A note on the strong and weak generative powers of formal systems

AbstractThis paper is a note on some relationships between the strong and weak generative powers of formal systems, in particular, from the point of view of squeezing more strong power out of a formal system without increasing its weak generative power. We will comment on some old and new results from this perspective. Our main goal of this note is to comment on the strong generative power of context-free grammars, lexicalized tree-adjoining grammars (and some of their variants) and Lambek grammars, especially in the context of crossing dependencies, in view of the recent work of Tiede (Ph.D. Dissertation, Indiana University, Bloomington, 1999)

Transformations in the Scale of Behaviour and the Global Optimisation of Constraints in Adaptive Networks

The natural energy minimisation behaviour of a dynamical system can be interpreted as a simple optimisation process, finding a locally optimal resolution of problem constraints. In human problem solving, high-dimensional problems are often made much easier by inferring a low-dimensional model of the system in which search is more effective. But this is an approach that seems to require top-down domain knowledge; not one amenable to the spontaneous energy minimisation behaviour of a natural dynamical system. However, in this paper we investigate the ability of distributed dynamical systems to improve their constraint resolution ability over time by self-organisation. We use a ‘self-modelling’ Hopfield network with a novel type of associative connection to illustrate how slowly changing relationships between system components can result in a transformation into a new system which is a low-dimensional caricature of the original system. The energy minimisation behaviour of this new system is significantly more effective at globally resolving the original system constraints. This model uses only very simple, and fully-distributed positive feedback mechanisms that are relevant to other ‘active linking’ and adaptive networks. We discuss how this neural network model helps us to understand transformations and emergent collective behaviour in various non-neural adaptive networks such as social, genetic and ecological networks

Aristotle on Epigenesis

It has become somewhat of a platitude to call Aristotle the first epigenesist insofar as he thought form and structure emerged gradually from an unorganized, amorphous embryo. But modern biology now recognizes two senses of “epigenesis”. The first is this more familiar idea about the gradual emergence of form and structure, which is traditionally opposed to the idea of preformationism. But modern biologists also use “epigenesis” to emphasize the context-dependency of the process itself. Used in this sense development is not simply the unfolding of a pre-determined sequence of changes specified in advance by the organism’s genotype. It is also sensitive to inputs from the internal and external environment, which help determine in real-time which of the many potential developmental pathways are actualized during the process. Within this paradigm developing embryos are viewed as dynamic and responsive systems that react to inputs from the internal and external environment ‘on the fly’. In this paper I argue that, while Aristotle was an epigenesist in the first sense, he would have rejected epigenesis in the more modern sense. First, Aristotle’s model of choice for a developing embryo is the automaton that executes a set of preset movements (GA 734b9-13, 741b7-15). The automatons he has in mind are not dynamic AI systems capable of modifying their behaviour on the fly in response to environmental cues but completely deterministic mechanisms whose movements are fixed by their original design. Second, given Aristotle’s views about the different kinds of causal powers there are, it looks like only intentional agents endowed with actual decision-making powers could be capable of the sort of plasticity at the core of a more dynamic epigenesis. For that kind of epigenesis requires powers for alternative outcomes, and Aristotle is explicit that such powers require rational desires (προαίρεσις) that control which of those alternatives to bring about. If I am right, then he could not have made sense of the idea of a developing embryo (as a non-intentional system) making adjustments to its phenotype on the fly in response to emerging problems and opportunities, given the conceptual resources available to him

Linguistics and some aspects of its underlying dynamics

In recent years, central components of a new approach to linguistics, the Minimalist Program (MP) have come closer to physics. Features of the Minimalist Program, such as the unconstrained nature of recursive Merge, the operation of the Labeling Algorithm that only operates at the interface of Narrow Syntax with the Conceptual-Intentional and the Sensory-Motor interfaces, the difference between pronounced and un-pronounced copies of elements in a sentence and the build-up of the Fibonacci sequence in the syntactic derivation of sentence structures, are directly accessible to representation in terms of algebraic formalism. Although in our scheme linguistic structures are classical ones, we find that an interesting and productive isomorphism can be established between the MP structure, algebraic structures and many-body field theory opening new avenues of inquiry on the dynamics underlying some central aspects of linguistics.Comment: 17 page

Shopping for new glasses: looking beyond jazz in the study of organization improvisation

This article calls for research on organizational improvisation to go beyond the currently dominant jazz metaphor in theory development. We recognize the important contribution that jazz improvisation has made and will no doubt continue to make in understanding the nature and complexity of organizational improvisation. This article therefore presents some key lessons from the jazz metaphor and then proceeds to identify the possible dangers of building scientific inquiry upon a single metaphor. We then present three alternative metaphors Indian music, therapy and role theory. We explore the nature of these metaphors and seek to identify ways in which they differ from the jazz metaphor. This analysis leads us to identify not merely how these alternative metaphors fill the gaps left by the jazz metaphor but also how they complement the contribution from the jazz metaphor thus further strengthening theory-building in this genre. Ultimately, our understanding of organizational improvisation will be sharpened by more incisive theoretical analysis and empirical research.