Shaving in a mirror with Ockham's razor

Abstract

Reflections in a simple looking glass are extraordinarily puzzling. The extensive literature, over millennia, of the philosophy and science of mirrors continues to be confused and confusing, especially over why reflections are horizontally but not vertically reversed when the optics are symmetrical. The diffculty for seeing what is happening may be the seductive temptations of many plausible kinds of explanations – optical, physiological, verbal – which are familiar and useful in other contexts. Optical ray diagrams are especially tempting, but they cannot distinguish horizontal from vertical – any more than a map can tell north without a compass – so although they are generally useful, they cannot answer this mirror question. Here we explore in detail one simple hypothesis for a complete explanation of a variety of such phenomena: only physical rotation is relevant. This may be rotation of the reflected object (from direct view of the back of objects) or rotation of the eyes of the observer (from direct view behind). All other considerations are excised by Ockham's razor, which accepts the simplest hypothesis while rejecting unnecessary postulates, even though based on truths. The special, indeed the unique case of one's own face is considered in detail for the first time. It is likely that mirror images are so puzzling because they cannot be explored by touch. This is evidence that interactive hands on experience is important for young children discovering the object world, and for enriching understanding of the principles of science in practical classes in schools and universities. This applies also to exploratory science centres attempting to introduce science to the public, for without initial guiding touch we see darkly.