What kind of analogies or "metaphors" to "real-life things" for rings and fields are there, if any? I'm studying for a final, was just wondering if there's anything concrete to help me wrap my head around these concepts. I understand the mathematical definitions, but I'm also having trouble "visualizing" them.
For example, someone used a language translation as an analogy for isomorphisms and other morphisms (like how an isomorphism is a perfect 1-1 language translation, while homomorphisms may translate from one lang. to another, but not necessarily back to the same word). Is there anything along that line for rings and fields? Thank you.