If you can't explain it simply, you don't understand it well enough. ---Albert Einstein
If there's anyone who dealt with extreme complexity in terms of mathematical equations, it was Albert Einstein. Yet he realized that in order to communicate his results effectively to others...even those in his own academic community...he needed to be able to express his findings in terms that they could understand. And this entailed simplifying his message, with the implication that anyone who was willing and able could check out his points on a more detailed and complicated level. I once saw a Big Bang Theory episode in which Sheldon the physicist derided a visiting popularizer of science who was giving talks about the nature of the universe...without the difficult mathematics that underpins the theories. I thought that Sheldon was in the wrong here, and I think that a lot of people in arcane professions are lacking in the ability to effectively convey their fields to people at large...and don't even try. I'm also convinced that, with some of these, that is a deliberate choice as it allows themselves the ego-swelling feeling of being exclusive and apart in their specialties. I also believe, from experience as a student over the years of my youth, that many teachers don't properly know their own area of instruction. How much effort really is involved in giving a short introductory lecture to the new class on the course they are beginning in general terms that captures the essence of what the students are about to be studying? Yet I can't recount a single time in all my years at school in which this was done, sadly...even vindictive, fictional Snape managed to accomplish this in the first Harry Potter movie. Stephen Covey once wrote that one of the first things you should do after learning something new is to turn around and teach it to another. I think his point was that by teaching another, it is forcing you into understand that essence, since you will need the other to be able to receive it. For me, this all makes since...yet I'm not so confident that, after studying the binomial theorem, matrix algebra or techniques of integration, I'm going to be able to turn right around and FIND someone willing to listen to me explain it, simply or not...
