All kinds of things meet that criteria -- the audio disc before CD, the written word, photographic film. And yes, there were even analog computers.
One definition for analog from the web is:
"Anything whose behavior corresponds with the behavior of something else, especially if the correspondence varies continuously rather than in steps. For example, the height of the liquid in a thermometer is an analog of the temperature. ..."
So what would be a modern day analog recorder for sound? Or more importantly, what could be transformed into a great analog recorder? What technology since the 1930s could we employ?
While I'd like realistic answers, at this moment I don't care completely about practicality and certainly not about return on investment.