Abstract
We consider processes of emergence within the conceptual framework of the Information Loss principle and the concepts of (1) systems conserving information; (2) systems compressing information; and (3) systems amplifying information. We deal with the supposed incompatibility between emergence and computability tout-court. We distinguish between computational emergence, when computation acquires properties, and emergent computation, when computation emerges as a property. The focus is on emergence processes occurring within computational processes. Violations of Turing-computability such as non-explicitness and incompleteness are intended to represent partially the properties of phenomenological emergence, such as logical openness, given by the observer’s cognitive role; structural dynamics where change regards rules rather than only values; and multi-modelling where multiple non-equivalent models are required to model such structural dynamics. In this way, we validate, from an epistemological viewpoint, models and simulations of phenomenological emergence where the sequence of events constitutes the natural, analogical non-Turing computation which a cognitive complex system can reproduce through learning. Reproducibility through learning is different from Turing-like computational iteration. This paper aims to open a new, non-reductionist understanding of the conceptual relationship between emergence and computability.
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Notes
A model may be defined as logically closed when (1) a formal description of the relationships between all the state variables is available in the model; (2) a complete and explicit description of system-environment interactions is available; (3) all possible structural features and asymptotic states are deducible from the information in (1) and (2). For instance, thermodynamically open systems such as dissipative structures may be described by logically closed models. Since the description of a given system is equivalent to assertions about its input and output processing, we may distinguish between (a) logically closed models related to explicit and completed input processing modalities; and (b) logically open models related to non-completed, non-explicit description of the system in case it is impossible to know, in principle, how the input–output will be processed. Therefore, it is impossible to know the asymptotic states of the system, if any. Examples are given by a computer program playing a game with a player and by the evolutionary paths of complex systems like ecosystems and biological collective behaviours where the environment plays a crucial role. Logical open models may be introduced on the basis of violation of as least one of the three criteria (1), (2), and (3) listed above to describe logical closed models.
In the sense of Bell (1987).
The cases where we consider to have authentic, so-called intrinsic or radical, emergence are (a) those in which the relationship with the environment and related processes of acquisition of emergent properties can not be modelled a priori in a single formal model. This is the case of structural dynamics given by the changing of variables to be considered, i.e., degrees of freedom. Structural dynamics can only be locally modelled by sequences of unrelated models. We have sequences of different but coherent different uniqueness; (b) ones in which the bonds are entirely independent of the rules (therefore, literally, “the rules of the game change”). In other words when, simply, something compatible with the “grid” of the laws happens, allowing, however, the emergence of properties.
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Appendix
Appendix
In this appendix we will briefly illustrate the concepts of completeness and incompleteness for systems.
For completeness, one can say that such a system is completely described by one or a finite number of models. The problem becomes more complicated when we consider dynamic systems, i.e., systems of differential equations describing the evolution of the system, often intractable analytically and thus we have to look at global properties of a system (families of solutions and structural facets).
For incompleteness, we have to use multiple non-equivalent models dynamically, i.e., for different instants and locally. In this case, however, models may describe the behaviour of the system in an incomplete way as with DYSAM (Minati and Pessa 2006). The dynamic usage of the models corresponds to the structural dynamics of the system.
Another way to deal with completeness and incompleteness consists of considering the states (configurations, parameters, etc.) reachable by the system. A system can be understood as complete when the number of reachable states is finite.
A system can be understood as incomplete when the set of achievable states is non-finite, when the next state is invented (not chosen among the available ones) by the system, e.g., by means of broken symmetry, given by logical openness, and they are not equivalent to, nor linearly deducible from, previous ones. Today, the focus is on coherence rather than on completeness. In other words, we use cognitive strategies to look for interesting configurations. In this case, the problem is not forecasting in a mathematical sense, but betting in the de Finetti sense (de Finetti 2008; Pavlov and Andreev 2013; Hosni et al. 2011). Computing is an essential tool for evaluating our chances of success.
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Licata, I., Minati, G. Emergence, Computation and the Freedom Degree Loss Information Principle in Complex Systems. Found Sci 22, 863–881 (2017). https://doi.org/10.1007/s10699-016-9503-x
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DOI: https://doi.org/10.1007/s10699-016-9503-x