The Meaning of Boundaries

Two landowners, Etgald and Lodfin, finally settled where to place the fence. They promptly cooperated to see it done.
"This will resolve all disputes," Etgald said as he admired it. "What's on this side is mine."
"And my parcel is over here," Lodfin said, tapping his fingers on his arm. "But."
"But?"
"The fence."
"Yeah?"
"Whose is that?"
"Why, I suppose I don't have an answer for that just at this particular moment."
That was the beginning of Etgald and Lodfin's grand adventure to learn the meaning of the space between. Not only did they revolutionize geometry and contribute to mathematics, they also defeated the terrible Hidden Tyrant. When they got back home, they were both heroes and fully tolerant of each other's company. They kept the fence, though.
Finis