Good, useful stuff, clearly presented. I love this kind of thinking.
It's logical, simple and easy to understand - once someone tells you how!
And it reminds me of one of my favorite anecdotes. (Forgive me

)
As the story goes, when Christopher Columbus returned from having discovered the new world, he attended a banquet. As wine flowed, the guests began to minimize his accomplishment: "All you did was sail west . . . if you hadn't, someone else would have . . . etc."
So Chris removed an egg from its basket and challenged the gathering to stand it on its end without use of any implement or grains of salt. Everyone at the table failed, and in their frustration, they all challenged him to do it. Chris took the egg in his hand, raised it above the table, and brought it down smartly, slightly crushing one end, where it rested "on end."
"You see how easy it is, once someone shows you how?" he said.