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    $\begingroup$ Height can actually be a multivalued function because of overhangs and such - I've seen contour lines on topo maps cross. But that just makes it an imperfect analogy. Potential is of course single-valued. $\endgroup$
    – David Z
    Commented Jan 5, 2012 at 3:28
  • $\begingroup$ Furthermore, it's imperfect without resorting to overhangs because you can have discontinuities in altitude (as you cross a cliff) but you can't have that in potential because then the magnitude of the electric field would have to be infinite at that point -- or think of it as something like a capacitor of zero width. $\endgroup$
    – ThePopMachine
    Commented Jan 6, 2012 at 4:14