> However, what are the general principle of this methodology and how do we apply to projects other than software. How do we really solve world problems, the agile way?
Most Agile derived or related processes actually have origins outside of software. Kanban, for instance, falls out of Lean which is a continuation of the Toyota Production System. DevOps (as originally described, not as a job title) follows largely from Goldratt's approach in Theory of Constraints, see his book The Goal for a similar novel to The Phoenix Project.
Lean, TPS, Theory of Constraints were all originally conceived in the context of physical manufacturing. Lean and TPS were also influenced by, and the result of, the work of W. Edwards Deming and his post-WWII work in Japan. You can see the Shewhart Cycle (popularly known as the Deming Cycle or PDCA - Plan-Do-Check-Act) as a very similar model to what most Agile processes emphasize. In particular, you can see how it influenced Scrum (taking each Sprint as an application of the PDCA cycle), but it was already somewhat common (though not as common as it should have been) in software and systems engineering before Agile was named Agile.
Theory of Constraints can be seen to influence how Kanban is used in software development, particularly taking note of work-in-progress limits and making the current load highly visible. It's also apparent in the move toward Continuous Integration/Continuous Deployment. Small but frequent batches versus big-bang annual (or further apart) releases.
