Invention of problem situations and experimental objects to study others’ thinking is a special kind of creativity worthy of scientific interest. The objects are considered in terms of Latour’s actor network theory (as nonhuman actants), cultural psychology (as cultural tools), and Gibson’s theory of affordances (as meta-affordances). A fundamental problem of validity in studies of curiosity and exploration is discussed. The author’s experience of inventions of exploratory objects to be experimented with is analyzed. An inter(trans)-disciplinary insight penetrating and integrating all levels of the work on an exploratory object is described. An example of participants’ revealing of an object’s unexpected faculties (“serendipities”) undesirable from the experimenter’s point of view is given. It is shown that an object designed to study thinking in one sample can be used in another sample with unexpected results. It is argued that automatic generation of problem posing-and-solving situations and exploratory objects, beginning from some levels of their novelty and complexity, is hardly possible because of fundamental limitations of “standard means to generate or score non-standard ends”.