Product Managers in both the Problem and Solution Spaces
Question: "Most of the product managers that I have been in contact with have to coexist in both the problem and solution spaces at different times. How can this be reconciled?"
This situation cannot be properly reconciled because the problem and the solution spaces each require very different and dramatically opposed competencies (Business Vs. Technical). One cannot be effective by assuming roles in both spaces at the same time. In simple terms, the answer is to be solely emerged in one space and fully disengage from the other space.
In many companies we find individuals mislabeled as product managers when they really are product architects who also do some problem space related tasks. This situation misleads many to rationalize the predicament and to incorrectly construe that product management resides in both the problem and solution spaces.
It is the role of the Product Architect to act as an interface between the problem and the solution spaces.
For more information, see the Blackblot Product Definition Team Model. This issue is explained at length in the "Blackblot Product Definition Team Model" chapter in the Blackblot PMTK Book.