> <i>The trick is that a normal distribution occurs when you sum independent, symmetric distributions.</i><p>It's not neccesary that the distribution is symmetric. You can try for example with 500 genes witn 10% of 0.00 extra height and 90% of 0.01 extra height. You will get again a gaussian but the center will be in 500*(.10*0.00+.90*0.01).
tl;dr: Gaussians show up when you add together enough small random effects. The notebook has some code and prose that shows why that's the case both for human height and for manufacturing wooden doors.