Economic 101 people
Good conclusion in the article, however the salient argument for reaching that conclusion wasn't clearly demonstrated - hence why there's a lot of people here producing arguments that miss the point. There's also the classic economists trick of jumping to look at a comparison to a counter factual or a rate of change rather than the cruder absolute amounts.
Hopefully this should make things clearer - I will do an example first - related to both IT and the environment as they seem popular round here, and then the models.
in 1980 I could produce a circuit board for a PC. However manufacturing was inefficient and I wasted 50% of the input materials. All sorts of nasty chemicals were the waste by products of production.
Today, due to technological advances, I can produce the same circuit board, with only 5% input material wastage. This allows me to produce more circuit boards today than 30 years ago. I'm still using resources but for the same output considerably less than before - and perhaps enough to be a sustainable level of input resources.
<pinch of salt>
Flying - it's evil...it fuels terrorism and despotism through money flows to undesirable states and spews filthy carbon like the halitosis of satan across the planet.</pinch of salt>
Until along comes a technological advance. We suddenly have new airplanes running of nuclear or some other non oil resource (Say what you like about nuclear safety, radiation etc you can't argue that it's not resource efficient, even including the extraction process.
Suddenly we could double the number of flights (growth) using no more of the preciously limited natural resource of oil on each journey. (Yes you need oil to make the plastics for the planes)
In this example we use a small amount of resources today to make the planes, but save a shed load in the future. Over the period as a hole we have achieved growth and used less resources.
Solow Growth from 1957 - note it is a model not a formula (It would never be dimensionally consistant!)
K = stock of human & Physical capital
L = unskilled labour
A = constant reflecting technological starting position
eu = rate of exogenous technology growth.
Endogenous theories - same as above but attempt to bring in technology growth as a result of education and capital investment.
CONCLUSION: Economics does not require us to be using more resources in 10 years time, just because we have grown.