division and the days when the height of the midday sun equals our latitude at Avebury being the other two. Unbelievable! But this is just typical of these ancient skywatchers, so in a way I’m not surprised.

      I need to get to grips a bit more with this luni-solar triangle on Green Street though. It might help me understand how their spherical trigonometry worked. It seems odd that they used the moon as well as the sun in calculations of latitude.

      I’m not sure whether this alignment is in any way connected with the sunroll or not. It seems unlikely at the moment but I wouldn’t dismiss the possibility entirely.

      Silbury Hill was built within the time when Avebury seems to have still been in active use. You can see some kind of a sunroll on it most times of the year, if you stand in the right place, and if the profile from your viewpoint is mostly open to the sky. The angle of sunrise or set isn’t always a perfect parallel with the side of the hill because it varies over the year by about 10°. The sunrise angle is steep at the equinoxes compared to the side of the hill, but the sun gets brighter as it rises due to the refraction effect, so it’s still very watchable and there are good scenic views to it. The first photo sequences I took of it were on the Spring Equinox 2009 but I had only just noticed the effect and so I just took the photos without having calculated any parallel.

      George Currie worked out a good parallel for a Silbury sunroll around 15th May in 2009 and a sequence of this sunset was photographed by Pete Glastonbury. It also works around the end of July from the same spot; George and Pete found a Neolithic viewpoint for their sunroll in the Kennet palisades. They do not claim that this proves that the effect was significant or intentional; they would say that it might have been noticed but it is clear that Silbury Hill cannot have been built in order to create the sunroll effect.

      I think this effect is likely to have been noticed by the architects after the hill was built.

      The nearer you are to the slope of Silbury Hill the more a bad parallel will show up (e.g. the sun will appear to get a flat tyre as it sets). You can get away with a lot more at a greater distance. It may be that once the builders noticed it they decided to use the effect from certain viewpoints. Maybe they even modified the slope of the hill accordingly, though I don’t know that there’s any evidence of this. In any case it works pretty well on the Summer Solstice from one of the Kennet palisades sites, and a line from there running towards Silbury Hill at the azimuth of Summer Solstice sunset can be seen on aerial maps of the palisades so this possibility can’t rightly be dismissed.

      George and Pete’s sunroll is the only one which has been calculated to establish a precise parallel with the side of Silbury Hill from the chosen viewpoint.

      In the Autumn of 2009 I discovered the sunbeams crossing the back stone in the West chamber of WKLB at sunrise on the equinox, and a year or two after George and Pete first did their sunroll I started going into West Kennet Long Barrow at sunrise to try to find out when the sunbeam that hits the back stone on the equinox from the south side of the ‘blocking stone’ would get in again from the north side of it.

      I started looking from around 1st May but no light was getting in. Eventually on 12th May and 15th May I saw that the sunbeam not only got into the barrow but into the south chamber as well. This looks impossible but it happens through an alignment of two small chinks. On the same evening of 15th May we were watching Pete G’s sunroll from the Kennet palisades.

      Silbury Hill was completed more than 1,000 years after the West Kennet Long Barrow. The azimuth of sunrise on the days (about four in a row) when the sunbeam gets into the South chamber of the WKLB starts at 58° and continues at least to 61°. The slopes of Silbury Hill do vary. It has been suggested that they average about 30° though I haven’t measured the exact angle from the horizontal of any of its slopes. The azimuth of the sunset on 15th May would be 30° South of West.

      The culture of the Silbury Hill people was not necessarily the same as the culture of the builders of the WKLB but it is of course possible for festival days to persist over many millennia and be adapted by a series of different religions.

      Christmas Day used to be the birthday of Horus after all.

      The Silbury Hill Palm Sunday gatherings also make sense in this context. Descriptions of them sound very like the Lughnasadh festivals said to have originated in Telltown in Ireland. If the year was divided into three then this would mean festivals on the Winter Solstice and around 21st April and 24th August as you suggest. I think this is entirely possible.

      Thank you very much for your thought-provoking comment!

      Marina

      Like

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