Levers. To me, they hold the key to all the mysteries of the universe. Why does one thing follow the last? Why is the speed of light – the speed of it, not light itself – immutable? How can an attribute be more fundamental than the thing itself? How can something come from nothing, and return to it? How can two things as different as mass and distance be so intimately intertwined?
Everyone knows the formulae involved; that’s not what I’m talking about. That work equals force times distance is definitional, and intuitively satisfying, given the ordinary meanings of the words in the equation. We can relate to pushing a one ton weight a distance of, say, ten meters. That’s work, by god! But just between you and me, those aren’t really words; in this case, they’re mathematical terms masquerading as words:
F = ma
W = Fd
For example, we accelerate a mass some distance by applying force to produce work, but we would never think of producing mass by dividing work by the product of acceleration and distance. How would we even go about such a division? Words literally fail us here! Not so mathematics:
m = W/ad
The disturbing thing here is that it’s perfectly true.