The emergence of life and evolution: Towards a categorical approach

Among the list of proposed questions in “Open Problems in Artificial Life” (Bedau et al. 2000) the first, “how does life arise from the nonliving?” is certainly one of the most difficult to answer. The first and main challenge in the understanding of the way that life emerged from the nonliving comes from our lack of knowledge of the living organism and paradoxically, the limitations which we impose to it, so that what we call organism remains a stillborn entity at best. The second challenge is creating a formal language suited to represent the organism while taking into account all its quantitative and qualitative characteristics. Consequently, to progress in the understanding of the organism, it is first essential to integrate two data. The first one being that both the questions “what is the living?” and “how does the living arise?” are connected. In other words, before being able to apprehend correctly the emergence of life, it would be necessary to know how to model it, almost through a theoretical biology approach. The second datum is related to finding an appropriate language which is capable of describing the organism in all its dimensions. In this present work, we want to find answers to the first list of Bedau's questions through a more integrative definition of the living which enables us to think of its mode of emergence from the nonliving in a coextensive way. For this, we propose a categorical model of the organism. This seems to be the most suitable language at the current stage of knowledge in describing such a phenomenon. To formalise our proposal, we use a branch of mathematics called category theory. A category is a structure that appears like a directed graph, which consists of objects and arrows between them. However, in a category, two paths from A to B may be declared equivalent in a commutative diagram. Beside, a functor is a mapping from one category to another that preserves the structures. As far as our main purpose is to unit entities in a special bigger one, this requires encoding interfaces, functional relationships, and transfer of data, extensive and intensive properties. In short, to convert an organism appearance into the ontology of category theory, we need concepts that allow us to group and lay out things. These concepts are best captured by pushout and its dual pullback expressed in terms of diagrams of arrows, which are special types of more general constructs known as colimit and limit respectively. In a category , the pushout (figure 1) for two morphisms f :A  B and g : A  C is an object D, and two morphisms j : B  D and k : C  D, such that the square commutes (f o g = j o k); and for any objet D’ and pair of morphisms j’: B  D’ and k’: C  D’ satisfying j’ o f = k’ o g, there is a unique morphism h : D  D’ such that diagram commutes. A dual is obtained by reversing the arrows. A complete presentation of category theory can be found in Lawvere and Schanuel (1997), and Ehresmann and Vanbremersch (2007).