Dimensionless numbers provide a powerful tool to approach mechanics. With mechanical duos, we defined "simple dimensionless numbers" in Episode 8 to offer a scaled orthogonal perspective on regimes. For trios, two possibilities emerge. Non-aligned trios produce events with objective coordinates set by the three mechanical quantities, such as the Ohnesorge length and time from Episode 9. Divided by these reference values, scaled kinematic variables yield dimensionless quantities that are not "simple," but can still be expressed through the underlying simple dimensionless numbers of the trio. Conversely, aligned trios (Episodes 12–13) produce no events, but give rise to a new type of dimensionless quantity: the Index, which depends solely on mechanical parameters. With quartets, we saw how the index structures the dynamics of the associated domain. Today, we make sense of these different kinds of dimensionless numbers, explain how they are related, and show how their connection is tied to the rich and fascinating history of science.