I'm reading about how a "straight line" depends on the geometry of space. While I think I understand this, the example people give is:
"Imagine a straight line on earth connecting two cities. It's actually curved because the earth is curved".
My response to that would be "Well no, because a truly straight line would cut through the earth. Like a straight string would cut through an apple".
So question: If two people took an infinitely strong and light string, stood on opposite ends of the earth, and pulled almost infinitely tightly, would the string curve around the earth a few feet above, or would it cut through to the core?