What I Wish I Knew When I Started My Career as a Software Developer:
Never ask for permission unless it would be reckless not to. Want to spend a week investigating something on your own initiative? Don't ask for permission. You won't get it. You might not actually be doing your boss a favor when you ask for permission; from their perspective, you're asking for the right to pass the buck if your project doesn't pan out. Since he can deny you and your buck-passing after-the-fact, in any case, because he outranks you, you don't really gain anything from such a promise you might extract in the first place. So there's no upside in asking for that permission. Of course, if you're going to do something that presents a real risk to the business or where his permission would be reasonably expected, then go ahead and ask for permission. If the loss is small and the risk is appropriate to your level in the company (and any programming job where you're not trusted with days to weeks of your own time is not worth having) then don't ask for permission. Just do it, and do it well.