Memorizing vs. Understanding (read: Data vs. Knowledge)

So how can I get the result of the arithmetic expression, e? Well, there are two ways: (i) if I'm lucky, and lazy (think: efficiency) I could have the value of e stored (as data) in some hashtable (a data dictionary) where I can use a key to pick-up the value of e anytime I need it (figure 1); The first method, let's call it the data/memorization method, does not require us to know how to compute e. That is, if the value of e is not memorized (and stored in some data storage), then the only way to get the value of e is to know that adding m to n is essentially adding n 1's to m and knowing that multiplying m by n is adding m to itself n times (and thus'multiplication' can be defined only after the more primitive function'addition' is defined). Crucially, then, the first method is limited to the data I have seen and memorized (i.e., stored in memory), while the second method does not have this limitation -- in fact, once I know the procedures of addition and multiplication (and other operations) then I'm ready for an infinite number of expressions. So we could, at this early juncture, describe the first method by "knowing what (is the value)" and the second method by "knowing how (to compute the value)" -- the first is fast (not to mention easy) but limited to the data I have seen and memorized (stored). The second is not limited to the data we have seen, but requires detailed knowledge (knowing how) of the procedures.