© 2004 Robert A. Freitas Jr. and Ralph C. Merkle. All Rights Reserved.

Robert A. Freitas Jr., Ralph C. Merkle, Kinematic Self-Replicating Machines, Landes Bioscience, Georgetown, TX, 2004.

5.1 General Taxonomy of Replicators

The somewhat controversial general theory of “autopoiesis” [455, 2350] – literally “the creation (or production) of self” – and autopoietic machines [455, 2351] may be of some theoretical and philosophical interest [455-457, 2352-2370]. For example, the canonical definition of an autopoietic machine was given by Maturana and Varela [455] who originated the neologism in 1971 (though anticipated in 1922 by Bogdanov’s “tektology” [2372]). They define autopoiesis as a concise set of six highly abstract criteria that apply to a given systemic “unity” of components (with clarifications kindly provided by Randall Whitaker [2351]) as follows:

(1) the unity has identifiable boundaries, via interactions with the boundary. Is it discrete? Does it exhibit “extent”? Can you circumscribe it? Can you specify where the unity stops and the environment begins?

(2) “...there are constitutive elements of the unity, that is, components of the unity.” Can the unity be seen as a set of “parts”? Do these “parts” comprise the whole?

(3) “...the unity is a mechanistic system, that is, the components’ properties are capable of satisfying certain relations that determine in the unity the interactions and transformations of these components.” Is the unity capable of acting on itself?

(4) “...the components that constitute the boundaries of the unity constitute these boundaries through preferential neighborhood relations and interactions between themselves, as determined by their properties in the space of their interactions.” Are the components of the apparent boundary participating in that boundary as a result of their interrelationships and interactions? Are the components of the apparent boundary discernible as such because of their participation in the processes of the composite unity?

(5) “...the components of the boundaries of the unity are produced by the interactions of the components of the unity, either transformation of previously produced components, or by transformations and/or coupling of non-component elements that enter the unity through its boundaries.” Are the components of the apparent boundary produced by the processes comprising the unity itself? Is the unity generating the components (of this apparent boundary) either from existing components or through accreting elements it appropriates from its environment?

(6) “...all the other components of the unity are also produced by the interactions of its components as in (5), and ... those which are not produced by the interactions of other components participate as necessary permanent constitutive components in the production of other components...” Are all the components of the unity produced by its components realizing processes within the unity itself? Do all of the unity’s components participate in the production of its components?

A somewhat simplified description of an “autopoietic machine” was later given by Maturana and Varela ([2356], p.79) as: “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 (ii) constitute it (the machine) as a concrete entity in the space in which they (the components) exist by specifying the topological domain of its realization as such a network.” Thus an autopoietic machine (which is self-maintaining and self-repairing, but may or may not be capable or self-replication, a very specialized ability) is composed of components which engage in a network of interactions that enable the continuous regeneration of these same components [2373]. (An “allopoietic” machine has as its product something different from itself.) Autopoiesis has been applied to communication [1853, 1856], management [1855, 1857], economics [2374], psychology [1854], and sociological [1850-1852] systems, as well as to biological and purely mechanistic systems.

While interesting, general philosophical discussions of autopoietic reproduction [2375-2378] and formal mathematical definitions of autopoiesis [2386], self-replication and self-reproduction [2387-2389] are beyond the limited scope of this engineering-oriented book, as are broad discussions of general systems theory as applied to replicating systems [2390-2396]. More useful to the replicating systems engineer are specific conceptual taxonomies that may provide guidance to investigations of the replicator design space. Thus we begin our analysis by summarizing a selection of replicator and replicator-relevant artificial life taxonomies that have been described in the past, including the Dawkins classification of replicators (Section 5.1.1), the Miller critical subsystems of living systems (Section 5.1.2), the Hasslacher-Tilden MAP survival space (Section 5.1.3), the Szathmary classification of replicators (Section 5.1.4), the POE model of bio-inspired hardware systems (Section 5.1.5), the Taylor categorization of reproducers (Section 5.1.6), the Bohringer taxonomy of microassembly (Section 5.1.7), and the Suthakorn-Chirikjian categorization of self-replicating robots (Section 5.1.8). The replication models of von Neumann and others have already been reviewed at length in Chapter 2. It should be emphasized that our review is only a selection and not a comprehensive survey of all such efforts, nor is our effort a “taxonomy of taxonomies” [2399], and any systematic consideration of purely computational artificial life entities [2400, 2401] or cellular automata arrays [383, 2402] is specifically excluded.

Our own replicator taxonomy, presented here for the first time (Section 5.1.9), constitutes perhaps the first crude but comprehensive map of the entire kinematic replication design space, subsuming all known prior work and providing a wealth of new design dimensions that may inform and inspire future engineering design efforts. Our design space at minimum identifies >10⁷⁰ theoretical distinct kinematic replicator subclasses, confirming our intuitive suspicion that the kinematic replicator design space* is truly vast – and, as yet, largely unexplored by human engineers.

* The design space of virtual replicators, particularly cellular automata, appears somewhat more amenable to analysis. Some automated explorations of this design space have already begun. For example, Lohn and Reggia [383] have used a genetic algorithm to automatically design self-replicating structures in cellular automata models, which “sheds light on the process of creating self-replicating structures, which could potentially lead to future studies on the discovery of novel self-replicating molecules and self-replicating assemblers in nanotechnology.” Koza [372] has pointed out that the design space of cellular automata may also be enormously vast, with the number of possible distinct 200,000-cell 29-state automata exceeding 10^292,480.

Last updated on 1 August 2005