Comment by AIPedant

This is where you are confused - in fact just plain wrong:

  A symbol is a discrete sign that has some sort of symbol table (explicit or not) describing the mapping of the sign to the intended interpretation

Symbols do not have to be discrete signs. You are thinking of inscriptions, not symbols. Symbols are impossible for humans to define. For an analog computer, the physical system of gears / etc symbolically represent the physical problem you are trying to solve. X turns of the gear symbolizes Y physical kilometers.