In the Data Ecologies 05 event, we were pleased to be visited by Tom Toffoli. A physicist, computer scientist and engineer, he has been immortalized for us with his comment that “Science is the stories that scientists tell about the games that scientists play.” We made a T-shirt, which people still wear , and were glad to have been able to host such a remarkable fellow. We have also noticed that the statement remains true for many different types of activity.
Earlier this year, a colleague at the Kepler uni suggested that we take some very old work of his and see if we can work out a way to write it as algebra. This seemed like a good idea, and has turned out to be. The idea is around something called reversible computation and has to to with physics, engineering, algebra and computers. Complicated stuff, needing some messy formalisms. We do things like the composition of two mappings in the image above, feeding outputs into inputs in a carefully controlled, information preserving way.
For those who want to read a short introduction, there is some context on the Theorem a Day blog, with links to related work and not too much technical stuff. For those who want to take the dive, there is the paper uploaded on the arXiv. And for those who want the polished version, we will let you know when the published version becomes available.
It has been a pleasure to work with Tom’s ideas, which have infused a lot of things over the past decade or two. Let’s see if these ideas help someone else find something interesting.