Give me an analogy, then tell me where it breaks

When you want an intuition for something abstract without picking up a wrong model.

Give me analogies for the concept below, and be honest about their limits.

For each of three analogies:
- The analogy, in two or three sentences.
- The mapping: which part of the analogy corresponds to which part of the real thing.
- **Where it breaks.** The specific way someone reasoning from this analogy would reach a wrong conclusion.

Then answer one question directly: is this a concept where analogy helps, or one where every analogy imports a misleading intuition and I would be better off with the literal definition? If it is the latter, say so and give me the literal definition instead.

Concept:

Explaining a concept. Getting an idea across at the depth you need, with analogies, origins and first principles.