If you think context switching activities is cheap, then just try saying two sentences; and then try interleaving those two sentences.  For example, I can say "I like kites" and "puppies are cute" in under 2 seconds. But to interleave them ("I puppies like are kites cute") took me about 10 seconds.

This is obviously a silly example, but it may be a helpful way to explain to some people why you don't want to be interupted in the middle of an intense thought-process to go handle some other random unrelated task.