Introduction

Symmetry has an undeniable heuristic value in physics, as is demonstrated throughout this volume. To see if the value is more than instrumental, that is, to see if the symmetries are somehow in nature itself, we should ask a transcendental question: what must the world be like such that symmetry would be so effective in understanding it?

I will describe two apparent conditions of symmetry: objectivity and design. It will turn out that only one of these, objectivity, can be securely linked to symmetry. But symmetry does not serve as evidence for design in nature. In fact, the very aspects of symmetry that link it to objectivity suggest that it is not the result of design. The two apparent implications of symmetry are incompatible, and there is clear reason to retain the notion of objectivity and give up design.

Symmetry and objectivity

The accomplishment of knowledge involves keeping track of relations between the permanent and the ephemeral. Sensations keep changing while the relevant categories to describe them stay the same, and we have empirical knowledge of the world when we can accurately associate the fleeting sensations with their more permanent concepts. Coordinate systems remain fixed as an object's position changes, and the science of kinematics is useful insofar as it can describe the variable positions in terms of the stable reference frame. In general, knowledge is intimately involved in the interplay between what changes and what doesn't.