Lab notebooks are great. I love them (and pens, and pencils, and, well... just geeking out at office supply stores).
But I switched to cloud-based documents for a few reasons: full text search, access from any (networked) computer, and I can type a lot faster than I can write. I am also able to keep a semi-useful GTD thing going just by using folders and documents on Google Drive. I recently discovered that drawing inside a Google doc isn't too bad and LucidChart is pretty cool too.
There are downsides from the perspectives of security and accessibility, for sure. And there's a tactile immediacy to writing on paper. So there will always be a place for paper and pencil in my world. But for storing and accessing the stuff that has left my scattered brain, it's hard to beat online technology.
I have a theory that it's impossible to prove anything, but I can't prove it.