Explanation:
A good analogy is a compromise between two conflicting goals: familiarity and representativeness.
Good analogies are familiar. They express an abstract idea in terms of a familiar one. The odometer and speedometer on a car are a good analogy for a function and its derivative, because we all understand how speedometers work, but maybe not calculus.
Concrete experiences are good breeding grounds for analogies because they can be appreciated by anyone. When I say voltage is to the electric force what height is to the gravitational force, that is helpful because height is more concrete than electric potential.
But a good analogy doesn’t need to be concrete, it only needs to be expressed in terms of an idea you already know deeply. One of my favorites was from an MIT ecology class which expressed the idea of biological niche as a section of an n-dimensional feature space. If you didn’t study linear algebra, that may not make any sense, but it was widely appreciated by the audience who had a stronger math background.
That latter fact is important when creating analogies for yourself. Concreteness is good, but as long as you understand the analogous domain well, anything works.
Good analogies are also representative. They match at least some of the features of the idea you’re trying to explain. More matches means the analogy has more intuitive power. Fewer means you need to be careful about applying the analogy to understand new situations.
Making new analogies is like making a key for a lock you haven’t seen before. You’re limited by your past experience as to what kind of keys you can make. New key designs take a lot longer to learn than borrowing old ones. That’s familiarity.
But you also want the key to fit the lock. If the key shape deviates too much, it won’t open the lock. That’s representativeness.
