THE AXIOM OF LOVE

Today Vincent tackled what is at one and the same time the simplest and most complex topic: unending love. Referring to how love can be measured and against which background, he made a distinction between algebraic numbers and transfinite numbers. The last line was delivered as a piece of advice to lovers who want to make an ultimate declaration of love. In his opinion, the proposition “I love you, my love, with an infinite love on the real numbers line” should do it. Those with a basic understanding of math are able to see why this is not only beautiful, but also very and verily simple, although there are the fewest who possess the right intuitive power to realize what is at stake in Cantor’s continuum hypothesis. In other words, how many people’s imagination can grasp endlessness without being deterred by endlessness itself?

The complexity of the topic arises when one poses a question that relies on cultural competence and recognition. To whom does one engage in making this ultimate declaration of love, as this presupposes that the other is able to identify what one is talking about. So love assessed in its simplest form, paradoxically enough, has little to do with numbers, and quite a lot with a gut feeling. Conversely, love assessed as a complex phenomenon is, paradoxically enough, the result of fallacious thinking about numbers. Vincent indirectly suggests that when lovers often want to know how infinite exactly this infinite love that they mutually declare is, they stupidly, or should I say, ignorantly, complicate the matter, insofar as they insist on seeing infinity as a number. But infinity is not a number, as Peano also beautifully demonstrated. If it were, then, the whole foundation of mathematics would come crumbling down – and so would our sense of culture beyond the world of mathematics.

Vincent said nothing about the implication of his declaration – which shows that he is a good mathematician who trusts himself. As he is primarily a logician, however, - or so he claims - one would like to know to what extent he sees trust in the other to understand what he understands as part of the set which, in group theory, all it requires is a value and an operator. Here, there are three obvious possibilities. Either one goes with Cantor, who followed St. Augustine’s declaration concerning the condition for the existence of the Absolute: “Every number is known to Him whose understanding cannot be numbered. Although the infinite series of numbers cannot be numbered, this infinity is not outside His comprehension. It must follow that every infinity is, in a way we cannot express, made finite to God. (St. Augustine, City of God, 496-7). Or goes with Dante: “That man should speak in nature’s doing; but whether thus or thus. . .” (Paradiso XXV). Or follows my advice: “Say 'Aleph One' without thinking it.” Ein-Sof.