Knowing that a directed graph is acyclic is useful. If you construct directed graphs in a certain way, then you can prove that they have no cycles. Design systems to produce constructable graphs, and you can take advantage of all of the theorems known to be true of DAGs. Alan Turing proved that there could not be a general procedure to determine whether an expression in first order predicate calculus is satisfyable. This extends Godel's Incompleteness Theorem by asserting not only that there are some true statements that cannot be proven, but also that there is no way to decide whether a statement in general even has a proof. In the process of constructing this proof, Alan Turing defined the Universal Machine, which can perform any mechanical computation. This is the genesis of the computers that we use today. Leslie Lamport finishes off his paper on Time, Clocks, and the Order of Events in a Distributed System by showing how to synchronize physical clocks. This is useful to avoid anom
