Sara Franceschelli

In the founding article of catastrophe theory, Thom states that the sources of his theory are twofold: on the one hand his research in topology and differential analysis, on the other hand the treatises of embryology, in particular the books of Conrad Hal Waddington and his notions of “epigenetic landscape” and “chreod”AQ1. These two notions were introduced by Waddington through images, even before definitions. In this chapter I defend the idea that the relation of catastrophe theory to biology, which—by Thom’s admission—cannot be subjected to experimental control, rests on the bet of its relevance as an expression in mathematical terms of the images constituting Waddington’s epigenetic landscape. After showing in what sense the notion of structural stability allows Thom to relate his theory to the epigenetic landscape, I consider the limits of this ambition but also the perspectives opened by the Thom-Waddington dialogue in the context of the recently renewed interest in Waddington’s voice as a theorist of developmental canalization.

I will propose a reading and an interpretation of Turing’s famous 1952 article “The Chemical Basis of Morphogenesis”. Many questions still arise for the reader of the original article: why did Turing not use any informational metaphor associated with the notion of “genetic program” in his work on morphogenesis, preferring instead to embark on a modelling approach based on a system of differential equations, using a mathematics that was far removed from his previous fields of work? Where did he draw his modelling inspiration from, both from the point of view of the mathematics employed and from the point of view of references to biology? In this essay I will address these questions by highlighting the morphological connotations of Turing’s work in biology, that can be easily related to Turing’s interest, from his youth, in D’Arcy Wentworth Thompson’s classic On Growth and Form (1917). After a presentation of what Turing does as a modeler, I will highlight two main features of Turing’s engagement with biological theory (morphology and holism). I will furthermore depict in more details three morphological signatures of his approach in relation with the kind of modelling he proposes (concerning the definition of morphogens, the study of the onset of instability, and the study of numerical solutions in a non-linear case).

Whereas computer simulations involve no direct physical interaction between the machine they are run on and the physical systems they are used to investigate, they are often used as experiments and yield data about these systems. It is commonly argued that they do so because they are implemented on physical machines. We claim that physicality is not necessary for their representational and predictive capacities and that the explanation of why computer simulations generate desired information about their target system is only to be found in the detailed analysis of their semantic levels. We provide such an analysis and we determine the actual consequences of physical implementation for simulations

Cellular Automata (CA) based simulations are widely used in a great variety of domains, fromstatistical physics to social science. They allow for spectacular displays and numerical predictions. Are they forall that a revolutionary modeling tool, allowing for “direct simulation”, or for the simulation of “the phenomenon itself”? Or are they merely models "of a phenomenological nature rather than of a fundamental one”? How do they compareto other modeling techniques? In order to answer these questions, we present a systematic exploration of CA’s various uses.

Digital practices in design, together with computer-assisted manufacturing (CAM), have inspired the reflection of philosophers, theorists, and historians over the last decades. Gilles Deleuze’s The Fold: Leibniz and the Baroque (1988) presents one of the first and most successful concepts created to think about these new design and manufacturing practices.1 Deleuze proposed a new concept of the technological object, which was inspired by Bernard Cache’s digital design practices and computer-assisted manufacturing. Deleuze compared Cache’s practices to Leibniz’s differential calculus-based notion of the parametric curve. From this perspective, the object is no longer an essential form: rather, it is functional, defined by a family of parametric curves. In Deleuze’s terms, it is an objectile. This definition grasps a particular aspect of modernity in the technological object, rendering possible the industrial production of “the unique object” (la pièce unique), while making obsolete the homogeneity that comes with industrial standardization. What follows introduces developmental biology into this design matrix, interrogating the relationship between parametric design and computer-assisted manufactory on the one hand and biological morphogenetic processes on the other. Is one necessary for the other? Does an architect need computation in order to render morphogenetic shapes? In answering these questions, this chapter displaces the centrality of digital technology in the design of shape-shifting forms within architecture and calls for a rethinking of design by way of analog prototypes. I argue that “thinking through analogs” offers another means of generating parametrically based morphogenetic forms.

Cette étude montre comment le météorologue Edward Lorenz, dans deux articles de 1963 et 1964, explore les propriétés des systèmes chaotiques par des allers-retours entre une déduction mathématique (basée sur la théorie des systèmes dynamiques) et une étude des solutions numériques du système dit « de Lorenz » dans un régime d’instabilité. This study aims at showing how the metereologist Edward Lorenz, in two papers of 1963 and 1964, explores the properties of chaotic systems thanks to the interplay between a mathematical deduction (based on dynamical systems theory) and a study of the mathematical solutions of the Lorenz system in an instability regime.

Determinism and unpredictability are compatible since deterministic flows can produce, if sensitive to initial conditions, unpredictable behaviors. Within this perspective, the notion of scenario to chaos transition offers a new form of predictability for the behavior of sensitive to initial condition systems under the variation of a control parameter. In this paper I first shed light on the genesis of this notion, based on a dynamical systems approach and on considerations of structural stability. I then suggest a link to the figure of epigenetic landscape, partially inspired by a dynamical systems perspective, and offering a theoretical framework to apprehend developmental noise.

Arguments of stability, intended in a wide sense, including the discussion of the conditions of the onset of instability and of stability changes, play a central role in the main theorizations of morphogenesis in 20th century theoretical biology. The aim of this essay is to shed light on concepts and images mobilized in the construction of arguments of stability in theorizing morphogenesis, since they are pivotal in establishing meaningful relationships between mathematical models and empirical morphologies.