I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong an…
Are we flat in the time dimension? Or what is our time size?
The best way to picture it is via Minkowski diagrams, you can find some neat visualizations in the wikipedia article: https://en.wikipedia.org/wiki/Relativity_of_simultaneity
Simply picture an extended object in the x direction, Lorentz transformations are going to rotate it slightly in the time direction causing it to become extended in the time direction.
[1] If you take it to the extreme you may consider that different parts of your body move with respect to each other and thus they are not in the same reference frame. In which case, not even with respect to yourself are totally "flat" in the time direction.