Common Schematic of Hierarchy of Space Dimensions
A given dimension is the result of the projection or motion of the previous dimension into a new direction. In the book, Concepts of Space, Max Jammer (Harvard University Press, 1969, p. 180) describes the steps 0–3 and then concludes that this kind of "...deduction comes to an end apparently because the conception of a motion of a three dimensional space as a whole lacks all intuition based on experience."
Massive Body with Accelerometers
According to the standard conceptions of matter, space, time and gravity, this picture is utterly static (neglecting the rocket flames). If we believe the accelerometers, it is a picture of motion, stationary motion: "A conception of a motion of a three-dimensional space as a whole with an abundance of intuition based on experience." Accelerometers seem to be telling us that the essence of matter and gravity is outward motion; movement into (or out from) the fourth dimension of space.