How big is too big? How fast is too fast?

It seems like prevalent economic theory says things can't be fine unless economic activity keeps growing at some very-hard-to-know appropriate rate. This sort of thinking has also been applied in the realm of energy, particularly in forcasting how much energy will be needed in the future to keep things running nicely. But there might be an invisible problem here . . .

The Invisible Research Institute has been picking up bits and pieces of information from various places for quite some time, and now believes that the current worldwide energy "consumption" rate for all purposes is about 13 TeraWatts. Various sources project this will grow to 50 TW in the next 45 years.

Going from 13 to 50 in 45 years is an annual growth rate of 3.0388%. That sounds like a nice, conservative, healthy growth rate, now doesn't it?

So if we start using 13 TW, and grow at this rate for say 1,600 years, we'd be using about 9 times as much energy as the entire sun produces - not just the energy that hits the earth, but all of it! - and 9 of them!

That seems unlikely, not to mention potentially unhealthy, so what's wrong? Surely 1,600 years is not the problem, as today we're fighting wars over ideas spawned roughly that long ago . . . and surely it can't be the growth rate since 3,0388% is so conservative and healthy. I wonder what it is?