My brain exploded trying to read the original post, and De Morgans laws seem like someone sense to anyone who has ever had to code a conditional.
I can't help but feel there's a bit of "Mathematic elitism" in this post, and I really disagree with it. I struggle to understand why this concept is "the most important" to programmers, yet I consider myself a pretty solid coder.
Currently I share a 100gig folder with my fiance. We both have everything we need in real time.
Dropbox has size limitations - you might be able to get around the 100gig limit by contacting them?