Hunting quanta

Abstract Thom considers that many of the dimensions of megalithic sites can be expressed in terms of a quantum of 6.44 ft (1.66 m). The problem of detecting a quantum when its size is not known in advance has been studied in pioneer papers by Broadbent (1955, 1956). With the greatly increased volume of evidence now available, a renewed attack on this problem seems called for, and a new approach, based on a Fourier analysis, will be outlined here. With samples of sufficient size, testing for the presence of a quantum is equivalent to testing a section of a realization of a Gaussian stochastic process, stationary under time shifts, for an unduly large supremum. If the test is not to be prejudiced by prior decisions about the fittings of ‘eggs’, ‘fans’, etc., then only data from circle-diameters can be used. This reduces the sample size, and so the asymptotic theory has to be supplemented by ‘ Monte Carlo ’ runs with simulated data (with and without a built-in quantum effect). It already seems clear that agreement on the data-set to be used in the analysis is the vital prerequisite for a decisive test of the quantum hypothesis.