This is a very good question and the previous answers covered most of what I would have liked to say. So the only point I would like to add is that there is a huge difference in how busy professors are. So for instance I would be happy to receive an intelligent question related to my work. However, there are some well known people who are presumably bombarded with emails and I am sure a lot of these emails are very reasonable emails. So I would avoid writing to such people unless I exhausted all other possibilities first and I am also sure that what I am writing will interest them. If I have doubts, I will not write them.
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