Douglas Heggie is a highly respected professor of mathematics and Alexander Thom was a highly respected professor of engineering – so who is right? Most archaeologists prefer to side with Heggie, almost certainly because the whole idea of a prehistoric unit of measurement is at odds with their view of Neolithic achievements. But archaeologists who have carefully reviewed Thom’s work in the field have a different view. For example, Tony Crerar, a researcher and engineer in Wales and Euan Mackie, an honorary Research Fellow at the Hunterian Institute in Scotland are strong supporters of the concept of the Megalithic Yard. Dr Mackie has recently said of Thom:
‘By exact surveying and statistical analysis he (Thom) demonstrated that most stone circles could have been set out much more accurately than previously supposed. Most are truly circular with diameters set out in units of a ‘megalithic yard’ of 0.829 metres or 2.72 feet. Other circles had more complex shapes like ellipses and flattened circles, whose dimensions appear to be based on pythagorean triangles, also measured in megalithic yards. By similar means he showed that many standing stone sites pointed at notches and mountain peaks on the horizon where the Sun or Moon rose or set at significant times. Not only does a sophisticated solar calendar seem to have been in use, but the Moon’s movements may have been studied carefully, even up to the level of eclipse prediction.’ 11
There were question marks over the Megalithic Yard but the challenge laid down by the late Professor Alexander Thom still remained. In our opinion there were only two main possibilities:
1. Thom’s data gathering and/or his analysis were flawed, and the Megalithic builders did not use the Megalithic Yard as a standard system of measurement.
2. Thom’s data and his analysis were both correct. The Megalithic builders did use this standard unit of measurement and it was applied with great accuracy.
‘Stick to Facts, sir!’
It is a matter of record that the academic establishment prefers a gentle evolution to revolution in its thinking. No academic authority enjoys having its finely-tuned paradigm challenged. But it is time to put the Megalithic Yard to the test. So, was there a way forward to resolve the authenticity or otherwise of Thom’s findings? Was it possible to investigate the suggested Megalithic Yard? The problem was that there was still a relative absence of informed opinion regarding this subject. The situation brought to mind the words of Mr Gradgrind in Charles Dickens’ Hard Times:
‘Now, what I want is, Facts... Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them… Stick to Facts, sir!’
Facts can be tricky things, as the point of view of the observer will always have a bearing on them. However, we came to the view that the only way to resolve the matter was to try to put some more facts on the table: facts that could help everyone concerned to have a more informed view. To do this we decided that we needed to try and discover how the Neolithic people could have produced the Megalithic Yard to such a high degree of accuracy across so large a geographical area and over such a long period of time. If we could find a realistic explanation of how the Megalithic unit of 0.8296656 metres could be created, it would justify a reappraisal of the existing paradigm of prehistory and potentially repair a substantial hole in the Great Wall of History.
1 http://news.bbc.co.uk/1/hi/sci/tech/975360.stm
2 http://nabataea.net/items.html
3 http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egypt.html
4 Knight, C. and Lomas, R.: Uriel’s Machine. Arrow, London, 2000.
5 Thom, A.: Megalithic Sites in Britain. Clarendon Press, London, 1967.
6 Thom A.: ‘A statistical examination of the Megalithic sites in Britain’. (1955) Journal of the Royal Statistical Society, A118, 275-91.
7 Thom and Thom: Megalithic Remains in Britain and Brittany. Oxford University Press, Oxford, 1978. Chapters 3, 4, 6, 7 & 8.
8 Thom, A.: Megalithic Sites in Britain. Oxford University Press, Oxford, 1968.
9 Heggie, D. C.: Megalithic Science: Ancient Mathematics and Astronomy in Northwest Europe. Thames and Hudson, London, 1981. See also: Renfrew, C. & Bahn, P. G.: Archaeology: Theory, Methods and Practice, Second Edition. Thames and Hudson, London, 1996.
10 Heggie, D. C.: Megalithic Science: Ancient Mathematics and Astronomy in Northwest Europe. Thames and Hudson, London, 1981.
11 Mackie, E. W.: July 30th 2003, see: http://www.dealbhadair.co.uk/athom.htm
CHAPTER 2
The Turning Earth
Does it really matter if Professor Thom was right about the Neolithic builders having used the finely-defined standard unit of length that he called the Megalithic Yard? Yes – it matters a great deal. If he was wrong, the subject of statistics needs a fundamental reappraisal; but if his findings were reliable, the subject of archaeology needs equally careful reassessment. Further – if Thom was right, the development of human civilization may have to be rewritten! We wanted to know, one way or the other: were Alexander Thom’s findings real?
The truth and the Earth
There were two possibilities: either Professor Thom’s Megalithic Yard was a genuine unit once used by Neolithic builders or it was an accidental consequence of statistical manipulation without any historical validity. We saw that the only hope of resolving the issue, once and for all, was to attempt to find a reason why this length of unit would have had meaning for Neolithic builders, and then to identify a methodology for reproducing such a length at different locations. It was a tall order, and failure to find a potentially meaningful origin of the Megalithic Yard and a feasible means of reproduction would still not confirm that it was a fabrication. Conversely, we recognized that success would not sufficiently prove that the measurement was real.
We have to admit that we had a starting point that suggested that Thom was correct, because Alan’s previous research had led him to believe that the Megalithic Yard was, and is, a geodetic unit. This means that it was derived from the geometry of the Earth itself – specifically, it was based on the polar circumference of the planet.1 After studying evidence from the Minoan culture that had developed on the Mediterranean island of Crete some 4,000 years ago, Alan had concluded that the Minoan astronomer-priests had regarded a circle as having 366 degrees rather than 360 degrees that we use today. The evidence also suggested that the Megalithic culture of Britain had done the same. Chris studied Alan’s earlier findings closely and could see a logical reason why any astronomically-based culture might consider that there should be 366 degrees in a circle – for the very good reason that there are 366 rotations of the Earth in a year.
Chris’s reasoning was straightforward. Everyone accepts that there are approximately 365 ¼ solar days in a year, and because we cannot have a quarter of a real day, our modern calendar has 365 days to the year with an extra leap day at the end of February every fourth year. There are also other subtle correctional mechanisms (for example, adding a leap year in millennium years but not in century years) designed to smooth out the oddities of the astronomical system that governs the progress of perceived time for daily purposes. While we are all relaxed about having a 365-day year, most people do not realize that the Earth actually makes just over 366 turns on its axis during the same period.
Such devoted Sun, Moon and star watchers as the Neolithic people of the British Isles and surrounding areas would have been acutely aware of the difference between the 365-day year and the 366 turns of the planet in a year. One difference was the day of the Sun and the other, of the stars.
Solar and sidereal days
There are various ways of defining a day and the two principal types are what we now call a ‘solar’ day and a ‘sidereal’ day. A solar day is that measured from the zenith (the highest point) of the Sun on two consecutive days. The average time of the Sun’s daily passage across the year is called a ‘mean solar day’ – it is this type of day that we use for our timekeeping tod
ay. A sidereal day is the time it takes for one revolution of the planet, measured by observing a star returning to the same point in the heavens on two consecutive nights. This is a real revolution because it is unaffected by the secondary motion of the Earth’s orbit around the Sun. This sidereal day, or rotation period, is 236 seconds shorter than a mean solar day, and over the year these lost seconds add up to exactly one extra day, giving a year of just over 366 sidereal days in terms of the Earth’s rotation about its axis.
In short, anyone who gauged the turning of Earth by watching the stars would know full well that the planet turns a little over 366 times in a year, so it follows that this number would have great significance for such star watchers. If they considered each complete turn of the Earth to be one degree of the great circle of heaven, within which the Sun, Moon and planets move, then they would also logically accept that there are 366 degrees in a circle.
There really are 366 degrees in the most important circle of them all – the Earth’s yearly orbit of the Sun. Anything else is an arbitrary convention. It seemed to us that this was so logical that the 360-degree circle may have been a later adjustment to make arithmetic easier, as it is divisible by far more numbers than the ‘real’ number of degrees in a year. In other words, the circle of geometry has become somehow detached from the circle of heaven. How right we were, and the truth of the situation would become all too clear to us as our research progressed.
Having satisfied ourselves that Alan’s conclusion about a 366-degree Neolithic circle was, at least, tenable we returned to the issue of the Megalithic Yard being a geodetically-derived concept. If it was indeed geodetic in origin it was implicit that the Neolithic peoples of western Europe had measured and understood the polar circumference of the Earth. At first view this may sound far-fetched – but it is not. In our opinion it is not unreasonable to assume that the astronomer-priests of this period did indeed achieve this feat. Few, if any, experts deny that many Megalithic sites were created for sky watching. Any culture that spent dozens of centuries studying the interplay of solar, lunar and stellar movements must surely have come to understand that the Earth is a giant ball. In the process it could quite readily have gained sufficient knowledge to gauge the Earth’s size.
Given that the human brain has enjoyed its current level of intellectual processing power for tens of thousands of years, it has to be acknowledged that prehistory must have had its share of individuals with the imagination and insight of Isaac Newton or Albert Einstein. It is not outlandish, therefore, to assume that the Megalithic builders would have established the true nature of the Earth, including measuring its dimensions using simple observational astronomy. Indeed, the Greek mathematician Eratosthenes is said to have single-handedly calculated the polar circumference of the Earth in 250 BC to an accuracy of 99 per cent without the considerable benefit of thousands of years of concentrated observational astronomy known to have been conducted by the people who built such sites as Stonehenge in England.
All this deduction seemed fair but one troublesome fact did cause us to wince a little. Having decided that there was no insurmountable difficulty in measuring the polar circumference of the planet in order to subdivide it into integer (whole number) units, we had to accept that the people concerned must have possessed a reliable unit of linear measure prior to the Megalithic Yard. Some presently unknown unit simply had to be in place to measure the polar circumference before this great distance could be recalibrated into a more useful geodetic subdivision. After some thought we realized that this was not a problem at all. All we had to do was to think about the relatively recent past to understand how the history of human endeavour repeats itself if facts become lost. The 18th-century French team that devised the metric system had done exactly the same thing in that they measured the polar circumference of the Earth in old French linear units before they could create the metre, which was then defined as one forty-millionth of the circumference of the circle that passed through both poles. What 18th-century Europeans could achieve, so too could the star watchers of the Neolithic Period. But the realization does add another level of surprising expertise to these otherwise apparently unsophisticated people.
Beautiful equations
Our next question was, ‘What is the modern estimate of the polar circumference of the Earth?’ Given that our planet has an uneven surface and is not entirely regular in every north-south cross-section, it would appear to be almost impossible to give an absolutely precise measurement for its polar dimensions. Inevitably estimates vary slightly, but the most common value quoted is 40,008 kilometres,2 a distance that converts to 48,221,838 Megalithic Yards (MY).
Our hypothetical 366-degree polar circumference would therefore give us 131,754 Megalithic Yards per degree – a number that does not sound very special. But Alan had reasons to believe that these early mathematicians had subdivided each degree into minutes and seconds of arc (part of the circumference of a circle), just as we do today. In this instance however, it appears they fixed upon 60 minutes to each degree of arc and 6 seconds to a minute of arc. This produced the following result:
full circle of the Earth
=
48,221,838 MY
Well, that did not look too exciting. Nor did the next two steps:
one degree (a 366th part)
=
131,754 MY
one minute (a 60th part)
=
2,196 MY
But the final breakdown was truly remarkable:
one second (a 6th part)
=
366 MY
According to this assumed system of 366-degree geometry, each second of arc of the entire planet is an amazingly precise 366 MY in length! It is incredibly neat, but is it real?
An astounding coincidence: the ‘Minoan foot’
Taking Thom’s Megalithic Yard of 0.8296656 metres we could reverse-engineer the process by multiplying it by 366 x 6 x 60 x 366, giving a supposed planetary circumference of a little under 40,010 kilometres. This is less than 0.005 per cent away from our modern estimate and it is so close as to be negligible. While there are no decipherable records from the Neolithic Period to confirm the use of this method of geometry, there is strong circumstantial evidence to suggest that the 366 x 60 x 6 principle of geometry was used by the Minoan culture that existed on the Mediterranean Island of Crete 4,000 years ago, which overlapped the time of the Neolithic cultures of Britain and France.
Canadian archaeologist, Professor J. Walter Graham of Princeton University discovered that a standard unit of length had been employed in the design and construction of palaces on Crete dating from the Minoan period, circa 2000 BC. Graham dubbed this unit a ‘Minoan foot’, which he stated was equal to 30.36 centimetres.3 This length held no particular significance for Professor Graham, as he had no reason to compare it to the units Thom claimed to have found on the other side of Europe.
It dawned on us, as we looked at Professor Graham’s findings, that there was something more than significant about the size of the Minoan foot, when looked at in conjunction with the Megalithic Yard and Megalithic geometry. Imagine our surprise when we realized that one second of arc in the assumed Megalithic system (366 MY) is equal to 303.6577 metres – which is exactly 1,000 Minoan feet (given that Graham did not provide a level of accuracy greater than a tenth of a millimetre). This fit could just be a very, very strange coincidence – but it has to be noted that several researchers now believe that the Minoan culture of Crete had ongoing contact with the people who were the Megalithic builders of the British Isles.4
It seemed highly unlikely that 366 MY and 1,000 Minoan feet should both fit our hypothetical Megalithic Second of arc so perfectly by sheer chance, given that they both appear to spring from the same geodetically sound principle. We were now feeling increasingly confident that the Megalithic Yard was a real unit of length and not a statistical blip as suggested by some archaeologists – who unfortunately have never taken the time to thoroughly investiga
te the issue.
Having determined that the Megalithic Yard had a potential reality, there was still the problem of how it could possibly have been reproduced at tens of thousands of different sites over thousands of years. We formed a hypothesis that a group of advanced Neolithic astronomers had calculated the Megalithic Yard from a detailed knowledge of the circumference of the planet, but they would need a means of formally recording the length of the unit and of disseminating it across time and distance for general use by the builders of hundreds or thousands of individual projects.
As we have demonstrated, the modern metre was derived from the polar circumference of the Earth and it was first recorded as the distance between two fine lines engraved onto a bar made of platinumiridium alloy. Later it was redefined in terms of the wavelength of red light from a krypton-86 source. Since 1983 the metre has been defined as the length of the path travelled by light in a vacuum during a time interval of one 299,792,458th part of a second.
We reasoned that the Megalithic Yard needed to be recorded in a way that was accessible to every builder, yet for the majority of the Megalithic Period this culture did not use metals of any kind. It is possible that two fine lines could have been cut into a rock at some significant location but such a procedure would be open to error and could not have produced the amazing accuracy found by Alexander Thom. As he himself observed, wooden measures would have been subject to damage from a host of different sources. Rather than keeping a ‘sample’, what our Megalithic mathematicians needed was a method of reproducing the Megalithic Yard that was simple to use, very accurate and available to people dispersed over a large distance and across a huge span of time.
Civilization One: The World is Not as You Thought it Was Page 3
