Constructing and understanding arguments is often difficult but key to both philosophyand other parts of the everyday life. Some methods to ease this task has been developed.One of the methods developed within informal reasoning is argument diagramming, amethod to structure and visualize arguments. This essay takes a complicated argumentabout the fate of the universe, put forward by futurist Ray Kurzweil in his book TheSingularity is Near, as well as some critique published against said argument, as a casestudy for the application of argument diagramming on unstructured arguments fromoutside the field of philosophy. To arrive at a diagram that can be easily grasped andread but still contains all information of the original argument, this essay developsa method of splitting sub-diagrams off of a main diagram. Analysing the resultingdiagrams shows that the plausibility of Kurzweil’s argument is heavily dependent on afew, critical premises at the lower levels of the diagram.