I vary between taking notes on paper versus on the computer. There are advantages and disadvantages to both.
For me, the biggest advantages to using paper for note-taking are speed and flexibility. I can write faster with a pen than a keyboard. And if the thought I’m trying to capture is visual, I can draw a little sketch on the spot. This combination of speed and flexibility makes pen and paper a much better extension of my mind than computers. I often get insights by sketching on paper that I wouldn’t have otherwise; the lines on the paper suggest new lines for exploration, and my hand is ready to articulate them.
Sounds ideal, right? However, there is a downside to paper-based note-taking: the sequence of notes is linear. If a thought occurs that is related to another topic, I must either find the last thread on that topic in my notebook and (if there is space) add it there, or break the current topic to start a new one. This results in sheets of paper covered in boxes and arrows.
Conversely, this is where digital note-taking shines: with computers my notes can be non-linear and cross-referential. If a thought related to a separate topic comes up, I can immediately refer to my last thread on that topic and add the note there. I can start with little or no structure, and move stuff around as patterns start manifesting. These emergent structures are a different means for exploration.
The trick is knowing when to use each type of note-taking. If I’m exploring a small set of ideas that lend themselves to linear thinking, paper usually works best. If I have a potentially large set of unstructured information, I use my computer. Of course, the two are not mutually exclusive; I will often start an exploration in my paper notebook, and move it to the computer halfway through to explore connections between things. This approach allows me to get the best of paper and the best of the computer without compromising either.