I was trying to think of a good way to explain to a friend recently why programming and meetings are so incompatible. The canonical reference for this is Paul Graham's Maker's Schedule, Manager's Schedule. Basically, programming needs big blocks of uninterrupted time, but managers tend to operate on small blocks. For managers, meetings are just another small block, but for programmers their whole big block is interrupted. That seems about right, but what it doesn't explain is why.
I'd like to propose another metaphor: programming is sleep-like. Sleep is a fairly odd phenomenon compared most of our behaviour. First, we have to engage in a certain degree of ritual to even get it going. We lie down somewhere dark and quiet, remove all external stimulation, empty our minds, and wait. Even when it comes, sleep is easily interrupted, and many short blocks of sleep don't work as well as fewer long blocks, no matter what the Ubermenschen will tell you.
Sleep comes in stages. The first is an essentially transitional light sleep, the second is a medium sleep that makes up the majority of the duration, the third is the deepest, so called slow-wave sleep (SWS). Finally, the much-hyped REM sleep, which is actually closest to light sleep in terms of brain activity. It used to be thought that REM was the most important stage, and then SWS, but presently the consensus is that they both work together.
Interestingly, programming also seems to involve stages. In my experience, the early stages involve acclimatising yourself to the code, getting all the different parts in your head, and generally setting up. With that done, you can then start thinking deeply about the problem. Once the solution occurs to you, you write the code for it, which looks like the hardest part but is actually the easiest.
Now, this is just a metaphor; there's no similarity at a neurological level between sleep and programming. That said, there are functional similarities. Being interrupted in the light stages is not so bad, but being interrupted in the deep stages means basically starting over. A certain amount of time is required to get through all the stages, and it has to be in one continuous block.
Most significantly, I feel like the main quality both sleep and programming share is that they thrive in a vacuum. To sleep effectively you have to get rid of everything that isn't sleep, and so too with programming. The main predictor of both good code and good sleep is long stretches of uninterrupted time.
Of course, programming isn't the only thing with this quality. Really, I that that any focused application of your mind would have similar characteristics, be that programming, writing, studying or something else. I suspect it's some unifying property of the way our brains work best; associations build on themselves, so you need to keep the spurious ones quiet and give the relevant ones time to build up.