An Inconvenient Puzzle: Global Warming, Genies and Torture

Oklahoma Sen. James M. Inhofe, the former chairman of the Environment and Public Works Committee, has called global warming "the greatest hoax perpetrated on the American people," and excoriates former Vice President Al Gore's movie "An Inconvenient Truth" every chance he gets.

And just recently, presidential aide Karl Rove has clashed sharply with environmental activists Sheryl Crow and Laurie David.

Inhofe and Rove are by no means alone. Skepticism about global warming and its causes is widespread. One overly kind reading of their position is that it is, to an extent, a consequence of the general problem of dealing with very big numbers and very small numbers. Such numbers are outside our familiar mid-size range, and so our intuition about them isn't well-developed.

A somewhat myopic focus on the day's mid-size happenings, although essential to our survival as people, and perhaps as U.S. senators and presidential aides, can nevertheless cause problems for us.

Ponzi Schemes and Discount Rates

Evolution would point to the enhanced survivability of organisms that respond quickly to local or near-term events. This quick response results in a steep temporal and spatial discount rate for distant or future events. The latter are discounted in the same way that money is. Suffering ordained for 25 years from now is, like a $10 million personal debt due in 2032, considerably easier to bear than is suffering, or bankruptcy, scheduled for tomorrow.

The relevance of this short-sightedness to greenhouse gases and extinct species should be obvious. Environmental despoliation may even be conceived of as a kind of global Ponzi scheme, the early "investors" (that is, us) doing well, the later ones losing everything.

Nevertheless, the "right" discount rates are not so easy to determine and vary from case to case. It's not that we shouldn't prize the here and now, but, as residents of a global village whose actions can reverberate for a long time, we may need a global reserve board to help decide on more rational discount rates to keep us from being our own Ponzis.

Imp in a Bottle

As I wrote in "A Mathematician Reads the Newspaper," Robert Louis Stevenson's story "The Imp in the Bottle" provides a fictional illustration of the psychology behind one sort of dismissal of global warming. It is the story of a genie in a bottle who will satisfy your every wish for love, money and power. You can buy this amazing bottle for any amount that you care to offer. The only constraint is that when you are finished with the bottle, you must sell it for a price strictly less than that you paid for it. If you don't sell it to someone for a lower price, you will lose everything and suffer everlasting torment in hell. What would you pay for such a bottle?

Certainly, you won't pay 1 cent for it because then you won't be able to sell it for a lower price. You won't pay 2 cents for it either because no one will buy it from you for 1 cent for the same reason. (Everyone knows that it must be sold for a price less than the price at which it is bought.) Neither will you pay 3 cents for it; the person to whom you would have to sell it for 2 cents would object to buying it at that price since he wouldn't be able to sell for 1 cent.

A similar argument applies to a price of 4 cents, 5 cents, 6 cents and so on. Mathematical induction can be used to formalize this argument, which proves conclusively that you shouldn't buy this magic bottle for any amount of money. Yet you would almost certainly buy it for $1,000. I know I would. At what point does the argument against buying the bottle become practically convincing?

Slow Torture

As the above thought experiment illustrates, the consequences of our decisions need not occur in the distant future for us to discount them. They can occur far away or after so many steps as to seem distant. Another example is provided by Derek Parfit in his book "Persons and Reasons," in which he discusses the case of someone strapped to a hospital bed with electrodes attached to his heart. Rotation of a dial in a distant location minisculely and imperceptibly increases the current in the electrodes and the stress on his heart.

Unfortunately, a free piece of candy is offered as a sweet incentive to anyone in the distant location who twists the dial. Assuming it takes 10,000 people, each rotating the dial once to electrocute the victim, what degree of guilt attaches to each individual dial-twister? Do these tiny guilt bits accumulate in any moral bank account?

The real question, of course, is, what is the impact of thousands of small environmental or personal abuses over time? In terms of this story, most environmentalists would probably opt to stop rotating the dial or at least to rotate very infrequently. They would also probably try to find other sources of candy or, better yet, try valiantly to substitute fruit for candy.

The Inhofes and Roves of the world, on the other hand, would perhaps argue that it takes many, many more than 10,000 twists of the dial to stop the victim's heart. Or perhaps they would argue that the free candy we get until the the eventual electrocution is worth it, or else they'd come up with some other rationale for indulging their sweet tooth.

The inconvenient truth is that the electrodes are attached to the heart of our planet.

John Allen Paulos, a professor of mathematics at Temple University, has written such best-sellers as "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on appears the first weekend of every month.