Hanson's paper is making the point that economic growth (measured as gross world product) has been increasing faster than exponentially for a long time, or more precisely that it can be modelled as an overlapping series of exponentials with rates that have increased with each characteristic epoch.

It doesn't say the same is true of population growth, at least recently, and certainly we're lucky that population growth is easing away from its previously exponential (in the recent past) and super-exponential (going further back) track.

But I really take issue with is the idea that because super-exponential growth has gone on for a long time, it's a priori plausible for it to continue for quite a while.  In fact, the more super-exponential the growth function, the less reasonable it is to extrapolate that way from the past!  In the extreme case, you could have a pattern of very little growth at all until the last 10 years, where you have hyperbolic growth taking off towards infinity in another 10 years.  Few people would suggest extrapolating on that basis.

As a side note, I'd bring up Jared Diamond's Collapse and point out that in many regional instances neither economies nor populations managed to maintain (super-)exponential growth.  Since until very recent centuries human history is a sum of generally isolated regional human histories, we would do very poorly to ignore these natural experiments now that we have in effect only one big population.

Now, I'm not arguing that economic growth as measured by world domestic product can't continue steady exponential growth, or perhaps even super-exponential growth, though I have severe doubts about the kind of Singularity Hanson appears to entertain purely from the models.  

(GDP/GWP may be a bad measure of economic activity going forward, but that's a whole other discussion)

But our ability to increase economic activity in that fashion is available only to the degree that we can divorce it from whatever physical limits the Earth presents us with. Nanotechnology, super-low-powered computing, virtual worlds (and the potential huge economies they could bring) are all wonderful things which may allow us to markedly increase our economic activity and personal utility ... but they don't do anything to solve the very pressing issues around energy and other physical resource issues (topsoil, water, etc.)  

Dropping energy per GDP is by itself of little use; there's no sign that rich countries are yet spending enough of their wealth on intangibles and services to stop increasing their total (or even per capita) ecological footprint.  We've been granted a demographic gift of a population that may stabilize on its own below 10 billion in this century, but that bit of luck will be of little use if we rely on luck (or price signals alone) to prevent the pain and dislocation of resource scarcity.

There's reason to believe that our population might not have been growing exponentially for a million years. Check out the transcript of this programme from the BBC: http://www.bbc.co.uk/science/horizon/1999/supervolcanoes_script.shtml

About four fifths of the way down the page they discuss a population bottle neck 70-80,000 years ago, based on miochondrial DNA evidence. It seems the human population may have numbered as few as 10,000 at that point. The time frame coincides with an erruption of the Sumatran supervolcano Toba 74,000 years ago, which would have had dramatic effects on the climate. That erruption was near the high end of the volcanic explosivity index, putting it at perhaps 10,000 times (or more) as intense as the erruption of Mount St Helens (if memory serves). For what it's worth, there's another supervolcano with similar explosive potential under Yellowstone Park. It seems to errupt about every 600,000 years, and the last erruption was 640,000 years ago. There are some things that make even peak oil look insignificant.

Human evolution happens to be one of my interests, Halfin, and talking about million year trends strikes me as a bit fantastic. One million years ago Homo erectus was running around just like any other animal making a living as best they could in their ecological niche. They certainly were not involved in any activities like those our species have engaged in from the beginning of the Holocene up to the present time.

Actually, there is good evidence that these same Homo erectus guys had thick, elongated skulls and large brow ridges because they (at least, the males) used to bash each other over the head to settle disputes (probably mostly over mating partners and territory). I won't dispute that a million years ago, these hominids were among the most dangerous predators then existing. Now, of course, Homo sapiens, having helped pushed Homo neanderthalensis into extinction, reigns supreme. And there is no doubt about what animal is the most dangerous predator on the Earth anymore. Taking the very long view in Geological Time, it would appear that Nature made a big mistake in the Pleistocene. Still, I'm sure that most of us are glad to be here even if the timespan for our continued existence is somewhat problematic--again taking the very long view.

So, maybe things haven't changed much.... Now we just prey on each other and the rest of the natural world.

I could provide hundreds of references if you like but don't ask. In any case, this tends to cast doubt on the source Robin Hansen you cite in your comment.