Why Gauge?

The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe handles though which systems couple: they represent real relational structures to which the experimentalist has access in measurement by supplying one of the relata in the measurement procedure itself. This observation leads to a physical interpretation for the ubiquity of gauge: it is a consequence of a relational structure of physical quantities.