We now turn our attention to a rather different kind of ABM: the Artificial Chemistries (ACs). For examples, see (Dittrich et al., 2001; McMullin, 1997a,b; Rasmussen et al., 2001; Fontana, 1991).
At first this will seem like a retrograde step, because ACs fall into the category of ABMs with closed agents. In fact, ACs do not normally even have the most limited evolutionary dynamics which we discussed in the section ABMs with Closed Agents. Prima facie then, the prospects for such systems to exhibit perpetual novelty seem extremely weak; but we will pursue the analysis nonetheless.
We must first characterize what we mean by ACs, and how they relate to the systems already described. As mentioned, ACs are ABMs with closed agents, and thus conform to the general framework shown in figure 1. However, the interpretation of the agents is now rather different. Instead of thinking of the agents as representing organisms, in ACs they are taken to denote atoms or (small) molecules (we will use the generic term ``particles''). The agent classes now represent elements and/or molecular species. The interactions between agents are motivated as--usually highly abstract--models of chemical reactions. In simple cases, this can result in the replacement of the reacting agents with different agents representing the appropriate reaction products. In more complex cases, there will be at least one kind of agent interaction which attempts to explicitly model chemical bonding: the effect is to establish agents into more or less stable aggregations--corresponding to larger scale macromolecules or molecular complexes.
Now, in contrast to the situation of the previous section, where the emphasis was on novelty on the part of individual agents, in ACs the agents are actually designed to have entirely immutable behaviours (methods); and, further, to have only a small number of distinct varieties (classes, types of agents). However, the new prospect is of novelty on a higher, or more macroscopic level: the level of the macromolecules or agent-aggregates.
This deliberate limitation of artificial chemistries at the level of agent variety is of course an attempt to mimic fundamental processes in nature which seem to operate exactly this way. The variety of chemical elements is essentially static, and relatively tiny compared to the stunning variety of higher level aggregates (molecules, cells, organisms, colonies etc.) which they give rise to--in processes which therefore surely have to be regarded as novelty producing. An ultimate goal of research with artificial chemistries is therefore to exhibit similar higher order structures and novelty creating processes in computer based systems.
So what specific types of novel behaviour may we hope to produce in ACs? We will want the AC to have the potential to dynamically create new macromolecular species, with novel functions and properties. In a sense, of course, the concept here is a generalisation of the original motivation underlying Tierra: starting from a relatively simple ``ur-chemistry,'' consisting of a few primitive agent classes (elements, primitive molecular species) only, we would hope that the complexity in such a system increases over time through the progressive emergence of new types of macromolecules, with new behaviours and which can relate and interact in new ways.
Note that while this ``ur-chemistry'' should ideally be maximally simple, some initial degree of complexity must presumably be supplied if certain functionalities are to emerge. For example, it is hard to imagine how enzymatic interactions could arise in a purely two dimensional chemistry.
In any case, it is clear that the implementation of bonding in an AC must be critical to the prospects for this open ended novelty at the macromolecular level. Let us therefore consider this in a little more detail.
A common, and conceptually simple, way to implement bonding in ACs is by specific and explicit state changes of the respective agents (McMullin, 1997b). Thus, particle A registers in its state variables that it is now bonded with particle B, and particle B records a precisely complementary relationship in its state variables. Bonded particles are then not different from unbonded particles in any other respect than that they are ``tagged'' in this way as being bonded; but, of course, the methods for implementing particle motion are explicitly programmed in such a way as to respect this bonding (i.e., to maintain the spatial juxtaposition of the bonded particles within some specified constraints). Similarly, the exact conditions for bond formation and rupture are explicitly specified in advance, within the various particle methods.
However, we would like to suggest that this form of explicitly programmed bonding seems unlikely to support the sorts of emergent novelty which we are in search of. The ``new'' higher level particle formed as a result of this kind of bonding is little more than a collection of its primitive components plus a few motion constraints which have been pre-conceived and explicitly pre-programmed. In this sense bonds--their formation, behaviour, rupture--are completely pre-specified, bottom-up phenomena; they exclusively stem from the explicitly programmed properties of the bonded particles, rather than being emergent effects of the molecular configuration per se. This seems distinctly unlike the formation of new molecular species in nature and it also restricts the potential for novelty creation in the model.
It seems that bonding in ACs might be much more interesting (with respect to the creation of novelty) if it were emergent, or a product of constraints that are top-down. We mean by this that bonding would not stem from explicit, pre-programmed, properties of the particles, but rather from the macroscopic or collective properties of the particle configurations.This is also the way nature seems to work. Bonding between particles would then not simply amount to tagging the participating particles and invoking extra rules which implement the constraints of bonded particles. If the top-down philosophy is followed, then bonding becomes a phenomenon that emerges from the interaction of particles, not the other way round, i.e., bonding is possible because there are constraints on the single particles. The collective should restrict the behaviour of the constituents to such a degree that they form a new whole. If the kind of constraint the whole exerts on the parts is very sensitive to the configuration of the parts, then it seems that this may be a potential source of variety and novelty.
The question is now whether strictly agent-based ACs with this property can be constructed. The snake has to bite its own tail. Is it possible to generate top-down constraints in bottom-up models? Note that in real chemistry exactly these kinds of top-down constraints arise and are one of the sources of novelty. Proteins, for example, are only composed of a handful of different types of atoms, yet are very different from one another. Size and configuration matters in the real world, and is a genuine source of novelty. If we manage to implement a similar kind of mechanism in an AC, then we might also hope for similar creation of novelty.
In order to better illustrate the idea of top-down constraints we will schematically outline the description of a minimal AC which exhibits them. Note that this is an imaginary toy-model devised just to illustrate this particular point. We do not suppose that it would, in fact, demonstrate any continuing creation of novelty (not, at least in this minimal form).
The AC is defined on a 2-dimensional square lattice and consists of only one type of particle (primitive agent). The particle exerts an attracting force in its immediate (Moore) neighbourhood, and a repelling force in the successive (Moore-like) neighbourhoods at distances 2 and 3. The corresponding potential field established by an isolated particle is indicated schematically in figure 2. The gradient of this field at any site would indicate the (vector) force imposed on a particle at that site. Potential fields from multiple particles are assumed to superpose linearly, as indicated in figure 3.
The underlying particle motion is imagined to be (approximately) newtonian--i.e., a conservative ``billiard ball'' mechanics.5 Thus given the right amount of energy a particle may penetrate the ``distant'' potential barrier of another particle, enter its ``near'' potential well, and the two particles will become ``bonded''. The configurations of figures 3 and 4 may represent such bonded particles (depending on the respective particle energies). If so, then this new (macro-)molecular configuration establishes a new collective potential field, quite different from that of either isolated particle. For example, it will offer distinctive, emergent, preferences for formation of further bonds.
This is already an example of a top-down constraint in our sense. Two or more particles which are trapped in each others potential wells become ``bonded''. Depending on the configuration, the (macro-)molecule might form further bonds with other particles or molecules. Which particles can bond with one another depends critically on the configuration of the whole. Likewise, the stability of the macromolecule will critically depend on how it is arranged, which itself increases the potential for the emergence of novel higher-level particles (macromolecules). Note that the bonding rules, the allowed configurations or the conditions under which bonds break are nowhere explicitly defined, but are emergent properties of the underlying mechanics of the AC and the distinctive potential field of the particles. A macromolecule will thus have properties which are not, in effect, already pre-figured in programmed bonding properties of the constituent particles. Even in this toy version, it seems that a two particle molecule may be capable of forming a further bond with a third particle; such bonding may, in turn, alter the collective potential field, so that the bonding between all three particles is stronger.
We thus see that bonding--and consequently higher order ``chemical'' properties--in such a model will not be pre-conceived or pre-programmed in any substantial way at the agent level, but rather emerge in a highly dynamic way. Already in this toy model we may observe a significant variety of macromolecular configurations and behaviour. The richness of the phenomenology of the model would, of course, be enhanced by introducing different classes of particles with different fields; this might then be a viable way to introduce novelty on an ongoing basis, through the creation of new types of macromolecules.
In some respects, of course, the avenue suggested here is fundamentally close to that of Rasmussen et al. (2001); but it is also still different in its suggested degree of abstraction and in its purpose. We do not propose attempting to model any particular chemical species and the described toy-model explicitly renounces any realism; this shift of attention allows to explore the generative power of more generalised artificial chemistries, but still with emergent bond formation. The emphasis is thus mainly on methodological aspects: The question at this point is not how a specific phenomenon can be modelled, but more general, how ACs with high or even perpetual novelty creation might be constructed.
At this stage it is unclear whether these approaches will ever lead to a model which supports the perpetual creation of novelty (the toy model certainly would not), but the ansatz at least seems to merit investigation to show whether it is fruitful or not.
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