[randomtoast]

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.

[robertlagrant]

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.

[randomtoast]

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.

[jimktrains2]

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.

[robertlagrant]

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

Ah - I missed this one.

[randomtoast]

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

[robertlagrant]

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.

[082349872349872]

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

[regularfry]

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