Consider two sentences:
- The llama was made out of watermelon flavored cactus.
- Policeman doe terminology star inconvenience recruit.
If I asked you to close this web page and then recall both sentences, you’d have an easier time with the first sentence. It has meaning and structure — even if a bit strange. I could make this still harder by adding a third sentence that’s just a jumble of letters. That would be less structured and even harder to recall.
Let’s say you’re reading a textbook, like Sedgewick’s The Algorithm Design Manual, and you come across the fact that \( \Theta(n \lg n) \) is the lowest possible complexity of a comparison sort algorithm. You could commit this to long-term memory as is — it’s true, after all. It would be connected to some other knowledge, like what you already know about sorting algorithms. This seems okay.
But, when doing something like this, you’re missing out on a whole lot of structure. If you forgot about the lower bound, you wouldn’t be able to regenerate it from what you already know. It’s connected to other knowledge, but it’s not recomputable. You’re forced to take Sedgewick’s word for the whole thing.
How can we absorb more of the structure of a piece of knowledge — to not be content with knowing a fact that someone else has stated, but to be able to recompute it, to solidly place it in our web of knowledge? The answer is the question, “Why?” There is a massive gulf between knowing that something is true and understanding why something is true. Being able to answer that why question makes all the difference — it forces you to absorb and understand deeper structural characteristics.
If I told you that 3 bits can represent 8 different values, you would not be able to answer the question, “How many bits do you need to represent 1729 different values?” But, if you understood why 3 bits can represent 8 values, that sort of question is trivial. It’s the difference between being able to regurgitate facts from Wikipedia and being able to solve novel problems — to understand the not yet seen.
Asking “Why is this so?” is an easy to implement strategy for absorbing a piece of knowledge, and connecting it to the rest of your beliefs in such a way that you can answer novel questions in the future.