I realized the other day that in my writing I consistently toe a fine line between generalization and simplification. Why is this important? I think generalization is a good short-term goal while simplification is preferred in the long-term.
The difference lies in the detail. A generalization ignores detail to apply an idea across as broad a range as possible. In contrast, simplification leverages detail to eliminate excess.
A quick example – what is calculus? The generalized answer is that calculus means complex math. This answer is 100% true. But does this help us understand calculus? All the generalization does here is strip away the detail that differentiates (!) calculus from analysis or advanced probability in order to compare it against arithmetic or geometry. We get it, but we don’t really have an idea of what calculus is.
The simplified answer is that calculus means rates of change. This answer is 100% true, as well, but it gives better insight into what calculus is. It uses the detail of the subject matter to define it while stripping away all the excess that is not required by the question.
For the most part, I think the general and the simple work hand in hand. As dismissive as I am of the general in the above example, I do admit that anyone who knows calculus as the subject studying rates of change will also know it as complex math. If there is an order of operations, the general should precede the simple.
The general is a good place to start but a bad place to finish. The trick, I suppose, is in knowing when to transition from the general to the simple. I think a lot of people wait too long and stunt their own learning process. It is fully understandable – someone speaking generally always has a fluency that is outwardly impressive. This creates the impression of full understanding and others will naturally want to mimic this level of expertise.
However, I think it is always better to dive into simplifying as quickly as possible. The process of simplifying always reveals gaps in understanding. Though embarrassing at times, these gaps are invaluable for the learning process. Without knowing what to study or think about next, the day of fully understanding the world around us will never arrive.
