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?
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 ABCNEWS.com appears the first weekend of every month.