## Moving Topoi: first cut.

As I described a few weeks ago here, I was invited to give a PechaKucha presentation, for the 11th version of the event in Bogotá. I finally settled on describing our ongoing joint project Moving Topoi with Roman Kossak, Wanda Kossak and María Clara Cortés.

The project starts as an attempt at creating a dialogue between two Mathematicians and two Artists. Originally intending to create some form of communication between two disciplines that have a hard time explaining away what they are – and after many partially failed attempts of dialogue (essays, seminars, presentations), we decided three months ago to do a completely new piece of something (maybe art, maybe a weird version of mathematics, maybe nothing : | ) between the four of us.

For reasons that are half-unfathomable, we ended up naming our joint project “topoi” (here is John Baez’s “in a nutshell” description of mathematical topoi – wikipedia has a reasonable take on that too) or “moving topoi”. Topoi (“places”, in Greek) in Mathematics are generalizations of the notion of space, abstractions of the notion of “being there”, useful ways of comparing and contrasting many structures (or situations, or actions) lying in apparently different, incomparable worlds.

The intent is to build directly new topoi, some mathematical, some artistic – but in many ways to open up common space, really common topoi made up slowly by the four of us, unfolding in time.

For now, the project is essentially photographic. Each of us makes a little set of 4 photographs and posts them to the rest of us – and elicits (or doesn’t) responses, all in the same format. NO verbal explanation of the photographs is given: just a keyword for the topos that is being opened, activated, created or answered to.

In its restrictiveness (no words, or almost no words – just sets of four images) there is something weird: after a while, topoi did start appearing, some of them consolidating sharply into lines – timelines of a topos, and the project started having its own life.

At the moment, after three months, we have about 440 photographs, about 40 or 50 new topoi – some of them quite developed, some of them just having appeared once. The project so far is best viewed as a timeline of sorts… there are however various different ways in which the project may be shown as new topoi appear, as some of them start evolving. At some point, showing some of the photographs in printed format, with some way of curating the show that enhances the topos aspect – or some other way of presenting this.

Or even breaking momentarily from our closed (4-ways) format… activating external topoi by inviting other people to participate in specific situations.

The inspiration has come from various sources and conversations. For the format, the Tales of Tono, that photographic book made some thirty years ago by Daido Moriyama, was essential. For some of the ideas, various conversations and reading seminars hinging on phenomenology has been instrumental. Samuel Todes…

Crucial in the whole conception (both intellectually but also formally) is the set of “dividing lines”, the $(2\times 2)^n$ dichotomies (2 Mathematicians, 2 Artists – 2 cities (Bogotá, New York), 2 places in the country (Chía, the Catskills) – 2 specific urban areas (Midtown Manhattan, Chapinero), 2 specific bucolic areas (Fonquetá, Fleischmann’s), 2 men – 2 women, 2 Europeans – 2 Latin Americans, etc. etc.)

The PechaKucha format (that I described here) was a “first cut”, an early test for topoi. I discussed with Roman, Wanda and MC various aspects of the presentation, and ended up giving a very distilled, very reduced glimpse of it.

The presention will be made public in PechaKucha’s website at some point.

Here are the images, meanwhile! (You could watch them as a presentation, leaving exactly 20″ per image, to get a feeling of the temporal aspect of the PechaKucha presentation… or wait until the official organization posts the actual presentation.) On slide 7, there is a handwritten list of the (so far) topoi, itself opening a topos – the picture of the handwritten note is part of our project.