Abstract I develop the idea that there exists a special dimension of depth, or of scale. The depth dimension is physically real and extends from the bottom micro-level to the ultimate macro-level of the Universe. The depth dimension, or the scales axis, complements the standard three spatial dimensions. I discuss the tentative qualities of the depth dimension and the universal arrangement of matter along this dimension. I suggest that all matter in the Universe, at least in the present cosmological epoch, (...) is in joint downward motion along the depth dimension. The joint downward motion manifests itself in the universal contraction of matter. The opposite direction of motion, upward the dimension, would cause the expansion of matter. The contraction of matter is a primary factor, whereas the shrinking of space in the vicinity of matter is a derivative phenomenon. The observed expansion of the Universe is explained by the fact that celestial bodies become smaller due to matter contraction, while the overall space remains predominantly intact. Thus, relative to the contracting material bodies, the total span of cosmic space appears to be becoming vaster. I attempt to explain how the contraction of matter engenders the effect of universal gravity. I use over thirty animated and graphical color visualizations in the text to make the explanation of the proposed ideas more lucid. Content Type Journal Article Category Original Paper Pages 1-39 DOI 10.1007/s10516-011-9178-4 Authors A. Alyushin, Department of Philosophy, The Higher School of Economics, 20 Myasnitskaya Street, 101000 Moscow, Russia Journal Axiomathes Online ISSN 1572-8390 Print ISSN 1122-1151. (shrink)