It's because we think in 3D, so we only really see three steps of exponential growth.
If we thought in 100D, we might have a better sense for it, because we'd be able to see a hundred of them.
Hypervolume grows exponentially.
One way to get a really rough idea is to try and control each and every joint individually.
Close your eyes and try to imagine that each joint, each muscle is a dimension along which you can move (by moving it), and your posture at any given moment is a point in that space. When you move, you make a line through it. Don't picture it, just feel it.
What is the shape of that space?
You can get an idea of what exponential growth is like by exploring how the shape of that space changes as you add more and more things you're controlling.