In 1968 Melzack and Kenneth Casey described pain in terms of its three dimensions: "Sensory-discriminative" (sense of the intensity, location, quality and duration of the pain), "Affective-motivational" (unpleasantness and urge to escape the unpleasantness), and "Cognitive-evaluative" (cognitions such as appraisal, cultural values, distraction and hypnotic suggestion). They theorized that pain intensity (the sensory discriminative dimension) and unpleasantness (the affective-motivational dimension) are not simply determined by the magnitude of the painful stimulus, but “higher” cognitive activities (the cognitive-evaluative dimension) can influence perceived intensity and unpleasantness. Cognitive activities "may affect both sensory and affective experience or they may modify primarily the affective-motivational dimension. Thus, excitement in games or war appears to block both dimensions of pain, while suggestion and placebos may modulate the affective-motivational dimension and leave the sensory-discriminative dimension relatively undisturbed." (p. 432) The paper ends with a call to action: "Pain can be treated not only by trying to cut down the sensory input by anesthetic block, surgical intervention and the like, but also by influencing the motivational-affective and cognitive factors as well." (p. 435)
The old children's story of the frog in the pot who is slowly being boiled alive reminds me of this self torturer puzzle. The frog may suddenly feel a sharp rise in pain once some threshold (psychological or otherwise) is reached and jump right out instead of being boiled alive. That would seem realistic and explanatory and thus dissolve the puzzle of the self torturer as well.
In 2002 Dr. Victor H. Hutchison, Professor Emeritus of Zoology at the University of Oklahoma, with a research interest in thermal relations of amphibians, said that "The legend is entirely incorrect!". He described how the critical thermal maximum for many frog species has been determined by contemporary research experiments: as the water is heated by about 2 °F, or 1.1 °C, per minute, the frog becomes increasingly active as it tries to escape, and eventually jumps out if the container allows it.