While the act of observation through apparatus is bound to measure in discreet excitation units, this doesn't negate the fact that certain aspects of reality are seemingly continuous. For example, the electromagnetic field is continuous; a photon is a discrete excitation of that field.

A field does not physicslly exist. It's an abstraction. We speak of waves and fields as first class objects, but this is reification. A field is a description of a pattern of relationships in the sequence finite states and possible state transitions. The intellect can grasp continuity but, physically, continuity can only be approximated. Because continuity is a concept. The fact that the intellect can grasp infinite and uncomputable things says something about the intellect, but it does not make infinite/continuous things physical. The invention of digital scarcity showed the requirements of a system implimenting conservation