Physicist: In a flat space local ideas about “parallel” and “perpendicular” are global. That is, if two lines are parallel, and you follow them for a while, then they’ll still be parallel. So you can have 2-d flat space, 3-d, 4-d, whatevs)An example of curved 2-d space is the surface of a ball (just the surface, don’t worry about the inside and outside). If you draw two parallel lines on the ball, then eventually they will cross. So if you’re sitting still (traveling forward in time), and no one applies a force to you, you’ll continue to sit still (travel forward in time).