There have several rounds of how to use analogies and how not to use analogies in the past few years.
These involved notions like agile is an untended garden. Actually and untended garden and called a weed patch.
Or we can't really stop and develop a strategy, because we're always putting out fires. Actually firemen rarely put out fires. They spend the majority of their time preventing fire with fire safety, inspections, fire inspections. Their job is to never have fires start.
And of course for false analogies of the double pendulum as a stand in for chaos and unpredictability. Since the equations of motion are easily defined - an exercise for any upper division physics student - and a MathLab plugin, you can plot the path of the double pendulum.
And my favorite the attractor analogy, in which it is presumed that some how in chaos theory the attractor attracts. Without understanding that those pretty pictures of the attractor are the result of the underlying equations for the system.
So with that in mind, there is a new book from one of my favorite authors, Douglas Hofstadter, Surfaces and Essences. In the book Hofstadter makes the case for analogy as the fuel for creative thinking. Using Robert Oppenheimer's quote...
whether or not we talk about discovery or of invention, analogy is inevitable in human thought, because we come to new things in science with what equipment we have, which is how we have learned to think, and above all how we learned to think about the relatedness of things.
But as always we need to take care to assure that those analogies we use to expand the conversation, don't violate the laws of physics, gardening, or mathematics.