The venerable Venn diagram is useful for showing overlapping areas between sets of things. A traditional representation of this type of diagram—translucent colored circles are an old favorite—is on the left, but tradition doesn't amount to a hill of beans when the elements of a set, or the sets themselves, don't lend themselves to any sane comparison.
For example, say you want to find out what would happen if you were to combine a sun, a blue moon, and a red lightning bolt. As you can see from a cursory examination of the intersecting areas in the Venn diagram on the right, the statistical likelihood of the Large Hadron Collider recreating the Big Bang is approximately that of two full moons within the same month.
In a similar way, combining a horse, a cow, and an octopus in a Venn diagram illustrates the difficulty of achieving meaningful results in today's DNA research facilities. Clearly, had humankind been intended for the task of creating new life forms, we would have more than two legs to stand on.
If necessity is the mother of invention, the Venn diagram is its father. Grafting common household appliances to plumbing fixtures can be a mind-numbing task, but diagramming the job beforehand keeps the numbness from ruining an otherwise sunny day. In the example on the right, the diagram tells me everything I need to know about the feasibility of combining a hair dryer, a coffeemaker, and a toilet.
In rare instances, even a Venn diagram isn't enough to keep chaos from raining on one's so-called picnic. If the sheer madness of certain combinations—the diagram on the left is only an example—proves one thing, it's that.