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Comment by ot1138 | Hacker News Reader

Please do so! This would be a fascinating experiment and perhaps a famous one, given that similar answers are the knee jerk reaction of armchair skeptics the world over.

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I asked GPT-4. It did the following calculation (summarized):

Let's consider Europe as roughly a 10 million square km area. The probability of a single point falling within a 50 km wide band (assuming the band runs the full length of Europe) is about 0.01581 (1.581%). The probability of seven points aligning within a 50 km wide band across Europe is approximately: 10^-14

Doesn't the first point have a probability of 1? It's the subsequent ones that become less and less likely.

Maybe my question was not right then. But my question was how likely is it that 7 randomly chosen points fall within a given 50 km band across europe. Because I want to test the hypotheses that the 7 cathedrals fall randomly in line that we see. And that one random point falls in that band is not 1.

It's pretty easy to Monte Carlo, even if you can't get there analytically.

Yes, but I suppose even if you have 7 that line up, they may not fall in your band.

To remove that constraint, so it's just any band, I think it should be more like: given a cathedral is in a particular place, how likely is it that six other cathedrals fall in a 50km wide band aross Europe.

Okay, GPT4 said there a just 189 non-overlapping 50km bands (horizontal, vertical, and diagnoal) in Europe and then continued to calculate the chance to land those 7 points in any of the 189 bands and gave a result in the order of 10^-12.

But diagonal at what angle? :)

I think if you set the probability of the first one at 1, then the rest works perfectly at any angle of band. I could be wrong, but intuitively that seems correct.

You could have two points in 2 of your non overlapping bands that are less than a band's width apart.

Also, the probability of the first 2 points will always be 100% because they define the line.

Also, it's not 7 random points, it's 7 of thousands of random points.

Alright, I suppose it's not as simple to formulate the question accurately and correctly.

> Also, it's not 7 random points, it's 7 of thousands of random points.

Ah - I missed this one.

search box tells me 600 choose 7 is 5e15, which implies (if google and GPT4 were correct) that there ought to be on the order of thousands of fat lines containing 7 actual cathedrals

This is an impressively irrelevant calculation, regardless of whether or not GPT did the arithmetic correctly. If you want to calculate something similar but actually useful, you could get a list of all "cathedrals" dedicated to st michael, find the line for each combination of 2 cathedrals, and then calculate the probability that 5 more also fall on that line.

But it turns out that we don't even have to go that far. The line found in TFA is about ~50km wide. Any given 50km wide line covers approximately 1% of europe's area. There are allegedly 800+ locations dedicated to st michael in the UK, so let's make a conservative estimate and say there are ~1000 in all of europe. This means that in any given 1% of europe's area, there are on average 10. Therefore literally any 50km wide line that crosses a substantial portion of europe has a solid chance at having 7 or more st michael dedications in it.

Edit: actually via a generalization of the pigeonhole principle, if we assume that europe is 3000km tall and contains 1000 sites dedicated to st michael, there must exist at least one 50km band that contains at least 17 sites.

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