Understanding can also be the ability to visualise or simulate what's happening in a concrete problem.  These kinds of simulations played a vital role in the achievements of Albert Einstein and Richard Feynman.

Understanding as concrete mental simulation

We all know the difference between memorising something we don't understand and the satisfaction of genuinely understanding something. To understand what it means to understand something is less clear. There are a few possibilities of what understanding might mean: <ul><li>Understanding as connected information</li><li>Understanding as flexible action</li><li>Understanding as an explanatory ability</li><li>Understanding as identifying broad, abstract principles</li><li>Understanding as concrete mental simulation</li></ul>

What it means to understand

We may view understanding as noticing deeper principles - the broad patterns that underlie an issue. Understanding is then a mental process rather than an outward result. Research shows that novices view physics problems in terms of superficial details (pulleys, inclined planes), but experts view the same problems in terms of principles (conservation of energy, momentum).

Understanding as identifying broad, abstract principles

To understand something means having many connections between it and its related ideas. We develop understanding by drawing relationships between what we already understand and what we are trying to understand. Analogies, metaphors, visualisations and associations can help to connect new and old knowledge. But it may not be sufficient to fully describe what understanding is.

Understanding as connected information

To understand something means to be able to apply it and various ways. Understanding chess means being able to play well from a variety of different positions. Understanding algebra means solving a wide range of algebra problems. Experts seem to rely on having many examples in memory to find the correct move.

Understanding as flexible action

There are many situations where we can behave flexibly but can't claim to have a deep understanding—for example, teaching someone how to tread water. Alternatively, we may think that explanation, and not action, is the key principle. For example, the Feynman Technique is an example of a tool that aims at self-explanation as the way to understand something. But, it is not complete, as understanding can always deepen.

Understanding as explanatory ability

There is no singular process behind understanding. <ul><li>Increased and varied exposure to an idea or skill should help to develop most forms of understanding.</li><li>The flexible action and explanatory ability show some overlap, but there are cases where you could foster one kind but not the other.</li></ul> Instead of trying to find one way of understanding, we should ask more guided questions about what we want to do with what we learn.

Practical consequences of ways of understanding

How do you know when you've truly understood an important idea? Here are five different ways we understand things and why it matters.