One of the best known of Zeno's paradoxes says that Achilles will never be able to overtake the tortoise in front of him, no matter how fast he runs. Why? Because Achilles must first reach the point from where the tortoise started, which means the tortoise is always ahead. It is a nice illustration of how easy it is to build abstract theories that hold little relation with reality.
Paul Krugman seems to have created some kind of a similar paradox with a recent New York Times article (“Slow Steaming and the Limits to Growth”) where he sets out to demonstrate that the world's gross domestic product (GDP) can continue growing even while reducing energy production. He does that by means of the example of “slow steaming.” Noting that the energy consumption of ships grows more than linearly as a function of speed, Krugman states that you can always save energy by slowing ships down and increasing their number. If the relation of speed to energy consumed is, let's say, quadratic, then by doubling the number of ships and halving their speed you reduce the energy consumed to a half. So, it is possible to maintain a constant economic throughput while reducing the input of energy to the system. Q.E.D.? Well, unfortunately things are not so simple.