Cache does rule everything, and the proof lies in the laws of physics. How fast can you access a bit of memory? The lower bound is the speed of light. How do

Cache does rule everything, and the proof lies in the laws of physics. How fast can you access a bit of memory? The lower bound is the speed of light. How do you organize your memory such that access is the fastest? In a sphere with the processor in the center. There is no more overall efficient packing of bits assuming that each bit takes up some finite "bit" of space (pun intended). This means that random access to memory can never be O(1) at the limit, it is actually O(n^.333)--the cube root, as the volume of a sphere is 4/3 pi r^3. Yes, even for hash tables. So random access memory always gets slower the more you have of it. Conversely, the less memory you have to access, the faster it can be. By putting more frequently accessed bits closer to the center of the sphere, you have created a cache.