Earlier quoted context omitted.
Much more important than the idea is the process you learn how to vet and research the idea. That is the 'support'. Now I can independently expand on my own ideas, and reject unpromising ones. Some are born with this skill, but many who think they have it... don't. A PhD isn't really about doing something useful, although that is typically a result. It's learning how to explore an idea and expand upon it. Your adviso…
> Now I can independently expand on my own ideas, and reject unpromising ones. Unpromising in what sense? Unpromising for you personally, or for the greater good of humanity? Research always comes with a risk. It is called "re-search" and not "re-find" for a reason. You can learn some heuristics that will help you explore, but it is certainly no guarantee for finding anything.
Agree. Those heuristics were precisely what I was alluding to. It is all about how you explore that space. The best researchers have an amazing ability to intuitively ascertain promising directions. Many smart folks I know constantly spin their wheels working on problems that are intractable.
To me, that ability is the principle value add of a senior PI (aside from funding, of course!)