Ingratitude is sooner or later fatal to its author

Ingratitude will do you in . . . so says a Twi proverb. Gratitude is good for you . . . so says positive psychologists.

To bring all the apparent paradoxes of positive psychology together, we need to learn some maths about planes rather than lines. Though not obviously connected, contemporary commentary on positive psychology hangs together when we listen to Mandelbrot and other mathematicians.