The software industry (at least the management) continues to treat the programming process like an assembly line. I think it's a lot more like writing a poem or painting a picture. But even if it is a mechanical process, it takes a lot of setup time to load up your mind with all of the relevent details (Physical psychology call this "working memory"). Then you can work on the problem. If, during this process, you are interrupted, even for a minute or two, the context evaporates and it will take varying amounts of time to recollect all the bits.

As an implementer (and now a manager myself) I have seen the most productive approach: give the programmer a problem to solve (not the solution) and leave them alone for at least a few days so they have time to think, to act, and to dream :-)

While I agree this can be tough, I've found it to be an acquired skill.
At my job, I am constantly bombarded with unrelated requests while developing software, and I've learned to manage it most of the time after 2 years.

at the end of the work, neither 'banana' or 'apple' would be complete. :)