Last week I started reading a book by Eugenia Cheng called Is Math Real? How Simple Questions Lead Us to Mathematics' Deepest Truths. Before I read this, I had always thought I was bad at math. But Cheng works in a field of mathematics in which they don't use numbers. Had I known there was such a thing, I would have been all over it as a teenager. And if I had read her book, I probably would have gone into the sciences.
Cheng explains that our brains have only so much space to work with (working memory?), so we need to simplify concepts down so we can ignore the hard parts and focus on the parts we understand. She defines math as "the logical study of how logical things work," and she posits that the indirect applications of math are actually more important than the direct ones but are largely ignored by schools.
With mathematical thinking we basically take what we do know and apply it to what we don't know and see if we can understand those things too. Much of life is a mixture of logic and chaos. Logic is very simple so it often won't apply to big concepts, but it can often apply to parts of concepts, making it possible for us to predict things that we couldn't before we applied the abstraction.
I had recently been reading Ashley Lilley's set of posts (starting at https://ashleylilley.com/2024/01/19/what-is-executive-function-part-1/) about executive function, which really helped me to understand just what it is and how it works in real life. Without the three facets of executive function working together we have trouble behaving "maturely". Those three facets are working memory, cognitive flexibility, and inhibitory control (a.k.a. emotional self control). What we see in people who struggle with these three pillars is a lot of behaviors that sabotage self, may hurt others, and make functioning in a thoughtful, present, mindful way very difficult.
Not surprisingly all of the facets of executive function come into play for working with math-- as well as with pretty much everything else in life. In math you need emotional self regulation in order to take the time to assess problems and hold yourself back from making unconsidered assumptions. Then you need to have the cognitive flexibility to think creatively about a problem, and finally you need working memory to hold the known information in your brain while working with it and comparing it to other information. These three pillars work together to wire the brain into understanding the world and shaping itself into a structure that notices, comprehends, and works with patterns.
Here's what blows my mind: this is what math is--and it has nothing to do with numbers, and... I do it all the time. Here's an example: Let's say I want to give a friend a gift. I need emotional self control in order to not make a thoughtless or random decision and possibly give an insulting or white elephant-type present to my friend. I need working memory and cognitive flexibility working together to take everything I know about my friend and put myself in her shoes and assess what might appeal to my friend or what she might need (empathy) and then compare what I learn from that empathy to the reality of my situation. Can I afford to buy that? Do I want to buy that? Will that survive shipping? Ultimately this complex set of equations are balanced out in my head and heart and I will choose a gift and send it.
No one I know would call gift giving "math". No one I know would call social relations with friends and relatives "math". Yet it seems we use "mathematical" thinking to understand and navigate our world every day.
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