Ramsey theory

Ramsey theory is a branch of mathematics that studies the conditions under which order must appear. It is named after the British mathematician and philosopher Frank P. Ramsey who discovered its foundational result, known as Ramsey's theorem.

Although there is some complex mathematics behind it all, basically it boils down to saying:

Given enough items to play with, you can find pretty much any pattern you want.

It is of enormous interest to skeptics and rational thinkers, because it can be used to dismiss more woo than any other branch of mathematics. Generally, whenever someone is claiming to have found some mysterious "order" in apparently random objects or items, Ramsey theory is in full effect.

Examples of this "order" include mysterious lines connecting ancient monoliths, random phrases emerging from analyses of the text in the Bible, and other such stuff which appears to be too precise to "have occurred by chance". Ramsey theory allows us to state — armed with the full authority of formal mathematical proof — that yes, whatever it was you think you have found could have occurred entirely by chance. With enough data, patterns are unavoidable.

The formal stuff
Ramsey theory comprises an entire subschool in the area of combinatorics. The initial finding, Ramsey's theorem (published in 1930) states that in any colouring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs. For two colours, Ramsey's theorem states that for any pair of positive integers (r,s), there exists a least positive integer R(r,s) such that for any complete graph on R(r,s) vertices, whose edges are coloured red or blue, there exists either a complete subgraph on r vertices which is entirely blue, or a complete subgraph on s vertices which is entirely red. Here R(r,s) signifies an integer that depends on both r and s.

Since the original theorem, many other findings have been published, all exploring the circumstances behind the emergence of particular types of order from apparent randomness. It remains an active field of mathematical research.

The anti-woo stuff
To witness Ramsey theory in full effect, a case study is illustrative.

In 2010, that fine bastion of objective British journalism, the Daily Mail, published an article entitled "How a prehistoric sat nav stopped our ancestors getting lost in Britain". The article presented research which analysed the location of 1,500 prehistoric monuments and found them all to be on a grid of isosceles triangles, with each pointing to the next. According to the researcher Tom Brooks, "Such patterns could only have been the work of highly intelligent surveyors and planners which throws into question all previous claims as to the origin of mathematics."

There is no doubt that Brooks did actually find the "mysterious" grid lines. Unfortunately, he did so by skipping over the vast majority of the sites, choosing only the few that happened to line up. Matt Parker of the University of London's School of Mathematics subsequently determined that there were 561,375,500 different possible "ley line triangles" using the 1500 monuments as a basis and that there was nowhere you could stand in the entire British Isles that was more than 58 metres away from a ley line intersection.

Parker later went on to "prove" the same theory about a prehistoric navigation system using the location of Woolworths supermarkets. He justified his research on the basis that, "if we analysed the sites we could learn more about what life was like in 2008 and how these people went about buying cheap kitchen accessories and discount CDs".

Ramsey theory says that such "apparent order" is not only likely, but that as the number of member elements increases, this "apparent order" actually becomes unavoidable. It is important to note that of all the total permutations, those which appear ordered will only represent a minuscule proportion. Hence a key aspect of woo arguments that exploit Ramsey theory is the fact that the vast majority of data is ignored in favour of the tiny set which meets whatever "apparent order" was wanted.