“When Is Better to Think Without Words?”
When we put words to a thought, we have to compress something that is like a web in our mind, filled with connections and associations going in all directions, turning that web into a sequential string of words; we have to compress what is high-dimensional into something low-dimensional.
[C]ompression is effortful. It takes intense concentration to find the right words (rather than the sloppy ones that first come to mind), and then to put them in the proper order.
If we can avoid the compression step, and do the manipulations directly in the high-dimensional, non-linguistic, conceptual space, we can move much faster. But this is a big if. Most people, myself included, have too weak mental models to do this kind of processing for complex problems, and so, our thoughts are riddled with contradictions and holes that we often don’t notice unless we try to write them down. We can move faster in wordless thought, but we’re moving at random. If, however, you have deep expertise in an area, like the mathematicians, it is possible to let go of the language compression and do a much faster search.
The insights arrived at wordlessly need to be submitted to the rigor of mathematical notation and logic, to test their validity. It is a sort of feedback mechanism: unless the intuition holds up on the page, it is a false intuition.
The written results also work as relay results. By writing something down and making sure it is solid, we can offload that thought from working memory and instead use it as a building block for the next step of the thought.
When writing, there are all sorts of details that need to be specified for our paragraphs to make sense, and if we don’t know what should go into a sentence, it is all too easy to fill in the uncertain parts with guesses. At least my brain has the most miraculous autocomplete function and supplies me with credible endings to any sentence I start—often credible nonsense. But when the nonsense is there on the page, next to thoughts I’ve settled through hard work, it looks respectable! It often takes considerable work to realize I’ve fooled myself.