Delete this question please.

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    $\begingroup$ Your method would be fine during any previous age, but game-changing advancements in science are now emerging so quickly, that old methods like per capita growth comparisons no longer rule absolutely. Sometime in the next few decades, some nation will master fusion, or age-reversal, or direct-light-to-electricity conversion, and when they do, it will not matter what their previous year GDP was. They will become a superpower overnight. $\endgroup$ – Henry Taylor May 5 '15 at 1:45
  • $\begingroup$ @HenryTaylor I should have been more specific, it's in the near future (2060) $\endgroup$ – Vincent May 5 '15 at 1:51
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    $\begingroup$ 2060? That's 45 years away. Right now the world looks very different from predictions that were made forty-five years ago. For one, the green revolution totally changed the game for the amount of people the world could support. But in 1970 plenty of people where predicting that we'd all be starving by now. $\endgroup$ – CoolCurry May 5 '15 at 2:08
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    $\begingroup$ @HenryTaylor Well, maybe. But odds are that any ground-breaking technology will come from a nation that's already a major power. No offense to the people of Sri Lanka or Tuvalu, but the chance that a small, poor country will suddenly invent a major new technology is small. For the same reasons why they are a poor, small country today: lack of infrastructure, established research facilities, etc. And even if they did, inventing a new technology and implementing a new technology are two different things. Suppose an isolated genius in Tuvalu suddenly came up with a way to pull off ... $\endgroup$ – Jay May 5 '15 at 6:46
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    $\begingroup$ ... cold fusion, for example. Then what? His country doesn't have the resources to start building a chain of power plants. And the existing powerful countries would likely quickly acquire the technology one way or another. Also, how is this different from past ages? What if some non-major-power had been the first to invent the steam engine, or the airplane, or the printing press, etc? $\endgroup$ – Jay May 5 '15 at 6:48

The United States today has economic growth rate of about 2 1/2%. This is historically low. The U.S. average from 1790 to 2014 was 3.73% according to this article: http://finance.townhall.com/columnists/danieljmitchell/2015/05/04/why-is-america-richer-than-kazakhstan-and-why-has-estonia-surpassed-croatia-n1993872/page/full

The fastest growing countries today are around 10%. Those are mostly poor countries, I presume it's easier to show a lot of improvement when you're starting from a low baseline. Among large countries, India and China are both growing at about 7%. The average for Europe is 1.4%. There are a number of countries showing negative growth, like Italy, Cyprus, and the Gaza Strip.

You could easily look up growth rates for various countries and project that forward 45 years. But that would be unlikely to give accurate projections: these rates tend to vary with all sorts of circumstances.

It certainly would be valid to look at historical rates to get a feel for what the standard of living might be in 45 years. If to get the standard of living you are projecting would require 20% per year growth for 45 years, that's very unlikely to happen. If you assume less than 2% you should be explaining why that country is stagnating.

As to who will be on top in 45 years ... of course one could speculate endlessly. I'd be surprised if a list of the major players was totally different from today, though it's likely some existing power will decline and some existing lower-tier nation will rise. Think how today compares to 1970, i.e. 45 years ago. Russia has declined sharply in power in that time. Besides that, any list of major powers is pretty similar.

On the other hand, compare 1935 to 1980. Britain and Germany were among the greatest powers in the world in 1935. Both were still important in 1980, but no longer the top of the heap. The U.S. rose considerably in that period. Etc.

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