The externalization of ideas helps overcome the limitations and biases of our minds. Ideas can be externalized through writing, symbols (in mathematics), diagrams, graphs, and drawings.
Each of these externalized mediums extends our memory, facilitates editing, and clarifies thinking. You can write down more than you can easily remember. Once ideas are made explicit on a page, their connections are open to critique and scrutinization. In this way, complex ideas can be more easily edited, manipulated, and organized into a coherent whole; word by word, sentence by sentence.
Ahrens, S. (2017). How to Take Smart Notes: One Simple Technique to Boost Writing, Learning and Thinking – for Students, Academics and Nonfiction Book Writers.
Richard Feynman on externalization as thinking
Richard Feynman once had a visitor in his office, a historian who wanted to interview him. When he spotted Feynman's notebooks, he said how delighted he was to see such "wonderful records of Feynman's thinking."
"No, no!" Feynman protested. "They aren't a record of my thinking process. They are my thinking process. I actually did the work on the paper."
"Well," the historian said, "the work was done in your head, but the record of it is still here."
Neil Levy on the necessity of note-taking"No, it's not a record, not really. It's working. You have to work on paper, and this is the paper."
"Notes on paper, or on a computer screen [...] do not make contemporary physics or other kinds of intellectual endeavour easier, they make it possible."
Niklas Luhmann
Jordan Peterson's Essay Writing Guide"It is not possible to think systematically without writing"
You can write down more than you can easily remember, so that your capacity to consider a number of ideas at the same time is broadened. Furthermore, once those ideas are written down, you can move them around and change them, word by word, sentence by sentence, and paragraph by paragraph. You can also reject ideas that appear substandard, after you consider them more carefully. If you reject substandard ideas, then all that you will have left will be good ideas. You can keep those, and use them. Then you will have good, original ideas at your fingertips, and you will be able to organize and communicate them.
Michael Nielsen's Extreme Thinking