A time to act and a time to think

Uncle Petros and Goldbach's Conjecture contains a passage that relates how for a mathematician to spend time away from the problem at hand is essential. Mentally to digest the work accomplished and process its results at an unconscious level requires leisure as well as exertion. In other words making progress requires more than the "application of perspiration" to the problem at hand. The spark of insight may come from "inside events", "outside events", or "other people" (for example a dream, the observation of an apple falling from a tree, or a chance conversation).
Professional mathematicians work in a way that reflects the nature of thought-work but unfortunately software teams often don't. To be most productive a developer requires time away from a keyboard and monitor, quietly reflecting or talking with colleagues. It can be hard for a client / sales / management representative to see the value being created in this time, but allowing developers the thinking time they need leads to higher quality work.
Reflection: What are the barriers to thought-time in your organisation? What forces or events caused those barriers to be erected? Can these forces be overcome in other ways?
(Thanks to Dave Farley for the conversation that stimulated this posting.)