You can ask these same questions about a lot of things we use every day. Do you have deep knowledge of how your car works, or just a superficial understanding of the basics to keep it running? How about your refrigerator? Household plumbing? Your computer? And how deep is "superficial"?

Another question to ask yourself is, "If it breaks, could you fix it?" And what is fixing it? Swapping parts, fiddling with function params, without knowing exactly what went wrong at a deep level? Paying someone to fix it for you? Is it "understanding" to know whom to pay for what repair?

I believe it is possible to have a thorough understanding of every aspect of every tool we use, but this would tend to limit the extent most of us would build up from it, as time spent learning these fundamentals is no longer available for deriving from them. If we assume humans have limited time and capacity for understanding what already is, it's by necessity that we use certain inventions as black boxes in order to build from them.

Or maybe the question is, "Should you be able to build your own toaster?"

http://www.ted.com/talks/thomas_thwaites_how_i_built_a_toast...