  We note the separation of a quantum description of an experiment into a
statement of results (as probabilities) and an explanation of these results (in
terms of linear operators). The inverse problem of choosing an explanation to
fit given results is analyzed, leading to the conclusion that any quantum
description comes as an element of a family of related descriptions, entailing
multiple statements of results and multiple explanations. Facing this
multiplicity opens avenues for exploration and consequences that are only
beginning to be explored. Among the consequences are these: (1) statements of
results impose topologies on control parameters, without resort to any quantum
explanation; (2) an endless source of distinct explanations forces an open
cycle of exploration and description bringing more and more control parameters
into play, and (3) ambiguity of description is essential to the concept of
invariance in physics.
