Von Neumann thought of his logical model of self-reproduction as an answer to
the observation that, unlike machines, biological organisms have an ability to
self-replicate while increasing their complexity without limit. Mechanical
artefacts are instead produced via more complicated factories (as opposed to self-
production) and can only degenerate in their complexity. He was searching for a
complexity threshold beyond which systems may self-reproduce (no outside
control) while possibly increasing their complexity.
Von Neumann concluded that this threshold entails a memory-stored description PHI(X) that can be interpreted by a universal constructor automaton A to produce any automaton X; if a description of A, PHI(A), is fed to A itself, then a new copy of A is obtained. However, to avoid a logical paradox of self-reference, the description, which cannot describe itself, must be both copied and translated into the described automaton. This way, in addition to the universal constructor, an automaton B capable of copying any description, PHI(X), is included in the self-replication scheme. A third automaton C is also included to effect all the manipulation of descriptions necessary -- a sort of operative system. To sum it up, the self-replicating system contains the set of automata (A + B + C) and a description PHI(A + B + C); the description is fed to B which copies it three times (assuming destruction of the original); one of these copies is then fed to A which produces another automaton (A + B + C); the second copy is then handled separately to the new automaton which together with this description is also able to self-reproduce; the third copy is kept so that the self-reproducing capability may be maintained (it is also assumed that A destroys utilized descriptions). Notice that the description, or program, is used in two different ways: it is both translated and copied. In the first role, it controls the construction of an automaton by causing a sequence of activities (active role of description). In the second role, it is simply copied (passive role of description). In other words, the interpreted description controls construction, and the uninterpreted description is copied separately, passing along its information (memory) to the next generation.
The notion of description-based self-replication implies a self-referential linguistic mechanism. A description must be cast on some symbol system while it must also be implemented by some physical structure. Since many realizations of the same symbol system are possible, viewing descriptions only as physical systems cannot explain the symbolic nature of the control of construction. When A interprets a description to construct some automaton, a semantic code is utilized to map instructions into construction commands to be performed. When B copies a description, only its syntactic aspects are replicated. Now, the language of this semantic code presupposes a set of primitives (e.g. parts and processes) for which the instructions are said to "stand for". Descriptions are not universal insofar as they refer to some building blocks which cannot be changed without altering the significance of the descriptions. These building blocks ultimately produce the dynamics, behavior, and/or functionality of the overall system, and may be material or computational (standing for some artificial materiality). In the genetic system, the parts are amino acids. Computational parts might be for example the building blocks of neural networks coded by genetic algorithms. We can see that a self-reproducing organism following this scheme is an entanglement of symbolic controls and dynamic constraints which is closed on its semantics. Howard Pattee calls such a principle of self-organization semantic closure.
Semantic closure requires the parts problem discussed above to be explicitly taken into account. The evolvability of a self-reproducing system, to be discussed below, depends on the dynamic parts used by the semantic code. If the parts are very simple, then the descriptions will have to be very complicated, whereas if the parts possess rich dynamic properties, the descriptions can be simpler since they will take for granted a lot of the dynamics that otherwise would have to be specified. In the genetic system, genes do not have to specify the functional characteristics of the proteins produced, but simply the string of amino acids that will produce that functionality “for free” [Moreno et al, 1994]. Furthermore, there is a trade-off between programmability and evolvability [Conrad, 1983, 1990] which renders some self-reproducing systems no evolutionary potential whatsoever. If descriptions require high programmability they will be very sensitive to damage (e.g. Langton’s self-reproducing loops). Low programmability grants self-reproducing systems the ability to change without destroying their own organization, though it also reduces the space of possible evolvable configurations. In computational realms this implies that we should move towards models that include both programmable and self-organizing components [Rocha, 1997]. We will discuss such systems later in this course.
Notice that changes in (A + B + C + D`) are not heritable, only changes in the description, PHI(A + B + C + D`), are inherited by the automaton's offspring and are thus relevant for evolution. This ability to transmit mutations is precisely at the core of the principle of natural selection of modern Darwinism. Through variation (mutation) populations of different organisms are produced; the statistical bias these mutations impose on reproduction rates of organisms will create survival differentials (fitness) on the population which define natural selection. In principle, if the language of description is rich enough (its material constraints are dynamically rich), an endless variety of organisms can be evolved. This is what open-ended emergent evolution means.
The threshold of complexity proposed by Von Neumann is taken by some (e.g. Pattee, Rosen, Cariani, Kampis see Rocha[1995]) as another category of self-organization which is capable of creative organization and selection from outside. Notice that the self-organizing systems we have been studying so far (random nets, Cellular Automata) are said to self-organize when they converge to small areas of their state spaces or attractors. This sort of evolution is constrained by the complexity of the attractor landscape of organisms seen as dynamical systems. It cannot evolve a truly novel dynamics. In Cariani's [1991] terms, it cannot evolve new functionalities (such as sensors). Non-trivial self-replicating systems rely instead on memory-based selected self-organization [Rocha, 1996, 1998; Henry and Rocha, 1996] which can be seen as a type complex adaptive systems that observe a principle of organization referred to as embodied, evolving semiosis [Rocha, 1997].
Further Readings and References:
Conrad. M. [1983], Adpatability. Plenum Press.
Conrad, M. [1990], “The geometry of evolutions”. In BioSystems Vol. 24, pp. 61-81.
Henry, C. and L.M.Rocha [1996]."Language theory: consensual selection of dynamics." In: Cybernetics and Systems'96. R.Trappl (Ed.).Austrian Society for Cybernetic Studies. pp. 477-482. To be reprinted in Cybernetics and Systems.
Moreno, A., A. Etxeberria, and J. Umerez [1994], “Universality Without Matter?”. In Artificial Life IV, R. Brooks and P. Maes (Eds). MIT Press. pp 406-410
Pattee, Howard H. [1982]."Cell psychology: an evolutionary approach to the symbol-matter problem." In: Cognition and Brain Theory Vol. 5, no. 4, pp 325-341.
Pollack, R. [1994]. Signs of Life: The Language and Meanings of DNA. Houghton Mifflin.
Rocha, Luis M.(Ed.) [1995]. special issue in Self-Reference in Biological and Cognitive Systems. Communication and Cognition - AI Vol. 12, nos. 1-2 .
Rocha, Luis M. [1996]." Eigenbehavior and symbols." In: Systems Research Vol. 12, No. 3 (In Press).
Rocha, Luis M. [1997]. Evidence Sets and Contextual Genetic Algorithms: Exploring Uncertainty, Context, and Embodiment in Cognitive and Biological Systems. PhD. Dissertation. SUNY Binghamton.
Rocha, Luis M. [1998]."Selected self-organization and the semiotics of Evolutionary Systems." In: Evolutionary Systems. S. Salthe and G. Van de Vijver (Eds.). Kluwer. (in press).
& nbsp; von Neumann, John [1966]. The Theory of Self-Reproducing Automata. Arthur Burks (Ed.) University of Illinois Press.
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