Megalithic Measures and Rhythms
Submitted by astro3 on Friday, 14 July 2006 Page Views: 16500
Alternative Archaeology
Excerpts of her correspondence with maths professor Jay Kappraff, twelve letters in all, are appended. One could wish her bibliography had included John Ivimy’s The Sphinx and the Megaliths, surely one of the more important works in tune with her endeavours.
It is good to hear a woman’s view on this topic, one whose work is marvellously infused with geometrical and musical considerations. The pages have John Martineau-type diagrams of regular geometrical figures imposed upon the megalithic structure-plans. Gerald Hawkins would have been the person to review this work, but alas that quiet-voiced elder has now departed. One would like to see an annual Anne Macaulay lecture set up, in which speakers grapple with these intractable and yet deeply important issues; and maybe combat in some degree the tides of Rugglesian scepticism now washing over academe.
Has she indeed discovered that the Megalithic Rod ( = 2.5 Megalithic Yards) ‘is identical to the ancient Greek fathom, which measures exactly seven Greek feet’ as the opening page of her text proclaims? Well, change ‘Greek’ to ‘Roman’ and it’s not a bad tie-up! As she writes, the MR = 6.80 Imperial feet = 2.072 metres while ‘The Greek foot is 0.296 metres.’ The great 19th-century metrologist Flinders Petrie found that the Stonehenge sarsens showed evidence for a foot in their construction, that was:
‘.. closely accordant with the Roman foot, which, though 11.64” in Rome, had a mean value of 11.68” ±0.01 in Greece, Africa & England. Not that this shows Stonehenge to be post-Roman, as the unit was the great Etrurian and Cyclopaen unit, originally derived from Egypt, and it may have been introduced at any date into Britain.’ [Ref 1]
Let’s here follow Petrie’s example, and also the advice which John Michell gives on this theme, of expressing the units in terms of English feet. If we use metres everyone will soon end up bored, baffled and bewildered. Taking Thom’s definition of the MY as 2.722 feet (and he reckoned he could obtain that four-digit accuracy) then one-seventh of a MR will be 11.66” i.e. a Roman foot.[Ref 2]
At this point, one wishes that AM had alluded to the precision measurement made by John Greaves back in 1639, of a ‘Roman foot’ kept in the Vatican garden in Rome. Greaves, an Oxford astronomy professor, found this Roman foot to be 11.66 inches [Ref 3]. This demonstates a powerful, four-figure tie-up for her fathom-MR argument, with the sole adjustment that it is the Roman not Greek foot that is involved. Let’s hope that some future megalithic-metrology conference will debate this matter. I like the fathom.
The Greek foot was between 12.16 and 12.17 inches, that being the ‘Olympic’ Greek foot: one hundred of these Greek feet comprised the width of the Acropolis and six hundred of them comprised a ‘stade’ equalling the length of the stadium (racetrack) in ancient Athens [Ref 4]. If we keep these measures in inches we may hope to avoid the dire error which reverberates through this book, of muddling up the Greek and Roman feet. One is less than the English foot, the other more, the two being forever interlocked in a 24:25 ratio.
Here’s a helpful comment by John Neal, the metrology expert: ‘It is glaringly obvious that the measures that were used in Britain were not introduced by any invader, or have any known source within recorded history. The Roman foot was in use in Britain in the Neolithic and the Bronze age … The Roman foot of .96 ft is known to have been in use from at least the third millenium BC, on the best of evidence.’ [Ref 5]
The diagrams are the meat of this work. That for the little-known ‘Milton of Clava’ at Inverness has a hexagon and pentagram define its circle radii. (p.43) [Ref 6]. AM explains, ‘The Milton of Clava pentagram [View Figure] is made using Fibonacci numbers and the central circle is formed by the junction of the arms of the pentagram.’ The two mean diameters given by Thom are in the ratio 57.8’/22.0’ = 2.627. That is the square of the golden ratio (to within 0.3%).
The presence of this pentagram-generated ratio in a Scottish stone-circle design is, I’d say, something more precious than gold or diamonds. I remain unconvinced, however, that this indicates a knowledge either of the Fibonacci series or of the golden ratio, as is here averred, on behalf of the megalith-builders. All it shows, is that the construction of a pentagram defined the ratio between the radii. How they constructed the pentagram, may not be known to us.
Only one stone remains of the alleged outer circle. AM’s construction thus directs further research, as to whether further remains can be detected, and will these give a radius estimate concordant with her regular-hexagon pattern? One could just say that this ratio is the square root of three - 100'/57.8' = 1.732 = √3 within 0.1%, but it might be better not to! The diameter of the main circle, measured by Thom at 57.8 feet, is meant to be 8.5 MR: at 8.494 MR that’s within 0.1%. [Ref 7] Marvellously, these precise geometric ratios lay unnoticed for millennia in a Scottish field, until Anne Macaulay came along. These megalithic mathematical constructs could well end up in math-history textbooks … in the first chapter!
This ‘Milton of Clava’ structure could be earlier than Stonehenge, or the pyramids. The British megaliths contain a first-beginning of human mathematics, and sceptics are going to have to harden themselves to face this disturbing fact. It is a theme of this book (as also of Ivimy’s Sphinx and the Megaliths) that the knowledge of the British megalith-builders (‘Hyperboreans’ [Ref 8]) infused into what became the Pythagorean tradition in ancient Greece.
At Shianbank in Perthshire [View Figure], two equal-sized circles lie some distance apart, and the line through their centres points to where the midsummer sun sets. Their tangents intersect at 45° (or, nearer to 46°): does that imply an octagonal pattern, and did the larger circles as shown in her diagram in any sense exist?
AM asks, ‘Would it be possible to examine the position of the unmarked outer rings with technologically advanced instruments, in order to search for possible wooden post holes … Neither Thom nor Burl had any idea of the size of the final geometry of these pairs.’ (p114) . Can traces be found to indicate that the two outer circles she has constructed, were an integral part of the design? She quotes Aubrey Burl, that ‘Paired rings such as these are not uncommon in central Scotland.’ The possible octagonal design here constructed has a wider interest, not least because of the presence of such at the core of the Stonehenge architecture, viz. its ‘station stone rectangle,’ linking the Aubrey circle of holes to that of the Sarsen ring of stones: did an octagon-design controll the size of its mighty ring of Sarsens?
AM quotes Thom as finding 104 MY as the diameter of Stonehenge’s Aubrey circle (its outer ring of holes), and taking a unit of 8 MY this will give the much-discussed 13-12-5 Pythagorean triangle in the ‘Station Stone rectangle,’ which stands on the Aubrey circle (p.52). Science historian John North found ‘No doubt’ [Ref 9] that the design of this rectangle embodied the MY units. The mean diameter of this circle is 104.2 MY [Ref 10] and so the measure of the 5-12-13 triangle may not ‘fit’ into it very exactly.
AM alluded to how ‘Keith Critchlow, the well-known authority on sacred architecture, recognised the presence of both an octagram and a heptagon on the Stonehenge plan, reinforced by the pattern of Aubrey holes: 7 x 8 = 56.’ [Ref 11] It is of interest to compare these constructions with the master-diagram of Stonehenge given by geometer John Martineau [Ref 12] [View Figure]. This shows, as its author tells us, how ‘the obvious eightfold geometry has been related to the astronomical siting of the site.’ This diagram links together the 5-12-13 rectangle, aligned to the Sun and Moon, and holding the Sarsen ring within it, with what is outside, the eight cardinal directions to which the monument is responsive. AM’s work surely deepens our ability to appreciate these things.
The notion of a star-heptagon construction within Stonehenge has seemed far-fetched [Ref 13], but if AM’s researches show that regular star-polygons are part of the design of British stone circles, then we need to reconsider it. A circle passing through the sarsen ring, through the centres of the stones, has a diameter AM found of 37.00 MY [Ref 14], a value remarkably close to that defined by the star-heptagon geometry, in fact within 0.3%. Using the above-given value for the Aubrey circle, a star-heptagon having its corners on every 8th hole in this circle intersects at a radius of 101.2’ or just over 37 MY diameter. In a sense this accord is too close, because the centres of the two circles, Aubrey and Sarsen, are two feet apart…
As Robin Heath suggested, we live today surrounded by mathematically-derived forms and dream about wild animals, whereas our early ancestors, surrounded by wild beasts, were attempting to dream about mathematics. AM’s book is about patterns in space not rhythms time, and barely alludes to astronomical rhythms. The symmetrical figures discerned by AM in the stones were a beginning of geo-metry, (earth-measure), and her work enables us to appreciate the scientia which did once exist, in prehistoric Britain.
Note on Mid Clyth: The most direct evidence for use of a unit of measure in prehistoric Britain appears to derive from ‘Mid Clyth’ in Caithness. Many rows of parallel stones there provide evidence for …what?. Heggie found that no-other UK site gave such strong evidence for an early unit of measure, adding ‘Thom found overwhelming support for a unit of 7.743 feet … It is a pity that this is not the megalithic yard, although it happens to be close to 20/7 MY.’ [Ref 15] AM proposed that this measure was equal to eight feet; these would then have to be, of 11.61 inches. This tends to endorse her seven-foot fathom, as equal to the MR, and shows the foot-unit used in megalithic-era Britain (p.39): ‘Roman,’ not Greek.
Megalithic Measures and Rhythms by Anne Macaulay is published by Floris Books and available from Amazon.co.uk.
At the time of writing, Dr Nick Kollerstrom was an Honorary Research Fellow at University College London in the Science and Technology Studies Department, read more of his writing on the Portal.
References
1. F.Petrie, Stonehenge: Plans, Descriptions and Theories, 1880, p.23.2. The 0.296 metres which AM cites, equals 11.65 inches.
3. J.Greaves, A Discourse of the Roman Foot, 1647, p.33.
4. www.ucl.ac.uk/sts/nk/stade.pdf
5. John Neil, All Done with Mirrors, 2000 p.105. See Note at end.
6. For a diagram of this formation see Thom and Thom, Megalithic Rings, Oxford, 1980 (collated by Aubrey Burl), p.248.
7. For frequency of occurrences of 1/2 MY, see Douglas Heggie, Megalithic Science 1981, p.49.
8. Or, 'happy Hyperboreans' as Gerald Hawkins called them, on account of their custom of dancing the night away to the sounds of the cithara, upon certain lunar periods, according to the Sicilian historian Diodorus: Hawkins, Stonehenge Decoded 1965 p.128.AM, p.178-182 discusses this ever-fascinating section of Diodorus' History: 'And there is also on the island both a magnificent sacred precinct of Apollo and a notable temple which is adorned with many votive offerings and is spherical in shape. Furthermore a city is there which is sacred to this god, and the majority of its inhabitants are players on the cithara.' That city, AM suggests, was Glastonbury, a mere forty miles from Stonehenge (p.179). On this view, its music-festival tradition is truly ancient! She interprets 'spherical' as alluding to astronomy, surely quite rightly; but alas does not comment on the way this text alludes to two different temples.
9. John North, Stonehenge, Neolithic Man and the Cosmos, 1996, p.329, p.478-480.
10. Euan Mackie, Science and Society in Prehistoric Britain, 1977, p.114: from, 283.6 feet.
11. Did he? He didn't do it in Time stands Still (1979), the only Critchlow opus here alluded to.
12. J.Martineau, A Book of Coincidence, 1995, p.107.
13. It was first proposed by C.A.Newham,.
14. John Michell (Ancient Metrology 1981, p.36) estimated the mean diameter of the sarsen ring as 100.83 feet, equivalent to 37.04 MY - agreeing to 0.1%.
15. Heggie (ref. 7), p.48.
Note: A review by Dr Nick Kollerstrom writing for the Megalithic Portal.
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