The key to understanding complicated things is knowing what not to look at.
Nothing brings fear to my heart more than a floating point number.
In engineering, as in other creative arts, we must learn to do analysis to support our efforts in synthesis. One cannot build a beautiful and functional bridge without a knowledge of steel and dirt, and a considerable mathematical technique for using this knowledge to compute the properties of structures. Similarly, one cannot build a beautiful computer system without a deep understanding of how to "previsualize" the process generated by the code one writes.
Being smart in the arts is the same as being smart in engineering is the same as being smart in writing is the same as being smart in anything, really. It's the ability to manipulate all the pieces of the puzzle in your mind, try to fit them together, and when they don't fit quite right... you sand the edges/corners and make them all fit.
A recursive definition does not necessarily lead to a recursive process.
The reason why people think of programming as being hard is because you're writing down a general rule which is going to be used for lots of instances that a particular instance must process correctly.
