> It's quite literally the symbols doing some of the thinking for you, specifically the symbols are doing the computing or calculating part of thinking. I was

> It's quite literally the symbols doing some of the thinking for you, specifically the symbols are doing the computing or calculating part of thinking. I was feeling bad earlier this week when thinking about taking the derivative of x^3. I, of course, didn't derive the answer geometrically. I did what most everyone does, I imagined the "3" symbol floating down and being replaced by n-1. But there is no reason to feel bad! I was outsourcing the computation to the symbols. The notation is good enough that some easily-remembered symbolic rules are just as good as (or actually equivalent to) the real computation.