I do not know why this keeps popping up. It basically goes like this:
Take the most recent piece of history, here recent is a maybe a quarter of the characteristic time scale of anything, say the economy, technology, population, … and proceed to extrapolate it into the far future.
The reason this never works is that everything has a natural limit set by the system. The extrapolation is always done at a point where the thing being extrapolated is just a minor player of insignificant but slightly noticeable value. Like the space rocket launches of the 1960s that were projected into the Jetsons. Nuclear power too cheap to meter. Microprocessors developing superhuman intelligence, etc. The current fascination is with the economic development of the BRIC countries. It say this is just not going to happen to the extent it is being extrapolated.
At some point in not too many years (10), BRIC will have grown to become such a large player that they will meet the same boundaries that are keeping other players like the US, Japan, and Europa from growing their towers into the sky. Since the sum total is limited by planetary constraints, what is actually going to happen is that the economy share of the latter will transfer in a slight fashion to the former.
The only way to grow exponentially is to discover virgin territory, and this actually does not last long given the geometric character of exponential growth.