Would you say it would be "better" (define that how you wish) to devote yourself to studying one thing in depth or studying anything and everything that captures your interest?
The ultimate goal is to contribute to the collective intellectual effort in a significant way.
Also,
study for its own sake vs study with a goal in mind.
study what makes sense to you vs study what doesn't.
study something physical vs study something non physical.
study going "in" or study going "out".
both is not a suitable answer (or if it is, provide real life examples...)
Are you an enneagram 1? The only people I know of who would want to ask "What career would be more useful to the world as a whole, because that's the career I want" are type 1. (I am included in there; sometimes I wish I wanted to be a doctor, because I'd be good at it and the world needs doctors, but the problem is that I'd be miserable.)
Here are my answers to each question specifically, keeping in mind that an ESTJ's answers are obviously going to be VERY different from an INTP's, and they depend a lot on what makes me happy -- because you can't pick a career path only based on whether it's "better" for the "collective intellectual effort", or else you won't live a happy life, and part of the goal is obviously for you to live a happy life because no one (including yourself) wants you to be miserable. (Jeez, that was a long disclaimer!) Anyhoo, I digress:
1) One thing in depth or anything/everything: One thing or a few things for your career, and whatever the hell you want outside of work. Or even better, pick the sort of career where all your interests could be of use. For example, my INTP dad did very well as the executive director of a small nonprofit in my hometown, because of his creativity, his exactitude, his big ideas, and his skill at delegating. Before he had that job, he had gotten a degree in arts management, and then worked in real estate for a while -- as well as being an amateur multimedia artist. All those things have come in handy throughout his life. (Of course, this is all under the assumption that you don't keep the same job for 20 years, xisnotx, and under the assumption that you don't have One True Passion -- because if you do, then you ought to be following it! because not a lot of people have One True Passion.)
2) If you study with a goal in mind, you're probably going to be disappointed. Either you'll never reach it (consider all the scientists who almost discovered the cure they were looking for, and then died mere years before it was discovered by someone who worked a lot less than them!), or you'll reach it midway through your career and then go "Okay, now what?" So, I'd say that if you have a goal, it should be pretty broad, i.e. broad enough that you don't expect to fulfill it 100% -- otherwise it'll drive you bonkers.
3) Depends on what you mean by "makes sense". A lot of things don't make sense to me because my brain doesn't work in the appropriate way for me to make sense of them, so I don't try to learn about them. But if they don't make sense purely because I don't know the required information for them to make sense, then I'll go and learn about them. In that second case, I'd say it links directly to #1.
4) Your choice! Both are equally "useful". I know you said not to say "both", but the thing is, both physical and non-physical study are required for a healthy life, and a healthy society, and without both, we'd be screwed.
5) I have no idea what this means.
