Back of the envelope analysis will work in cases where the system as a whole will temporarily converge to a steady state. It's easy to tell if a system will temporarily converge, but not when.

For more in-depth analysis without having to result to numbers, Nassim Taleb says that Poincare helped develop the field of analysis in situ where qualitative properties of systems can be rigorously discussed, but not computed. I have not researched this.

But here's a small example, I think, of a back of the envelope analysis without numbers. If you are certain to die, but you do not know when, how does this impact your disposition toward living a human life?

Interesting opinion piece in the latest Time magazine called "Excluding the Extremist" by Justin Fox. He is referring to the financial advice of Peter Schiff and others who aren't necessarily mainstream.

"But there's a thriving line of academic research showing that including divergent opinions and models of how the world works makes groups better at solving problems"

That puts it fairly succinctly and I still think the quantitative analysis is possible. Unfortunately, the financial quants have given the term quantitative a bad rap.

BTW, Justin Fox has a book coming out next month called "The Myth of the Rational Market".