Woodworking is one of my many non-technical hobbies, used to switch off from the world. In particular, I will set out to make a 'thing' of non-critical nature, and abandon all measurement equipment. I'll still use a marking gauge without index markings, allowing me to mark a straight line, or a half way point, but that's it. Removing numbers from the process, for me, is a fantastic way to switch from an engineering mindset, to a purely creative one.
Reminds me of a traditional harpsichord builder I heard of. When starting a new instrument, he defines the "inch" for that instrument which is the width of the key. He sets his calibers for that, measures 8 inches for the width of an octave. And so on, everything is done geometrically, like they used to do in the "good old days" before this fixation of numeric methods. His instruments are of very good quality.
