Let's talk about the space without time - for simplicity, if this makes sense at all.
I want to grasp the space bending caused by massive objects with examples on 2-D space. I'm not sure if the 2-D space geometry and physics works the same way, but let's assume they are - like some kind of "projection" of a 3-D world.
Let's assume that we have a simulation of an empty 2-D surface where we can visualize the space with a grid of lines always following the same direction - and bending together with the space.
Is it eligible way to show the curvature? Is it possible to see the curvature of space if we place some massive 2-D object on our surface? Or is it relative to each object's perspective of perception and we will "see" nothing from outside?
If it still makes sense and we can "see" the curvature, then "where" is space actually curved? If we place the measuring tool (like a ruler) onto the surface it will curve with it. But we can clearly see the curvature from the "outside" (like on the screen of simulation): the grid of curved lines is different from initial straight lines - and we can measure the difference with our ruler from outside of simulation.
Does this imply that 2-D space curvature exists inside some kind of 3-D or 2.5-D space? And if not then how can we tell in the first place if space is curved or not, if there is not any kind of reference uncurved 2-D surface?
I understand to some extent that the space geometry is kind of mathematical concept that describes well the physical observations and experiments, but my questions are about visualization of this concept in some meaningful way - the simpler the better, but still almost fully relevant to our real perceived 3-D space.