Complex Systems

Landgrebe and Smith (2022) have recently offered an important mathematical argument against the possibility of Artificial General Intelligence (AGI): human intelligence is a complex system; complex systems have some properties that cannot be modelled mathematically; hence we have no viable way to build an AI that would be able to emulate human intelligence. The issue of complexity is thus at the heart of the Landgrebe and Smith approach, and they tackle this issue by postulating a set of conditions, derived from (...) mathematics, for a system to be complex. I argue that Hayek’s “Theory of Complex Phenomena” offers an interesting alternative path to understanding what makes complex systems complex. This offers an argument complementary to that of Landgrebe and Smith, which approaches the issue of complexity from an ontological angle, and which is designed to show that AI systems are not the right kind of entity that may interact meaningfully with complex systems. (shrink)

This Special Issue of Journal of Critical Realism (JCR) is dedicated to the 2022 International Association for Critical Realism (IACR) Conference, which was hosted by the International Institute of...

In our book, Why Machines Will Never Rule the World, Jobst Landgrebe and I argue that we can engineer machines that can emulate the behaviours only of simple systems, which means: only of those systems whose behaviour we can predict mathematically. The human brain is an example of a complex system, and thus its behaviour cannot be emulated by a machine. We use this argument to debunk the claims of those who believe that large language models are poised to achieve (...) a level of intelligence that will equal or even surpass that of the human brain. The essay was published under the title "Why Machines Will Never Rule the World". (shrink)

I argue for an inferentialist account of the meaning of causal claims, which draws on the writings of Sellars and Brandom. The account is meant to be widely applicable. In this work, it is motivated and defended with reference to complex systems sciences, i.e., sciences that study the behaviour of systems with many components interacting at various levels of organisation (e.g. cells, brain, social groups). Here are three, seemingly-uncontroversial platitudes about causality. (1) Causal relations are objective, mind-independent relations and, as (...) such, analysable in objective, mind-independent terms. (2) There is a tight connection between our practice of predicting, explaining and controlling phenomena, and the use of causal notions. (3) The second platitude should be explained in terms of the first. Contrary to this widely-held stance, I suggest that we reverse the order of analysis, by taking our activities of agents as the raw material in terms of which to account for the obtaining of causal relations. To this end, I propose and defend an inferentialist account of causality. Causality is a ‘category’ that the knowing subject employs to ‘mediate’ between himself and the world. In inferentialist terms, this mediation is the result of the concept of cause figuring in a network of inferences, used in our practice of gathering evidence and using it to explain, predict and intervene. Complexity only makes the mediation more difficult, thereby rendering the meaning of causality more evident. (shrink)

On montre d’abord qu’il est nécessaire de caractériser une simulation informatique à un niveau plus fin que celui des modèles formels : celui des symboles et de leurs divers modes de référer. C’est particulièrement vrai pour celles qui intègrent des modèles et des formalismes hétérogènes. On s’interroge ensuite sur les causes ontologiques qui pourraient expliquer leur succès épistémique. Il est montré qu’elles peuvent s’expliquer commodément si l’on adopte une conception de la nature à la fois discontinuiste et finitiste. Cette dernière (...) thèse se trouve renforcer une position métaphysique naturaliste en invalidant, à sa racine, l’argument formulé par le matérialisme spéculatif à l’encontre d’une approche scientifique du monde physique procédant, comme les simulations, par représentations et opérations finitistes. (shrink)

Since the 1980s chaos has been the subject of great interest both in scientific research and in public consciousness. Chaos as played roles in books and movies such as Jurassic Park and Bellwether and has been the subject of numerous popularizations. But what is chaos—better characterized as chaotic dynamics—really? How much of an impact does it have on everyday life? This book explores these questions and more, introducing you to the basics of chaos as mathematicians and scientists study it and (...) apply it. There are a lot of buzzwords surrounding chaotic dynamics such as “butterfly effect” and “strange attractors,” and much discussion about whether chaos has shattered scientific dreams of a predictable world. This book will help you understand these buzzwords and their excitement, what limitations there are for predictability, and the wisdom scientists have learned from studying chaos. You will come away with a deeper appreciation of the intricacy and surprising order of our world. (shrink)

This book brings together contributions from leading researchers in the field of agent-based modelling and simulation. This approach has grown out of some recent and innovative ideas in the social sciences, computer sciences, life sciences, physics and game theory. It is proving helpful in understanding complexity in many domains. The opportunities it offers to explore the experimental approach to social and human behaviour is proving of theoretical and empirical value across a wide range of fields. With contributions from researchers whose (...) work has served to define this new field such as Nigel Gilbert, Robert Axtell (in economics and social science) and Jacques Ferber (in multi-agent systems), as well as practitioners who are working at the cutting edge of the new domain, this collection of essays has been assembled by two of its leading exponents: Frédéric Amblard and Denis Phan. The research, case studies and theoretical approaches discussed in this book are designed to introduce beginners and experts alike to the current state of play in this new and exciting field of social science. (shrink)

The book you hold in your hands is the outcome of the "ISCS 2013: Interdisciplinary Symposium on Complex Systems" held at the historical capital of Bohemia as a continuation of our series of symposia in the science of complex systems. Prague, one of the most beautiful European cities, has its own beautiful genius loci. Here, a great number of important discoveries were made and many important scientists spent fruitful and creative years to leave unforgettable traces. The perhaps most significant period (...) was the time of Rudolf II who was a great supporter of the art and the science and attracted a great number of prominent minds to Prague. This trend would continue. Tycho Brahe, Niels Henrik Abel, Johannes Kepler, Bernard Bolzano, August Cauchy Christian Doppler, Ernst Mach, Albert Einstein and many others followed developing fundamental mathematical and physical theories or expanding them. Thus in the beginning of the 17th century, Kepler formulated here the first two of his three laws of planetary motion on the basis of Tycho Brahe’s observations. In the 19th century, nowhere differentiable continuous functions (of a fractal character) were constructed here by Bolzano along with a treatise on infinite sets, titled “Paradoxes of Infinity” (1851). Weierstrass would later publish a similar function in 1872. In 1842, Doppler as a professor of mathematics at the Technical University of Prague here first lectured about a physical effect to bear his name later. And the epoch-making physicist Albert Einstein – while being a chaired professor of theoretical physics at the German University of Prague – arrived at the decisive steps of his later finished theory of general relativity during the years 1911–1912. In Prague, also many famous philosophers and writers accomplished their works; for instance, playwright arel ape coined the word "robot" in Prague (“robot” comes from the Czech word “robota” which means “forced labor”). (shrink)

What do a short car trip, a pandemic, the wood-wide fungal web, a challenging learning experience, a storm, transport logistics, and the language(s) we speak have in common? All of them are systems, or multiple sets of systems within systems. What happens in any set of circumstances will depend on a mix of initial conditions, complexity dynamics, and the odd wild card (e.g., a chance event). While it is possible to model and predict what might or perhaps should happen, it (...) is impossible to be certain. "It depends" thinking needs to be applied. Future-focused literature identifies complex systems thinking as an essential capability for citizenship, and this book sets out to show teachers how they might foster it-for themselves as well as for their students. There are implications for pedagogy, curriculum, and assessment. Multiple examples show what changes might look like, for students of different ages, and in different subject contexts. This is a book of several layers: It is both practical and philosophical. There is explicit discussion of parallels between complexity science and indigenous knowledge systems (specifically mātauranga Māori in the New Zealand context). The many examples are designed to appeal to general readers with an interest in the complex challenges facing contemporary societies, as well as to teachers at all levels of the education system. (shrink)

The book’s core argument is that an artificial intelligence that could equal or exceed human intelligence—sometimes called artificial general intelligence (AGI)—is for mathematical reasons impossible. It offers two specific reasons for this claim: Human intelligence is a capability of a complex dynamic system—the human brain and central nervous system. Systems of this sort cannot be modelled mathematically in a way that allows them to operate inside a computer. In supporting their claim, the authors, Jobst Landgrebe and Barry Smith, marshal evidence (...) from mathematics, physics, computer science, philosophy, linguistics, and biology, setting up their book around three central questions: What are the essential marks of human intelligence? What is it that researchers try to do when they attempt to achieve "artificial intelligence" (AI)? And why, after more than 50 years, are our most common interactions with AI, for example with our bank’s computers, still so unsatisfactory? Landgrebe and Smith show how a widespread fear about AI’s potential to bring about radical changes in the nature of human beings and in the human social order is founded on an error. There is still, as they demonstrate in a final chapter, a great deal that AI can achieve which will benefit humanity. But these benefits will be achieved without the aid of systems that are more powerful than humans, which are as impossible as AI systems that are intrinsically "evil" or able to "will" a takeover of human society. (shrink)

When we deal with complex things, like human subjects or organizations, we deal with identity – that which makes a person or an organization what it is and distinguishes him/her/it from other persons or organizations, a kind of “self”. Our identity determines how we think about and interact with others. It will be argued in this chapter that the self is constituted relationally. Moreover, when we are in the realm of the self, we are always already in the realm of (...) engaging with and mediating differences – the realm of ethics. The position which will be developed argues that approaching identity as a complex system allows us to resist thinking of identity as an easily identifiable and static entity. Identity is always being constituted within a complex and contingent world, where we have to make choices based on contingent values rather than on universal knowledge or the outcome of rational calculations. As a result, we have to keep in mind that our daily practices always already have an ethical component, and our decisions need to be continually evaluated and re-evaluated in the light of our (and others’) varying identities. (shrink)

Explores complexity theory and systems thinking to better understand how complex systems drift into failure. This book develops a vocabulary that allows us to harness complexity and find different ways of managing drift.

Is human free will compatible with the natural laws of the universe? To “compatibilists” who see free actions as emanating from the wants and reasons of human agents, free will looks perfectly plausible. However, “incompatibilists” claim to see the more ultimate sources of human action. The wants and reasons of agents are said to be caused by physical processes which are themselves mere natural results of the previous state of the world and the natural laws which govern it. This paper (...) argues that the incompatibilists make a mistake in appealing to such non-agent sources of human action. They fail to realize that free will may exist at one scale, but not at the scales where they look. When free will is considered from the correctly scaled perspective, it does seem compatible with determinism and natural laws. (shrink)

In this article, after a historical introduction, we give an epistemological point of view of the physics of complex systems. Complex systems are epistemologically interesting because of the fundamental interaction experiment/observer and physicists in their everyday life can experience the paradoxes given by this interaction. Here we describe some of these paradoxes, we make a parallel with quantum mechanics and give a possible philosophical solution, based on notorious physicists/philosopher from the past, transposing and reinterpreting their ideas to modern times. In (...) particular, we analyse the interaction with a complex system such as the living cell, and therefore we also analyse some biophysical implications of complexity. (shrink)

Community detection is a major issue in network analysis. This paper combines a socio-historical approach with an experimental reconstruction of programs to investigate the early automation of clique detection algorithms, which remains one of the unsolved NP-complete problems today. The research led by the archaeologist Jean-Claude Gardin from the 1950s on non-numerical information and graph analysis is retraced to demonstrate the early contributions of social sciences and humanities. The limited recognition and reception of Gardin's innovative computer application to the humanities (...) are addressed through two factors, in addition to the effects of historiography and bibliographies on the recording, discoverability, and reuse of scientific productions: (1) funding policies, evidenced by the transfer of research effort on graph applications from temporary interdisciplinary spaces to disciplinary organizations related to the then-emerging field of computer science; and (2) the erratic careers of algorithms, in which efficiency, flaws, corrections, and authors’ status, were determining factors. (shrink)

Typically, fair machine learning research focuses on a single decision maker and assumes that the underlying population is stationary. However, many of the critical domains motivating this work are characterized by competitive marketplaces with many decision makers. Realistically, we might expect only a subset of them to adopt any non-compulsory fairness-conscious policy, a situation that political philosophers call partial compliance. This possibility raises important questions: how does partial compliance and the consequent strategic behavior of decision subjects affect the allocation outcomes? (...) If k% of employers were to voluntarily adopt a fairness-promoting intervention, should we expect k% progress (in aggregate) towards the benefits of universal adoption, or will the dynamics of partial compliance wash out the hoped-for benefits? How might adopting a global (versus local) perspective impact the conclusions of an auditor? In this paper, we propose a simple model of an employment market, leveraging simulation as a tool to explore the impact of both interaction effects and incentive effects on outcomes and auditing metrics. Our key findings are that at equilibrium: (1) partial compliance by k% of employers can result in far less than proportional (k%) progress towards the full compliance outcomes; (2) the gap is more severe when fair employers match global (vs local) statistics; (3) choices of local vs global statistics can paint dramatically different pictures of the performance vis-a-vis fairness desiderata of compliant versus non-compliant employers; (4) partial compliance based on local parity measures can induce extreme segregation. Finally, we discuss implications for auditors and insights concerning the design of regulatory frameworks. (shrink)

The hard problem of consciousness has been a perennially vexing issue for the study of consciousness, particularly in giving a scientific and naturalized account of phenomenal experience. At the heart of the hard problem is an often-overlooked argument, which is at the core of the hard problem, and that is the structure and dynamics (S&D) argument. In this essay, I will argue that we have good reason to suspect that the S&D argument given by David Chalmers rests on a limited (...) conception of S&D properties, what in this essay I’m calling extrinsic structure and dynamics. I argue that if we take recent insights from the complexity sciences and from recent developments in Integrated Information Theory (IIT) of Consciousness, that we get a more nuanced picture of S&D, specifically, a class of properties I’m calling intrinsic structure and dynamics. This I think opens the door to a broader class of properties with which we might naturally and scientifically explain phenomenal experience, as well as the relationship between syntactic, semantic, and intrinsic notions of information. I argue that Chalmers’ characterization of structure and dynamics in his S&D argument paints them with too broad a brush and fails to account for important nuances, especially when considering accounting for a system’s intrinsic properties. Ultimately, my hope is to vindicate a certain species of explanation from the S&D argument, and by extension dissolve the hard problem of consciousness at its core, by showing that not all structure and dynamics are equal. (shrink)

The history of economic thought witnessed several prominent economists who took seriously models and concepts in physics for the elucidation and prediction of economic phenomena. Econophysics is an emerging discipline at the intersection of heterodox economics and the physics of complex systems, with practitioners typically engaged in two overlapping but distinct methodological programs. The first is to export mathematical methods used in physics for the purposes of studying economic phenomena. The second is to export mechanisms in physics into economics. A (...) conclusion is drawn that physics transfer is often justified at the level of mathematical transfer but unjustified at the level of mechanistic transfer. (shrink)

This paper discusses the epistemic status of biology from the standpoint of the systemic approach to living systems based on the notion of biological autonomy. This approach aims to provide an understanding of the distinctive character of biological systems and this paper analyses its theoretical and epistemological dimensions. The paper argues that, considered from this perspective, biological systems are examples of emergent phenomena, that the biological domain exhibits special features with respect to other domains, and that biology as a discipline (...) employs some core concepts, such as teleology, function, regulation among others, that are irreducible to those employed in physics and chemistry. It addresses the claim made by Jacques Monod that biology as a science is marginal. It argues that biology is general insofar as it constitutes a paradigmatic example of complexity science, both in terms of how it defines the theoretical object of study and of the epistemology and heuristics employed. As such, biology may provide lessons that can be applied more widely to develop an epistemology of complex systems. (shrink)

This article aims to describe the last 10 years of the collaborative scientific endeavors on polarization in particular and collective problem-solving in general by our multidisciplinary research team. We describe the team’s disciplinary composition—social psychology, political science, social philosophy/epistemology, and complex systems science— highlighting the shared and unique skill sets of our group members and how each discipline contributes to studying polarization and collective problem-solving. With an eye to the literature on team dynamics, we describe team logistics and processes that (...) we believe make our multidisciplinary team persistent and productive. We emphasize challenges and difficulties caused by disciplinary differences in terms of terminology, units/levels of analysis, methodology, and theoretical assumptions. We then explain how work disambiguating the concepts of polarization and developing an integrative theoretical and methodological framework with complex systems perspectives has helped us overcome these challenges. We summarize the major findings that our research has produced over the past decade, and describe our current research and future directions. Last, we discuss lessons we have learned, including difficulties in a “three models” project and how we addressed them, with suggestions for effective multidisciplinary team research. (shrink)

Eshel Ben-Jacob’s manuscript entitled ‘Bacterial wisdom, Gödel’s theorem and creative genomic webs’ summarizes decades of work demonstrating adaptive mutagenesis in bacterial genomes. Bacterial genomes, each an essential part of a Kantian whole that is a single bacterium, are thus not independent of the environment as sensed; and a single bacterium is therefore a semiotic entity. Ben-Jacob suggests this but errs in 1) assigning autonomy to the genome, and 2) analogizing through computation without making clear whether he is doing so for (...) illustrative purposes or making committed ontological propositions. We reinterpret adaptive mutagenesis and related phenomena in ways both metaphysically rigorous and revealing. We conclude that bacteria are much farther removed from the ‘self-organizing’ world of inanimate process than from the Peircian world of signs; and a critical reappraisal of existing knowledge can enhance our understanding of selfhood, semiosis, and the roots of subjective experience. (shrink)

We live in a world full of mysteries. How do our brains create consciousness? Which animals are conscious, and which are not? How can we have free-will in a deterministic universe? What are the fundamental Laws of Nature? What caused the Big Bang? How can we make sense of Quantum Mechanics? Why is the universe so finely-tuned for Life? And how did Life begin? Despite investigating such mysteries for decades or more, scientists and philosophers are no closer to finding clear (...) and convincing answers that everyone can agree upon. The big question is: why do such mysteries exist, and can they ever be solved? -/- In Life, the Universe and Consciousness, A. T. Bollands introduces us to twelve so-called intractable problems, demonstrating how each one arises from a conflict between beliefs. And yet, beliefs that are in conflict cannot all be true, which means that one or more of them must be false. To solve each problem, therefore, all we need to do is work out which of our beliefs are false and correct them. This may sound easy, but these beliefs include the most fundamental assumptions of modern science. If that wasn’t enough, it turns out that these twelve intractable problems are related, such that we cannot solve any one of them satisfactorily until we have solved all twelve within the same coherent worldview. -/- Examining each of these problems in turn, we finally arrive at our twelfth intractable problem: What is Life? A. T. Bollands proposes a new definition for Life, and with it a new way of understanding the physical world – a scientific worldview he calls Universal Life. Armed with this new worldview, he proceeds to solve all twelve intractable problems one by one, thereby developing the Theory of Universal Life and the solution to the “Big Problem of 20th Century Science”. By successfully solving each problem, he shows that Universal Life offers us a simpler, more natural, more coherent and hence more credible explanation for ourselves and the world we live in than our current scientific worldview ever can. (shrink)

We have recently started to understand that fundamental aspects of complex systems such as emergence, the measurement problem, inherent uncertainty, complex causality in connection with unpredictable determinism, time­irreversibility and non­locality all highlight the observer's participatory role in determining their workings. In addition, the principle of 'limited universality' in complex systems, which prompts us to search for the appropriate 'level of description in which unification and universality can be expected', looks like a version of Bohr's 'complementarity principle'. It is more or (...) less certain that the different levels of description possible of a complex whole ­­ actually partial objectifications ­­ are projected on to and even redefine its constituent parts. Thus it is interesting that these fundamental complexity issues don't just bear a formal resemblance to, but reveal a profound connection with, quantum mechanics. Indeed, they point to a common origin on a deeper level of description. (shrink)

In a previous paper we outlined a series of historical touchpoints between classical aether theories and modern theoretical physics which showed a shared conceptual lineage for the modern tools and methods of the most common interpretations and fluid based “Hydrodynamic” treatments of an electromagnetic medium. It was proposed that, though the weight of modern experimentation leaves an extremely narrow and convoluted window for even a reconceptualization of a medium, all of modern physics recognizes a plethora of behaviors and attributes for (...) free space and these physics are interchangeable with modern methods for treating superfluid-like continuums. Thus the mathematical equivalence of the methods do not comprise alternative physics but an alternative interpretation of the same physics. Though many individual components describing a “neo-aether” or “quintessence” are available, an overarching structural outline of how these tools can work together to provide an alternative working overview of modern physics has remained undefined. This paper will propose a set of introductory concepts in the first outline of a toy model which will later connect the alternative tools and conceptualizations with their modern counterparts. This introductory paper provides the simpler “100-miles out” overview of the whole of physics from this perspective, in an easily comprehensible, familiar and intuitive, informal dialog fashion. While this paper grants the largest and loosest introductory overview, subsequent papers in this series will address the finite connections between modern physics and this hydrodynamic view. (shrink)

In this paper, I defend an epistemological pluralism that moves away from universal and absolute rationality, as well as from a radical and arbitrary relativism, where any criterion is valid for decision making. Such epistemological pluralism maintains that subjects know the world in which they live according to different conceptual schemes. We posit a notion of truth linked to the justification process and practical effectiveness. Then we present the importance of traditional knowledge in the socio-ecological field and relative to complex (...) systems. Finally, we explain the relevance of epistemic equity between traditional and scientific knowledges in order to anticipate consequences and to make decisions less uncertain. (shrink)

The continued failure of our civilisation to mobilise an adequate response to the crisis of climate change is traced to a pathological condition of culture analogous to addiction in the case of an individual. The exponential increase in the use of fossil fuel energy has both fuelled, and been driven by, an increasingly mechanistic and materialistic world-outlook that is inimical to acceptance of the measures needed to prevent catastrophic anthropogenic climate change. A holistic view of nature, drawn from such disciplines (...) as chaos theory, complexity theory and Gaia theory, and allied to a spiritual outlook grounded in the Buddhist view of interdependence and kindred paradigms, is emerging as a response to the crisis that could form the basis of a rapid 'state-shift' of the human social / economic / cultural system, comparable to cases of spontaneous remission from cancer that is unresponsive to conventional treatment regimes. (shrink)

The goal of creating Artificial General Intelligence (AGI) – or in other words of creating Turing machines (modern computers) that can behave in a way that mimics human intelligence – has occupied AI researchers ever since the idea of AI was first proposed. One common theme in these discussions is the thesis that the ability of a machine to conduct convincing dialogues with human beings can serve as at least a sufficient criterion of AGI. We argue that this very ability (...) should be accepted also as a necessary condition of AGI, and we provide a description of the nature of human dialogue in particular and of human language in general against this background. We then argue that it is for mathematical reasons impossible to program a machine in such a way that it could master human dialogue behaviour in its full generality. This is (1) because there are no traditional explicitly designed mathematical models that could be used as a starting point for creating such programs; and (2) because even the sorts of automated models generated by using machine learning, which have been used successfully in areas such as machine translation, cannot be extended to cope with human dialogue. If this is so, then we can conclude that a Turing machine also cannot possess AGI, because it fails to fulfil a necessary condition thereof. At the same time, however, we acknowledge the potential of Turing machines to master dialogue behaviour in highly restricted contexts, where what is called “narrow” AI can still be of considerable utility. (shrink)

Among the very architects of the recent re-emergence of emergentism in the physical sciences, Robert B. Laughlin certainly occupies a prominent place. Through a series of works beginning as early as his Nobel lecture in 1998, a lecture given after having been awarded, together with Störmer and Tsui, the Nobel prize in physics for its contribution in the elucidation of the fractional quantum Hall effect, Laughlin openly and relentlessly advocated a strongly anti-reductionistic view of physics – and, more particularly, of (...) the interface between condensed matter and particles physics – which culminated in what can be considered his emergentist manifesto: A Different Universe. Reinventing Physics from the Bottom Down (2005). In spite of this prominent role in the vindication of emergentism, rare are the philosophers, among whom even those sympathetic to the idea of emergence, who have paid serious attention to Laughlin’s insights. The subtleties of his view – it is true, often concealed in many technicalities – have accordingly, and somewhat unfortunately, mainly passed unnoticed. (shrink)

We critically analyse the point of view for which laws of nature are just a mean to compress data. Discussing some basic notions of dynamical systems and information theory, we show that the idea that the analysis of large amount of data by means of an algorithm of compression is equivalent to the knowledge one can have from scientific laws, is rather naive. In particular we discuss the subtle conceptual topic of the initial conditions of phenomena which are generally incompressible. (...) Starting from this point, we argue that laws of nature represent more than a pure compression of data, and that the availability of large amount of data, in general, is not particularly useful to understand the behaviour of complex phenomena. (shrink)

This essay furthers debate about the burgeoning science of Probabilistic Event Attribution (PEA) and its relevance to imminent climate policy decisions. It critically examines Allen Thompson and Friederike Otto’s recent arguments concerning the implications of PEA studies for how the United Nations Framework Convention on Climate Change (UNFCCC) policy framework should be revised during the 2016 ‘review and decision.’ I show that their contention that PEA studies cannot usefully inform decision-making about adaptation policies and strategies is misguided and argue that (...) the current UNFCCC treaty, the “Paris Agreement,” supersedes their proposed revision. (shrink)

Various processes are often classified as both deterministic and random or chaotic. The main difficulty in analysing the randomness of such processes is the apparent tension between the notions of randomness and determinism: what type of randomness could exist in a deterministic process? Ergodic theory seems to offer a particularly promising theoretical tool for tackling this problem by positing a hierarchy, the so-called ‘ergodic hierarchy’, which is commonly assumed to provide a hierarchy of increasing degrees of randomness. However, that notion (...) of randomness requires clarification. The mathematical definition of EH does not make explicit appeal to randomness; nor does the usual way of presenting EH involve a specification of the notion of randomness that is supposed to underlie the hierarchy. In this paper we argue that EH is best understood as a hierarchy of random behaviour if randomness is explicated in terms of unpredictability. We then show that, contrary to common wisdom, EH is useful in characterising the behaviour of Hamiltonian dynamical systems. (shrink)

We consider an integrable, nonlocal and nonlinear, Schrödinger equation as a model for building space–time patchings in inhomogeneous loop quantum cosmology. We briefly review exact solutions of the NNSE, specially those obtained through “geometric equivalence” methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of Shannon's (...) communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)