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Sunday, 15 May 2011

Sacred geometry or playschool games?

Not long ago I came across this extraordinary web site:

and I have had some interesting Email exchanges with Geoff, the originator.  I was interested to discover the amount of effort which is put in by some mathematicians and "astroarchaeology" or "archaeoastronomy" researchers into understanding alignments, orientations, lunar and solar observations and predictions etc, with respect to Stonehenge and other sites.  I don't have a problem with Neolithic man lining up stones with horizon positions for summer solstice sunrises or midwinter sunsets, or even for lunar positions -- or even for the Pole Star in the heavens.  And I quite like the idea of Stonehenge and other monuments being astronomical observatories, calendars or maybe even calculators related to seasonal rhythms -- so long as these ideas are not stretched ad absurdam.  But I do have major problems with this strange thing called "sacred geometry" -- as preached by Gerald Hawkins, Alexander Thom, John Michell and Robin Heath, among others.  Richard Atkinson was VERY sceptical about all this sort of stuff, as was Aubrey Burl, and this scepticism is shared by many modern archaeologists like Clive Ruggles who have studied STONEHENGE.

Let's quote Matt Parker and refer to my previous post about Woolworths stores.  " any sufficiently large set of random data it is possible to find meaningless patterns of any required accuracy.”

In any set of points plotted on a map (such as a map of Neolithic or megalithic sites in the UK) you can simply skip over the vast majority of the sites that happen to be inconvenient, and home in on the few that happen to coincide with the lines or corners of whatever triangle or other shape that you choose to demonstrate as "meaningful."  The more data or plotted points you have, the greater is your ability to pull meaningless patterns from them.

Matt Parker had the locations of 800 Woolworth stores to work with.  He was still able to find close "fits" with his chosen lines, distances, and geometric shapes, just as Robin Heath and others have done with their maps.  The more random or precisely positioned points you have on the map, the greater the chance of finding "meaningful" patterns.  If you just plot standing stones, or Neolithic henges, on a map, some geometric patterns will be found; but if you then add long barrows, round barrows, causeways, etc, your data set is greatly enlarged, and more and more "patterns" can be "discovered." If you want to increase your prospects of finding patterns even further, you can add in ALL prehistoric features, or "meaningful points in the landscape", such as Carn Meini, Glastonbury Tor, Lundy Island, Bardsey island, Caldey Island, or the tips of peninsulas or river mouths.  You end up with hundreds if not thousands of points in the landscape, enabling you to find patterns everywhere, with close matches for triangles of various shapes and sizes, circles, straight lines, and curves.

You can play little games, just as they do in Playgroups and primary schools with very small children, by creating predetermined shapes (such as triangles of circles) and moving them around on your map with thousands of random points in it, and finding "fits."  If the points of your triangle do not EXACTLY coincide with the "meaningful places" on your map, you can explain this away by using some pseudo-scientific phrase relating to degrees of confidence, or by saying "the fit is accurate to within 0.5%" or "the fit is almost perfect" -- or even by saying that the map itself is inaccurate, or that coastal erosion since the Neolithic has moved your crucial point from A to B.  This is quite wonderful!  You can do almost anything, and find "meaning" and "ancient wisdom" or "sacred geometry" in almost anything, as Matt Parker has pointed out.

This is not science.  It is pseudo-science, pure and simple. Put another way, it is a little game that one might play with one's grandchildren.  What is amazing is that some people actually write books about this sort of stuff, and that people buy them and read them, and are apparently swept away into a state of wonderment.  What does it tell us about the human condition?  Well, it tells us, I suppose, that the yearning for a rediscovery of "ancient wisdom" is still as strong as ever, that people have a strong sense of spatial awareness, and want to find patterns or "sacred geometry" in landscapes, or order where there is chaos.  It also tells us that people are remarkably poorly educated and that they are just as gullible as our ancestors were in the Middle Ages.

Thinking of which, I have been dipping into Robin Heath's book called "Bluestone Magic" -- I am amazed, and I will shortly post a review.

In the meantime, and returning to the "Lunation Triangle" illustrated above, I discovered this in the field of "Geomantics":

Robin Heath -- "The Marriage of the Sun and Moon"


"The large Lunation Triangle, shown incorporated into a huge cardinally aligned 5:12 rectangle, includes the location of the bluestone site, and the exact north-south and east-west lines complete a right angled triangle via Lundy and Caldey Island. In Old Welsh, Lundy is called Ynys Elen, the 'island of the elbow, or right-angle'. I suggest that this may be the reason why Stonehenge is located where it is - as the only man-made construction in this geomantic message about calendar wisdom? (Figure 5.2, Sun, Moon & Stonehenge, page 76)"

Now what is all that about?  What on earth is this "Lunation Triangle" with sides 5:12:13?  We can remind ourselves that exactly this same triangle can be located in an almost infinite number of positions, with Stonehenge at one of its points.  It can be flipped and swivelled all over the map of Southern Britain, and fitted to an almost infinite number of other points on the map. Some of those points will be north, west, south or east of Stonehenge.  Amazing!

Robin is actually suggesting that Stonehenge was built where it is because it was the only point which exactly fitted this triangle, in exactly the position where he chooses to place it.  So he assumes that the builders knew what they were doing, or did something unconsciously, driven by some irresistible urge or geomantic guidance.  From whom or what?  All very strange.  Let's look at the triangle. I tried the same exercise, and the "Lundy point" is not on the island at all, but in the sea to the north-west.  And what about Carn Meini?  You can play silly games in the eastern Preseli, and put your point wherever you want it.  We know that the stones did not all come from Carn Meini anyway, but from at least 30 different places, including Pont Saeson.  If there was sacred guidance here, how come the source of all this esoteric guidance and wisdom got the geology all wrong? 

To quote Geoff:  "But how did they (the builders of Stonehenge) do it, if they actually did?  When was it possible to know you were on a Lat. as specific as 51 53 00?  The problem here is that the ability to have that kind of exactitude seems to postdate some apparent model activity - if there ever actually was any such model.  Things, names and people turn up at precise model points before the precision to do it existed.  And that's a puzzle.  It's almost worth conjecturing a pre-OS survey/mapping here, perhaps?  OS only really gets going after 1800 AD, but our model will find accurate activity from the 1750s and earlier - but then, as the investigation developed, I found some things that looked old were actually fairly recent in situ - and the more recent the placement, of course, the easier the explaining any accuracy - were such, of course, intentional."

Elsewhere in his writings, Geoff (in spite of being predisposed to accept much of this "sacred geometry" system of belief) finds things that don't quite fit -- with points not quite where they are supposed to be, angles just slightly awry from those cited with certainty, and other associations which sound very learned until you explore them in detail and find that they are just plain wrong...........

So what's going on here with all this geomantic / sacred geometry literature?  It is certainly packed with pseudo-science and mumbo-jumbo.  Are those who write it all down and flog it to a gullible readership just deluded themselves, or are they charlatans?  I couldn't possibly comment......


Tony Hinchliffe said...

Very interesting,Brian. You seem to be finding lots of instances where things are not QUITE an exact match, or not quite as they seem to be to the enthusiasts/ fanatics who peddle this stuff.Your example of how the Stonehenge/ Lundy Island straight line turns out (from your check-ups) to to be a near miss, ending in the sea is very revealing!

I have a Robin Heath/ John Michell specific example from down here in Wiltshire. My FIRST abiding interest is local history/ archaeology/ historical geography, so though I was at initially fascinated by these gentlemens' statements, I compared them to the more prosaic statements of that great academic local historian, Professor W.G.Hoskins, in relation to a site in the Vale of Pewsey, between Avebury & Stonehenge, at or near the village of Alton Priors.

Ken Watts' admirable book for walkers, "The Marlborough Downs" (2003), has a section on Anglo-Saxon Estate Boundaries. Watts states (p65):

"The Saxon estate boundaries often become parish boundaries and Professor Hoskins has drawn attention to their survival at Alton Priors on the south side of the Marlborough Downs where some of the boundary marks may still be seen. In Winding Combe (the Saxon "Woncomb) there is a reference in the Charter to a stone with a hole in it, and until recently we could see this large sarcen almost nine feet across complete with hole which the Saxon surveyor took as his boundary marker in 825 when he defined the boundaries of this estate which King Egbert granted to a Winchester church."

Contrast this with the Robin Heath & John Michell version of events from "The Measure of Albion", Bluestone (!#)Press, 2004, page 106

"Alton Priors church. Built on a mound with ancient yew trees, a large stone with a hole bored into it may be discovered under a trap door in the nave....over which the church was built. The stone has a large hole bored into it and is surely the original mark-stone. a surveyor's point on the Stonehenge- Avebury axis. It stands 25,920 feet from the start line at Avebury".

Two rather different versions of events, one prosaic and Anglo Saxon, the other Prehistoric and highly poetic, to put it mildly.
I wrote down the Robin Heath version in pencil at the front of my copy of Ken Watts' book, as a perpetual reminder not to be so easily seduced by 1970's New Age ramblings in future!

BRIAN JOHN said...

I tried another exercise many years ago, when ley lines were all the rage. I found that many of the "sacred sites" purportedly on ley lines were sort of / approximately / almost on them, but not quite. You could force these places onto the lines by using a very small-scale map and a VERY thick pencil. Enough said.

Constantinos Ragazas said...


I couldn't agree with you more on this. When I was five growing up in Greece I would often lay back on the grass with friends looking endlessly at clouds. Each of us could see many variety of 'gods and heroes' in the clouds. That each of us saw something different convinced me at a very young age that all these were just projections of our imagination.


Tony Hinchliffe said...

Cue some immortal lines about clouds from Joni Mitchell's "Both Sides Now" song, Kostas!

Tony Hinchliffe said...

Do all you Welsh Speakers actually concur with Robin Heath's claim that the Old Welsh for Lundy (see text), Yns Elen, DOES mean "island of the elbow, or right-angle"? Thought this might be worth checking. I was aware that Lundy derives from Viking for Puffin. Please confirm or not, someone.

Tony Hinchliffe said...

A colleague who worked in the print room of our Council had at his fingertips all the large scale negative maps of Wiltshire. In quieter periods, he was given to drawing lines between ancient monuments in various parts of our ancient land.

When he attempted to present his findings to the County Archaeologist, he was given very short shrift!

I guess this was another case of 'staring up at the clouds', metaphorically speaking, even when entombed in an airless municipal building.

BRIAN JOHN said...

Ynys Elen? Not sure where that came from. Rachel Bromwich, the expert on the Triads and the Mabinogion, says: "Ynys Wair (Gwair) was also an old name for Lundy island and I understand that this name for Lundy still survives in the speech of the locality." That sounds to me as if the old Welsh name was not Ynys Elen at all, but Ynys Gwair.

Gwair is a personal name. He was the son of somebody called Geirioedd -- mentioned in Triad 52..

BRIAN JOHN said...

Other people say that Lundy was called Ynys Elen, after a Welsh saint. There may also be references to it being Ynys Annwn -- as a gateway to the Otherworld. Or Ynys Nectan, who may have been the resident saint in the Age of the Saints. Elin (with the letter i) in Welsh means elbow, angle or bend. It doesn't necessarily mean a right angle -- and the word is not the same as the name of the Welsh saint.

Tony Hinchliffe said...

Sounds like the jury's still out on Robin Heath's "island of the elbow" claim. St Nectan. whom Brian has mentions, also has a Church dedicated to him/her at Hartland parish, that northern tip of North Devon known to Ptolemy etc as Hercules Promontery.

Tony Hinchliffe said...

I see that both the old and the newer Church on Lundy are indeed dedicated to St. Helen: so I think we can safely give Robin Heath's notion of "island of the elbow"..........the elbow!

geoffss said...

I am not, actually, wedded to any Sacred Geometry. My view is that that it is only termed "sacred" because so much of it is about religious sites.

Heath's 5-12-13 is nonsense because it is 2-D on a 3-D reality: take a piece of A4 and apply it to a tennis ball and see what happens to any right-angled triangle you may have on the A4.

You point your readers at my speculative Moving Menhirs page when your queries to me were about the Stonehenge Station Stones page and Robin Heath? Whatever, I found Robin's grid coordinates c/o his Satnav differed from mine c/o Multimap (which used to give OS and Atlas co-ords - so you you translate them, assuming the conversion was accurate). I have his Pembroke siting fairly near Temple Druid and Gors Fawr in the Preselis: using his figures I get, variously, SN123278 for SN132285 (Multimap's OS value for his co-ordinates) and (his GPS) SN126121 for which I get a (2-D) 5-12-13 based on his figures to generate SN137282. It might (or not!) interest you to know that the area was called "the thicket of Solomon" ... and the Lat. could be 51 55 15.
Shove all OS coords into OS "getamap" to see the various places.

Were you to duplicate Michell's Circle of Perpetual Choirs, then vesica it, then superimpose 2-D hexagon/pentagon maths, this is about where you would be.

I'd appreciate it if you'd do me the common courtesy of running any references to me by me before you air them in future.


BRIAN JOHN said...

Hi Geoff -- sorry if I have offended you or misrepresented you. Unintentional, I assure you -- I called your site "extraordinary" because I was (and am!) very impressed by the sheer amount of effort and mathematical skill you have put in to it. OK -- it's a sort of "thinking aloud" site -- but if you put it on the web, it's on the web, and people will look at it and comment on it. They can't refer back to you every time they make a comment. God knows what rude things people have said about my site here and there across the web and the blogosphere........

I don't think I suggested you were wedded to "sacred geometry" -- but I suggested that you were at least inclined to take it seriously. You must be taking it seriously to devote so much time to investigating it!

Anyway, none of this actually MATTERS -- so let's just enjoy some good-humoured debate.

david gregg said...

There is indeed a significant lunatic fringe associated with 'astroarchaeology' which allows sceptics to dismiss even significant results. However some of your comments surprise me. You label Thom and Hawkins as advocates of 'sacred geometry'
a label not to be confirmed from any of their writings. This labelling might give your readers the impression that their work, particularly Thom's, can be lightly dismised. Since these gentlemen died it appears to be open season on them ...with attacks often led by
'archaeological' academics who should know better and do not themselves hold back from unfounded hyper-speculation.

I am also surprised that you label as 'pseudo-scientific' attempts to apply statistics and probability theory to this area. A statistical approach is exactly the way to deal with a population of ancient sites...for example in trying to establish the existence or not of a unit of measurement or common underlying geometrical design principles. If statistics can identify such patterns then it matters not what one calls them.

Science begins with the detection of patterns. What distinguishes it from mumbo-jumbo is the step of testing the patterns to destruction against the data using mathematics. A third step is to seek to broaden the data base and repeat the testing, etc,etc. I am
surprised somebody with a degree, even if non-numerate, does not understand this.

Professor D P Gregg (retired)

BRIAN JOHN said...

David -- thanks for the post. It's always good to have comments from those who have not contributed before. I'm not sure I would agree with you about a lunatic fringe -- I would prefer to avoid the word "lunatic' and would prefer to see the views of certain people as misguided or mischievous -- or maybe as arising from an obsession with proving a theory, come hell or high water.

Regarding Thom and Hawkins, OK -- maybe I should not have lumped them together with Heath and Michell, but there doesn't seem to be much doubt that they were seeking to establish a sophisticated geometry for megalithic sites and a link with astronomical observations. So they should not have been surprised that their pursuit of ancient wisdom and "ancient geometry" led others to find something sacred in their numbers and patterns.....

I agree that current archaeologists have been having a go at both Thom and Hawkins -- but I'm not sure they are shown a greater degree of disrespect than is accorded to others who have passed on. Even greater disrepect is shown to people like Jehu and Judd.

You say: "I am also surprised that you label as 'pseudo-scientific' attempts to apply statistics and probability theory to this area". I do nothing of the sort -- I have great respect for statistical methods and theories in sorting out core issues and getting rid of the noise around the edges. What I DO find irritating is the mis-application of such techniques, in which data is manipulated and selected in order to fit into hypothetical patterns.

Please don't patronise me with accusations that I do not understand scientific method. You can test patterns and hypotheses numerically if you want, but very often to can demonstrate the falsehood of hypotheses simply by the process of observation on the ground.