Ley line

Ley lines, attributed to ancient dodmen, allegedly join geographical points resonating special psychic energy. They may relate to traditional religious sites (such as Stonehenge and other megalith structures), and/or to recognised landscape features such as high or prominent mountains.

Ley lines were discovered by Alfred Watkins, who first made his theories public at a meeting of the Woolhope Club of Hereford in September 1921. His actual discovery took place on June 30, 1921 when he visited Blackwardine, Herefordshire. He was looking at map when he noticed key places were aligned. "The whole thing came to me in a flash" he explained to his son afterwards.

His ideas were taken up by the occultist Dion Fortune who featured them in her 1936 novel The Goat-footed God.

Mapping ley lines, according to New Age geomancers, can foster harmony with the "planet" or reveal pre-historic trade routes.

Theories of magnetic interactions however, appear unproven to date, leading to suspicions that leys belong in the realms of pseudoscience or magic (or magick) .

History of British ley line hunting

Books:

By Alfred Watkins:

Early British Trackways (1922)
The Old Straight Track (1925)
The Ley Hunter's Manual (1927)

By Tony Wedd:

Skyways and Landmarks (1961)

to be written

Skeptical critiques of ley lines

Various skeptics have suggested that ley lines are a product of human fancy.

One suggestion is that thanks to the high density of historic and prehistoric sites in Britain and other parts of Europe, that finding straight lines that "connect" sites (usually selected to make them "fit") is trivial and nothing more than coincidence. However, others claim that the patterns of shrines and monuments in the Aymara territory of Bolivia, as shown in the photographs of Tony Morrison in his 1978 book Pathways of the Gods offer convincing evidence.

Computer simulations appear to show that pseudo-random points on a plane form alignments in similar numbers to Watkins' significant places, suggesting that Watkins' ley lines may also be generated by chance. Many Chaos magicians delight in this as scientific proof not only of the existence of ley lines, but also of the generative power of chance.

It is obvious that finding ley lines on a landscape gets progressively easier as the length of ley line to be considered increases. This is because if one stops progressing along the line no more significant points can be discovered, where as if one proceeds further there is always a chance that another significant site will be discovered.

Expected numbers of ley lines through random points

For those interested in the mathematics, the following is a very approximate estimate of the probability of "ley line"-like alignments, assuming a plane covered with uniformly distributed "significant" points.

80 4-point leylines pass near 137 random points

Consider a set of n points in an area with area $d^{2}$ and approximate diameter d. Consider a valid ley line to be one where every point is within distance w/2 of the line (that is, lies on a straight track of width w).

Consider all the unordered sets (known as combinations) of k points from the n points, of which there are (see factorial for the notation used):

{\frac {n!}{(n-k)!k!}}

What is the probability that any given set of points fits a ley line? Let's very roughly consider the line drawn through the "leftmost" and "rightmost" two points of the k selected points (for some arbitrary left/right axis: we can choose top and bottom for the exceptional vertical case). These two points are by definition on this line. For each of the remaining k-2 points, the probability that the point is "near enough" to the line is roughly w/d.

So, the expected number of k-point ley lines is very roughly

{\frac {n!}{(n-k)!k!}}\left({\frac {w}{d}}\right)^{k-2}

With the assumption of constant density, and for values of d where n >> k this value can be shown to be roughly proportional in $d^{k+2}$ . Thus, contrary to intuition, the number of k-point lines expected from random chance increases much more than linearly with the size of the area considered.

In addition, it can be noted that even small increases in w greatly increase the number of expected lines. For example, allowing the use of "large" features such as stone circles has the effect of increasing the effective value of w.

Numerical results

607 4-point ley lines pass near 269 random points

Plugging in some typical values for the variables, and using the exact formula for combinations, rather than the approximation:

w = 50m, the width corresponding to a 1mm pencil line on a 50000:1 map

d = 100km

α = 5.5 × 10^-8m^-2 (50 points in a 30km square area)

then n is 550 and the number of leys predicted is of the order of 1000, with the longest leys expected to be 6-point leys. The number of predicted ley lines increases sharply as the size of the area considered increases.

According to this argument, the existence of long-distance ley line alignments in the English landscape should not surprise us.

External links

A ley line map
http://www.magonia.demon.co.uk/arc/80/leyhistory.html
Ley Lines and Coincidence: discussion and computer simulation results
Skeptic's Dictionary entry on Ley Lines