by Kim Pederson…….
I miss math. Crazy I know for someone who never got beyond basic high school trigonometry and calculus and has retained pretty much none of it. Even so, I’ve been thinking about math recently and remembering that it was actually sort of fun to do geometry and work out equations in a world where the rules and the operations are clear, pristine, and consistent and the answers or solutions (at least at my level) were something everyone could agree were correct.
What prompted this remembrance and reflection was picking up a copy of Eugenia Cheng’s How to Bake π: An Edible Exploration of the Mathematics of Mathematics. She had me with the opening recipe for clotted cream and this promise and explanation:
I need to clear up some misunderstandings about what math is in the first place. Indeed, not only is math not just about numbers, but the branch of math I’m going to describe is actually not about numbers at all. It’s called “Category Theory” and it can be thought of as the “mathematics of mathematics.” It’s about relationships, contexts, processes, principles, structures, cakes, custard.
She had me, that is, up to “mathematics of mathematics” and then my eyes glazed over until “cakes, custards.” There’s nothing like food in general and dessert in particular to get and keep your attention, something she obviously figured out in writing the book.
While I have yet to delve deeper into Pi-making, Cheng’s writing has already prompted a revelation of sorts. What appeals to me most about math and the sciences in general these days is its focus, as opposed to politics and religion, on logic. In her words, mathematicians stick to studying “anything that obeys the rules of logic.”
The logic she mentions has to do with inference, the mental act or process of reaching a conclusion based on specific evidence. You may have seen an example like this before:
1. Premise 1: If it’s raining then it’s cloudy.
2. Premise 2: It’s raining.
3. Conclusion: It’s cloudy.
In this instance, you have a proven fact followed by an observation followed by a logical conclusion based on knowledge of the fact. It’s obvious that we need more of this behavior in our world. We need, in short, to insist, as math does, that everyone think and act according to the rules of logic.
Such a transformation would exponentially increase the chances of people agreeing on issues rather than fighting over them. I know this sounds like crazy Utopian thinking, and it probably is crazy Utopian thinking. But hey, the way things are going anything seems worth a try. We need a leader, though, who can sell the idea to America and the world. That just leaves one question: How do we bring Spock back from the dead?
*”Commutative diagram for morphism” by User:Cepheus. Own work, based on en:Image:MorphismComposition-01.png. Licensed under Public Domain via Commons.
Visit Kim Pederson’s blog RatBlurt: Mostly Random Short-Attention-Span Musings.