The example I like to use is sudoku. Often, after a day of programming, it takes me a while to "come out of it" and I explain that to my SO as if she'd been doing hours of sudoku and then had to jump into a social situation.

Similarly, if you are interrupted in the middle of a "solve" it may be difficult to jump back in - especially if the puzzle hasn't been created correctly and you are trying to "debug" which numbers conflict. Some puzzles are harder than others. At times you don't have a pen and paper so you have to keep a mental model of the whole puzzle in your head which makes an interruption that much more jarring.

Not a perfect analogy, but close enough to get me a 15 minute buffer at the end of the day and fewer knocks on the office door :D