Is Washington DC more important than NYC or any city in Silicon Valley? I'm not convinced that capitals are the most important city.
You can talk about the culture, economy, and history of a country without ever talking about the capital. Capitals are usually (not always) where the government sits, but that's only a small part of what you can learn about a country.
It surely has a lot of influence on economy, history (culture is a different thing in a country-continent like the USA, but most countries are the size of a state, not the Union). Is * important to understand the state of *?
Texas City^H^H Austin of Texas
Los Angeles^H^H Sacramento of California
Anchorage^H^H Juneau of Alaska
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Edited to fix the initial bad example.
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Screw it, USA states have their capitals assigned to the weirdest cities instead of the largest ones. No wonder that you don't understand why capitals are important to normal countries.
We definitely have an odd way of assigning importance to subdivisions of land. I live in an area where one of the "cities" is a mansion rented out for events with a few businesses and homes built to support it: https://en.wikipedia.org/wiki/Carl,_Georgia
