I carry a small spiral-bound memo book with me all the time for short-term notes. In the case of random thoughts, it’s generally just a title.
Every morning, I move everything from the memo book into other systems and tear out the used pages. For ideas, this means putting the title at the top of a blank sheet of paper and free writing until I either run out of things to say or reach the bottom of the page.
About once a week, I file all the new notes in a binder sorted by title and put an index card for each one in a Leitner box for reviewing in the future.
When working through reviews, if I find a note interesting it gets promoted all the way to the front section of the box, and otherwise it gets pushed back one, so that its review cycle gets longer. I also use the review as an opportunity to ensure the note is recorded properly in a topical index.
