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I think that is a very good intuitive of viewing it. ∇is measuring the gradientI read in another forum (unfortunately I no longer remember where) the following idea: An intuitive justification for having [itex] \nabla g=0 [/itex] is, if you move a meter stick around a room and the meter stick grows or shrinks as you move, it will still measure one meter in length if what you're using to measure it is the meter stick itself.

*with respect to*g. Therefore g has no gradient itself.