Averages and Liturgy

Averaging is a common way to arrive at a description of a group of particulars. But in obtaining an average, we necessarily lose that which distinguishes any one particular from the more general underlying form, if, indeed, there is an underlying form. There may not be. The average number of legs on a human is less than two, so the average there is not a good representation of some kind of ideal Platonic human form.

Many people have met images such as the two faces below. They are derived by a process of averaging over many images of individual faces. I recall the first time I saw such composites, and what struck me was, I guess, unremarkable. I recognised that the average face was beautiful in an odd sense, as it lacked any real character. It seemed to show a kind of ideal beauty.


What I may have taken longer to recognise is that the faces that went into these composites are not particularly representative of humanity. Indeed they are particularly white. So whoever created these images also performed an act of selection which determines the character of the final result.

Of course this was noticed by many people, and face averaging became popular. A casual Google search will bring up many average faces drawn from specific classes. One such example is this, which produces faces that are indexed by nationality.


With this, one might think the non-representativeness of the first picture was improved upon. I suggest that the opposite is the case. Where the first two faces were averages from an unknown population, these seem to be from quite determinate groups. Yet it is abundantly clear that in creating these, the creator has chosen faces that fit a pre-existing national stereotype. For example, there are many people who are Irish citizens, born and raised here, but who look nothing like the mono-ethnic stereotype shown above under the term “Irish.” The selection has thus acted to construct and reinforce national racial stereotypes, which is anything but a neutral act. It is a kind if use of data that we ought to be sensitive to, but which sadly often goes unnoticed. (Most studies of such images have taken the “attractiveness of the female face” as a theme to explore, thus creating a perfect storm of nationalism, racism and sexism in one fell swoop.) There is room for a strong critique here of the practices of data scientists and data mungers of all kinds, but I wish to explore a rather different thought.

Faces are an important index of identity. We value our faces, they represent us, we present our faces to others, and take great care that our faces are seen in the best possible light. In a culture in which the selfie and the avatar do so much representation on our behalf, the centrality of the face in the assertion of identity has never been more important. But we assert our identity in other ways too. We enact our identity in ritual for example, whether it be the solemn ritual of liturgy or the more light hearted chanting of supporters on the football terraces.

Some liturgies give rise to very stable forms, forms that are repeated with only minor variation on innumerable occasions. The consecration of the bread and wine in a Catholic mass is a ritual that has survived for centuries, since the words “Do this in memory of me” were uttered (perhaps). Rituals provide invariance in a world of variation. Invariance in a sea of change has been difficult to characterise satisfactorily. Invariants of all kinds have been sought by perceptual psychologists to account for how we come to identify stable objects and events in a world of sensorimotor flux, for example.  Heinz Von Foerster referred to stable forms as Eigenforms, in reference to the mathematical notion of invariance across transformation.

So I asked myself if one could do for liturgy what was done above for faces. Could one identify stable recurring forms across all the messy particulars of individual rites and rituals. The images below are composites, each based on 10 instances of the mass, each centered on the elevation of the host at the moment of transubstantiation, as this moment is central to the ritual in an intuitive way, just as pictures of faces are aligned with the eyes.





I think the stability of such forms and their role in the enactment of common ground bears further exploration.

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