On the face of it writing can be a substantive aid to thinking to the extent that one might regard the writing as actually being the thinking.
For example:
When historian Charles Weiner looked over a pile of Richard Feynman’s notebooks, he called them a wonderful ‘record of his day-to-day work’.
“No, no!”, Feynman objected strongly.
“They aren’t a record of my thinking process. They are my thinking process. I actually did the work on the paper.”
“Well,” Weiner said, “The work was done in your head, but the record of it is still here.”
“No, it’s not a record, not really. It’s working. You have to work on paper and this is the paper. Okay?”, Feynman explained. (Clive Thompson (2014): Smarter Than You Think. p. 7)
All, or almost all, students of mathematics have experienced an offload of thought onto the written page when working memory becomes overloaded. For example, (à suivre)