On Complexity and Emergence

Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and Shannon Entropy measures widely used as complexity measures, yet addresses a number of concerns raised against these measures. However, the price of doing this is to introduce context dependence into the definition of complexity. It is argued that such context dependence is an inherent property of complexity, and related concepts such as entropy and emergence. Scientists are uncomfortable with such context dependence, which smacks of subjectivity, and this is perhaps the reason why little agreement has been found on the meaning of these terms.Comment: submitted to Complexity Internationa

Evolution in the Multiverse

In the {\em Many Worlds Interpretation} of quantum mechanics, the range of possible worlds (or histories) provides variation, and the Anthropic Principle is a selective principle analogous to natural selection. When looked on in this way, the ``process'' by which the laws and constants of physics is determined not too different from the process that gave rise to our current biodiversity, i.e. Darwinian evolution. This has implications for the fields of SETI and Artificial Life, which are based on a philosophy of the inevitability of life.Comment: 4 pages; submitted to Complexity International (http://www.csu.edu.au/ci/ci.html

Some Techniques for the Measurement of Complexity in Tierra

Recently, Adami and coworkers have been able to measure the information content of digital organisms living in their {\em Avida} artificial life system. They show that over time, the organisms behave like Maxwell's demon, accreting information (or complexity) as they evolve. In {\em Avida} the organisms don't interact with each other, merely reproduce at a particular rate (their fitness), and attempt to evaluate an externally given arithmetic function in order win bonus fitness points. Measuring the information content of a digital organism is essentially a process of counting the number of genotypes that give rise to the same phenotype. Whilst Avidan organisms have a particularly simple phenotype, Tierran organisms interact with each other, giving rise to an ecology of phenotypes. In this paper, I discuss techniques for comparing pairs of Tierran organisms to determine if they are phenotypically equivalent. I then discuss a method for computing an estimate of the number of phenotypically equivalent genotypes that is more accurate than the ``hot site'' estimate used by Adami's group. Finally, I report on an experimental analysis of a Tierra run.Comment: 5 pages; 1 figure; European Conference on Artificial Lif

An Ecolab Perspective on the Bedau Evolutionary Statistics

At Alife VI, Mark Bedau proposed some evolutionary statistics as a means of classifying different evolutionary systems. Ecolab, whilst not an artificial life system, is a model of an evolving ecology that has advantages of mathematical tractability and computational simplicity. The Bedau statistics are well defined for Ecolab, and this paper reports statistics measured for typical Ecolab runs, as a function of mutation rate. The behaviour ranges from class 1 (when mutation is switched off), through class 3 at intermediate mutation rates (corresponding to scale free dynamics) to class 2 at high mutation rates. The class 3/class 2 transition corresponds to an error threshold. Class 4 behaviour, which is typified by the Biosphere, is characterised by unbounded growth in diversity. It turns out that Ecolab is governed by an inverse relationship between diversity and connectivity, which also seems likely of the Biosphere. In Ecolab, the mutation operator is conservative with respect to connectivity, which explains the boundedness of diversity. The only way to get class 4 behaviour in Ecolab is to develop an evolutionary dynamics that reduces connectivity of time.Comment: 5 pages; 3 figures; accepted for Artificial Life VI

Network Complexity of Foodwebs

In previous work, I have developed an information theoretic complexity measure of networks. When applied to several real world food webs, there is a distinct difference in complexity between the real food web, and randomised control networks obtained by shuffling the network links. One hypothesis is that this complexity surplus represents information captured by the evolutionary process that generated the network. In this paper, I test this idea by applying the same complexity measure to several well-known artificial life models that exhibit ecological networks: Tierra, EcoLab and Webworld. Contrary to what was found in real networks, the artificial life generated foodwebs had little information difference between itself and randomly shuffled versions

Tierra's missing neutrality: case solved

The concept of neutral evolutionary networks being a significant factor in evolutionary dynamics was first proposed by Huynen {\em et al.} about 7 years ago. In one sense, the principle is easy to state -- because most mutations to an organism are deleterious, one would expect that neutral mutations that don't affect the phenotype will have disproportionately greater representation amongst successor organisms than one would expect if each mutation was equally likely. So it was with great surprise that I noted neutral mutations being very rare in a visualisation of phylogenetic trees generated in {\em Tierra}, since I already knew that there was a significant amount of neutrality in the Tierra genotype-phenotype map. It turns out that competition for resources between host and parasite inhibits neutral evolution.Comment: Accepted for ALife IX; final M

The Role of Innovation within Economics

This paper discusses dynamic evolutionary economics, and introduces a model of such.Comment: 20 pages; 5 figure

SuperNOVA: a novel algorithm for graph automorphism calculations

The graph isomorphism problem is of practical importance, as well as being a theoretical curiosity in computational complexity theory in that it is not known whether it is $NP$-complete or $P$. However, for many graphs, the problem is tractable, and related to the problem of finding the automorphism group of the graph. Perhaps the most well known state-of-the art implementation for finding the automorphism group is Nauty. However, Nauty is particularly susceptible to poor performance on star configurations, where the spokes of the star are isomorphic with each other. In this work, I present an algorithm that explodes these star configurations, reducing the problem to a sequence of simpler automorphism group calculations.Comment: This paper was rejected for publication, primarily because it implements known techniques. I have updated the manuscript with experimental data comparing the algorithm with other well known automorphism implementation

The influence of parsimony and randomness on complexity growth in Tierra

The issue of how to create open-ended evolution in an artificial system is one the open problems in artificial life. This paper examines two of the factors that have some bearing on this issue, using the Tierra artificial life system. {\em Parsimony pressure} is a tendency to penalise more complex organisms by the extra cost needed to reproduce longer genotypes, encouraging simplification to happen. In Tierra, parsimony is controlled by the \verb+SlicePow+ parameter. When full parsimony is selected, evolution optimises the ancestral organism to produce extremely simple organisms. With parsimony completely relaxed, organisms grow larger, but not more complex. They fill up with ``junk''. This paper looks at scanning a range of \verb+SlicePow+ from 0.9 to 1 to see if there is an optimal value for generating complexity. Tierra (along with most ALife systems) use pseudo random number generators. Algorithms can never create information, only destroy it. So the total complexity of the Tierra system is bounded by the initial complexity, implying that the individual organism complexity is bounded. Biological systems, however, have plenty of sources of randomness, ultimately dependent on quantum randomness, so do not have this complexity limit. Sources of real random numbers exist for computers called {\em entropy gatherers} -- this paper reports on the effect of changing Tierra's pseudo random number generator for an entropy gatherer

Diversity Evolution

Bedau has developed a general set of evolutionary statistics that quantify the adaptive component of evolutionary processes. On the basis of these measures, he has proposed a set of 4 classes of evolutionary system. All artificial life sytems so far looked at fall into the first 3 classes, whereas the biosphere, and possibly the human economy belongs to the 4th class. The challenge to the artificial life community is to identify exactly what is difference between these natural evolutionary systems, and existing artificial life systems. At ALife VII, I presented a study using an artificial evolutionary ecology called \EcoLab. Bedau's statistics captured the qualitative behaviour of the model. \EcoLab{} exhibited behaviour from the first 3 classes, but not class 4, which is characterised by unbounded growth in diversity. \EcoLab{} exhibits a critical surface given by an inverse relationship between connectivity and diversity, above which the model cannot tarry long. Thus in order to get unbounded diversity increase, there needs to be a corresponding connectivity reducing (or food web pruning) process. This paper reexamines this question in light of two possible processes that reduce ecosystem connectivity: a tendency for specialisation and increase in biogeographic zones through continental drift