UX of Mathematics

 

potter

The acronym "UX" stands for User Experience. What does this have to do with mathematics, and the disciplines that grew out of math (e.g., science and engineering)? What is mathematics? Mathematics is an ancient discipline that formalizes our abstract concepts about the world. So, for example, algebra or set theory are collections of abstract ideas whose realizations occur everywhere. Mathematics has nothing to do with notation. So when you see symbols on the screen, that is not mathematics -- it reflects a standardized, and economical, representation of mathematical thought. These notations have changed over time and are well-documented by Florian Cajori. So, y = ax^2 +b is not math? No, it isn't. This is a modern and efficient way to communicate about math with other people. So, if this expression is not mathematics, where is the math? Mathematics is a mental phenomenon. But having said this, there are now two paths we can follow when we do create representations of mathematical structure: (1) create representations that use traditional notation, or (2) create other representations. Both of these paths are useful, but I would like to suggest that mathematics as humans practice it has embodied interaction at the core. So, if you think about adding two numbers together, there are hundreds of ways to express this, interactively--using your bodily affordances. I mention some of this in section 26.2.2 of a chapter on aesthetic computing. The way in which you express addition is part of doing mathematics. To find a philosophical treatment consistent with this view, read Lakoff and Nunez's Where Mathematics Comes From. Similar arguments can be made for representations in computer science. How does one represent the concept of iteration? It is easy, but problematic, to get caught up in specific typographic notations such as "for (i=0; i<10;i++) {...}" to iterate from 0 to 9, but this has nothing fundamentally to do with iteration. How we express iteration can take on a huge number of forms and varieties. Iteration is a mental concept, which can be realized through multiple, creatively-derived representations. UX lives at the center of mathematics as we practice it. We have a tendency to dismiss the body, at large, in mathematics and computer science -- as if mathematics does not require a body; a disembodied "brain in a vat." And yet, we do have bodies, and a deep understanding of mathematics requires them.