<i>The concept of &quot;curvature of space&quot; is obvious nonsense because curvature is measured with respect to space.</i><p>This is not really true. If you take a flat two dimensional space, a sheet of paper, this space has no intrinsic curvature. You surely now imagine this sheet of paper laying flat on a table in front of you embedded in our usual three dimensional space. Now pick it up and role it to form a cylinder. This gives extrinsic curvature to the space, curvature in the space the sheet is embedded in. But the sheet has still no intrinsic curvature, if you were a two dimensional creature living on the sheet you can not tell whether it is laying flat on the table or is rolled up to a cylinder, at least ignoring the fact that the cylinder connects two opposite edges of the space.<p>The surface of the earth on the other hand has intrinsic curvature, angles of triangles don&#x27;t add up to 180 degrees for example. And this intrinsic curvature is a feature of the space not of the embedding into a higher dimensional space. It is not easy to visualize if possible at all, but spaces can have intrinsic curvature independent or even without an embedding, our three dimensional space can be curved without being embedded in a higher dimensional space and the same of course holds for space-time.