Applying a modern Spreadsheet to prove the Megalithic Yard
Submitted by astro3 on Monday, 23 February 2009 Page Views: 14389
Discoveries
The statistician Prof David Kendall claimed to show that a quantum unit of diameter 5.44 feet (two Megalithic Yards) ‘rose up above the sea of random noise…’ (p122). This all seemed rather complicated. These days, a lot of people are sceptical.
Let’s keep things simple, and only include megalithic stone circles, not ellipses or other shapes, and only those circles where we reliably believe that the stones have not been moved and are reliable indicators of the Megalithic designs. This means that we have only one single measure for each construction, viz the radius, or rather diameter. Exactly this was done by the two authors John Barnett and Gordon Moir, in their article, ‘Stone Circles and Megalithic Mathematics’ published in Proceedings of the Prehistoric Society (1984), 50, pp. 197-216. This gave them a list, of sixty such circles, English and Scottish. The diameters were measured in feet, and these averaged 79 feet. Thom had surmised that their radii were measured in ‘Megalithic yards,’ which he always claimed was 2.72 feet in length.
These authors concluded that their test on these sixty circles, a sub-group of all of Thom’s data, did ‘not generally provide sufficient data of adequate quality to sustain his hypothesis.’ I wish to argue that this merely shows they did not look carefully enough at the data. Or, maybe it shows that these things are now a lot simpler in the age of the computer spreadsheet.
We here plot a quantum-unit of circle diameter, which we allow to vary, and see if it gives any best-fit value for this ‘Megalithic circle’ data-set. For each of these 60 values, the integer-multiple of the quantum unit is taken, that comes nearest to it, either just less or just more. Then the deviation of each Megalithic diameter from this nearest integer value is found, and these are summed, all sixty of them. Then, varying the value of the quantum-unit, the sum of all residues will be different each time, and can be plotted against it.
The result of this is shown in the graph. It is clear that a minimum occurs where Alexander Thom said it should be.
The enclosed graph shows a minimum in residuals around one single value and no other, viz. 2.72 feet the MY value, or rather double that for the radii here investigated. If there had been an intention on the part of the megalithic builders to employ a unit of measure for these radii, then there would have to be one value at which these deviations would descend to a minimum. Clearly, that is the case. Q.E.D.
This result is unequivocal, and it rules out the agnostic conclusion drawn by Barnatt and Moir back in ‘84. It demonstrates that, millennia ago, a single unit of measure was indeed used for these sixty radii, or some substantial proportion of them. It confirms that this primal, original measure was more or less just what Alexander Thom said it was, viz. 2.72 feet. A higher magnification of this graph indicated that the best-fit value (i.e. giving a minimal sum of residual values) was around 2.718 feet, but one may doubt whether such four-figure accuracy is warranted on this data-set.
I would welcome discussion as to whether this list of circle-diameters compiled back in 1984 can be improved in any way.
Nick Kollerstrom PhD
Note: New research from Nick Kollerstrom, comments welcome
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