The Somerset projectLey lines, or the arithmetic of dots?
Real monuments, random monuments, and a fairer kind of random that changes the answer.
The learner downloads the Historic England list of scheduled monuments and keeps the 233 whose centre points fall inside the Mendip district. With 233 points there are 2,081,156 different sets of three. A set counts as a straight line when one monument sits between the other two and within 25 metres of the line joining them. The program checks every set and finds 14,569 alignments. That sounds astonishing, until you ask the only question that matters: how many would random dots give?
To answer it, the program scatters 233 random dots over Mendip using rejection sampling. It picks a random spot in the rectangle around the district, keeps it if it falls inside the boundary and throws it away if not. About 60.6 per cent of spots are kept, so each dot takes about 1.65 tries. Twenty scatterings of random dots give between 5,746 and 6,910 alignments, averaging about 6,326.
Near-straight triples within 25 metres, our runs of 26 September 2026| Set of 233 points | Straight triples | What it tells you |
|---|
| Real Mendip monuments | 14,569 | The number to explain |
| Random dots, spread evenly | About 6,326 | Monuments beat plain chance by more than two to one |
| Each monument moved up to 3 km | About 11,217 | Keeping the clumps explains much of the gap |
| Each monument moved up to 500 m | About 13,159 | Most of the excess is simply clumping |
Evenly spread random dots are an unfair comparison, because real monuments are not spread evenly: their typical distance to the nearest neighbour is 354 metres, against 844 for random dots, and 94 of the 233 are bowl barrows, which often sit in groups. Points packed into clumps make far more straight triples. So the program builds a fairer kind of random: each real monument is moved to a random spot within 500 metres of where it is. That keeps the clumps and scrambles any deliberate lines, and it produces about 13,159 alignments. Most of the excess over even chance was clumping all along.
A small gap remains: 14,569 against a highest value of 13,479 across ten scrambled runs. That could mean some monuments really were placed in rows, such as barrows along a ridge or sites beside an old route, or it could come from how the centre points of large monuments are calculated. The honest conclusion is not "ley lines are real" or "ley lines are nonsense", but that the evidence for deliberate lines is far weaker than the raw count suggests, and that finding the real cause means looking closely at the few triples that remain.
Ages 9 to 12
Throw twenty counters on a map, draw every straight line through three of them, and count how many you find without trying.
Ages 12 to 15
Write the three-point line test in Python, scatter random dots with rejection sampling, and count the lines they make.
Ages 15 and up
Run the full comparison with the real monuments, build the clustered random model, and explain what the remaining gap could and could not mean.
What is recorded and what is ours
The monuments and their names come from Historic England's National Heritage List, and the Mendip boundary from the ONS. The alignment rule, the random models and every count in the table are ours, and a different width or rule would give different numbers. Nothing here says anything about what the monuments meant to the people who built them.
