According to a quote from a past Physics Forums article, 4D spacetime can be embedded isometrically (preserving the metric) in 90-dimensional flat spacetime: My intuition is that smaller regions of spacetime will require many fewer dimensions. By analogy: a 2D torus requires 3D for an embedding, but any small enough section can be embedded in 2D. My question is whether there is some kind of limit theorem of the form: For any 4D spacetime, every point belongs to an open set that can be isometrically embedded in flat spacetime of N dimensions or fewer. where N is some number much smaller than 90. (If we drop the "isometrically", then the answer is clearly N=4, because every 4D manifold is by definition made up of 4D sections stitched.) together.