Blending in mathematics

Abstract

Mathematics is one of the richest, if more abstruse, areas of higher human cognition. It is a formal system, founded on a minimum of primitive concepts, but involving cognitive mechanisms, such as blending and framing, in an iterative manner, which lead to the rich structure of “higher” mathematics. The use of such cognitive mechanisms is done in a very controlled way, so as to maintain the rigor of the discipline. It is suggested that blending and other such mechanisms are incorporated into the formal structure of the discipline. This thesis is examined via a number of examples. This has the effect that blends are easy to make in mathematics. On the other hand, before blends and other processes were incorporated into mathematics, some blends that are obvious, even necessary, in hindsight, have taken a long time — sometimes centuries — to be realized. We hypothesis there is a cognitive cost to actualizing blends, which must be overcome. This phenomenon is investigated via the historical record.