Matt Parker ("Stand up Maths" channel on YouTube) gave a very informative and entertaining lecture in 2010 titled "Clutching at Random Straws" [0], which, among other things, covered something similar. From the subtitle of the video: "Did aliens help prehistoric Britons find the ancient Woolworths civilisation?" The answer is "no". Given enough data points, you can find all sorts of patterns.
I've got to assume that this is partly a Birthday Problem - that the probability of something unlikely being true grows rapidly as the population grows. Probability of 3 random churches lining up? Small, probability of 3 churches lining up when there are 100,000 churches in Europe? Basically 100%
That's one of the examples he goes into in his talk, at a high level anyway. I'd love to find a write-up of someone who has done the detailed calculations of how likely alignments and shape occurrences are.
Another thing that would be interesting is to look at the effect of non-uniformly distributed birthdays. For example, the day that's nine months after valentine's day or christmas might (?) have a slightly higher number of births than an average day. Then you could look at what kind of an effect this would have on the probability of a common birthday as a function of group size.
Thanks for the link. Gist was that with enough data, lots of patterns are inevitable.
He gave example from some text taken out of bible with spaces removed. That's lots of letters on one screen, and from those letters he was able find his name, date and topic of the talk, when joining letters at equal distance.
Finding unbelievable patterns is not as amazing as we think.
He also covered this in a more recent talk [1] which has some better audio and a direct feed of the slides. It also comes with an entirely different set of interesting stories for anyone inclined to listen :)
Check it :-) Other popular saints and devotions are "Mary", "Joseph", "Paul", "Sacred Heart", ... can you easily get seven sufficiently special ones on a line for those?
0: https://www.youtube.com/watch?v=sf5OrthVRPA