1:16:57 On metrics that don't measure and hair-dressers! See Intransitive dice . See Tensor Fields and Simplicial Complexes and observable in nlab : In physics and in the theory of dynamical systems (deterministic, stochastic, quantum, autonomous, non-autonomous, open, closed, discrete, continuous, with finite or infinite number of degrees of freedom…), an observable is a quantity in some theoretical framework whose value can be measured and observed in principle. Any good theoretical framework of physical phenomena should come with carefully established notion of an observable. ... See also measurement in nlab : In principle, any interaction between two physical systems is a measurement, whereby each system measures the state of the other. In practice, we break the symmetry by treating one system as the real physical system S of study and the other system as merely a measuring apparatus A with the sole purpose of measuring S. If the properties of A are mo...