Understanding

Sometimes, people make a fuss about the difference between knowledge and understanding.

Recently, an explanation of this difference occurred to me which I had not considered before.

The Slate Star Codex article Right is the New Left  explains fashion with cellular automata. It's a model of society which has about ten moving parts, yet has behaviors which resemble those of a whole society.

This made me think that understanding is essentially explaining something with a model small enough to fit in working memory.

Consider the extremely detailed weather model which meteorologists use to produce forecasts.

Now, consider the highly simplified explanation based on air masses, warm and cold fronts and so on which is commonly illustrated with weather maps.

The first gives us more accurate predictions, but the second one gives us more understanding. If a scientist was able to use the detailed mathematical weather model but did not think in terms of storm fronts and so on, he/she could not answer questions such as "why" it is raining. In the detailed physical model, "why" is almost meaningless: the causes of any particular event are huge in number.

This notion of understanding has several implications.

What constitutes understanding will depend on the mind doing the understanding, whereas knowledge is more objective in nature. I can achieve understanding of a system by putting it in terms I am familiar with. Suppose I am trying to understand an esoteric branch of chemistry known as semi-equilibrium Z-theory. I might learn all the statements belinging to SEZ theory by heart, and gain the ability to solve SEZ equations and get the correct answer, and still feel that I have little understanding. Yet, if I can relate SEZ theory to more familiar subjects, I will feel I've "put it in terms I can understand".

Assume I was an apple farmer before learning chemistry.

Let's say an experienced SEZ-theoretician gives me an analogy in which a SEZ-frubian (a central object of SEZ theory) is a rotten apple, and a SEZ-nite (another important concept in SEZ theory) is a worm slowly eating the apple. If the analogy works well enough, I feel I've gained an understanding: now when I'm solving the equations, I imagine that they are telling me things about this worm munching away happily at the core of the apple. I've now got a model with a few moving parts which allows me to make heuristic predictions much more effectively.

However, someone with no experience of apples and worms will not be helped very much by this analogy. It's placed SEZ-theory into my mental landscape, but the same explanation may not be useful to others.

Even a superhuman intelligence would have use for understanding: the actual universe is far too complex for a mind-within-universe to fully model. However, the understanding it achieves would be far beyond us. The "small" heuristic models would be too large to fit into our working memory (the mythical seven-plus-or-minus-two). Its weather maps would likely look more like our "detailed" physical simulations of the weather.