I can understand a concept very quickly. Usually I figure it out before a test, regardless of the fact I didn’t pay attention in class. But if its just a math equation (no concepts) I cannot do the same thing, regardless of how simple it is. Why is that? I’m in high school.
Concepts are relatively easy to form. We can tell each other stories to inform, use metaphors and analogies to explain, and use elaboration or imagery as well as narrative devices to reinforce.
A mathematical equation is a bare-bones formulation. Sometimes it’s hard to believe that our wonderful, thrilling, all singing all dancing concept can be reduced to a handful of symbols. Other times it’s unbelievable that simple concepts need such a huge plethora of symbols!
The trick is to imbue the symbols with the meanings from the concept. Some of us are better at this than others. The really good ones have an internal life that is god-like: the prologue to Ian Stewart’s Nature’s Numbers describes a Yahweh-like being issuing Genesis-style commands that create a universe. This segues into a sequence reminiscent of the virtual reality computers in Minority Report – though not without a hint of Homer Simpson’s Halloween trip to 3D-land – as the being explores and manipulates his new universe. It’s then revealed that this is an average morning’s work for a mathematician. On paper or with the help of computers, this is how they ‘see’ each problem they work on – as a miniature universe, twisting and turning on itself with every tweak of a symbol.
I’d love to be able to see that. Unfortunately, all I see is.