From my list on mathematical approaches to complex systems.
Why are we passionate about this?
An accident of professional life led us, Jean-Paul Vanbremeersch and Andrée Ehresmann, to meet in 1979. Jean-Paul was then a young physician who was also interested in problems of emergence and complexity. Andrée was a mathematician working in Analysis and, more recently, in Category Theory with Charles Ehresmann (her late husband). With Charles, she shared the idea that: “a category theory approach could open a wealth of possibilities to the understanding of complex processes of any kind.”This idea appealed to Jean-Paul who suggested that we both try applying it to problems of emergence, complexity, and cognition. It led to our 40 years old development of MES.
Andrée and Jean-Paul's book list on mathematical approaches to complex systems
Why Andrée and Jean-Paul loves this book
We appreciate this book because it helped us to introduce the concept of a ‘hierarchical category,’ which is necessary to describe our MES. We accomplished this by translating Koestler's concept of a "hierarchy of holons," where a holon embodies a 'hybrid nature' akin to a two-faced Janus.
Technically, a hierarchical category organizes objects into numbered levels (0 to m). An object at level n is dual-faced: 'simple' compared to levels above n, but 'complex' compared to levels < n, this object being the "colimit" (or combination) of linked objects < n. Within a hierarchical category, we compute the 'complexity order' for each object. The category aligns with pure reductionism if it lacks objects with a complexity order greater than 1.
1 author picked Janus as one of their favorite books, and they share why you should read it.
Excellent Book
- Coming soon!