Or “A very short investigation of the mental dynamics of feeling suddenly stupid”.
Every week I have a couple of experiences that play out as follows:
Involved and intricate discussion on non-trivial subject, usually but not always mathematical and/or abstract in nature, involving an attempt to make a deduction about the same, resulting in a sudden and complete blanking of the mind, the contents of which are replaced by an image of reflective self-awareness at losing the plot. Having lived through this a few hundred times, I’m beginning to understand in greater resolution what is happening during the “blanking” stage. It’s not really that all relevant concepts pack up and vacate the imagination. For the most part, they’re around. The strongest “chunks”, clusters of densely interconnected atoms of understanding, they continue to persist as chunks too. What disappear under mental overload are the thinly formed (i.e. new) bridges connecting these islands, leaving in their wake local pockets of orphaned and completely inapplicable concepts.
This realization is helpful in that it tells me where I should be exerting my efforts: Not on learning new ideas, but on creating as many independent routes between new and old ones as I can. In a field like mathematics that deals with generalities, for example, this means spending less time on definitions or theorems and more on applying them to as many other mathematical constructs as I can, hopefully proving something I already know to be true in a new way.
For long-lasting learning, pieces of knowledge should support each other through their connections. For when we remember a fact or use an idea, we activate connected facts and ideas and solidify them in our minds. Our knowledge lives best in infinite, self-supporting clusters. But if we learn facts and ideas in isolation, we make dots without bonds…So, for long-lasting learning and understanding, make bonds; connect each new fact and idea to what you already know. Use your reasoning tools to weave a richly connected, durable tapestry of knowledge.
-The Art of Insight in Science and Engineering