# Historical Background and Physical Motivations

Let us consider the free *surface* of a glass covering a table. And let us idealize it as being *planar*. What is its *volume*? Clearly *zero* since it has no height. An uninteresting answer to an uninteresting question. What is its *length*? Clearly *infinity*. One more uninteresting answer to another uninteresting question. Now, if we ask what is its *area*, we will have a meaningful answer, say 2 m^{2}. A *finite* answer. Not zero, not infinity – correct but poorly informative features. A *finite* answer for a measurable quantity, as expected from good theoretical physics, good experimental physics, and good mathematics. Who “told” us that the interesting question for this problem was the *area*? *The system did!* Its planar geometrical nature did. If we were focusing on a fractal, the interesting question would of course be its measure in d_{f} dimensions, d_{f} being the corresponding *fractal* or *Hausdorff dimension*.

## Keywords

Black Hole Historical Background Maximal Lyapunov Exponent Continuous Phase Transition Physical Motivation## Preview

Unable to display preview. Download preview PDF.