I agree that the 1 mile is too rigid. There are only going to be about 3,000 people within a mile radius of me (~1K/sq mile) whereas in Manhattan you would exp

I agree that the 1 mile is too rigid. There are only going to be about 3,000 people within a mile radius of me (~1K/sq mile) whereas in Manhattan you would expect around 210,000 (~70K people/sq mile). To get a similar expectation, I would need a radius of about 8 miles. Though of course, as I expand the radius to the south near NYC the population density gets a bit higher, and as I expand my radius to the north it gets lower and 8 miles is enough to bring about changes.