&gt; Use a sheet of paper as your Flatland. Draw two points, measure the distance. Crinkle up the paper. There&#x27;s still the same &#x27;distance&#x27; of paper between the two points.<p>Because the paper is not elastic. Spacetime is; it stretches. So a better analogy would be the rubber sheet with masses rolling around on it, and deforming it, which is often invoked in popular introductions to spacetime curvature. Like all analogies, it has its limitations, but it does capture the essence of the classic Wheeler quote: &quot;Mass tells space-time how to curve, and space-time tells mass how to move.&quot;<p>&gt; If gravity wells stretch and contract _matter_ (rather than space), then this fits my mental model.<p>Gravity stretches and contracts space AND matter, the latter to the extent that it can overcome the chemical bonds (and other forces) trying to keep matter together (gravity is weak, so that takes a lot of mass). We see the stretching of matter all the time as tides. Moons torn apart by it when they get too close to their planets (the Roche limit) is a more dramatic example. Spagettification of matter falling into a black hole an even more dramatic one. You can think of gravitational waves as an oscillating, self-sustaining tide traveling at the speed of light.<p>By the way, there is a thread of thought which takes the analogy of spacetime with an elastic solid quite seriously: <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;gr-qc&#x2F;0408051" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;gr-qc&#x2F;0408051</a>