Well, I watch Vsauce, and correct me if you think of my theory otherwise.
We can't TOUCH anything. What we feel is the pressure of the atoms against our skin. And if you cut something, you simply push the ATOMS aside, so cutting something if pushing the atoms aside, matter, etcetera, and increasing the density of the two pieces. So if the fourth dimension is for the ability to push matter/atoms aside. So scissors have the fourth dimension, I think...
Correct me if I'm wrong, I just had a thought