Suppose there is a medical device that enables doctors to apply electric current to the body in increments so tiny that the patient cannot feel them. The device has 1001 settings: 0 (off) and 1 … 1000. Suppose someone (call him the self-torturer) agrees to have the device, in some conveniently portable form, attached to him in return for the following conditions: The device is initially set at 0. At the start of each week he is allowed a period of free experimentation in which he may try out and compare different settings, after which the dial is returned to its previous position. At any other time, he has only two options – to stay put or to advance the dial one setting. But he may advance only one step each week, and he may never retreat. At each advance he gets $10,000.

Since the self-torturer cannot feel any difference in comfort between adjacent settings, he appears to have a clear and repeatable reason to increase the voltage each week. The trouble is that there are noticeable differences in comfort between settings that are sufficiently far apart. Indeed, if he keeps advancing, he can see that he will eventually reach settings that will be so painful that he would then gladly relinquish his fortune and return to 0.

The self-torturer is not alone in his predicament. Most of us are like him in one way or another. We like to eat but also care about our appearance.