I wrote a program in the 1980's to find 'ley-lines'. Specifically, it allowed one to input the map references of 'points of interest' on a 1:50000 map and then search then entire entry list for alignments. It took every possible pair or points, plotted a straight line and worked out the perpendicular distance of every other point from the line. More than '3' counted as a 'ley'.
On the other hand, items that appear at first glance to be related, such as "earthworks" may be separated in age by 3,000 years and be from different cultures and belief systems. Of four "ancient earthworks", one may be defensive, one funerary, one agricultural, and one ritual.
They're also large, compared with, for example a standing stone. Even a small earthwork, say 50 yards across can line up with a startling number of other points. Badbury rings will align with half of Dorset.
Of course you can 'align' with the outer edge or anywhere in between. That was awkward to program for, but it was the case that earthworks cropped up in a lot of alignments. When the program created random points, seeded on the original map data, I relocated the whole earthwork.
Any two points will always be in a straight line relative to each other. The chance that a third random point is within a degree either side of that line is 1/180. That's not rare. if I had a 1/180chance of being knocked off my motorbike every ride, I would not ride it.
The chance of a fourth point being within 1 degree of the same line is also 1/180, so the chance of points 3 and 4 both being within a degree of the line between points 1 and 2 is 1/(180*180) which is 1/32,400 which is a small chance.
From memory that was pretty much the ratio of 3 point alignments to 4 point from map data. A five point alignment (that didn't have two earth works in it ] was a very rare occurrence in real or randomised data. The program never found one which didn't have a fat earthwork (or two) in it somewhere.
There is a way to consider every possible straight line in an area and check the distance of all the point from every theoretical line. I've got a note of in in the loft somewhere, but my little Amstrad didn't have the power to run it and deriving it is beyond my addled maths capabilities these days.
However, if you allow yourself the freedom to look for any and all possible alignments, then the more random points you have, the more alignments you will find, because every pair of points is a new line that a third or fourth point may also be on. It's like the thing with birthdays: the chance of a single random stranger having the same birthday as you is around 1/365, but if you have 50 people in the room, it is extremely likely that two of them will have the same birthday as each other.
Yesterday I evoked something called the Orthoténie, and, because my ufologic memories are more than rusty, I attributed this theory/technique to Jacques Valée, when the correct is Aimé Michel. Michel was inspired, by the way, by another Jacques, Jacques Bergier, that showed him the significance of observing phenomena that could be found happening three or four times on a straight line. Michel tried this hypothesis on the UFO sightings over France on a giving date, 24/09/1954 : he found that, on a straight line, from Bayonne to Vichy (485 km), not only 3 or 4 sightings could be marked, but 6, all in the same night. Michel tried this method on many other sightings on a giving period of 24 or 48 hours, always succeeding in plotting a number of phenomena over straight lines between cities or regions. Again, inspired by Bergier, Michel found that he could cross this lines and find a single intersection point. Giving a mathematic background to the method, an American, Alexander Mebane, found that the alignment of 3 or 4 phenomena/sightings could be dismissed as coincidence, but 6 phenomena aligned had a probability between 1/500000 and 1/400000000.
All this argumentation was refuted, in a way or another, by scientific magazines and publications, and the Orthoténie was forgotten on the rusty memory of teenage wannabe ufologists.
It would be interesting applying this method to lay lines. It would be, also, proof of scientific rigour to submit the ley lines theories to the many refutations once endured by the Orthoténie.
But, you know what - as (probable) illusions go, ley-hunting is potentially an incredibly educational one. I spent hours poring over maps and learned an awful lot about the geography and history of my locality. I also learned to love that locality - and to read a map. (By coincidence, I lived very near to Arbor Low, which is a great nexus for the avid ley hunter.)
I've always loved a map, and I can't help wondering now if it was maybe that early enthusiasm which inspired that attraction - and I don't resent a moment spent on it. It may all be in our imagination - but I'd say that this is one instance where that is not necessarily a bad thing.
I liked this opening for an article by Paul Devereux about ley lines in Fortean Times of June 2007:
Ever since Alfred Watkins announced his discovery of a network of ancient alignments crisscrossing the British countryside, the history of leys has been less of an old straight track and more of a long and winding road, one that has taken detours into everything from ufology to dowsing.
Poor Watkins! He was only trying to put some sort of order system into mapping remarkable places and things really spiraled out of control. This happens quite often as conceptual concepts related to actual factual or scientific concepts lose original meaning and clarity, or the terms get conflated.
And costs about the same. But looks fascinating....must resssiiisssstttt!!!
When you are standing at a high point in the White Peak area of the UK Peak District, where I was fortunate enough to be brought up - and where every hill, bump and rise seems to have a burial mound plonked on its ridge - it's actually quite hard not to see some sort of pattern in those ancient additions to the landscape. I'd hasten to add that I'm commenting on human nature, rather than actually suggesting that there is actually a system to the placement.
However, I've often wondered if human nature has also played a part in the initial acts, as well as their interpretation. If you were burying an important figure on a hill between two others which already had mounds on top, might it not seem somehow natural to place the new one at a point along the line that connects the other two? And might it not be that this possibly unconscious, but very simple desire, for some sort of order has been entirely misconstrued, forming the later conviction that much more complex forces were at play.
Sheer conjecture - which may simply be a reflection my own tidy nature, of course.