The world science describes tends to have a very strange look. We can’t see atoms or force fields, nor are they imaginable within visualizable categories, so neither can we even imagine what the world must be like according to recent physical theories. That tension, between what science depicts as reality and how things appear to us, though it is more striking now, has been with us since modern science began. It can be addressed, and perhaps alleviated by inquiring into how science represents nature. In general, representation is selective, the selection is of what is relevant to the purpose at hand, and success may even require distortion. From this point of view, the constraint on science, that it must ‘save the phenomena’, takes on a new form. The question to be faced is how the perspectival character of the appearances (that is, contents of measurement outcomes) can be related to the hidden structure that the sciences postulate. In the competing interpretations of quantum mechanics we can see how certain traditional ideals and constraints are left behind. Specifically, Carlo Rovelli’s Relational Quantum Mechanics offers a probative example of the freedom of scientific representation.