The prismatic principle

Occam’s razor is a long-lasting principle regarding rational explanations. It is often stated as “entities must not be multiplied beyond necessity”. It’s a clear call to parsimony and to hold to the simplest explanation. Some interpret the maxim in terms of truth, claiming that the simplest explanation tends to be true. This is still valid for our times, but there is caveat. The “simplest” explanation must be chosen acknowledging a minimum degree of complexity. Let’s call this the prismatic principle. Before an explanation can be chosen for its simplicity among others a degree of complexity must be granted. What does this mean? That the subject at stake must be explained showing its different perspectives and transformations. We can learn a lesson from current mathematics. A mathematical object includes all its possible variations and transformations as long as some invariant is preserved. An object is not simply identical to itself; it is equivalent throughout all its transformations. Objects are neither static nor reducible to some unique mode of appearance. Take a mathematical knot. They are defined as continuously deformable closed curves, like “rubber rings”, embedded in ambient space (R3). They can thus be “manipulated”, i.e., stretched, twisted or compacted remaining the same. The only forbidden actions are cutting and gluing. To obtain a knot take the shoelace of your sneakers and join the loose ends. It cannot be undone without cutting or gluing, but you can play with it, transform it in several ways. A knot has infinite modes of appearance. It can be modified (by the so-called Redemeister moves). And yet, if no cutting or gluing is involved, it remains the same. Likewise, the prismatic principle considers an object, a problem or an issue as a set of transformations with an invariant. This principle is prior to Occam’s razor. If we follow the latter too soon, we will miss the richness of the object, and its different perspectives, even if they seem irreconcilable prima facie.