# An Upper Bound on Human Memory A loose upper bound on human memory can be established from a simple counting argument. Suppose a brain of mass \(m\) fits in a sphere of radius \(r\). Then, the mass-energy of the brain is at most \(E=mc^{2}\). Applying Bekenstein's bound, the maximum information in that sphere is: \[ I\leq\frac{2\pi Er}{\hbar c\ln 2} \] Thus, the brain can have no more than \(2^{I}\) distinct states. If a distinct memory minimally requires a distinct state, then the brain can have no more than \(2^{I}\) distinct memories. This, for a brain of mass \(1.4\) kg that fits in a sphere of radius \(0.1\) m, is approximately: \[ 2^{3.6\times 10^{42}} \]