Beauty fascinates me although it is not at a purely aesthetic level or in any visceral approximation to emotional experience and desire with which our culturally-mediated experience of self and subjectivity endows us. Consider that there have been a number of cross-cultural and ethnically-diverse academic studies that demonstrate that the faces which are considered to be most attractive in any context are also those that tend towards some geometric property of median values. Put slightly simpler – the greatest beauty is that which most closely approximates to an average value calculated over all possible geometries of facial structure.
Ouch! It is not what you think, though. Approximation to a numerical or geometric average is a quantitative measurement across all possible geometries that is quite profoundly NOT the same thing as a qualitative (or emotional) assertion of “average”. What an observation of convergence towards an average indicates is that there are subtle cues and implicit feedback loops (inside minds, languages, systems of visual representation and – indeed – the cognitive hyper-extension of technology) that naturally and autonomously self-gravitate around a central pivot or focal point.
So, if you were to get out your ruler and start measuring the facial geometries of reputedly beautiful celebrities (for instance), you would very likely discover that they all possess remarkably similar facial properties. Why does such an underlying bias towards a central average or geometric mean exist? It is probably a property of the ways in which sociocultural (and cognitive or subjective) information-processing systems autonomously orient themselves towards methods of optimally-resilient sustainable continuity and self-replication.
It is attributed to Francis Bacon to have penned an observation that “there is no great beauty that hath no strangeness of proportion”. It may be that the underlying mathematical systems of pattern recognition that occur in brains (and are distributed in cultures) possess second-order convergences to other statistical averages of geometry.
Or, it might just be that some faces are truly gorgeous.