Feature - No pain, no gain: Pleasure and suffering in technologies of leidenschaft

Training for bodybuilding competition is clearly a serious business that inflicts serious demands on the competitor. Not only did Francis commit time and money to compete, but he also arguably put winning before his physical well-being—enduring pain and suffering from his injury. Bodybuilding may seem like an extreme example, but it is not the only activity in which people suffer in pursuit of their goals. Boxers fight each other in the ring; soccer players risk knee and ankle injuries, sometimes playing despite being hurt; and mountaineers risk their lives in dangerous climbs. In the arts there are many examples of people suffering to achieve their goals: Beethoven kept composing, conducting, and performing despite his hearing loss; van Gogh grappled with depression but kept painting, finding fame only posthumously; and Mozart lived the final years of his life impoverished but still composing. These examples show that many great achievements come at a price: severe suffering...

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.