While I appreciate the beauty this piece, I can't help but think of the irony of such a complicated piece to explain something which mechanics and engineers, who actually use gears, understand completely intuitively.
I had the same feeling, hoping to receive an epiphany, perhaps on the bevel of the gear teeth, but nope. Then I thought, ok, surely there's an insight to be gained regarding helical gears, but it was never discussed.
I'm not sure this is intuitive for many mechanics. I can remember studying for the ASVABs in high school (it has, or at least it did, have a whole section on spatial orientation and gears and pulleys), and it was pretty common for people to be flummoxed by the questions about picking which direction a gear in a set would turn when another was rotated. And this was with a set of people that tended to tinker on cars and snowmobiles all the time for fun.