The role of complex systems theory in cognitive science (original) (raw)
Contextual emergence of mental states from neurodynamics
The emergence of mental states from neural states by partitioning the neural phase space is analyzed in terms of symbolic dynamics. Well-defined mental states provide contexts inducing a criterion of structural stability for the neurodynamics that can be implemented by particular partitions. This leads to distinguished subshifts of finite type that are either cyclic or irreducible. Cyclic shifts correspond to asymptotically stable fixed points or limit tori whereas irreducible shifts are obtained from generating partitions of mixing hyperbolic systems. These stability criteria are applied to the discussion of neural correlates of consiousness, to the definition of macroscopic neural states, and to aspects of the symbol grounding problem. In particular, it is shown that compatible mental descriptions, topologically equivalent to the neurodynamical description, emerge if the partition of the neural phase space is generating. If this is not the case, mental descriptions are incompatible or complementary. Consequences of this result for an integration or unification of cognitive science or psychology, respectively, will be indicated.
Dynamical Systems Theory in Cognition: Are We Really Gaining?
2011
Dynamical Systems Theory (DST) claims to be an epistemological weapon particularly broad and rich in providing a fair explanatory account of the operations of our mind. However, the very features that this DST espouses as reasons for having an edge over Computational Theory of Mind (CTM) and Artificial Neural Networks (ANN), are the ones that are causing trouble in the philosophy of science speculation, especially regarding issues of Explanation. This paper aims to suggest some possible problems that could arise from the application of DST’s characteristically abstract mathematical framework to the study of the mind. As I have not found anything that suggests something like this, my aim is to at least show the reasonability of a possibility.
Complex Systems, Brain, and Consciousness (Reading Group Syllabus)
An a priori definition of complexity cannot be given, nor is it viable to propose one for the reason that every complex system differs in character and organization. Thus, the only possible course of action in understanding complex systems is by observing the characteristics those systems exhibit. However, some features have been deemed necessary (although not sufficient) for regarding a system complex as opposite to complicated or merely simple systems. A working definition of this sort describes a complex system as a composite organization of many interdependent parts that are displaying rich array of nonlinear interactions and/or adaptive relations that result in complex ('emergent') collective behavior. In this sense, it is important to distinguish complex from complicated systems since complicated systems can and often do have many components and perform highly sophisticated operations. For example, the Large Hadron Collider is a complicated system; we can deconstruct it to its constituent parts and account for their function within a system. By doing so we are able to predict the systems behavior. On the other hand, a flock of birds is a complex system. Given the part's properties, i.e. single bird, one cannot fully account for the properties of the whole, i.e. the flock, making those systems more than just the sum of their parts. Complexity talk has become fashionable over the recent decade or so. Its applications are numerous. One of them is in the Cognitive Neuroscience research project. This is mostly done through the framework of complex dynamical systems which presents a radical shift of methodology. However, there are two problems emerging from this and, thus, two main aims of this reading group. Firstly, the very concept of 'complexity' is complex. Can we talk about complexity as an umbrella term or are there only specific cases of complexity? Similarly, should this, and in what way, change the application of the theory itself to the particular systems? In addition, complex systems theory uses opaque concepts such as emergence that are heavily burden philosophically. Hence, the first order of business is to understand complex systems and, subsequently, examine them from a philosophical perspective. On the other hand, theories like Integrated Information Theory (IIT) have recently emerged in this framework. These theories aim to account for phenomenology and capture the notion of consciousness. However, the main issue remains the same throughout the theories: the very application to " higher order " cognitive processes is questionable, since complex dynamical systems don't necessarily account for 'how things work' or 'why things happen'. Hence, our second aim is to examine some of these theories more closely.
A complex-systems perspective on the" computation vs. dynamics" debate in cognitive science
1998
Abstract I review the purported opposition between computational and dynamical approaches in cognitive science. I argue that both computational and dynamical notions will be necessary for a full explanatory account of cognition, and give a perspective on how recent research in complex systems can lead to a much needed rapprochement between computational and dynamical styles of explanation.
The Physics of Mind and Thought
Activitas Nervosa Superior, 2019
Regular physics is unsatisfactory in that it fails to take into consideration phenomena relating to mind and meaning, whereas on the other side of the cultural divide such constructs have been studied in detail. This paper discusses a possible synthesis of the two perspectives. Crucial is the way systems realising mental function can develop step by step on the basis of the scaffolding mechanisms of Hoffmeyer, in a way that can be clarified by consideration of the phenomenon of language. Taking into account such constructs, aspects of which are apparent even with simple systems such as acoustically excited water, as with cymatics, potentially opens up a window into a world of mentality excluded from conventional physics as a result of the primary focus of the latter on the matter-like aspect of reality.
Discrete Dynamics in Nature and Society, 1999
The language of nonlinear dynamical systems and ergodic theory is used to present a theoretical framework for the study of mind. The basic spaceXconsists of the collection of all brain images (clusters of activated neurons) that are relevant to consciousness. The dynamics of the brain is modelled by means of a discrete time transformationTwhich takes a cluster of activated brain cells into another cluster of activated brain cells. The spaceXis partitioned into subcollections of brain images, namely those generated by the five senses and by other processes that produce brain images relevant to consciousness. It is argued thatTis a Markov transformation with respect to this partition ofX. This leads to the existence of an objectμ, referred to as an SRB measure which possesses properties that make it a candidate for mind:μis ‘aware’ of the brain images in its support;μis time-invariant and acts as an attractor into which all orbits of (conscious) brain images settle. Furthermore, the d...
Physics of mind: Experimental confirmations of theoretical predictions
Physics of life reviews, 2018
What is common among Newtonian mechanics, statistical physics, thermodynamics, quantum physics, the theory of relativity, astrophysics and the theory of superstrings? All these areas of physics have in common a methodology, which is discussed in the first few lines of the review. Is a physics of the mind possible? Is it possible to describe how a mind adapts in real time to changes in the physical world through a theory based on a few basic laws? From perception and elementary cognition to emotions and abstract ideas allowing high-level cognition and executive functioning, at nearly all levels of study, the mind shows variability and uncertainties. Is it possible to turn psychology and neuroscience into so-called "hard" sciences? This review discusses several established first principles for the description of mind and their mathematical formulations. A mathematical model of mind is derived from these principles. This model includes mechanisms of instincts, emotions, behav...
Elsevier SSRN
The computational mind approach was conforming to neural models of material mind based on theories like Neural Correlates of Consciousness. Thinkers like Chalmers posed the Hard Problem of consciousness arguing on the theme of an extended mind going beyond the brain. Gödel incompleteness theorem, called into question the power of mathematics to explain all of reality — along with the hypothesis that the mind works like a formal system, or a mathematical machine. Gödel’s incompleteness theorem made Penrose to remark that mind is no algorithmic machine. .To Hofstadter, the mystery of subjectivity can only be explained with the concept of self-reference. The idea that consciousness emerges from self-modeling is supported by thinkers like Judea Pearl, whose causal calculus forms the backbone of one of today’s most respected consciousness theories, integrated information theory. Integrated Information Theory of Tononi and Koch is also inspired by ancient mystic ideas of panpsychism or universal mind ,as well as concepts in more recent times like complexity,modularity ,hierarchical structures and interactive dynamics. This can be approximately abstracted by mathematical topology to suggest complex entities of an imaginary nature in a mind space of an ideational nature, with its possible material interphases with physicalism in microdomain nature of Planckian order quantum gravity medium. The study of the similarities and differences between polynomial-time algorithms and the functioning of the mind is a concrete matter,and not merely philosophical. Topology in the mathematical sense has been used by cognitive scientists in work on the mathematical properties of connectionist networks. Using algebraic topology to study the way neurons group together to form geometrical shapes, revealed a universe of complex multi-dimensional geometric structures. The topological background of Husserl's work makes itself felt already in his theory of dependence. It comes to the fore above all however in his treatment of the notion of phenomenal fusion. Thus phenomenal space is compositional with respect to quasi-elements. We may assume that conscious experience is structured along multiple interdependent layers. The local-global interdependency of experience is mirrored in the mereological and topological structure of phenomenal space. Analogously,perhaps Hoffman and Chetan Prakash pursued the mathematical theories of agent dynamics. The paper discusses how mind matter interphases in phenomenological and psychological states of cognitive conditions are being mathematically abstracted as topological approximations that represent complex ideation or imaginal and phenomenological spaces, rather corresponding to or conforming to models of conscious entities and agent dynamics at Planckian or near Planckian orders ,giving rise to mind and matter interphases and physical phenomenological continuum states