this link is _fantastic_ , thank you for sharing it, i haven't heard this argument before .

First: For a given constant T > 0 there exists C > 0 such that Temp(earth) <= T implies Energy(earth) <= C

  > Right, if you plot the U.S. energy consumption in all forms from 1650 until
  > now, you see a phenomenally faithful exponential at about 3% per year over
  > that whole span. The situation for the whole world is similar. So how long
  > do you think we might be able to continue this trend?

  > Alright, the Earth has only one mechanism for releasing heat to space, and
  > that’s via (infrared) radiation. We understand the phenomenon perfectly
  > well, and can predict the surface temperature of the planet as a function of
  > how much energy the human race produces. The upshot is that at a 2.3% growth
  > rate (conveniently chosen to represent a 10× increase every century), we
  > would reach boiling temperature in about 400 years. [Pained expression from
  > economist.] And this statement is independent of technology. Even if we
  > don’t have a name for the energy source yet, as long as it obeys
  > thermodynamics, we cook ourselves with perpetual energy increase.

  > At that 2.3% growth rate [of global energy consumption], we would be using
  > energy at a rate corresponding to the total solar input striking Earth in a
  > little over 400 years. We would consume something comparable to the entire
  > sun in 1400 years from now. By 2500 years, we would use energy at the rate
  > of the entire Milky Way galaxy—100 billion stars! I think you can see the
  > absurdity of continued energy growth. 2500 years is not that long, from a
  > historical perspective. We know what we were doing 2500 years ago. I think
  > I know what we’re not going to be doing 2500 years hence.

  > If we tried to generate energy at a rate commensurate with that of the Sun
  > in 1400 years, and did this on Earth, physics demands that the surface of
  > the Earth must be hotter than the (much larger) surface of the Sun.

Second: Energy(earth) / GDP(earth) >= K > 0

  > Then in order to have real GDP growth on top of flat energy, the fractional
  > cost of energy goes down relative to the GDP as a whole.
  > How far do you imagine this can go? Will energy get to 1% of GDP? 0.1%? Is
  > there a limit?
  > if energy became arbitrarily cheap, someone could buy all of it, and
  > suddenly the activities that comprise the economy would grind to a halt

That is, assuming we want Temp(earth) <= T for some constant temperature T, then there exist positive constants C > 0, K > 0 such that Energy(earth) <= C and Energy(earth) / GDP(earth) >= K > 0 . Therefore GDP(earth) <= C / K .