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Megalithic Mathematics 9.

Avebury- alternative designs.

3.9.1  Thom's Avebury design may not be the only approach to resolving this complex figure. Below is an alternative proposed by John Smout, a London designer. For the full development of this alternative please go to John Smout's website and download his Macromedia Flash presentation: jsdesign.co.uk/avebury2

John Smout, 2004.

Arguments against a rational design for Avebury's great stone ring. 3.9.2  Archaeological thinking on Avebury does not favour the likely hood that the outer stone ring has been laid out to precise arcs. Rather it is believed that the ditch was originally dug by several parties, working independently and somewhat sloppily, creating their best efforts at circularity. The stones of the outer ring were then thought to have been erected in a best-fit pattern following the line of the ditch.

3.9.3  However the discoveries of Harold St. George Gray made during five seasons of excavations of the Avebury ditch between 1908 and 1922 do not suggest a haphazard approach to the construction of this great earthwork.

Aubrey Burl. 'Prehistoric Avebury'. p63. The walls also were well cut and Gray wrote of 'no toolmarks on the walls', a 'vertical and smooth face', and the 'finest example of cut chalk', and he wondered how it had been possible to break away and work the solid, dense chalk with tools of antler. 'The hardest chalk must have been loosened, at least to some extent, by the blows of flint hammers and mauls.'..........the floor uncovered nearly ten metres below ground level, so deep that had a telegraph pole been stood upright on the bottom it would not have shown above the top. To someone standing on the floor, the rim of the ditch would have been higher than the chimney-pots of a modern house. It was obvious that the prehistoric diggers had taken great care in their work. Although the ditch varied a lot in depth yet in cutting after cutting near the entrance Gray's workmen came to a floor so smooth that sections might have been levelled using a water-trough as an improvised spirit-level.

Only in Cutting VIII near the Barber's Stone and farthest from the entrance was the floor irregular, perhaps because of the 'poor quality of the rock in this position, which consisted of a soft, smooth, rotten, pale greenish-grey chalk'. This desire to create an impressive, well-finished entrance was emphasised in the workmanship uncovered in Cutting IX on the eastern side of the causeway. Here the ditch was even deeper, a full eleven metres below the surface, and the almost sheer lower faces had been 'squared off with the sides of the fosse [ditch], and not rounded off. The face of the solid chalk was excellently cut'.

Gray also noticed an apparent pathway along the inner edge of the ditch-bottom trodden by workers carrying rubble to the ditch-end where baskets were hauled up by ropes that left 'two very shallow open channels, or "shutes" scored in each corner.

3.9.4  The primary turf bank core. A further critiscism to theories of intentional design is presented by archaeological examination of the low pre-cursor bank discovered underlying the present great earthwork. This small heap of turves is thought to be an initial marker bank laid to delineate the course of the great bank later heaped over. It is thought that parts of this bank lay exposed to weathering for perhaps up to 100 years before the present great bank was completed and the stones of the great ring erected.

Aubrey Burl. 'Prehistoric Avebury'. 1979. '..........excavations by Major and Mrs.Vatcher on Avebury's bank near the west Entrance showed that, just as Leslie had recorded in the Meux cutting on the opposite side of the earthwork, there had been a primary turf core at the heart of the bank with layers of rock and soil above it. This could have been an earlier bank but as it was set so far back from it's little ditch with an unnecessarily wide stretch of ground between them it was more probably put up as a guide line for the people who later heaped the huge bank-dumps over it. This would have taken years. Much of the marker bank would have become grass-grown over the generation or so before it was covered but if the imposing North and South Entrances were constructed first this would explain why Gray's bank-cutting near the entrance had no trace of an internal turf-line. Grass would not have had time to grow before the ditch was deepened and the final bank built. If this interpretation is correct then it follows that the design of Avebury was based not on the shape of the megalithic rings or of the present ditch but on the inner, concealed core of the bank.'

3.9.5  This observation of Burl's would seem to contradict the notion that the great bank was thrown up without a considered guide. The small turf pre-cursor bank may have been located with reference to the great ring which was first laid out with timber markers as could the inner edge of the great ditch where the work would commence. It may have taken several decades to complete the digging of the ditch and heaping of the bank but a timber version of the great ring could well have survived intact for this period. Oak and European larch stakes many decades old can still be found giving good service in fences not yet entirely replaced by vacuum tannalised timber. Such stakes would not have measured more than 6 inches thick originally.

3.9.6  The inner rings. The inner circles of the Avebury complex are generally believed to be older than the great outer ring of stones. Arguments to the thesis that the outer ring is laid out with a series of precise arcs point out that the presence of the older, inner rings would hamper rope-and-stake scribing of the arcs.

3.9.7  Whilst this is true it is not unthinkable that these stones could have been worked around. If rope-scribing the radii could be laid between the stones to draw sufficient short stretches on the intended perimeter. If a more mathematical approach was employed the practice of off-setting may be used to work past obstacles in order to locate accurate points on the perimeter.

3.9.8  Limits of rope scribing. A greater obstacle to rope-and-peg scribing of the great ring of Avebury is pointed out by Thom himself. He does not think that arcs of these dimensions could be laid to the precision found using ropes nor even modern surveyor's tape.

A.Thom,'Megalithic Sites in Britain' p.1 The surveys must be made with the same accuracy as was used in the original setting out and it will be shown that some sites, for example Avebury, were set out with an accuracy approaching 1 in 1000. Only an experienced surveyor with good equipment is likely to attain this kind of accuracy. The differences in tension applied to an ordinary measuring tape by different individuals can produce variations in length of this amount or even more. The necessity for this kind of accuracy has not in the past been appreciated and has in fact only become apparent as the work recorded here progressed.

3.9.9  Thom has surmised that these large arcs could only have been established by a mathematical method of survey. He has suggested that the builders had a good working knowledge of the relationships between the chord of a circle and it's sagitta. See Maths 8, 3.8.10.With this understanding, and the ability to section circles accurately, as seen in the D, egg and compound rings, a simpler construction approach to the Avebury outer stone ring may be suggested. On the following page a construction set for this ring is proposed which requires no long rope scribing. It depends on accurate base line surveying with sighting through ranging poles and may throw some light on the empirical methods the ring builders used to find their appropriate dimensions and the choice of base units employed.

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