This is super fun, but the result isn’t surprising from a geometric point of view. The configuration space of n points in the plane (that is, all the possible pictures we can make with n points) is an algebraic manifold of dimension n!. Fixing the mean, median, correlation and some other parameters of those points only removes one degree of freedom for every property we fix. As n! is very large, and we only fix a handful of properties, we still have an enormous amount of space to move in and create images that are obviously completely different.
but the result isn’t surprising from a geometric point of view.
In this case I myself would go for the ‘did I see it coming’ definition of surprise, rather than ‘is it unlikely to occur’. Otherwise, no maths could ever be surprising, could it? I’m personally fond of the phrase ‘surprising yet inevitable’ – I got it from Howard Tayler talking about fiction writing, and apparently it was first said by Aristoteles, but it’s neat for this sort of thing, too.
Also, thanks for the n!-based explanation, that was new (and surprising!) to me.
For me, it was more a layperson view on it. I watch news articles post contradictory statistics all the time. They seem easy enough to massage to prove about any BS you want. That they can get different datasets to produce the same means or whatever is unsurprising from that perspective of “statistical results are easy to fake or mislead with if audience isn’t a statistics expert reviewing their methodology and data.”
This is super fun, but the result isn’t surprising from a geometric point of view. The configuration space of n points in the plane (that is, all the possible pictures we can make with n points) is an algebraic manifold of dimension n!. Fixing the mean, median, correlation and some other parameters of those points only removes one degree of freedom for every property we fix. As n! is very large, and we only fix a handful of properties, we still have an enormous amount of space to move in and create images that are obviously completely different.
In this case I myself would go for the ‘did I see it coming’ definition of surprise, rather than ‘is it unlikely to occur’. Otherwise, no maths could ever be surprising, could it? I’m personally fond of the phrase ‘surprising yet inevitable’ – I got it from Howard Tayler talking about fiction writing, and apparently it was first said by Aristoteles, but it’s neat for this sort of thing, too.
Also, thanks for the n!-based explanation, that was new (and surprising!) to me.
Yeah, I should have said “can be explained”. :)
For me, it was more a layperson view on it. I watch news articles post contradictory statistics all the time. They seem easy enough to massage to prove about any BS you want. That they can get different datasets to produce the same means or whatever is unsurprising from that perspective of “statistical results are easy to fake or mislead with if audience isn’t a statistics expert reviewing their methodology and data.”
The visualizations were still cool, though.