Adjustments
When you’re cutting up vegetables or meat and you need to adjust to get a different angle or position, you can move three things:
the knife
the food
your body
The knife moves, of course, as you make the series of cuts along a piece of food. Some small adjustments can be made, but mostly you want the knife to stay in the same area—where your grip is sure and your hand and wrist are comfortable. Where you can confidently control the knife; where you can make smooth and efficient strokes. Think of working your way down a carrot.
Moving the food instead of the knife is necessary when you’re finished with one piece and grab another (duh), or when the cut requires a knife angle that you can’t easily or safely accommodate. Think of dicing a potato or an onion.
Moving your body is usually reserved for big or awkward tasks that don’t lend themselves well to moving the food. But it’s not because you need to change the grip on the knife, necessarily. It’s more likely because you need to see the food better and it might be simpler to move yourself than move the food. Think of moving around to cut up a pork shoulder or getting yourself over the top of a large squash to slice it in half.
Knife, food, eye. Put another way: tool, problem, perspective.