I started out writing music on the computer, from day one. Originally, it was notation software (Finale Printmusic at the time), then eventually I transferred over to a DAW (Cubase). The vast majority of music I’ve composed was an entirely digital proceeding. Until rather recently, that is.
I generally come up with musical ideas on the piano or cello, and then jump to the computer and hurriedly attempt to get them in. This doesn’t always work right, as ideas slip away, unable to make the transfer, and the original concept slowly dissolves. Sometimes that’s a good thing. The computer allows a different method of thinking. Being able to hear different instruments interact can take it in new directions I wouldn’t have thought of at the piano.
A while back, I decided to try something new. I printed out some blank sheet music, and sat down at the piano, this time with a pencil ready to scribble down some notes. The result was a simple piano solo (you can hear it here), but the idea stuck. A few months later, I was brought on to compose the score to Episode 3 of Youtupolis. Rather than using my MIDI keyboard and Cubase to record some ideas, I went with the pencil approach. 
Two weeks ago, I put myself to the test, and wrote an entire orchestral track by hand, spanning 14 pages and about 120 measures, in a few hours. It was quite a satisfying accomplishment. The sense of freedom and ease is exhilarating! Then I transferred it into Cubase, and got the final result: The Discovery by Jeremiah Pena
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Delighted to read your post, regarding the rediscovery of the process of writing music by hand and indeed to hear the recording of your composition “Discovery” on SoundCloud. It is a landmark in my present exploration. I recently read “The Act of Writing” by media theorist Daniel Chandler. That contains some interesting observations on “writing tools” and methods, though in the context of literature rather than music.