Original sentence: (Although the number of transformations is infinite, the number of classes of transformation is finite--just 1 class, the addition of the gradient of a scalar function.A common illustration of this fact is the sight of a small bird perched on a high voltage power line without electrocution, because the bird is insulated from the ground (as long as it doesn't complete the circuit by accidentally touching another wire or some grounded structure).In contrast, if some symmetry could be defined arbitrarily from one position to the next, that would be a local gauge symmetry.In fact, the example above (of electromagnetism) is actually a local gauge symmetry where the particular transformation of the potential of the electric field is just the constant one (a global symmetry is a local one but not vice versa); there are an infinite number of transformations of the electromagnetic field's potential A that are not constant but can be made consistent as explained below.The absolute value of the potential is immaterial; what matters to circuit operation is the potential differences across the components of the circuit.The definition of electrical ground in an electric circuit is an example of a gauge symmetry.The definition of the ground point is arbitrary, but once that point is set, then that definition must be followed globally.This is called a global gauge symmetry.When the electric potentials at all points in a circuit are raised by the same amount, the circuit will still operate identically, as the potential differences (voltages) in the circuit are unchanged