As I was sitting having my morning coffee and whittlin a bit, a thought came to me. Years ago my father-in-law explained billiards as nothing more than geometry. This morning as I was using my knife to remove a slice of wood up to a stop cut I got to thinking what I was really doing. I had set my thumb and knife up as a simple machine, the lever.
The lever is the knife, while the fulcrum is my thumb, or the pivot point, and is used to multiply the mechanical force (effort) that can be applied. And, the pivot point (thumb) lets you control the amount of force you apply. If you don't believe this, try to make the slice cut up to a stop cut, without the thumb in use as a pivot point. Learn to control the amount of "force" that you apply with the knife, because it's multiplied at the cut; and you'll begin to master your knife.