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- Bruce Edmonds, Understanding Observed Complex Systems – the Hard Complexity Problem.bruce@edmonds.name http://bruce.edmonds.name Abstract. Two kinds of problem are distinguished: the first of finding processes which produce complex outcomes from the interaction of simple parts, and the second of finding which process resulted in an observed complex outcome. The former I call the easy complexity problem and the later the hard complexity problem. It is often assumed that progress with the easy problem will aid process with the hard problem. However this assumes that the “reverse engineering” problem, of determining the process from the outcomes is feasible. Taking a couple of simple models of reverse engineering, I show that this task is infeasible in the general case. Hence it cannot be assumed that reverse engineering is possible, and hence that most of the time progress on the easy problem will not help with the hard problem unless there are special properties of a particular set of processes that make it feasible. Assuming that complexity science is not merely an academic “game” and given the analysis of this paper, some criteria for the kinds of paper that have a reasonable chance of being eventually useful for understanding observed complex systems are outlined. Many complexity papers do not fare well against these critieria.
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The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is the first example of an exact estimation of the degree of natural complex logics, i.e. logics whose deducibility relation cannot be represented by a single matrix. The remaining examples of complex logics are more artificial, having been constructed for the purpose of checking some theoretical possibilities.
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| | Other links: jstor.org | Scholar | At my library | More options ... In this chapter we want to provide philosophical tools for understanding and reasoning about complex systems. Classical thinking, which is taught at most schools and universities, has several problems for coping with complexity. We review classical thinking and its drawbacks when dealing with complexity, for then presenting ways of thinking which allow the better understanding of complex systems. Examples illustrate the ideas presented. This chapter does not deal with specific tools and techniques for managing complex systems, but we try to bring forth ideas that facilitate the thinking and speaking about complex systems.
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| | Other links: cogprints.org | Scholar | At my library | More options ... Complexly organized systems include biological and cognitive systems, as well as many of the everyday systems that form our environment. They are both common and important, but are not well understood. A complex system is, roughly, one that cannot be fully understood via analytic methods alone. An organized system is one that shows spatio-temporal correlations that are not determined by purely local conditions, though organization can be more or less localizable within a system. Organization and complexity can vary independently to some extent, but they are interconnected: organisation requires some complexity, but complexity cannot be maximum in an organized system. I will define complexity and organization more precisely, and show how these definitions imply the above properties. Next I will discuss how organized complexity can be modelled, with an eye to limitations on the tractability of both the models and the modelling process. I will finish with some remarks on the limits of our possible understanding of complexly organized systems. Keywords: complexity, organization, modelling, holism, information theory..
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| | Scholar | More options ... The philosophical mind-body problem, which Chalmers has named the 'Hard Problem', concerns the nature of the mind and the body. Physicalist approaches have been explored intensively in recent years but have brought us no consensual solution. Dualistic approaches have also been scrutinised since Descartes, but without consensual success. Mentalism has received little attention, yet it offers an elegantly simple solution to the hard problem.
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| | Other links: peterblloyd.org | Scholar | More options ... A short review of complexity research from the perspective of history and philosophy of biology is presented. Complexity and its emergence has scientific and metaphysical meanings. From its beginning, biology was a science of complex systems, but with the advent of electronic computing and the possibility of simulating mathematical models of complicated systems, new intuitions of complexity emerged, together with attempts to devise quantitative measures of complexity. But can we quantify the complex?
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| | Scholar | More options ... This paper explores the meaning and possibility of a theory of knowledge vis-a-vis the non linear complex systems. The thesis hereafter defended is that knowledge of complex systems has to do more with possibilities than with factual reality. Therefore, knowledge is characterized by incompletness, incomputability and randomness, and so computer acquires a relevant role in the study of complex systems. Towards the end, the place and the very complexity of human beings as a complex problem is considered.
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| | Scholar | More options ... The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem of computational complexity of the Ramsey quantifier for which the phrase “A is big relatively to the universe” is interpreted as containing at least one representative of each equivalence class, for some given equvalence relation. In this work we consider quantifiers Rf, for which “A is big relatively to the universe” means “card(A) > f (n), where n is the size of the universe”. Following [Blass, Gurevich 1986] we call R mighty if Rx, yH(x, y) defines N P – complete class of finite models. Similarly we say that Rf is N P –hard if the corresponding class is N P –hard. We prove the following theorems.
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| | Other links: jakubszymanik.com | Scholar | At my library | More options ... Biology deals, notoriously, with complex systems. In discussing biological methodology, all three papers in this symposium honor the complexity of biological subject matter by preferring models and theories built to reflect the details of complex systems to models based on broad general principles or laws. Rheinberger's paper, the most programmatic of the three, provides a framework for the epistemology of discovery in complex systems. A fundamental problem is raised for Rheinberger's epistemology, namely, how to understand the referential continuity of the theoretical terms and concepts employed in typical case studies involving complex systems.
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| | Other links: jstor.org journals.uchicago.edu dx.doi.org | Scholar | At my library | More options ... In a simple economic decision problem with multi-tasking the dimensionality of the problem is neither a necessary nor a sufficient measure of complexity. Rather, dimension is good measure of complexity when there is an aggregate resource constraint that creates an interaction between the different activities, resulting in a problem with high algorithmic complexity.
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| | Scholar | At my library | More options ... Introduction to complexity and complex systems -- Introduction to large linear systems -- Introduction to biochemical oscillators and nonlinear biochemical systems -- Modularity, redundancy, degeneracy, pleiotropy and robustness in complex biological systems -- The evolution of biological complexity; invertebrate immune systems -- Irreducible and specified complexity in living systems -- The complex adaptive and innate human immune systems -- Complexity in quasispecies : microRNAs -- Introduction to complexity in economic systems -- Complexity in quasispecies : micrornas -- Dealing with complexity.
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| | Scholar | At my library | More options ... Discussion of Bruce Edmonds, Understanding observed complex systems – the hard complexity problem
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