Thank you, JoAnne Growney

My talk at the Évora conference was about the abstract/concrete dimension of mathematics, illustrated by examples from my work. In the course of preparing it, I came across the following, from the book Mathematics, Poetry and Beauty, by Ron Aharoni:

… the heart of the poem is given to the concrete, and it is in this direction that the poem goes. This is the diametric opposite of the ping-pong of mathematics, in which the last shot is always towards the abstract.

I don’t think it is quite so simple; but never mind, he points out a connection between mathematics and poetry, which is my subject for this post.

There is a genre of “mathematical poetry”, which contains at least the following three types of poem:

• poems with a mathematical structure, such as some of those produced by the French group Oulipo;
• poems about mathematicians;
• poems employing mathematical imagery.

These are not mutually exclusive, and probably not exhaustive.

Here is a small detour, which you are welcome to skip if you are a non-mathematician (like Neill).

Next week is the Permutation Patterns conference in St Andrews. My take on this is that a permutation consists of a set with two total orders on it. The first order serves to identify the n points with {1,…,n}, and the second gives the images of these points under the permutation. There are at least two benefits of thinking of them that way:

• People working in permutation patterns have the notion of one permutation being contained or involved in another, which newcomers sometimes find a little mysterious. In my formulation, this is just the concept “induced substructure”.
• The definition works equally well in the infinite case, so allows us to define infinite permutations in such a way that their finite substructures are finite permutations.

The last point allows us to define a countably infinite universal homogeneous permutation, where “universal” means that every finite permutation is a substructure of it and “homogeneous” means that every isomorphism between finite substructures extends to an automorphism of the whole structure. By Fraïssé’s theorem, there is a unique such object: it has the properties

• each of the two total orders is isomorphic to the rational numbers;
• any interval in either order, no matter how small, is dense in the other.

I consider this a good metaphor for two lovers embracing: each part of either lover’s body, no matter how small, is fully aware of the entirety of the other. However, I never succeeded in making a poem based on or using this; the idea is a bit remote even from most mathematicians.

End of detour.

Anyway, this brings me to JoAnne Growney, to whom I am grateful for many things as well as her poetry. She wrote the tagline of this blog, and she co-edited a lovely book of mathematical love poetry entitled Strange Attractors. Like me, she grew up on a farm.

As I mentioned, I was at the third Theoretical and Computational Algebra conference in Évora, Portugal, about which I will certainly have more to say. But the organisers put in a huge amount of work to give me a number of presents, both material (including a book on the remarkable azulejos in the lecture halls of the mediaeval university (including one in the Metaphysics Hall which I will also say more about later) and immaterial (a really wonderful collection of messages from collaborators, students, and other members of my mathematical family, which I will also say more about later).

But one of these gifts was to ask JoAnne for a poem.

Rather than say more, I will simply refer you to this post on JoAnne’s blog. Please do take a look, and if you like it, explore the other treasures on her blog. She, much more than I, has integrated poetry and mathematics.

Thank you JoAnne! and thank you Poyi for making this happen!