Truly innovative ideas are supposed to come to us in an “A-HA!” moment. That rarely happens though. Most good ideas are simply cross application of other ideas. Great ideas on the other hand require hard work and time to develop.
Sir Isaac Newton was a brilliant man to be sure, but when asked how he invented calculus his response was that he had simply taken the time to think deeply about it for long enough to figure it out when others just simply hadn’t thought about it before.
This seems to be a theme for many difficult tasks. Taking the time to really wrap your mind around something and go deep enough that you can fully understand things opens up new doors.
Discovery also happens when you take the time to explore with an open mind. I have worked on many projects where we have learned so much about how to build a particular type of system during development that by the time it was finished we wanted to go back and re-implement everything with what we had learned. There are technical choices that cannot be fixed easily with simple re-factoring.
Some aspect of ‘wandering’ to try to feel out a particular idea can really help nail down a stronger direction for a project. Maybe you consider this a prototype stage (but all too often I’ve seen prototypes turn into production systems).
Wandering promotes more risk taking, more throwing out of bad ideas. I think wandering allows you to be more critical of the ideas you come up with and that in turn leads you to better innovation.