Asymmetry

In Manila, Pope Francis returned to a concept that he first introduced in Evangelii Gaudium - that of the polyhedron being the ideal of social interaction instead of the, seemingly more perfect, sphere. There, speaking about "ideological colonization," he said:

"[W]hen conditions are imposed by [...] colonizing empires they seek to make peoples forget their own identity and make them (all) equal. This is the globalization of the sphere - all the points are equidistant from the center. But the true globalization [...] is not the sphere. It is important to globalize [...] not like the sphere, but like the polyhedron. Namely that every people, every part, conserves its own identity without being ideologically colonized."

To make more sense of the sphere-polyhedron distinction, let's go back to Evangelii Gaudium, where it is presented in the context of strategies for contributing to the common good and peace in society. There, Francis gives preference to time over space (§222-225), unity over conflict (§226-230), realities over ideas (§231-233) and finally the whole over the part. However, he is quick to argue that the part is not negated or subsumed in the whole, but that they mutually enrich each other (§235):

"The whole is greater than the part, but it is also greater than the sum of its parts. There is no need, then, to be overly obsessed with limited and particular questions. We constantly have to broaden our horizons and see the greater good which will benefit us all. But this has to be done without evasion or uprooting. We need to sink our roots deeper into the fertile soil and history of our native place, which is a gift of God. We can work on a small scale, in our own neighborhood, but with a larger perspective. Nor do people who wholeheartedly enter into the life of a community need to lose their individualism or hide their identity; instead, they receive new impulses to personal growth. The global need not stifle, nor the particular prove barren."

And it is in the context of how the whole and its parts can be thought of without the former stifling the latter that the concept of the polyhedron comes into play (§236):

"Here our model is not the sphere, which is no greater than its parts, where every point is equidistant from the centre, and there are no differences between them. Instead, it is the polyhedron, which reflects the convergence of all its parts, each of which preserves its distinctiveness. Pastoral and political activity alike seek to gather in this polyhedron the best of each. There is a place for the poor and their culture, their aspirations and their potential. Even people who can be considered dubious on account of their errors have something to offer which must not be overlooked. It is the convergence of peoples who, within the universal order, maintain their own individuality; it is the sum total of persons within a society which pursues the common good, which truly has a place for everyone."

Reading the above, I believe, that the image of a polyhedron also points to another fundamental feature, implicit in the distinction between sphere and polyhedron, which is that of asymmetry.

Purely on geometric grounds, an obvious distinction between a sphere and any polyhedron is that the former abounds in symmetry: an infinity of rotation symmetries around the sphere's center, an infinity of reflection symmetries with respect to any plane containing the sphere's center and a central point symmetry, also with respect to its center, not to mention a host of other symmetry groups. On the other hand, a polyhedron, in general, has no guaranteed symmetry whatsoever, where each of its vertices may relate to all the others in a unique way and where even subsets of the polyhedron's vertices may form geometries distinct from those of other vertex subsets. As a result, the polyhedron formed by a set of vertices, edges and faces is both a unique whole and one whose nature depends on where each one of its components is located, potentially without any symmetry at all. In fact, the absence of symmetry can also be though of as an expression of the non-redundancy of the polyhedron's parts, since any, even partial symmetries or repetitions would allow for a representation of the polyhedron that no longer requires a reliance on all of its parts. The sphere here represents an extreme, where the infinite continuum of points that form its surface can be reduced just to the coordinates of its center and its radius. Incidentally this line of thinking also resonates with Pope Francis' early insistence on the importance of peripheries, expressed by him saying that “We understand reality better not from the center, but from the peripheries.” To understand a polyhedron requires traversing its vertices, edges and faces that form its perimeter, while a sphere can be "understood" from its center and radius, since its surface can be inferred from them, without ever being traversed.

Asymmetry not only means that each member is necessary for the identity of the resulting whole, but it is also a principle that is deeply embedded in Jesus' life and teaching. His incarnation itself is vastly asymmetrical, since it is the infinite, unbounded God making Himself spatiotemporally finite, as is His death on the cross, where his one life is given "so that everyone who believes in him might not perish but might have eternal life." (John 3:16). The all becomes one to save the many.

Jesus' teaching too is full of asymmetry, starting with the following, emphatic passage:

“But to you who hear I say, love your enemies, do good to those who hate you, bless those who curse you, pray for those who mistreat you. To the person who strikes you on one cheek, offer the other one as well, and from the person who takes your cloak, do not withhold even your tunic. Give to everyone who asks of you, and from the one who takes what is yours do not demand it back." (Luke 6:27-30)

In St. Matthew's account of the same speech, we then hear Jesus adding: "If anyone wants to go to law with you over your tunic, hand him your cloak as well. Should anyone press you into service for one mile, go with him for two miles." (Matthew 5:40-41).

Love-hate, bless-curse, pray-mistreat, strike-offer, take-give, tunic-tunic+cloak.

And the madness doesn't stop there! The asymmetrical rewards offered in the parable of the workers in the vineyard have those who have worked a full day complain to the owner: "These last ones worked only one hour, and you have made them equal to us, who bore the day’s burden and the heat." (Matthew 20:12). The pittance offered by a poor widow is valued above the large sums contributed by the rich (cf. Mark 12:41-44) and asymmetry is also at the heart of Jesus' exhortation to "be shrewd as serpents and simple as doves" (Matthew 10:16).

Not only are action and reaction, action and reward asymmetrical, but asymmetry is at the very heart of God's own inner life and at the core of love as such. The gratuity of love and the very concept of a gift hinge on asymmetry. I give without expecting anything in return, for if I did, my gift would not be a gift at all, but - at least implicitly - an exchange, a transaction, a symmetrical process. In the Trinity the Father gives all of Himself to the Son, without holding back or without requiring prior guarantees of equal recompense. The Son too gives Himself to the Father unreservedly and totally, making Himself nothing to Himself and all as gift to the Father. The Holy Spirit makes Himself empty unconditionally to allow for the love of the Father and the Son to find space in Him. Each Person of the Trinity is ultimately asymmetrical: a gift of self outside oneself, for the other; nothing and everything. It is only on this asymmetry that Father, Son and Holy Spirit are one - a one that is dynamic (instead of being static), varied (instead of being monotonous) and communion (instead of being regimented).

A consequence of the asymmetry of love is also a difference in what to expect of oneself versus others. For my actions to be gratuitous and an expression of love, their end must remain their being love, gift and a benefit for the other. If they get reciprocated, my neighbor and I share in the life of the Trinity and we become one without either of us being annihilated.

I believe it is for these same reasons that St. John Paul II used to say: "Be strict to yourself and lenient with everyone else." and that I choose to constrain what I say and do, out of love for my neighbors, without wanting to impose those same constraints on them. For by imposing them, I would preclude them from freely choosing to self-apply them out of love for me.