Dynamical Systems

The concepts and powerful mathematical tools of Dynamical Systems Theory (DST) yield illuminating methods of studying cognitive processes, and are even claimed by some to enable us to bridge the notorious explanatory gap separating mind and matter. This article includes an analysis of some of the conceptual and empirical progress Dynamical Systems Theory is claimed to accomodate. While sympathetic to the dynamicist program in principle, this article will attempt to formulate a series of problems the proponents of the approach in (...) question will need to face if they wish to prolong their optimism. The main points to be addressed involve the reductive tendencies inherent in Dynamical Systems Theory, its somewhat muddled position relative to connectionism, the metaphorical nature DST-C exhibits which hinders its explanatory potential, and DST-C's problematic account of causality. Brief discussions of the mathematical and philosophical backgrounds of DST, seminal experimental work and possible adaptations of the theory or alternative suggestions (dynamicist connectionism, neurophenomenology, R&D theory) are included. (shrink)

Dasein is one of several twentieth-century notions which paint a portrait of the “post-Cartesian subject.” Critics of cognitivism such as Dreyfus have invoked Dasein in arguing that computational models cannot be sufficient to account for situated cognition. Van Gelder argues that dynamic systems theory provides an empirical model of cognition as practical activity which avoids the Cartesianism implicit in the computational approach. I assess Van Gelder’s claim for dynamic systems as a model of being-in-the-world. Contra Van Gelder, I argue that (...) the force of the “Dasein objection” is that the significance of a mental process, whether representational or not, depends on a lived background of value. While dynamic systems can help model the diachronic interplay between organism and environment, the semantic context for this interplay is no more accounted for here than in traditional computer models. (shrink)

I explore the possibility that mentality can be characterized as a level in between the functional and the neurological, namely as a physical system exhibiting a specific kind of chaos. The argument is meant to make a case for this kind of characterization rather than giving one in specific detail.

A new layer of complexity, constituted of networks of information token recurrence, has been identified in socio-technical systems such as the Wikipedia online community and the Zooniverse citizen science platform. The identification of this complexity reveals that our current understanding of the actual structure of those systems, and consequently the structure of the entire World Wide Web, is incomplete, which raises novel questions for data science research but also from the perspective of social epistemology. Here we establish the principled foundations (...) and practical advantages of analyzing information diffusion within and across Web systems with Transcendental Information Cascades, and outline resulting directions for future study in the area of socio-technical systems. We also suggest that Transcendental Information Cascades may be applicable to any kind of time-evolving system that can be observed using digital technologies, and that the structures found in such systems comprise properties common to all naturally occurring complex systems. (shrink)

The Gestalt psychologists adopted a set of positions on mind-body issues that seem like an odd mix. They sought to combine a version of naturalism and physiological reductionism with an insistence on the reality of the phenomenal and the attribution of meanings to objects as natural characteristics. After reviewing basic positions in contemporary philosophy of mind, we examine the Gestalt position, characterizing it m terms of phenomenal realism and programmatic reductionism. We then distinguish Gestalt philosophy of mind from instrumentalism and (...) computational functionalism, and examine Gestalt attributions of meaning and value to perceived objects. Finally, we consider a metatheoretical moral from Gestalt theory, which commends the search for commensurate description of mental phenomena and their physiological counterparts. (shrink)

Traditionally, computational theory (CT) and dynamical systems theory (DST) have presented themselves as opposed and incompatible paradigms in cognitive science. There have been some efforts to reconcile these paradigms, mainly, by assimilating DST to CT at the expenses of its anti-representationalist commitments. In this paper, building on Piccinini’s mechanistic account of computation and the notion of functional closure, we explore an alternative conciliatory strategy. We try to assimilate CT to DST by dropping its representationalist commitments, and by inviting CT to (...) recognize the functionally closed nature of some computational systems. (shrink)

We present simulation results of an olfactory cortex model complementing the results presented in Wright & Liley's target article. We show how the cortical dynamics as expressed in EEG can be regulated by neuromodulation and discuss how the system can attain global stability without cortical-subcortical interaction, as presumed necessary by Wright & Liley. Network structure is shown to be crucial.

In this paper we prove that the reachability problem is BSS-undecidable for o-minimal dynamical systems.

Recent years have seen an increasing interest in the study of continuous-time computational models. However, not so much has been done with respect to setting up a complexity theoretic framework for such models. The present paper intends to go a step into this direction. We consider problems over the real numbers which we try to relate to Lyapunov theory for dynamical systems: The global minimizers of particular energy functions are supposed to give solutions of the problem. The structure of such (...) energy functions leads to the introduction of problem classes U and NU; for the systems we are considering they parallel the classical complexity classes P and NP. We then introduce a notion of reducibility among problems and show existence of complete problems for NU and for PU, a polynomial hierarchy of continuous-time problems.For previous work on the computational capabilities of continuous-time systems see the surveys by Cris Moore [9] and by Pekka Orponen [10]. Our paper presents a step into the direction of creating a general framework for a complexity theory of continuous-time systems as outlined in [10]. It is closely related to work done by A. Ben-Hur, H. Siegelmann, and S. Fishman [12, 11]. (shrink)

Open peer commentary on the article “A Cybernetic Computational Model for Learning and Skill Acquisition” by Bernard Scott & Abhinav Bansal. Upshot: The target paper acknowledges some early computer modelling that I did in the years 1966–1968 when working with Pask at System Research Ltd in Richmond. In the commentary, I revisit the roots of this kind of modelling and follow the trajectory from then to today’s growing understanding of the dynamics of cognitive systems.

According to the age-of-acquisition hypothesis, words acquired early in life are processed faster and more accurately than words acquired later. Connectionist models have begun to explore the influence of the age/order of acquisition of items (and also their frequency of encounter). This study attempts to reconcile two different methodological and theoretical approaches (proposed by Lambon Ralph & Ehsan, 2006 and Zevin & Seidenberg, 2002) to age-limited learning effects. The current simulations extend the findings reported by Zevin and Seidenberg (2002) that (...) have shown that frequency trajectories (FTs) have limited and specific effects on word-reading tasks. Using the methodological framework proposed by Lambon Ralph and Ehsan (2006), which makes it possible to compare word-reading and picture-naming tasks in connectionist networks, we were able to show that FT has a considerable influence on age-limited learning effects in a picture naming task. The findings show that when the input–output mappings are arbitrary (simulating picture naming tasks), the links formed by the network become entrenched as a result of early experience and that subsequent variations in frequency of exposure of the items have only a minor impact. In contrast, when the mappings between input-output are quasi-systematic or systematic (simulating word-reading tasks), the training of new items was generalized and resulted in the suppression of age-limited learning effects. At a theoretical level, we suggest that FT, which simultaneously takes account of time and the level of exposure across time, represents a more precise and modulated measure compared with the order of introduction of the items and may lead to innovative hypotheses in the field of age-limited learning effects. (shrink)

Philosophical and scientific investigations of the proprietary aspects of self—mineness or mental ownership—often presuppose that searching for unique constituents is a productive strategy. But there seem not to be any unique constituents. Here, it is argued that the “self-specificity” paradigm, which emphasizes subjective perspective, fails. Previously, it was argued that mode of access also fails to explain mineness. Fortunately, these failures, when leavened by other findings (those that exhibit varieties and vagaries of mineness), intimate an approach better suited to searching (...) for an explanation. Having an alternative in hand, one that shows promise of achieving explanatory adequacy, provides an additional reason to suspend the search for unique constituents. In short, a negative and a positive thesis are developed: we should cease looking for unique constituents and should seek to explain mineness in accord with the model developed here. This model rejects attempts to explain the phenomenon in terms of either a narrative or a minimal sense of self; it seeks to explain at a “molecular” level, one that appeals to multiple, interacting dimensions. The molecular-level model allows for the possibility that subjective perspective is distinct from a stark perspective (one that does not imply mineness). It proposes that the confounding of tacit expectations plays an important role in explaining mental ownership and its complement, disownership. But the confounding of tacit expectations is not sufficient. Because we are able to be aware of the existence of mental states that do not belong to self, we require a mechanism for determining degree of self-relatedness. One such mechanism is proposed here, and it is shown how this mechanism can be integrated into a general model of mental ownership. In the spirit of suggesting how this model might be able to help resolve outstanding problems, the question as to whether inserted thoughts belong to the patient who reports them is also considered. (shrink)

This article discusses how sequential sampling models can be integrated in a cognitive architecture. The new theory Retrieval by Accumulating Evidence in an Architecture (RACE/A) combines the level of detail typically provided by sequential sampling models with the level of task complexity typically provided by cognitive architectures. We will use RACE/A to model data from two variants of a picture–word interference task in a psychological refractory period design. These models will demonstrate how RACE/A enables interactions between sequential sampling and long-term (...) declarative learning, and between sequential sampling and task control. In a traditional sequential sampling model, the onset of the process within the task is unclear, as is the number of sampling processes. RACE/A provides a theoretical basis for estimating the onset of sequential sampling processes during task execution and allows for easy modeling of multiple sequential sampling processes within a task. (shrink)

In this collection of essays, which is Volume 19 in the University of Western Ontario Series in Philosophy of Science, Laudan examines, in a very engaging manner, the fortunes of the method of hypothesis in the 17th, 18th, and 19th centuries. Most of the essays have appeared elsewhere, but some are published here for the first time. Although there is no introductory or concluding essay that attempts to tie all of the articles together, this collection still succeeds in presenting itself (...) as a unified examination of the important topic of the method of hypothesis. Laudan's expressed intent is to "identify some of the recurrent themes associated with debates about the method of hypothesis and to examine some of the specific causes for its changing fortunes". He does more in this collection than merely fulfill his rather modest intent. In each of his essays, Laudan succeeds in presenting both a clear statement of his particular theme and also a concise and often convincing argument for his particular interpretation of each theme concerning the history of the method of hypothesis. (shrink)

The central claim of computationalism is generally taken to be that the brain is a computer, and that any computer implementing the appropriate program would ipso facto have a mind. In this paper I argue for the following propositions: (1) The central claim of computationalism is not about computers, a concept too imprecise for a scienti c claim of this sort, but is about physical calculi (instantiated discrete formal systems). (2) In matters of formality, interpretability, and so forth, analog computation (...) and digital computation are not essentially di erent, and so arguments such as Searle's hold or not as well for one as for the other. (3) Whether or not a biological system (such as the brain) is computational is a scienti c matter of fact. (4) A substantive scienti c question for cognitive science is whether cognition is better modeled by discrete representations or by continuous representations. (5) Cognitive science and AI need a theoretical construct that is the continuous analog of a calculus. The discussion of these propositions will illuminate several terminology traps, in which it's all too easy to become ensnared. (shrink)

We propose a new dynamical mechanism for information processing in mind and brain. We emphasize that a hermeneutic process is one of the key processes manifesting the functions of the brain and that it can be formulated as an itinerant motion in ultrahigh dimensional dynamical systems, which may give a new realm of the dynamic information processing. Our discussions are based on the notion of chaotic information processing and the observations of biological chaos.

We argue that the propositional and link-based approaches to human contingency learning represent different levels of analysis because propositional reasoning requires a basis, which is plausibly provided by a link-based architecture. Moreover, in their attempt to compare two general classes of models (link-based and propositional), Mitchell et al. refer to only two generic models and ignore the large variety of different models within each class.

Beer’s (2003) paper is a tour de force of detailed comments on the more general notion of “situated- dynamical modeling, and provides a concrete sample ness”, Beer suggests that “on this view, situated action of the kinds of understanding dynamicists may realis- is the fundamental concern and cognition is … one tically hope to achieve. The analysis is thus, as Beer resource among many that can be brought to bear as an states, a “tool for building intuition”, and in this (...) it suc- agent encounters its world”. In the worked example of ceeds brilliantly. But it is also an attempt to show that an agent that approaches circles and avoids diamonds, dynamical approaches can get a foothold in the expla- we see direct evidence of this in the claim that a certain nation of “minimally cognitive behaviors”; that is to three-dimensional projection provides a potent analytic say, behaviors that seem, on the surface at least, good tool. For this projection happens to be one that involves contenders for more traditional forms of problem de- one environmental state variable (vertical object posi- composition and analysis. In these brief comments, I tion), one body state variable (horizontal position rela- want to focus on one important question that I think tive to the object) and one neuronal state variable remains unanswered, and that bears rather directly on (output of interneuron 9). By dispensing with talk of this enterprise of “scaling up”. representations and their contents, and restricting the The question concerns the notion of an integrated depiction of the inner realm to a depiction of inner state dynamical explanation itself. The point about such alone (section 9.3), the dynamicist makes it easy to.. (shrink)

Van Gelder seeks to distinguish between the computational and the dynamical hypotheses primarily on the basis of ontic criteria – the kind of systems cognitive agents really are. I suggest that this meets with mixed success. By shifting to epistemic criteria – what kind of explanations we require to understand cognitive agents – I suggest there is an easier and more intuitive way to distinguish between these two competing views of cognitive agents.

A consideration of underlying neural dynamics and the evolutionary process producing cognitive agents should complement the development of dynamical models of behavior. The geometrical aspects of dynamical systems theory which make it useful in the description of systems acting in an environment are less useful in understanding agents interacting with a range of environments, and may call for supplementation by evolutionary insights.

One of the most foundational and continually contested questions in the cognitive sciences is the degree to which the functional organization of the brain can be understood as modular. In its classic formulation, a module was defined as a cognitive sub-system with nine specific properties; the classic module is, among other things, domain specific, encapsulated, and implemented in dedicated neural substrates. Most of the examinations—and especially the criticisms—of the modularity thesis have focused on these properties individually, for instance by finding (...) counterexamples in which otherwise good candidates for cognitive modules are shown to lack domain specificity or encapsulation. The current paper goes beyond the usual approach by asking what some of the broad architectural implications of the modularity thesis might be, and attempting to test for these. The evidence does not favor a modular architecture for the cortex. Moreover, the evidence suggests that best way to approach the understanding of cognition is not by analyzing and modelling different functional domains in isolation from the others, but rather by looking for points of overlap in their neural implementations, and exploiting these to guide the analysis and decomposition of the functions in question. This has significant implications for the question of how to approach the design and implementation of intelligent artifacts in general, and language-using robots in particular. (shrink)

This paper is devoted to stress the importance of the contribution of Gaetano Kanizsato contemporary psychology. His theoretical ideas have in many respects been truly seminal. In particular, are emphasized his distinction between the primary and secondary process, his criticism of the concept ofPrägnanz, and his focus on self-organisation in a dynamic approach. To continue his work, the main task is to identify the rules and constraints that enable us to see the world as it appears. In the last years (...) of his scientific work, his insight was that the non-linear dynamic approach may be the best way to achieve this goal, giving a more sound sense to the intuitions of Gestalt psychologie.Unfortunately, he died before he could reap the fruits of this insight. Here are reviewed the first results that some among his direct and indirect pupils have obtained in this direction. (shrink)

. Interpreted dynamical systems are dynamical systems with an additional interpretation mapping by which propositional formulas are assigned to system states. The dynamics of such systems may be described in terms of qualitative laws for which a satisfaction clause is defined. We show that the systems Cand CL of nonmonotonic logic are adequate with respect to the corresponding description of the classes of interpreted ordered and interpreted hierarchical systems, respectively. Inhibition networks, artificial neural networks, logic programs, and evolutionary systems are (...) instances of such interpreted dynamical systems, and thus our results entail that each of them may be described correctly and, in a sense, even completely by qualitative laws that obey the rules of a nonmonotonic logic system. (shrink)