Asking 'silly' questions to doctoral supervisor

Every PhD student "lacks technical fundamentals" in some respect. That is why you are a PhD student and not a senior researcher (though they probably lack more "technical fundamentals" than you would guess, also). You aren't going to trick your supervisor into thinking you know everything by never asking questions that might be "silly".

But learning to find answers on your own is an essential skill, so it's good that you are practicing doing this. I don't know why you say it is "suffering".

I think a good compromise is to spend a reasonable amount of time trying to find the answer yourself. If you can't, then ask your supervisor, and mention what you tried or what sources you consulted. A reasonable PhD supervisor should not "think less of you" for this, and in any case, it's almost certainly better for your supervisor to have an accurate view of what you know.

If you are in the middle of a meeting and you need to know the answer now in order to proceed with a meaningful discussion, then it is reasonable to ask the question on the spot. Again, it is better to be honest about what you do and don't know, than to potentially waste everyone's time by proceeding with a discussion you don't understand.

If you find yourself spending too much time chasing down answers to random questions, then prioritize them. It's okay to say to yourself: "This is an interesting question, but I don't need to know the answer right now; let me set it aside and come back to it in the future when I have more time."

This is a good question, and probably more subtle than many grad students imagine. (And perhaps subtler than some faculty would like to acknowledge, having some expert-blindness, as well as wishful thinking, and false memories/ideas of how "good" grad students can/do/should operate.)

First, I don't see how a novice can really know whether a question is "silly" or not.

Second, right, many things are either not readily google-able, if only because a novice does not know the key-words. Worse, naive or archaic versions of (e.g., mathematics) tend to swamp sophisticated (and perhaps more likely correct) versions, as though by a popularity contest. This also tends to be the case in Wiki, still. (Don't get me wrong, I strongly support Wiki, and send them money, and they're much, much better than 15 years ago, but, still, due to the nature of the situation, they're prey to enthusiastic-but-naive/misguided people...)

Third, yes, one can rightly feel that there is some sort of both moral and professional virtue for "finding out things for oneself". On the other hand, it is easy to go too far with this, and slide down a slippery slope into extreme inefficiency (i.e., not using a presumed expert who has offered their consultative services to you!)

So, e.g., I tell my students to ask me all the "silly" questions they want, since, if they're truly silly, I presumably can answer them instantly, and/or tell them that the questions are not silly, where to read about it (e.g., my own notes of various sorts), or that it's not documented anywhere (despite possibly mythology otherwise).

Still, collectively, yes, students are reticent about talking to faculty. Some of this is visibly due to the drift of conversational styles and related things over years, but, in any case, I claim it's an unfortunate waste of resources.

(Sure, some faculty simply don't want to engage in activities like "talking to students", which may be uncomfortable to everyone involved. Sure, some students want to "be independent", even if this means they'll be out of touch with state-of-the-art. Such things.)

So, obviously, it depends on the personalities of everyone involved... Oop, no good answer. :)

I have actually directly said to my supervisor that I think some of my questions might be silly, but I must ask because I am lost. He says always to me that my questions are not silly and he'd rather I asked than wasted time or made a mistake. From talking to other colleagues I learned that everybody at some point felt like they did silly things or asked silly questions. I think it's normal to wonder if to ask or not, given that supervisors are busy etc. My algorithm: google and if no answer - ask other phd students and if no answer - ask professor. Then my conscience is clear and I can honestly say I've done all I could before going to supervisor. Hope that helps.