I am going to show, that blow-ups of solutions, that usually are treated as something very bad, can in fact describe some self-organization phenomena, "positive" (like healing) or "negative" (like society polarization). Mathematically it is going to be the theory of integro-differential equations that is applied to processes in Social Sciences (opinion formation), Economics ("lemons and cherries" theory), Biology (DNA denaturation), Medicine (tendon healing process - collagen remodelling) and the redistribution in a lift.