Classical physics and, by implication, all modern sciences studying biological (broadly defined) phenomena and systems are "flat" in the sense that they are largely unaware and thus do not make use of such a "dimension" as scale and the simmetries associated with the scale dimension. Any biological system, from proteins and cells to societies and ecologies, is a multiscale arrangement of energy/matter flows, in which multiple interdependent scales contribute to and are required for proper functioning and competitive performance of the biological whole. The holistic nature and multiscaleness of biological organization require and thus imply the existence of an economically efficient physical system of communication and transport that integrate energy/matter flows both within and across scales inside any given biological whole. The only geometry that satisfies the demands of economy and efficiency, while integrating multiple spatiotemporal scales in an interdependent and mutually informing manner, is fractal geometry - hence, "The Fractal Geometry of Nature" of Benoit Mandelbrot, hence allometric scaling laws in biology, hence disruption of fractal geometry, uncoupling of scales, and deterioration of long-range correlations in disease and aging.
This short video provides an introduction to the ideas of i) unity of living matter; ii) fractal organization of living matter; iii) self-similarity and nestedness of scales withing living matter; and iv) scale as the fifth dimension.