Abstract
In this paper Peter Sain ley Berry discusses aspects of the intangible Neolithic heritage that may be deduced from the pattern of ancient sites in the Vale of Glamorgan - a centre of Neolithic civilisation - and elsewhere. Area and linear measures that fit this pattern appear derived from the circumference of the earth. The hypothesis is therefore that the Neolithic people successfully measured the earth. The project proposed involves attempting to calculate the circumference of the earth using a method that the Neolithic people might have employed - viz. by using a reflected ray of sunlight to measure the earth's curvature across the Bristol Channel. Project duration is expected to be about a year with a cost of some £6,000. This might be recouped from television interest. Partners might be a University Department, or a Science Museum such as Techniquest.

Introduction
To speak of an intangible Neolithic heritage may seem like a contradiction in terms. Surely all that is left of the great Neolithic civilisation that once stretched in an unbroken arc down the European Atlantic seaboard from the Hebrides to Spanish Galicia are the menhirs and dolmens, the stone circles and the burial cairns? And they are pretty tangible after all. Clearly a society that persisted for some two and a half thousand years - from around 4500 - 2000 BC must once have had an intangible heritage - but no music songs, poetry, language, customs have come down to us. Surely that has now all been lost - if indeed anything existed.

For it is remarkable how apparently little we know of these people. We have found a few of their tools and a few shards of their pottery. We know they had the power of quarrying and erecting stones, even transporting stones over great distances. But culture? Decoration? Even the most elaborate of burial cairns, over at New Grange in Ireland can only boast geometric spirals - hardly much to stir the soul.

Some people hold that well known sites such as Stonehenge and Amesbury are astronomical calendars constructed with great cleverness and indeed many such astronomical connections have been found, though all seem a little random. Even today we have only a sketchy notion of the real purpose of these great sites. Such gaps in our understanding are compounded by a distinctly racist attitude towards our forebears expressed in the sentiment: "they couldn't have done that - they wouldn't have had the intelligence." All this leads to the widely held view that the Neolithic people were really not very civilised - or indeed very clever - at all. That they were no more than simple farmers, just settled out of a hunter-gathering existence.

True we are impressed in a mildly condescending sort of way at the tangible heritage these folk left behind, but lacking comprehension we are inclined to dismiss them as intellectual inferiors from the pages of pre-history. Indeed the very term 'stone-age' has come to epitomise cultural and technological barrenness.

Here in Wales we are blessed with a rich Neolithic heritage. It is a good place to search for a greater understanding of these people and indeed for some of the less tangible aspects of the Neolithic heritage itself.

My Own Research
Some twenty years ago I was living in the little Vale of Glamorgan village of Colwinston. Looking at the map one day I noticed that the churches in Colwinston, and in the neighbouring village of Llysworney, were both an identical distance from the church in another village called Llandow. The three churches formed an arrowhead that pointed directly to Nash Point - a prominent local geographical feature.

Now it is generally accepted that ancient sites were frequently reused as one civilisation succeeded another. The three churches above are no exception. Of course, that particular finding could have been pure chance, but I found similar patterns all over the Vale. In this part of Wales at least there can be no doubt that the pattern of ancient sites is intricately associated with landscape features including hilltops, coastal points and river mouths.

I soon also discovered that the distances between the sites - which one would expect to be haphazard - were frequently regular. Moreover, sites often lay along straight lines of fixed length in such a way that a prominent site would divide the line into an easy ratio - such as 3 to 5 or 6 to 2.

The Tinkinswood Burial Cairn at St Nicholas - reputed to have the largest capstone in Britain - is fixed by two lines that it bisects exactly in the ratio 3 to 5. One line runs from the mouth of the Col-Hugh river to the mouth of the river Usk; the other runs from a prominent hilltop near Llantwit Fardre (inevitably today the site of a mobile phone mast) to Cold Knap Point, near Barry.

Again this might be of only minor significance were it not for the fact that one of these lines is exactly one thousandth of the earth's circumference while the other is precisely half this length. Now it is too much to suppose that this combination of lengths and ratios could have occurred by chance and it points to great sophistication in the selection of Tinkinswood's location.

From the above you can calculate that Tinkinswood must be 0.000375 of the earth's circumference from the mouth of the Col-Hugh river. This is not a handy figure to work with; fortunately, it equates to 15 kilometres, for a reason we shall see in a moment.

Now we know the mouth of the Col-Hugh river was a sacred site. In Celtic times chieftains were buried there. Their memorial crosses can be found today in the nearby church at Llantwit Major. Here, then, is evidence that the site was also sacred in earlier times. The Celtic burials also support the theory that a religious site continues to be used as civilisation succeeds civilisation.

But Tinkinswood is not the only cairn to be located 15 kilometres from the Col-Hugh river. If we draw an arc of this radius then it will intersect the location of two further cairns - that at Laleston and that at Coity. There are only about six such cairns in the whole of the Vale and three lie on this arc. Again this can hardly be coincidence.

Moreover, we find other burial cairns located at just the same 15 kilometres from the mouths of the Usk and the Taff rivers, though that relating to the Usk was lost during construction of the M4.

Now it might be argued that the mouth of the Usk, or the Col-Hugh, is (at least today) a vague and undefined point. True - but we can work backwards from the arc connecting the burial cairns to find a precise point in both Col-Hugh and Usk estuaries. And it is these two precise points that form the ends of the line - one thousandth of the earth's circumference in length - that the Tinkinswood cairn bisects in the ratio of three to five.

Building these secondary burial cairns therefore allowed the Tinkinswood builders some fine-tuning to construct a line that was exactly one thousandth of the earth's circumference in length.

It is hard to escape the conclusion that such lines of one thousandth, or one two-thousandth, of the earth's circumference, were chosen other than deliberately and presumably after a great deal of mapping and survey work. There are at least three such major lines in the Vale. So one is led inexorably to the conclusion that the Neolithic people must actually have measured the circumference of the earth. For to have hit arbitrarily on a unit that just happened to be a thousandth of the earth's circumference surely stretches credulity.

It is always necessary to choose the simplest hypothesis - and the simplest hypothesis in this case is that they did in fact measure, successfully and with fair accuracy, the circumference of the earth.

The Neolithic Measures - the Pole and the Acre
The fact that the radius of the burial cairn arc is 15 kilometres suggests that the Neolithic measurement of the earth's circumference must have been very close to 40,000 kilometres, which is, of course, the late eighteenth century measurement from which the kilometre is derived. Naturally, the Neolithic people did not use kilometres.
We can't know for sure what they used. But two measures whose origins are lost in the sands of antiquity do fit the measurement of Neolithic settlement surprisingly well. These are the Pole and the Acre. Both are related to the circumference of the earth and, of course, to each other.

The Imperial Pole is fixed today at 198 inches - a quarter of a chain of 22 yards. The Neolithic pole seems to have been a little shorter: my calculations make the Neolithic pole 196.8 inches or virtually one two hundredth of a kilometre. This being the case the earth's circumference then measures 8,000,000 poles - a figure that is not necessarily any more arbitrary than 40,000.

One thousandth of the earth's circumference is therefore 8,000 poles and the standard river mouth-burial cairn distance becomes 3,000 poles. This fits in to a general pattern, for many of the distances between ancient sites in the Vale of Glamorgan can be expressed in terms of regular number of poles - 100, 500, 1,000, 2,000 etc.

Neolithic Measures and the Circumference of the Earth
While the Neolithic people appear to have evolved a numerical system that counted in tens, their metrology seems to have been based on 2s and 4s and 8s and 16s. The reason for this may lie in the fact that the surface area of a sphere is four times the surface area of a circle of the same radius. The Neolithic people chose the acre to be - as it is today - 160 square poles. They did so for an intriguing reason apart from the obvious one of being easily divisible by two, four and eight: an elegant reason having to do with simplicity of calculation in a world without calculators or a fixed value for p.

If the earth's circumference is taken as 8,000,000 poles and the acre as 160 square poles then there are exactly 100,000 times the number of acres making up the surface of the earth as there are poles in the earth's radius. This relationship enables a simple calculation of the area of a circle without needing to know - and indeed be able to use - a value for p.

For all normal purposes if you square the radius of a circle measured in poles, double it and then divide by 100, you will arrive at the area of the circle given in acres. The beauty of the system is that the numbers stay the same - though the orders of magnitude differ - as the radius increases.

Thus a circle of 16 poles radius will have an area of 5 acres; a circle of 160 poles radius will have an area of 500 acres; a circle of 1600 poles, an acreage of 50,000 and so on. A radius of 7 poles produces a circle one acre in area; 70 poles will give us 100 acres.

The results are not exact - they are up to 2 per cent out - but for practical purposes this is not a problem.

My work has suggested that not only did the Neolithic people build according to linear measure but they also took advantage of this pole/acre correspondence to use spatial measures as well.

Thus if we take the outermost (heel stone) circle at Stonehenge we find (within the normal limits of measuring accuracy) that it has a radius of 16 poles, a circumference of 100 poles and of course an area of 5 acres. Indeed, all the circles at Stonehenge show this elegant correspondence of circumference, radius and area when measured in poles. (Nothing remotely similar can be found if the currently fashionable megalithic yard unit - really just one sixth of a Neolithic pole - is used). There is also no area measure linked to the megalithic yard.

The Intangible Heritage
So here we have the beginnings of an intangible heritage and that heritage is the spatial geometry that the Neolithic people wrote into the landscape with their religious and other sites. 6,000 years ago these people seemed to have evolved a decimal system of counting, appear to have measured the circumference of the earth and used this to devise a linear measure - the Pole - and its area counterpart - the Acre. They also appear to have mastered the techniques of surveying and mapping (which suggests in addition that they were familiar with Pythagorean geometry) and also of constructing edifices from large stones.

This intangible heritage can have a practical use today. Because Neolithic alignments frequently began on the coast and are of commonly fixed lengths, we can plot where the coast must have been before six thousand years of coastal erosion took their toll. Other alignments - there are four such in the Vale - run North-South and appear to be focused on the pole star, or magnetic north for each differs from grid north by a few degrees. These data could yield valuable historical astronomical information.

We can also use the data to plot the age of sites. In the Vale, the Tinkinswood Burial cairn seems to be the oldest and most important feature. It is the bisector of alignments and sites seem to be built in relation to it, rather than it to them. The exception is the site now occupied by Llandaff Cathedral. The ratios suggest that this was in use before Tinkinswood was built: that that site is even older than the 6,000 year old Tinkinswood.

The Project
Was it possible for the Neolithic people to measure the earth's circumference? That is the first piece of practical research that needs to be done. There are various ways of measuring the earth's circumference. (And here let us dispose of the fallacy that these people were like children who believe the earth is flat.) One way is to shine a light across a body of water that curves with the earth. Clearly, if the light source is at sea-level then the observer on the far side must be slightly elevated to see over the 'hump' caused by the curvature of the earth. From the extent of this elevation and the distance across the water the height of the 'hump' and therefore the curvature of the earth can be calculated.

The Neolithic people did not have lights (so far as we know). But they did have the sun and they did have a very handy body of water that flows east-west so that the sun can shine across it. This is, of course, the Bristol Channel. The Channel is ideal for this purpose, wide enough for the earth's curvature to be perceived, but not so wide that you cannot see, or signal, across it on a clear day. Probably they didn't have mirrors - but they would have had polished flints or quartz from which a satisfactory reflector could be made.

This then is the project - simple and self-contained. It is to attempt to measure the earth's circumference as the Neolithic people might have done 60 centuries ago. The project might take about a year from start to finish. It would not cost a great deal - £6,000 perhaps - though this is a guess. A University engineering department or a Science Museum such as Techniquest could be approached to run it. It may be possible to attract interest from the media, such as a television programme. They might even fund the study. This could help to publicise UNESCO in Wales.

Should it prove possible to derive a reasonably accurate figure for the earth's circumference by this or a similar method then it will represent a major step forward in our understanding of the Neolithic people and of their mathematical and technological capability. It will provide the springboard for a far greater body of research into the sophistication of our ancestors and the enigmatic artefacts that they bequeathed to us.

Conclusion
But the really exciting theoretical possibility is that if the Neolithic people were as sophisticated as their intangible heritage appears to show, then it really begs the question of how they were able to make detailed mathematical calculations, map the countryside over large distances, give orders for structures to be built in precise locations and to even more precise dimensions, without the benefit of writing.

But of course, at this time - six thousand years ago - writing had not been 'invented,' at least so far as current fashionable theory would have us believe. The question is left - was writing developed here in the Vale of Glamorgan - and no doubt elsewhere in the Neolithic civilisation - before it evolved in Mesopotamia? We should not entirely discount the possibility.

Peter Sain ley Berry
Cowbridge
17 October 2005

Footnote - Answers to some of the objections made to the hypothesis above.

Writing
If writing did develop here, why then is there no trace of it?

I don't find that difficult to answer. When a civilisation collapses, especially if it is invaded whether by an enemy, or by disease, or even by a succession of bad harvests caused perhaps by global cooling as a result of volcanic eruption, almost everything vanishes. Writing was perhaps held to be so sacred that literacy was confined to an elite group that deliberately did not let its precious symbols appear more widely. And if they wrote on any organic material that would long since have perished. We do not know what form the writing took, anyway. Even something carved in stone would have eroded by now.

None of this appears in the classical literature
It is also surely wrong to think that mankind has developed in a straight line with each generation becoming cleverer than the one before. Is it not rather a question of civilisations developing and then collapsing? We lose types of skills and technology almost as fast as we discover new ones. Who now, for instance, could navigate a fleet under sail? Or work stone - or gold - like the Incas? This Neolithic technology was developed four thousand years before the Romans arrived in the Vale of Glamorgan. And in the intervening period the knowledge was simply lost.

How would they have known the earth was round?
And as for not knowing that the earth was round, surely this is nothing more than common sense? Is the moon not round and have you never shone a light at an egg?

It is the concept of the flat earth that is the heresy that insults the intelligence. Bear in mind that mankind has been around, with much the same brains and emotions as you and I, for at least 60,000 years. We are talking here of going back 6,000. Surely in the intervening 54,000 years, people would have woken up to the fact that the earth didn't have an edge?

PSLB