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The entrance to Wayland's Smithy, one of the Cotswold-Severn Group Neolithic stone structures, seems primitive but megalithic mathematics can be found here, and experimental archaeology proves it. Source: Msemmett / CC BY-SA 3.0

Megalithic Mathematics Revealed at the Cotswold Severn Long Barrows!

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During the British Neolithic, circa 4000-2500 BC, we witness the appearance of numerous ceremonial and domestic monuments dominating the prehistoric landscape. Providing an absolute total of how many were built during this period is not possible. Undoubtedly, we could be looking at a figure in the thousands. And, if we accept the opinion of archaeologist Andrew Flemming, then the architectural form of these structures was so designed that their appearance visibly indicated the specific types of ritual or other usage that could be legitimately held there. Accordingly, their respective designs would have had to been well thought out: their architecture had to meet the visual and experiential expectations of the people. All in all, one is led to consider the possibility that any style of monument was the result of deliberate planning and that the prehistoric builders were using megalithic mathematics to help them with design. But this is where we hit the major drawback to this assertion which this article attempts to tackle.

The British Neolithic communities were preliterate, and they have left behind no written records or sculptured schematics of any kind that could be interpreted as evidence of prehistoric metrology (the science of measurements). In short, archaeologists have yet to recover any material evidence of deliberate measuring or megalithic mathematics.

Thus, we are left with the impression that the British Neolithic communities were illiterate and no better than “savage, ignorant builders” who could neither think, count nor measure and yet they still somehow managed to construct complex monuments such as Stonehenge. Surely, this is not the case?

The front area of West Kennet Long Barrow in Wiltshire, which was also used by the author to reveal Neolithic megalithic mathematics in a time when no written communication existed! (Jarkeld / CC BY-SA 4.0)

The front area of West Kennet Long Barrow in Wiltshire, which was also used by the author to reveal Neolithic megalithic mathematics in a time when no written communication existed! (Jarkeld / CC BY-SA 4.0 )

Experimental Archaeology Can Reveal Megalithic Mathematics

Without a doubt, British Archaeology does not have a happy relationship with the idea as to whether or not intentional metrology or megalithic mathematics were involved in the construction of Neolithic structures. Suggestions that there might have been “gifted individuals,” such as Neolithic architects performing complex arithmetic are not very welcome, especially across the world of academia. At best, academic attention towards such intellectual architects tend to be glossed over or, at worst, simply ignored.

Thus, when it comes to analyzing evidence for those measuring systems that built complex structures, such as the Cotswold Severn long barrows , then it is so much easier to avoid mentioning metrology. In fact, avoiding the subject is the best strategy. Otherwise, one will have the difficulty of both explaining and demonstrating the existence of Neolithic numeracy across prehistoric Britain, for which there is no immediate “hard” evidence.

So where does one look for justification? I am an archaeologist who has spent over 25 years reconstructing the architectural designs of numerous British Neolithic monuments. To do so, I firstly survey an extant Neolithic structure . Secondly, I scrutinize my survey results, looking for measurements “proportional to the whole.” Thirdly, I attempt to reconstruct its ground plan using three experimental methods which, I believe, the prehistoric communities were capable of performing.

My starting position with the reconstructions is to utilize measured lengths of ropes to set out on the ground the designs for my intended reconstructions. Certainly, it can be accepted that the people of the Neolithic were making rope. Perhaps the earliest evidence for the use of ropes during the British Neolithic can be implied from the numerous attrition marks found at the Cissbury, Grimes Graves and Blackpatch Neolithic flint mines, circa 4000-3000 BC. Undoubtedly, the rope was used to haul the quarried flint from deep inside the mines towards the surface.

My next position states that the Neolithic communities orientated the design of their monuments by using the sun’s shadow as cast at midday in order to identify the direction of true north. Whilst there may be no immediate archaeological evidence to suggest that the British prehistoric communities were using this particular technique for orientation, it does seem to have been a well-known, universal, age-old practice for determining the direction of north. Incidentally, the technique of finding a north-south line by using the midday sun was a method traditionally employed by the English church’s builders for setting out their building works: a technique that was continuously utilized for almost the last two thousand years.

The final position accepts that the people used a rudimentary form of finger reckoning for working out how their ropes should be folded when setting out such structures. Simply put, that the prehistoric communities might have folded their measured ropes into shorter lengths using finger reckoning, that is counting on their fingers to calculate the number of folds required for setting out the design of the intended structure to be built i.e., fold the rope once equals one finger; fold it twice equals two fingers; and so on. Let me now explain how these three experimental methods can be used to reconstruct the trapezoidal shape of a Cotswold Severn long barrow.

The Megalithic Mathematics of the Cotswold Severn Long Barrows

It was the archaeologist Glyn Daniel who first coined the term the “Cotswolds Severn Group” to categorize the architectural similarities amongst a number of Early Neolithic long barrows found in regions of North and Southeastern Wales, the Cotswold, Somerset, Wiltshire, and Berkshire. These long barrows were built very early in the Neolithic, circa 3850 BC.

And they fell out of use around 3400 BC. Providing a definitive total as to how many Cotswold Severn long barrows might have been built is not possible but there could have been as many as 200 of them. The architectural similarities between them were consistent with their trapezoidal-shaped earthen cairns covering a combination of megalithic stone-lined passageway(s) and chamber(s). The West Kennet long barrow (Wiltshire) being, perhaps, the most famous British barrow of this kind (Figure 1B & 1C).

Figure 1. A: location of the Capel Garmon and West Kennet long barrows; B: external view of West Kennet; C: internal view of West Kennet. (Author provided)

Figure 1. A: location of the Capel Garmon and West Kennet long barrows; B: external view of West Kennet; C: internal view of West Kennet. (Author provided)

Case Study: Analyzing the Capel Garmon Long Barrow

In the following case study, I will discuss the Capel Garmon ( Denbighshire) long barrow, circa 3500 BC (Figure 2). A typical Cotswold Severn design with side entrance and three stone-built, internal chambers. Its orientation is east/west, with the wider proximal end facing east. After performing a survey at this extant long barrow, I concluded that it could be reconstructed in its entirety using a length of rope 48 feet long (14.64 meters).

In other words, the dimensions of all its architectural features (i.e., the length of the covering cairn, its passageway, entrance, three chambers, two horns and both its proximal and distal ends) were all proportional to a whole measurement equal to 48 feet long. Therefore, it was just a matter of folding the 48 foot length of rope accordingly in a specific sequence of shorter lengths to set out its full architectural design (see Figure 6).

However, for this case study we will confine our reconstruction exercise to the setting out of the barrow’s outer shape, that is, its distinctive trapezoidal shape (Figure 2 inset). I realize that the reader may not have access to physically reconstruct this shape on a large sports field but, alternatively, you can scale it down accordingly and draw its geometrical shape onto paper (see Figure 4).

Figure 2. The Capel Garmon long barrow; Inset: barrow plan. (Author provided)

Figure 2. The Capel Garmon long barrow; Inset: barrow plan. (Author provided)

The first task is to set out a large circle with a radius of 48 ft (14.64 meters). Next, place one stick at the circle’s center and at midday note the direction of the stick’s shadow as cast by the sun. At midday, the shadow reduces in length to its shortest point, and thus indicates the direction of true North (Figure 3).

Now use the shadow to act as a line of sight and have a helper place a second stick at the true North position on the circumference line of the large circle. Use these two sticks to act as a line of sight so that you can place a third stick in a straight alignment, due South on the circumference line of the large circle.

Then, stand at the center of the large circle, facing true North and hold out both your arms so that they are at parallel with the ground and at right angles to true North. Your outstretched arms now determine the directions of both due West and East. Then place two more sticks on the circumference line of the large circle (i.e., West points in the direction of your left arm, East points in the direction of your right arm). You have now identified the four cardinal points on your large circle.

Figure 3. The simple way of identifying the cardinal points. (Author provided)

Figure 3. The simple way of identifying the cardinal points . (Author provided)

Next fold the 48 foot of rope in half and set out a circle with a radius of 24 feet (7.32 meters) standing at the East cardinal point. Place two markers at the two points where the second circle crossed the first circle i.e., shown as positions B1 and B2 in Fig. 3. This procedure identifies the width for the proximal end. Next, fold the 48 foot rope into a quarter and set out a third circle with a radius of 12 feet (3.66 meters) standing at the West cardinal point again placing markers at the two points where the third circle crossed the first circle i.e., positions C1 and C2 as shown in Figure 4. This procedure identifies the width for the distal end (narrow end).

The final sequence is to then use line of sight between the four markers (B1, B2, C1 and C2) and mark out two lines (i.e., B1 to C1, B2 to C2) so that the edges of the cairn can be marked out.

Figure 4. Schematic plan of a reconstruction for the Capel Garmon long barrow.

Figure 4. Schematic plan of a reconstruction for the Capel Garmon long barrow .

Figure 5. The trapezoidal shape of the Capel Garmon long barrow. (Author provided)

Figure 5. The trapezoidal shape of the Capel Garmon long barrow . (Author provided)

In Figure 5 we see the same result as marked out on a sports field. So, congratulations, you have just reconstructed the trapezoidal shape of a Cotswold Severn long barrow using a length of rope that need only be folded three times by counting on three fingers of your hand, rudimentary practical megalithic mathematics!

Discussion: Proving Deliberate Megalithic Planning

Of course, on the one hand, there is no evidence to state that the builders of these long barrows were actually using these experimental methods to set-out their designs. But, on the other hand, it cannot be denied that the Neolithic builders were deliberately planning their long barrows, perhaps using the very similar megalithic mathematical methods to those I have discussed here. For how can it be explained that I can accurately recreate the design of any Cotswold Severn long barrow simply using a single length of rope, the sun’s shadow at midday and finger reckoning mathematics (see Figure 6). Moreover, my own survey data collected from other Cotswold Severn long barrows further supports the type of proportional mathematics I have just described in this case study, and in Table 1. I show the relationship between a barrow’s distal and its proximal ends for seven other long barrows.

Table 1. A sample of the proportional measurements surveyed at other long barrows .

With all the examples listed in the above table, the mathematical correspondences between a barrow’s distal and proximal ends can be explained by folding a single, measured length of rope in similar sequences to which I have demonstrated with the Capel Garmon reconstruction.

Undoubtedly, experiments like the one I offer here can explain how the Neolithic builders could have accurately set out on the ground the designs of their long barrows. Certainly, the people would have had access to those ropes which could have been used for measuring, perhaps, in similar ways in which many other ancient cultures used their ropes for surveying and measuring, for instance, the well-known Egyptian rope stretchers comes to mind.

Finally, folding a length of rope over and over to determine the dimensions of the intended structure to be built is indicative of both elements of Neolithic metrology and numeracy. Moreover, this principle of counting can also explain why the prehistoric finger reckoning mathematics would not have left any “hard” evidence in the archaeological record. Thus, the fact that we do not have any physical proof of prehistoric metrology, “written in stone,” does not mean that the concept of numeracy did not exist, and definitely reconstructions such the one discussed here can demonstrate just how capable the Neolithic communities were at counting and measuring.

Figure 6. Folding a single length of measured rope, over and over, reproduces the design of the Capel Garmon long barrow. (Author provided)

Figure 6. Folding a single length of measured rope, over and over, reproduces the design of the Capel Garmon long barrow. (Author provided)

Dr. Hill’s book,  The Recumbent Stone Circles of Aberdeenshire: Archaeology, Design, Astronomy and Methods  is available at:   https://www.cambridgescholars.com/product/978-1-5275-6585-2

Top image: The entrance to Wayland's Smithy, one of the Cotswold-Severn Group Neolithic stone structures, seems primitive but megalithic mathematics can be found here, and experimental archaeology proves it. Source: Msemmett / CC BY-SA 3.0

By Dr John Hill

Comments

I have no doubt they had the brains for the job. They would have had the brawn too. But the time? That's harder to fathom. Either their lives must have been easier than we think or there were more of them. Or they used more advanced techniques than we are willing to attribute to them. This applies to a range of ancient megastructures

It’s absurd to think our ancestors weren’t able to do rudimentary engineering or math.  By the time these people were building structures, humans had been watching the skies and estimating when the next season would occur for thousands, perhaps, tens of thousands of years.

Look at the magnificent placing of the stones at Stonehenge and tell me our ancestors didn’t know what they were doing.  It’s too much of a cop out to say they were “illiterate, preliterate, or savages.  I expect better from your writers and website.

Pete Wagner's picture

They were certainly intelligent.  A good old ‘story stick’ might have been all they needed to use.  The other big question is, how long did their elder leaders live?  Maybe a lot longer than today.  What could be better than one who built it, or lived in it, or survived it?   

Nobody gets paid to tell the truth.

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