Mappings

Abstract

As in the previous chapter, we will continue to look for small spatial stories and conceptual blending to see how those mental patterns contribute to the effectiveness and fecundity of mathematics. The subject of focus of this chapter is mathematical mapping, described in the quotation below as “the single, most important and universal notion.” We will find that at least three small spatial stories are prompted in our handbook as a way of constructing the meaning of mapping. Or, to use the terms introduced in Sect. 2.2, three small spatial stories become input spaces in the conceptual integration network where the meaning of mathematical mapping emerges. As we mentioned above, the input small spatial stories are always easier to spot than the mostly unconscious process of conceptual blending, but we will see several traces of it as well. A rather surprising secondary conclusion of the present chapter is that the official, “rigorous” definition of mapping as a set of ordered pairs is in fact fully circular, which—taking into account the crucial importance of mapping—should result in the whole discipline being completely barren. Instead, mathematics thrives, and its effectiveness is constantly confirmed by new applications in all areas of science and industry. In the following section will be able to see how conceptual blending and its input small spatial stories contribute to these accomplishments.