The Linear Dream was originally written in about 1975 as a sceptical statistical response to various popular books about ley lines which were on the market at the time – notably John Michell’s The View Over Atlantis, Paul Screeton’s Quicksilver Heritage, and Janet and Colin Bord’s Mysterious Britain. Basically it set out to show that the alignments which these authors thought provided good evidence of deliberate design were actually consistent with chance alignment. The study was never published, except in an edited version by Chris Hutton-Squire in Undercurrents (issue 18, pp. 33–35.) Our aim here is to publish The Linear Dream in its full, original form, and then to provide links to comments on various aspects of it in the light of recent developments.
The first part of the original study dealt with 10 interesting cases of ley hunting, and it used a formula which had been devised by Peter Furness. At the time I believed the Furness Formula to be correct, and indeed it remains a reasonable first approximation to what chance can achieve, alignment-wise, but it is wrong, as a computer simulation showed as early as 1976, and as a number of computer simulations done in the past year confirm.
It has always been known that whatever model is used in any theoretical treatment, it is limited by the assumption of a uniformly random distribution of the ancient sites on a map. This is known not to be true, but to derive a model with a non-uniform site-distribution is a theoretical nightmare, so that models which assume a uniform distribution remain, in effect, our best effort. Nevertheless, the results are instructive in revealing the extraordinary power of chance alignment
The present study, then, consists of the original Linear Dream, together with links to pages containing an analysis of the Furness Formula, and the testing of that formula using a much larger number of computer simulations than was possible with the computer power of the mid 1970s. Oddly enough, despite the incorrectness of the Furness Formula, it remains a fact that the main thrust of the original study was valid: chance can produce more extraordinary alignments than most people would expect, and the activities of ley hunters remain suspect for the most part.
With the study of the Coldrum Ley done for the BBC in 1985, it became clear that computer simulation – which could be run with non-uniform site distributions matching those of the real sites on a map – was the best way forward, thus rendering any theoretical treatment rather redundant. In a sense, then, updating The Linear Dream as we are doing it here is a redundancy, though the computer simulations of the 10 case studies do enable a testing of the formula approach. (It is to be noted that in the 10 case studies only the total numbers of sites on the maps were counted, with no account taken of their spatial distribution, so that these simulations effectively use a uniform distribution over their respective maps. They thus test the formulae, but are not as realistic as they would be if we went back to the maps and studied the spatial distributions, grid-square-wise, as outlined in the Coldrum study.)
The second part of the original version of The Linear Dream attempted to test some examples of Sacred Geometry (hypothesised geometrical arrangements of ancient sites, such as equilateral triangles or circular arrangements) and the alleged association of phenomena like UFOs with ley lines. My early attempts were admittedly crude, and so this part of the study has had to be considerably updated in the supplied links, and with the addition of further computer simulations.
Though the original Linear Dream was solely by me, the updates to it are effectively a joint effort by Michael Behrend and myself.