A popular science article begins like this:
[…] imagine a company of drunken students who wander in the streets, and whenever they come to an intersection one of them just spins around and they all go down the path that ends up being in front of the spinning student’s eyes.
In this way the author, Oliver Nagy, makes the mathematical concept of ‘random movement’ concrete. That’s an arbitrary route in a network. Random movement is used, among other things, to describe stock prices and the distribution of pollen.
Is your subject also abstract and do you communicate with a wide audience?
Then it really helps to use a concrete metaphor.
But how do you come up with that?
Usually it helps to articulate the underlying idea first.
In Oliver’s case: sequential, random movements on nodes.
The next step is to brainstorm where you encounter that idea in a familiar sensory setting.
Streets and intersections make the network physical in a logical way. And drunken wandering is a beautiful depiction of random movements.
The metaphor allows Oliver to quickly explain later what distribution is (places where the students can be and the probability that they are indeed in that place) and mixing time (the time that elapses until it no longer matters for the distribution what the starting point – the pub – was).
PPS Oliver’s article is meant for people with a basic knowledge of mathematics.