Monday, 31 December 2012

A mathematical paradox of Christmas

Rembrandt nativity

An aspect of Christmas that is closest to my heart is that, where A is any set and where H is the set of all humans, it is also about the following:1, 2
!∃ A: A ⊄ Q ⇒ Q ⊂ Q ∧ Q ⊃ Q
H ⊂ Q
∃ h: h ∈ H ∧ h = Q ⇒ Q ∈ H ∧ H ∈ Q
In other words,3 God (an aspect of whom is represented here by Q), who includes and exceeds everything (which is beautifully put by the Islamic expression Allāhu Akbar - الله أكبر): “God is greater”), has become an individual human person (h) - i. e., a member of one of the myriad sets whose strict superset He is. The resulting recursive, infinite regress of divine in human in divine ... is a fundamental aspect of what Christians believe and celebrate at Christmas. Yes, there is a lot more to it and, no, I am not attempting either a reduction or any sort of proof here, but, I believe the mathematical representation of what happened at Christmas just makes the enormity and irregularity of it stand out more starkly than using any other means.

God - the transcendent beyond, has become a man - a finite creature, while retaining His transcendence and immanence simultaneously. This paradox (and it strictly is a paradox since it amounts to a finiteness and infinity that cannot be resolved) is a mind-boggling event regardless of the specific circumstances under which it took place and would in any case have shown God's love for humanity. His choice of coming into being as a human from the moment of conception (which Christians celebrate on the feast of the Annunciation and when the above paradox actually took place), being born the way all humans are and doing so under the humblest of circumstances just eases our comprehension of this extraordinary event and of the inexhaustible love that God has for us - a love that can also be read from the above set theoretic notation.

Another level of recursive infinity is introduced when Jesus institutes the Eucharist (making his divine-human self present in a transubstantiated, finite quantity of bread and wine), when it is He Himself who is present among any set of two or more humans who follow his words, and when it is He Himself who is also present in each human being. This makes not only God be transcendent-immanent but every single one if us too, by participation in His life. The ontological configuration that the incarnation introduces is truly a source of constant wonder for me and I hope that I managed to share some of that with you here.

Merry Christmas!

1 Thanks to my bestie PM for fixing my initially muddled notation!
2 Yes, I know I am using Cantor’s naïve set theory here and not Zermelo–Fraenkel (ZF or ZFC), but I do so since the latter has been designed to avoid the occurrence of paradox, which in most cases makes good sense, while Cantor’s system is more unconstrained and is precisely what the expression of the Christmas paradox calls for. Also, note that the term “naïve” here merely means non-axiomatic as opposed to implying any derogatory connotations.
3 In case you are not familiar with (this) set theoretic notation, it reads as: “No set A exists such that A is not a strict subset of Q (where a set X is another set Y’s strict subset if and only if all of the members of X are also members of Y and Y has at least one member that is not a member of X), therefore Q is a strict subset and also a strict superset of itself. H is a strict subset of Q. There exists a h that is a member of H and that is identical with Q, therefore Q is a member of H and H is a member of Q.”