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That's a pretty interesting way to look at it. It also makes sense given that it'll take longer than that to exploit our own solar system, given that it's got millions of times the accessible resources of Earth.
The vertical axis of the graph on page 6 is in log scale - it already accounts for exponential growth, considering we get there in 600 years, which is, IMHO, a very reasonable (and I dare to say, optimistic) extrapolation.

Consider you need more than access to raw materials: you need the manufacturing capacity to harness the power source. Covering the Moon with 100% efficient solar panels wouldn't even put us on 1 at the Kardashev scale.

This paper appears to assume that no revolutionary changes in energy production make it vastly more available. Am I misreading it? With projects like polywell fusion reactors[1] showing great promise, I'm not sure if the conclusions drawn on that assumption are very predictive.

[1] http://en.wikipedia.org/wiki/Polywell

"calculated based on 27 years of data on historic energy trends, societal priorities, required mission energy, and the implications of the Incessant Obsolescence Postulate "

Yes, you're right. He's assuming everything proceeds growing the way it is now. You gotta start somewhere when predicting the future.

The problem is, that things like these create a misguided perception in the general public. Papers like these should be full of disclaimers that making predictions about any technology 200 years in the future is at best highly speculative. Ultimately I would argue the value of a constructed research like this is very little more than the work of a scifi author who just makes up some story based on the last 27 years of his life experience. The choice ultimately comes down to what method one prefers for speculating on what is going to happen 200 years from now.
They assume an upper limit with 100% efficient conversion of matter to energy, so changing the energy production method shouldn't make a material difference. EDIT/UPDATE: Realized you might be talking about the total energy budget (i.e., their total energy budget that is then multiplied by the "Space Devotion Ratio.") Yeah, that could advance the timetable by some amount.
Additionally, the only mention I see of matter to energy conversion is an aside about efficiency of propulsion technology, not energy generation; it doesn't appear that they evaluate matter-energy conversion as an actual energy source at all.
What if there is a social upper limit on energy development? Ever-greater energy generation density and capacity means that any mistakes are likely to have correspondingly larger consequences.

We should be using our remaining fossil fuels to fund the development of advanced nuclear power, which has much greater power density and capacity. Instead huge portions of society are pushing for solar and wind and geothermal etc, which are less dense and lower capacity. There simply is not the appetite to accept any nuclear fission accidents. And let's face it, accidents are inevitable on a long enough time span with complex new technologies.

But we're not going to cross interstellar space on solar and wind.

> There simply is not the appetite to accept any nuclear fission accidents

Well, that's part of the reason why fusion is attractive.

Interestingly, the author dismisses the 0.3c matter-antimatter possibility in favor of a much more modest 0.03c, and then goes on to list "earlier", "nominal", and "later" scenarios while ignoring an entire order of magnitude of velocity.
It's an interesting analysis, but I'm extremely dubious about the degree of extrapolation going on here. It's hard to imagine that the past 25 years have been typical in human history, or for that matter that the past 125 years have been. Is it really safe to make any quantitative assumptions about how technology and society will support spaceflight 200 years from now?

Those concerns are only magnified by the author's willingness to list a "nominal readiness date" of the year 5000 for humanity to be able to capture and use 100% of the entire galaxy's energy output (last line of Table 5). It would take 20 times that long just for us to reach the other edge of the galaxy, even assuming light speed travel.

"We are not going to be able to operate our Spaceship Earth successfully nor for much longer unless we see it as a whole spaceship and our fate as common. It has to be everybody or nobody."

--Buckminster Fuller

http://en.wikipedia.org/wiki/Spaceship_Earth