The identification problem. Suppose that we do have a full-fledged discrete geometry and suppose that we replace the classical geometry of a physical theory with the discrete version. We will now be talking about hodons and chronons. The “natural” question that arises is what is to be identified with what? Imagine that, in line with Silberstein, we are a bit naïve and would be tempted to identify the hodon with the Planck length, \(l_{p} = 10^{-35}\text{m}\) and the chronon with Planck time, \(t_{p} = 10^{-43}\text{s}\). If one now accepts that the maximum speed is one hodon per chronon, then what comes out of this identification is that the maximum speed is indeed \(c = 3.10^{8}\text{m/s}\). (Note: nothing amazing is happening here, since in classical physics, \(l_{p}\) is defined as \(\sqrt{\hbar G/c^3},\) and \(t_{p}\) as \(\sqrt{\hbar G/c^5},\) so that it is immediately obvious that \(l_{p}/t_{p} = c\). Now ask the simple question what the next speed will be, just below \(c\)? The answer must be: one hodon per two chronons, but that means a velocity of \(c/2\). We seem to have missed out the whole range between \(c/2\) and \(c\). There is a way out, but it supposes that “jerky” motion is considered possible, an aesthetically quite ugly idea. An object moves two hodons in two chronons and then waits for one chronon and then repeats the same motion. The average velocity is then \(2c/3\). One possible way out, that will be briefly mentioned in section 3.2, is to introduce an element of randomness into the structure. For an appreciation of the full complexity of this topic, going beyond merely numerical relationships, see the excellent overview and discussion of Hagar (2014).