gulf
As a White Belt your are completely unaware of exactly what you don't know, almost blissfully so in retrospect. The idea that you think you have a clue of what you are doing and that you think you can replicate what the higher belts are doing is a complete pipe-dream.
As a Purple Belt, you start to realize the depth and span of what you don't know. Take a brief moment and look at current White Belts and look back to when you were a White Belt, how much of a blessing was that ignorance? The literal wealth of knowledge you need to possess to become a black belt is frightening and potentially off-putting to a beginner. I still find that it is slightly disconcerting to think about.
Just as soon as I feel comfortable and think that I know what I am doing, suddenly its like a curtain is pulled back revealing a gulf waiting to be filled with knowledge (with my Professor, comfortably on the other side). Except he doesn't carry you across. He will show you the way, providing the teaching and tools, but you have to do the work and execute the technique.