You have to get the people there. This is something that "organic" cities like London, New York and Paris can do well, because there is a "virtuous circle" in action - people want to be at the centre of culture, culture costs money, these cities can attract the wealth creators who want to spend their wealth, and so it continues. Culture being whatever you're into, art, opera, fashion, publishing, fine dining... Cities like these are dynamos of both productivity and pleasure.

But in a sterile, planned city, that is initially empty... How do you get the ball rolling? How do you initially attract the people who can work anywhere in the world? The three cities I mentioned, and a few others, have solved that.

You say solved, but there was nothing to solve in your example cities since they were not planned or built from whole cloth (yes there were plans - the NYC grid, the Paris hub-and-spoke - but the cities, as you point out, grew and evolved).

Of course there was something to solve. London is 2000 years old, but NYC is much more recent. How did it become the hub for finance and media when there's Boston to the north and Washington to the south?

NYC had a better port. Back when this mattered, a deep-water port at the end of the Hudson river was a big deal (D.C. was never in the running, but up until 1815 or so Boston and Philly were bigger commercial centers than NYC.) For the first 100-150 years of its existence the early colonies traded more with England than with each other, so a good port was a necessity for a city but it did not need much else beyond that. Post-revolution most trade was still external rather than internal but England and France shut down most of this trade during the Napoleonic wars. At this point the advantage went to NYC because by sitting at the end of the Hudson river it was able to serve as the trans-shipment point for goods coming down from the Hudson river valley out to the other states. After the Gibbons v. Ogden court case established federalist supremacy over interstate commerce the maritime merchants of NYC were better positioned than their competitors in Boston, Philly, or Baltimore to take advantage of this explosion of commercial opportunity.

The reason people gathered at a certain buttonwood tree in lower manhattan was to trade shipping interests -- early finance was all about commercial shipping and the fact that NYC was an early leader in shipping led to the development of a finance hub and the two sides of the same coin propped each other up.

So how would you do this today? A better airport?

Here in England there is growing concern that Heathrow is stifling growth in London as it doesn't have capacity anymore and expanding it is politically infeasible. So it's not a far-fetched scenario...

The question that comes to mind - are they building a new NYC every 12 days or are they putting up a whole lot of building every 12 days? To borrow a cliche, NYC was not built in a day (or even 12 days) - it's an accretion and a culture. How does that change the question 'will NYC cease to be relevant'?

That was what I was thinking: just as nine women can't have a baby in one month, you cannot create a seething furnace of urban synergy by just throwing a bunch of infrastructure together. It's like giving a kid a cupcake liner filled with raw batter: you're going to make him cry.

I don't see NYC or any of the other regions mentioned—London, Tokyo, the Valley—becoming irrelevant anytime soon. I doubt any city is going to steal the title of "Capital of X" from any of them, though the industries that drive the success of these cities may wane—and wax and wane and wax and…—new cities (or existing cities) will rise to prominence due to the development of new industries and new ways of working.

One of the ironies that always struck me about the Valley was that much of it was built on the dream on making distance no longer matter. Instant, global, paperless, tele-blah, and on and on. Yet the Valley continued (and continues) to matter.

What we think of as technology really isn't technology any longer, in any meaningful sense. Pencils and paper are technology, yet CTOs don't control the stationary cabinet. I've asked, sarcastically, CTOs why they don't show more interest in the legal pads and ballpoint pens, to make a point: computers and phones are no longer perceived as technology but as things.

And as things, along with other newly-just-a-thing things like web apps and virtualized servers and storage and clusters, the history and dynamics that favor the Valley don't necessarily support the sort of innovations that are going to make a big difference.

That's why the New Yorker article on Nick Denton, who, according to the article, is trying to bring a television-like time model to web advertising—and is working to kill the impression model—is so interesting. It details a guy that's using technology—yawn, programmers—but has internalized and is working to forward the interests of a completely different culture.

Of course, the existing web advertising mindset is a product of the application of the paper publishing world's advertising models, which just goes to show that as time passes it's less about how any given technology technology wants us to think but how we make sense of that technology.

So maybe the sorts of things that come out of the Valley will change. There's an understatement. Of course they've already changed!

Place has a huge role in shaping what happens. Where you live affects the way you think about the world. The way you think about the world affects where you want to live. (See Slate's "The Big Sort" coverage.) Until a city has a distinct worldview, a Weltanschauung, that draws people and changes them—and the rest of the world—it doesn't really matter.