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Characterizing Autopoiesis in the Game of Life

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Characterizing Autopoiesis in the Game of Life Characterizing Autopoiesis in the Randall D. Beer* Game of Life Indiana University Keywords Autopoiesis, organizational closure, artificial chemistry, cellular automata Abstract Maturana and Varelaʼs concept of autopoiesis defines the essential organization of living systems and serves as a foundation for their biology of cognition and the enactive approach to cognitive science. As an initial step toward a more formal analysis of autopoiesis, Downloaded from http://direct.mit.edu/artl/article-pdf/21/1/1/1665049/artl_a_00143.pdf by guest on 23 September 2021 this article investigates its application to the compact, recurrent spatiotemporal patterns that arise in Conwayʼs Game-of-Life cellular automaton. In particular, we demonstrate how such entities can be formulated as self-constructing networks of interdependent processes that maintain their own boundaries. We then characterize the specific organizations of several such entities, suggest a way to simplify the descriptions of these organizations, and briefly consider the transformation of such organizations over time. 1 Introduction Everyone agrees that a biological cell is alive, but why? Upon what criteria do we base this assertion? How we choose to answer this fundamental question determines not only what the subject matter of biology actually is, but also how we approach many practical biological endeavors such as investigating possible pathways for the origin of life [36, 41], testing for extraterrestrial life [11, 29], or creating synthetic life [10, 22]. On the rare occasions when this question is even raised in the biological literature, proposed answers typically take the form of either a list of components (e.g., carbon chemistry, RNA/DNA, phospholipid bilayer) or a list of properties (e.g., growth, reproduction, evolution). Neither of these answers is particularly satisfying theoretically. The first list seems overly tied to the specific material con- stitution of life as we have so far encountered it, and exceptions to the second list are easily found. Unsatisfiedwithsuchlists,theChileanbiologists Humberto Maturana and Francisco Varela proposed that what distinguishes a living system from a nonliving one is not its material structure, but the particular organization of processes supported by that structure [39, 40, 51]. On their view, the observed properties of living systems are consequences or further elaborations of this basic organization, which they termed autopoietic (self-producing) [39, p. 78]: An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and * Cognitive Science Program, School of Informatics and Computing, 840 Eigenmann, 119 East 10th Street, Indiana University, Bloomington, IN 47406. E-mail: [email protected] © 2015 Massachusetts Institute of Technology Artificial Life 21: 1–19 (2015) doi:10.1162/ARTL_a_00143 R. D. Beer Characterizing Autopoiesis in the Game of Life (ii) constitute it (the machine) as a concrete unity in the space in which they (the components) exist by specifying the topological domain of its realization as such a network. To put it mildly, this is not an easy definition to understand on first reading. It is quite abstract, makes use of somewhat idiosyncratic terminology, depends upon a larger background of unfamiliar concepts, and exhibits an essential circularity that can be difficult to assimilate. There are also key differences in how subsequent authors have interpreted various aspects of this definition, and even Maturana and Varela later diverged somewhat in their opinion of its scope and consequences [25, 44, 55]. Nevertheless, autopoiesis stands as an important example of how to formulate a definition of living systems that goes beyond lists of components or properties. It is also representative of a number of other such attempts [34], for example in chemistry [27], theoretical biology [24, 32, 45], and philosophy [31]. Furthermore, the concept of autopoiesis serves as the foundation for the growing enactive approach to cognition [47, 48, 53]. Thus, despite its difficulties, it is worth trying Downloaded from http://direct.mit.edu/artl/article-pdf/21/1/1/1665049/artl_a_00143.pdf by guest on 23 September 2021 to understand and explore this notion in depth. Consider the paradigmatic example of an autopoietic system: the living cell. A typical cell consists of a large number of protein and water molecules bounded by a semipermeable membrane formed from a bilayer of phospholipid molecules [4]. The material structure of such a cell is thus given by the physical details of these molecular components: their type, position, orientation, bonds, modes of vi- bration, and so on. However, the cell itself cannot be equated with this totality of material properties, because these properties are constantly changing. Over time, individual molecules move, rotate, and enter and leave the cell, while chemical bonds are continually being broken and re-formed through reactions. And yet, despite this ongoing material change, the cell itself, as a delimited spatiotemporal organization of processes, persists. This persistence of identity in the face of material change is exactly what the notion of autopoiesis attempts to capture. More specifically, Maturana and Varelaʼs definition states two conditions that a network of processes must satisfy in order to be considered autopoietic. The closure condition demands that the network of processes must produce the components whose interactions generate and maintain that very same network. The boundary condition demands that the spatial boundary that distinguishes an autopoietic system from its background must itself be generated and maintained by the network of processes and in turn must play a central role in enabling those same processes. This basic circularity of autopoiesis is illustrated in Figure 1. In order to go beyond this rough characterization of autopoiesis, we need to examine in con- siderably more depth an application of this concept to a simple concrete system. Since even the simplest biological system is still quite complex, we turn to models for this purpose. There is a long history of computational modeling of autopoiesis [7, 13, 21, 42, 52, 60]. However, these models are Figure 1. An illustration of the central circularity of autopoiesis. A bounded system generates a network of processes that produces the components that determine the very same bounded system. Although organizationally closed, such a system is both materially and interactionally open to its environment. Adapted from [35]. 2 Artificial Life Volume 21, Number 1 R. D. Beer Characterizing Autopoiesis in the Game of Life typically designed a priori to satisfy the definition of autopoiesis. In contrast, the goal of this article is to assess the extent to which the definition can be applied to a system that was not designed specifically to exhibit autopoiesis. In particular, building on a previous proposal [8], I investigate the conditions under which spatiotemporal patterns that arise in the well-known Game of Life (GoL) cellular automaton can be considered to be autopoietic. Note that the intent here is not to argue that such patterns are “really” alive or that they capture all relevant characteristics of living systems. Rather, I wish merely to utilize GoL as a simple model universe in which we can explore in detail the many issues raised when attempting to apply the definition of autopoiesis to a concrete system. This article is organized as follows. Section 2 introduces the game of Life and suggests a way to describe the patterns that arise within this cellular automaton as collections of interacting processes. Sections 3 and 4 then show how to formulate the closure and boundary conditions, respectively, of autopoiesis in such a way that they can be applied to the patterns that arise in GoL. Section 5 then examines simplified descriptions of GoL organizations that are more analogous to the formalism of Downloaded from http://direct.mit.edu/artl/article-pdf/21/1/1/1665049/artl_a_00143.pdf by guest on 23 September 2021 theoretical chemistry, and Section 6 briefly explores the transformation of organizations over time. Finally, Section 7 considers the broader implications of our analysis for the concept of autopoiesis and its various applications and extensions. 2 The Game of Life Cellular automata are a well-known class of simple models of spatiotemporal processes in which state, time, and space are all discrete. Conwayʼs game of Life is a binary outer totalistic cellular automaton defined on a rectangular lattice L, whose exploration has been widely publicized [2, 12, 28, 43]. Descriptions of GoL are typically couched in biological terms (e.g., individual elements of the lattice are “cells” that can be “born” due to “reproduction” and can “die” due to “overcrowding” or “loneliness”). However, this biological vocabulary is strictly metaphorical. For our purposes here, it is better to think of GoL as a simple discretized physics [50] whose single dynamical law can be tþ1 P t P t L ¼ y ; þ L y ; L most compactly written as x; y 3 x; y x; y 2 x; y ,where x;y is the state of the lattice cell (x, y) ∑ ʼ at time t, x, y is the number of 1-cells in that cell s Moore neighborhood (the eight lattice cells sur- y = rounding it), and i, j is the Kronecker delta function (which takes on the value 1 when i j and 0 otherwise). On this view, any potential “biological” entities arise as self-perpetuating networks of processes grounded in the underlying GoL physics. A typical GoL time evolution is shown in Figure 2A for a 100 × 100 lattice with periodic bound- ary conditions. On the left is a random initial configuration with a 1-density U0 of 0.5. On the right is the same lattice after 1000 applications of the GoL physics; here the 1-density has decayed to U = 1000 0.037.
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