The yardstick that may be a mirage

Claim (verbatim)

Alexander Thom, surveying hundreds of British and Breton stone circles and rows, argued that their dimensions are built on a single unit, the 'megalithic yard' of about 2.72 feet, used with remarkable consistency across the islands - a claimed prehistoric metrology, and one of the few lost-knowledge hypotheses that comes with a closed corpus of precise measurements and a genuinely decidable statistic. David Kendall answered it in 1974 with a 'broadness of a trousers-quantum' test, asking whether the diameters really cluster on multiples of a common unit more tightly than chance, and later reanalyses (Freeman and others) have gone back and forth. The virtue here is that nothing is unmeasurable: Thom published the numbers, and the question - is there a quantum, and is it 2.72 feet? - is answerable by statistics alone. The famous debate is worth reopening not by re-posing it but by pinning new arithmetic to a pre-registered subset, because the original result is vulnerable to selection of which monuments count and to the flexibility of the quantum-hunting statistic. The missing knowledge is whether a shared unit of length existed in the third millennium BCE; it is decidable on Thom's own table with a modern, honestly-priored test.

Prediction clause (verbatim)

Prediction: taking Thom's published diameters for a pre-specified, homogeneous subset (for example only the Scottish recumbent stone circles, or only true circles with a stated survey accuracy) and applying a Bayesian quantum analysis with a broad prior over unit length, the posterior will NOT concentrate a quantum near 2.72 feet - the Bayes factor for a quantised model against a no-quantum (continuous-diameter) model will fall below 3, and any favoured unit's credible interval will exclude the megalithic yard or be too wide to identify it (primary clause: Bayes factor < 3 for quantisation in the pre-registered subset). Disambiguation: the subset and the prior are fixed before computation to bar quantum-hunting flexibility. Coverage guard: if the homogeneous subset contains fewer than 40 monuments with stated accuracies the test voids rather than resolving.

Kill-dataset (verbatim)

Kill: Thom's "Megalithic Sites in Britain" (1967) diameter tables (and the Thom survey corpus), analysed with Kendall's (1974, "Hunting Quanta") and Freeman's quantum-detection framework re-run as a pre-registered Bayesian model comparison on a fixed homogeneous monument subset - the operation is the Bayes factor for a quantised versus continuous diameter distribution and the credible interval on the unit.

Novelty / leakage triage

already answered in the literature

The Bayesian analysis the conjecture proposes has substantially been done. Kendall (1974, 'Hunting Quanta,' Phil. Trans. R. Soc. A 276) found any quantal signal resides almost entirely in the Scottish circles and is marginal; and decisively Freeman (1976, 'A Bayesian Analysis of the Megalithic Yard,' JRSS A 139/1) ran a Bayesian model on Thom's data and found two other unit lengths fit the Scottish diameters about as well as 2.72 ft and no evidence for a single quantum in the stone rows. The conjecture's conclusion - no robustly identifiable megalithic-yard quantum, the favoured unit's credible interval too wide or excluding the MY - is the published Bayesian result; a pre-registered subset re-run would refine, not first establish it.

• D.G. Kendall, 'Hunting Quanta,' Philosophical Transactions of the Royal Society of London A 276 (1974): 231-266
• P.R. Freeman, 'A Bayesian Analysis of the Megalithic Yard,' Journal of the Royal Statistical Society, Series A 139(1) (1976): 20-55
• A. Thom, Megalithic Sites in Britain (Oxford: Clarendon Press, 1967)

Predictions

No prediction registered yet.