On the relationship between explanation and understanding

Is it possible to be able to explain a thing without understanding it? Or to have and understanding of a thing without being able to explain it? We've probably all experienced one or both of these, but prima facia it seems paradoxical that these should be so easily divorced from each other.

Literature often has an understanding without an explanation, science often has an explanation without understanding.

When you read a story like Adventures of Huckleberry Finn you have spent your time watching the battle between Huck’s morality and society’s. You have explored a theme, well set up for controversy by a thoughtful author, and you come away with a bit more understanding. No where in the book does Mark Twain explain racism to the reader but he none the less imparts understanding.

If you read the scientific paper by Watson & Crick first describing the double helix shape of the DNA molecule, you will read a fascinating, elegant and true explanation of a thing… with zero understanding of it. The entire field of quantum physics is explanations without understanding. I occasionally take apart old electronics with my oldest son before we throw them away because we share that excitement of finding out what all the little bits and pieces look like. It is well within my power to make detailed, thorough and true descriptions of what all the little green and silver and black pieces are, but that gets me no closer to knowing what they do.

When you teach a student something and they have a ‘lightbulb’ moment, they have gained an understanding of a thing, but that hardly correlates with them having an explanation of it. Many students will have written and verbalized an explanation several times and then … click… they have the understanding to match it. Others will have the light turn on and still be at a loss as to the explanation.

Our language only gives us to tools to create explanations, a magic incantation, a string of words that I can speak out loud and if the magic works right, then you have a new thought in your brain (and it’s the thought I intended. It is frustrating when that spell doesn’t work right, but if an explanation doesn’t generate understanding, we’ve done all our language is capable of and we need to seek other ways to generate understanding. This perspective doesn’t hint at where else we can look, but I think illuminating the paradox is worthwhile none the less.