To me, the greatest appeal of analog computing is in representing equations in mechanical, visual, directly modifiable, 'hands on' forms. Having different concrete representations or implementations of abstract concepts makes them so much easier to understand. I've read somewhere that the technicians working at MIT with Vannevar Bush's mechanical differential analyzer quickly learned advanced calculus and "debugged" the math of university professors that would use the machines for various computations. It is not the continuous nature of the variables that is so interesting, it is the concept of computing by analogy and the benefits to understanding that come with that.