I guess one of the best ways to see the limitations of one's knowledge is to get a PhD. The usual description of the path to a doctor of philosophy degree is to get a bachelor's degree at a four year college, get a master's degree in a year or two (sometimes more) and get the doctor's degree in 3 or more years.
Several people have described the final exam for a doctorate as an occasion of being quite aware of all the things one does not know. That final exam is often an oral one. One's advisor invites professors from one's major and minor. I had two minors, philosophy and psychology. I don't actually remember what philosophy and psychology professors attended my orals. I do remember the realization that those men could ask me ANYTHING !
The usual format is an hour or so of committee questions, then a short discussion while the candidate is not in the room. If the answer is "yes, he qualifies", the person fetching the candidate from where he is waiting, often signals the candidate's success by greeting him with an extended hand and the words, "Congratulations, Dr. _____________" Of course, there is no guarantee that the candidate will be able to answer all the questions. There may be disagreements generally as to the correct answers.
