This week we had MRC@Cupertino. This was great! Since I had issues with tachycardia and could not go to Beaver Hollow at the end of May, some of the participants of our Mathematical Research Community (MRC) came over to work with me. We were a bit unlucky with the weather, it was far too hot to stay outside and work in the Memorial Park, as I thought we would. But the air conditioning at the Quinlan Center where we had our official meetings worked well and we've managed several sessions of recap and discussion.
The four groups we had organized for the MRC (Dialectica and Poly, Dialectica and Lenses, Dialectica and Games, Petri Processes and implementations) had representatives and we have made some progress in these four themes. Everyone is planning to submit abstracts for the JMM in January 2023, the deadline is in two days.
As usual, I had hoped to be much further along on our discussions and wanted to be able to write something about the `Dialectica Extended Family' to complement the old papers Dialectica and Chu constructions: cousins? and Hofstra's The dialectica monad and its cousins as well as the blogposts Dialectica categories and polynomial functors (Part 1) (Nelson Niu) and Lenses for Philosophers (Jules Hedges) and Sean Moss' talk in the Polynomial Workshop 2022 Dependent products of polynomials. But I am very slow, even more so after the cardiac issues earlier this year.
Also collaborative research has perks (you can get much more done), but also drawbacks: you must learn from the differences. So it doesn't go as you want it, it goes as all of you want it, to go. Collaborators have ideas and agendas of their own, which is wonderful. And it is also true that research in general doesn't go the way you expect it: if it always did, it wouldn't be research, but simply development. I am very aware that I need to let go of some of my old fashioned wishes for the Dialectica categories.
