Celebrating the 12 days of Christmas
with short reflections on 12 gifts
Did you hate math class? OK, you econometrics, engineering, IT, math and physics majors reading this (all five of you!) are excused from answering this one. You arts, education and business types — how did you feel about math class? Endless hours of tedious, incomprehensible and purposeless stuff, right?
What a shame. Worse, what a failure of imagination — if not in individual math teachers then in curriculum designers. Mathematical concepts can clarify our day-to-day thinking in areas as diverse as public policy discussions and proposal writing. Join me in celebrating just two such…
The ‘necessary but not sufficient’ construct, in which we distinguish between conditions that are surely required, yet not by themselves enough, to bring about a desired outcome. How much argumentation about social problems and solutions could be avoided by adopting this simple phrase and, by extension, admitting that complex problems often do not have single solutions?
The ‘disjoint set’, in which we carve up the universe of things into mutually exclusive categories that cover all instances. Think of the ‘animal, vegetable, mineral’ of the Twenty Questions game we played as kids (And who knew those categories originated with Linnaeus? Thanks again to Wikipedia!). Simple categorizations help us cover all the bases, while keeping ‘like’ with ‘like’ and ‘different’ somewhere else! To see the quintessential example of a non-disjoint set (albeit likely an artificial one), check out this supposed ancient Chinese taxonomy of animals, and contrast it with what Linnaeus did.
No matter where we find its tools — even in math class — may we treasure the gift of clear thinking.