symmetry and ignorance

Confronted with total ignorance we expect symmetry: If we do not know anything about a process except for its set of possible outcomes, then we assume that all outcomes are equally likely. In other words, we use the most symmetrical probability distribution as an expression of total ignorance.

Confronted with symmetry we expect ignorance: Presence of symmetry, by definition, means that there are certain transformations (whose kinds depend on the nature of the symmetry) of the underlying substrata that leaves everything observable unchanged. In other words, we have no hope of being able to tell whether the substrata is currently being subject to such transformations.

Hence, in some sense, use of symmetric designs in the interior decorations of mosques is very appropriate. They remind us the state of ignorance that all mortals are in.