The Hypothetical Framework
1. The Rational Distribution Hypothesis
The Rational Distribution hypothesis suggests that:
1. The perimeters of stone circles are rationally divided such that the gaps are common fractions of a revolution in a whole number of a circumferential unit, also referred to here as the perimetric unit.
2. All stone circles are set out with a common circumferential unit that is equal to one-sixteenth of a Megalithic Yard multiplied by π. It is suggested that this is the reason why Thom found the Megalithic Yard in samples of stone circle diameters.
3. It is therefore possible, where circles are reasonably defined, to determine the size of the perimetric unit as locally implemented and, thus, the imputed site Megalithic Yard, and assess its variance against the results of Thom’s statistical analysis.
2. The Bi-Metric Hypothesis
The Bi-Metric Hypothesis serves a dual purpose:
1. Providing a means to convert a perceived circumferential unit derived from Rational Distribution Analysis, as above, into a diametric unit. This is central to the research question: could there be a common unit on stone circle perimeters that produces the Megalithic Yard on diameters?
2. Introduces the possibility that the megalith builders did not think about circles in the same way that we do - this being potentially borne out by observations at a number of sites discussed.
The suggestion is that two units related by a factor of π may have been in use, one being employed to measure diameters and the other to measure circumferences such that there would be as many perimetric units on the circumference as there are diametric units on the diameter.
Such a system and procedure would overcome problems related to the incommensurability of π and would facilitate the calculation of lengths of arc were these to be subtended by a common fraction of a revolution. For example, an arc of one-tenth of a revolution on a radius of ten diametric units would have a length of two circumferential units - a straightforward calculation that does not involve π.
3. A Conceptual Astronomy?
Should stone circles be aligned to the cardinal points of the compass then one consequence of rational distribution would be that the axis would potentially bear at a common fraction of a revolution from one of these cardinal points. This would therefore potentially apply to astronomically aligned axes.
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