When looking at a map of North America, we can actually get a good estimate of the prosperity of large cities simply by evaluating the size of the city and the geographic reasoning behind it's location.
As the continent was being settled, it was fairly predictible where cities would form. The site of New York City is not only a very good location for a harbor (harbour), but also has a plentiful supply of fresh water from the Hudson River. Cape Cod forms an ideal natural harbour (harbor), and it is perfectly logical that a city like Boston would grow up there. If we sail up the St. Lawrence River until we encounter the obstacle of the Lachine Rapids, we find an easily defensible island with a hill in the river and it should come as no surprise that it formed a natural site for Montreal.
When pioneers settled the west, they could go no further than the Pacific Ocean and a city would form where they stopped that is today called Los Angeles. Further north, along the same coast, there was an ideal harbor (harbour) and another city grew there, San Francisco. A similar scenario applies further north, with Seattle, Vancouver and, Victoria. Those pioneers would be delayed as they crossed the plains and encountered the Rocky Mountains, and there we have Denver.
Settlers would also go as far south into Florida that they could go, and there we find Miami.
A lake forms an ideal waterway, and since Lake Michigan extends far into America's agricultural heartland we might expect to find a city like Chicago at it's end. Lake Erie was another natural waterway, and Buffalo and Toledo grew at it's opposite ends. In a similar way, we find Hamilton at the western end of Lake Ontario.
Inland, we would expect to see cities roughly evenly-spaced across the hinterland, such as Columbus and Indianapolis, and a series of cities along a river like the Mississippi. Where America's largest river meets the sea, we would logically find a city, and there we have New Orleans. Where two rivers meet, we might expect to find a city like Pittsburgh.
However, I notice that prosperity is another factor. The Inverse Geographic Prosperity Principle is that when the size of a large city exceeds the geographic logic of it's location, the difference can be explained by the prosperity of the city.
The city that first made me think of this is Toronto. The geographic reasoning is simply not there for such a large city to be located where it is. The Toronto Islands, just off the shore in Lake Ontario, form a harbour (harbor), but the city's basic industry is banking and the harbor (harbour) is much less significant than that of Hamilton, to the west. So, the only possible explanation for such a big city to be located on the northern shore of Lake Ontario, without the geographic foundation of the continent's other big cities, is that Toronto is a very prosperous place. Prosperity brings growth as well as does geographical logic.
Atlanta is another city that has grown out of proportion to the geographic logic for it's existence. Atlanta, which is not on the coast, makes sense as a hub city in the hinterland, sorrounded by smaller cities, towns and, farms, but it has clearly grown well beyond what we would expect such a hinterland city to be and this can only be explained by prosperity.
What about deserts? For a city to grow in the desert, it must be prosperous. There cannot be a big and poor city in the middle of the desert. The only thing that can bring about a city, where geography would seem to dictate that there really shouldn't be a city, is prosperity.
Thus, we can say that the population of a city, at least in North America or other freely settled domains, is equal to the geographic logic for it's existence plus it's prosperity.
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