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Most towns in the Midwest were platted around proposed or newly-constructed railroads. The Illinois Central was the most extreme example, and actually used the exact same plat map to lay out a couple dozen towns between Chicago and the Kentucky/Missouri line. Hence “Oak Street” and “Locust Street” are always on the opposite side of the tracks as “Walnut Street.”

The variance between town spacing is also a function of railroad geometry. The more intersecting lines you have, the bigger your city gets. Bigger cities, in turn, can serve a wider market area (there’s more stuff there to justify the trip). So, for instance, in the middle of Illinois you have a bunch of small cities slugging it out (Decatur, Danville, Bloomington, Springfield) but as you get closer to the “poles” (Chi and StL) you have a reduction in density before the sprawl starts. Hence Dwight, IL is a truckstop while Joliet (inside the Chicago commutershed) has the historic industrial base.

Paved roads (auto trails) only showed up after the railroads had determined population distribution. US numbered highways followed the paved roads, and Interstates followed the most popular US routes, so you have an iterative winner-take-all system in which the city with favorable rail service in 1885 ends up being the city with a couple of freeways in 1960.

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South of that, the South of Market grid bends around until it’s almost north-south-east-west, with 3rd street crossing all the streets above 15th at right angles. Further south, there’s another grid, which is about 20 degrees off the cardinal directions; here the streets are alphabetical in *both* directions.

The western half of the City has a grid over most of its area, once again, not *quite* in the cardinal directions. The north-south streets are numbered “Avenues” (repeating numbers used in the numbered “Streets” on the east side), while the east-west ones are alphabetical. Except the streets which border Golden Gate Park.

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Well it takes a lot more confusion to get lost in a little place like Bremen after all.

The main plan of German cities that started from villages accreting around missionary churches, which is all of them but the few that were Celtic oppida before the Roman conquest, is a star-shaped net of avenues leading out from the central square and cathedral. If you get lost, the first thing to do is to head inward to the center of town, because all the roads out originate there.

NYC is the opposite; it has no center. It is the 19th century equivalent of LA.

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When this stuff was being laid out the only thing that mattered was ease of surveying. The area was basically trackless wilderness by this time (Earlier it had been farmed and settled, but there was a big die-off.)

“No one is going to place a town in the middle of a field just to meet an arbitrary distance.”

This was not a consideration when the area was basically trackless wilderness, especially since the flatness of the terrain permits siting a town, building a road, or platting fields out just about any way people felt like doing it.

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I believe that Philadelphia, Allentown, Scranton, Binghamton, Syracuse, Kingston also form a line.

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For more than 3 points, you can adjust for multiple comparisons. That’s fine if multiple lines show up, but what if 4 points form a line? That is not interesting as 4 separate lines, but because it is stronger evidence of a line. So probably you should introduce a new measure L4 of how close the 4 points are to a line. Perhaps simply the sum of the old L of all 4 subsets of 3 lines.

But should we stop and 4 points? Or should we look at all configurations of 10 points? Literally looking at all subsets of 10 is not computationally tractable. And it leads to a terrible multiple comparisons correction. I worry that the Bonferroni correction is too pessimistic because of the correlations. But whatever procedure you come up with – say, working your way up the number of points by throwing out n-tuples with too high Ln – you can test it on data generated by your null hypothesis to get a p-value.

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