In today’s Dilbert comic, another opportunity to highlight something about how math is held in society.
Dilbert, rather desperately, is trying to convince his audience of something. And, somehow, he does! He invokes the Authority of Mathematical Gobbledygook, represented in the comic strip by an officious-looking pie-chart. The bald-headed guy even says: “It must be true, because..” He is convinced by a (somewhat math-related) demonstration.
Yet Dilbert can see that his audience is convinced for dubious reasons. Mathematical ideas can convince in ways that are entirely different from smiting your audience with a well-aimed mathematical authority or mathematical spell. A mathematical idea can engage the other person, in such a way that the other person sees for himself or herself and can check for himself or herself.
Let me try to show this with a rather simple (but by no means trivial) example. Below, I show two odd numbers, one on the left, and one on the right. You can see they are odd numbers since they are represented by a number of squares, and the squares are organized in groups of two, one above the other – except there is an “odd” one left over at the end, the “odd one out”. The picture also shows each odd number folded in a way that makes it hard to see exactly what odd number is shown. From the picture, you can easily see that if these two odd numbers are put together – that is, added – you end up with an even edge, with the two “odd ones out” combining nicely to form a whole set of these groups of two. Two odd numbers add up to an even number: I claim that the picture, through the folds, lets me see that any two odd numbers add up to an even number. The representation of odd numbers used in the picture lets me see that the part that matters is the pairing of squares and the fact that one squares sticks out. For the sticking-out squares to “dock” together, it matters not how many pairs the sticking-out squares are connected to.
Whether or not you agree that this demonstration is fully effective, wouldn’t you agree that the appeal this demonstration makes is of an entirely different kind than smiting somebody with a spell? Whatever capacity it is that this demonstration tries to engage in you, it is this capacity that I would call mathematical thinking, engaging in mathematical ideas. However, society at large tends to arrange its members in the various roles around Dilbert’s table. Mathematics is not widely seen as a game of participation.