Our universe is both chaotic and (most likely) infinite in space and time. But it is within this setting that we must make moral decisions. This presents problems. The first: due to our universe's chaotic nature, our actions often have long-lasting, unpredictable effects; and this means we typically cannot say which of two actions will turn out best in the long run. The second problem: due to the universe's infinite dimensions, and infinite population therein, we cannot compare outcomes by simply (...) adding up their total moral values - those totals will typically be infinite or undefined. Each of these problems poses a threat to aggregative moral theories. But, for each, we have solutions: a proposal from Greaves let us overcome the problem of chaos, and proposals from the infinite aggregation literature let us overcome the problem of infinite value. But a further problem emerges. If our universe is both chaotic and infinite, those solutions no longer work - outcomes that are infinite and differ by chaotic effects are incomparable, even by those proposals. In this paper, I show that we can overcome this further problem. But, to do so, we must accept some peculiar implications about how aggregation works. (shrink)
Common wisdom holds that communication is impossible when messages are costless and communicators have totally opposed interests. This article demonstrates that such wisdom is false. Non-convergent dynamics can sustain partial information transfer even in a zero-sum signalling game. In particular, I investigate a signalling game in which messages are free, the state-act payoffs resemble rock–paper–scissors, and senders and receivers adjust their strategies according to the replicator dynamic. This system exhibits Hamiltonian chaos and trajectories do not converge to equilibria. This (...) persistent out-of-equilibrium behaviour results in messages that do not perfectly reveal the sender's private information, but do transfer information as quantified by the Kullback–Leibler divergence. This finding shows that adaptive dynamics can enable information transmission even though messages at equilibria are meaningless. This suggests a new explanation for the evolution or spontaneous emergence of meaning: non-convergent adaptive dynamics. (shrink)
Chaotic dynamics has been hailed as the third great scientific revolution in physics this century, comparable to relativity and quantum mechanics. In this book, Peter Smith takes a cool, critical look at such claims. He cuts through the hype and rhetoric by explaining some of the basic mathematical ideas in a clear and accessible way, and by carefully discussing the methodological issues which arise. In particular, he explores the new kinds of explanation of empirical phenomena which modern dynamics can deliver. (...) Explaining Chaos will be compulsory reading for philosophers of science and for anyone who has wondered about the conceptual foundations of chaos theory. (shrink)
A vast amount of ink has been spilled in both the physics and the philosophy literature on the measurement problem in quantum mechanics. Important as it is, this problem is but one aspect of the more general issue of how, if at all, classical properties can emerge from the quantum descriptions of physical systems. In this paper we will study another aspect of the more general issue-the emergence of classical chaos-which has been receiving increasing attention from physicists but which (...) has largely been neglected by philosophers of science. (shrink)
A dynamical system is called chaotic if small changes to its initial conditions can create large changes in its behavior. By analogy, we call a dynamical system structurally chaotic if small changes to the equations describing the evolution of the system produce large changes in its behavior. Although there are many definitions of “chaos,” there are few mathematically precise candidate definitions of “structural chaos.” I propose a definition, and I explain two new theorems that show that a set (...) of models is structurally chaotic if it contains a chaotic function. I conclude by discussing the relationship between structural chaos and structural stability. (shrink)
Explaining Chaos provides both a succinct and accurate introduction to the physics and mathematics of chaotic dynamical systems along with a number of pertinent philosophical commentaries on the scientific results. The book provides the clearest and most sensible treatment of chaos theory from a philosophical perspective available in the literature.
The big news about chaos is supposed to be that the smallest of changes in a system can result in very large differences in that system's behavior. The so-called butterfly effect has become one of the most popular images of chaos. The idea is that the flapping of a butterfly's wings in Argentina could cause a tornado in Texas three weeks later. By contrast, in an identical copy of the world sans the Argentinian butterfly, no such storm would (...) have arisen in Texas. The mathematical version of this property is known as sensitive dependence. However, it turns out that sensitive dependence is somewhat old news, so some of the implications flowing from it are perhaps not such “big news” after all. Still, chaos studies have highlighted these implications in fresh ways and led to thinking about other implications as well. -/- In addition to exhibiting sensitive dependence, chaotic systems possess two other properties: they are deterministic and nonlinear (Smith 2007). This entry discusses systems exhibiting these three properties and what their philosophical implications might be for theories and theoretical understanding, confirmation, explanation, realism, determinism, free will and consciousness, and human and divine action. (shrink)
Instead of treating art as a unique creation that requires reason and refined taste to appreciate, Elizabeth Grosz argues that art-especially architecture, music, and painting-is born from the disruptive forces of sexual selection.
Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, (...) the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs. (shrink)
This paper considers definitions of classical dynamical chaos that focus primarily on notions of predictability and computability, sometimes called algorithmic complexity definitions of chaos. I argue that accounts of this type are seriously flawed. They focus on a likely consequence of chaos, namely, randomness in behavior which gets characterized in terms of the unpredictability or uncomputability of final given initial states. In doing so, however, they can overlook the definitive feature of dynamical chaos--the fact that the (...) underlying motion generating the behavior exhibits extreme trajectory instability. I formulate a simple criterion of adequacy for any definition of chaos and show how such accounts fail to satisfy it. (shrink)
In recent years, the research of chaos theory has developed from simple cognition and analysis to practical engineering application. In particular, hyperchaotic systems with more complex and changeable chaotic characteristics are more sensitive and unpredictable, so they are widely used in more fields. In this paper, two important engineering applications based on hyperchaos pseudorandom number generator and image encryption are studied. Firstly, the coupling 6D memristive hyperchaotic system and a 2D SF-SIMM discrete hyperchaotic mapping are used as the double (...) entropy source structure. The double entropy source structure can realize a new PRNG that meets the security requirements, which can pass the NIST statistical test when the XOR postprocessing method is used. Secondly, based on the double entropy source structure, a new image encryption algorithm is proposed. The algorithm uses the diffusion-scrambling-diffusion encryption scheme to realize the conversion from the original plaintext image to the ciphertext image. Finally, we analyze the security of the proposed PRNG and image encryption mechanism, respectively. The results show that the proposed PRNG has good statistical output characteristics and the proposed image encryption scheme has high security, so they can be effectively applied in the field of information security and encryption system. (shrink)
A recent noninterventionist account of divine agency has been proposed that marries the probabilistic nature of quantum mechanics to the instability of chaos theory. On this account, God is able to bring about observable effects in the macroscopic world by determining the outcome quantum events. When this determination occurs in the presence of chaos, the ability to influence large systems is multiplied. This paper argues that although the proposal is highly intuitive, current research in dynamics shows that it (...) is far less plausible than previously thought. Chaos coupled to quantum mechanics proves to be a shaky foundation for models of divine agency. (shrink)
Two examples demonstrate the possibility of extremely complicated non-convergent behavior in evolutionary game dynamics. For the Taylor-Jonker flow, the stable orbits for three strategies were investigated by Zeeman. Chaos does not occur with three strategies. This papers presents numerical evidence that chaotic dynamics on a strange attractor does occur with four strategies. Thus phenomenon is closely related to known examples of complicated behavior in Lotka-Volterra ecological models.
In his recent book, Explaining Chaos, Peter Smith presents a new problem in the foundations of chaos theory. Specifically, he argues that the standard ways of justifying idealizations in mathematical models fail when it comes to the infinite intricacy found in strange attractors. I argue that Smith's analysis undermines much of the explanatory power of chaos theory. A better approach is developed by drawing analogies from the models found in continuum mechanics.
Some irrational numbers are "random" in a sense which implies that no algorithm can compute their decimal expansions to an arbitrarily high degree of accuracy. This feature of (most) irrational numbers has been claimed to be at the heart of the deterministic, but chaotic, behavior exhibited by many nonlinear dynamical systems. In this paper, a number of now classical chaotic systems are shown to remain chaotic when their domains are restricted to the computable real numbers, providing counterexamples to the above (...) claim. More fundamentally, the randomness view of chaos is shown to be based upon a confusion between a chaotic function on a phase space and its numerical representation in Rn. (shrink)
ABSTRACT This introduction attempts to draw together the various threads which comprise this special issue and place them in the context of recent disruptions to the political order occasioned by the rise of populist politics, the resurgence of widespread racial tensions in a number of polities and the emergence of a global pandemic. Central to the challenges thrown up by these ‘events’ and a motive force, has been the incremental advancement of libertarianism with its capacity to disorient and displace a (...) more socially oriented liberalism. Together with a range of changes to our technological capacities these moves offer significant challenges to the advancement of a moral education that is sufficiently robust. The discussion moves from the development of historico-political readings of our present situation and challenge, through some important epistemic questions about truth-telling, integrity and sociality, and on to practical questions about the relationship between technology and personal moral capacities. This last challenge is explored with respect to the need to maintain the very analogue capacity of judgement in the face of a digitally mediated world. Moreover, this introduction also explores the structural and political challenges posed by narrow specialisation in the field of moral education, the evolution of bio-technology/materials and consciousness. (shrink)
This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators to search for semiclassical signatures of chaos. Here I am concerned with the status of semiclassical mechanics as a distinct third theory of the (...) asymptotic domain between classical and quantum mechanics. I discuss in some detail the meaning of such crucial locutions as the " classical counterpart to a quantum system " and a quantum system ' s " underlying classical motion ". A proper elucidation of these concepts requires a semiclassical association between phase space surfaces and wave - functions. This significance of this association is discussed in some detail. (shrink)
This book presents a broad-ranging and fascinating examination of attitudes: how we form them; how we organize them towards others; and whether they are inherently human or could also be developed by computers. Professor Eiser suggests there are fundamental objections to the idea of a computer having a sense of self or a set of attitutdes.
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)
Our aim is to discover whether the notion of algorithmic orbit-complexity can serve to define “chaos” in a dynamical system. We begin with a mostly expository discussion of algorithmic complexity and certain results of Brudno, Pesin, and Ruelle (BRP theorems) which relate the degree of exponential instability of a dynamical system to the average algorithmic complexity of its orbits. When one speaks of predicting the behavior of a dynamical system, one usually has in mind one or more variables in (...) the phase space that are of particular interest. To say that the system is unpredictable is, roughly, to say that one cannot feasibly determine future values of these variables from an approximation of the initial conditions of the system. We introduce the notions of restrictedexponential instability and conditionalorbit-complexity, and announce a new and rather general result, similar in spirit to the BRP theorems, establishing average conditional orbit-complexity as a lower bound for the degree of restricted exponential instability in a dynamical system. The BRP theorems require the phase space to be compact and metrizable. We construct a noncompact kicked rotor dynamical system of physical interest, and show that the relationship between orbit-complexity and exponential instability fails to hold for this system. We conclude that orbit-complexity cannot serve as a general definition of “chaos.”. (shrink)
From the beginning of chaos research until today, the unpredictability of chaos has been a central theme. It is widely believed and claimed by philosophers, mathematicians and physicists alike that chaos has a new implication for unpredictability, meaning that chaotic systems are unpredictable in a way that other deterministic systems are not. Hence, one might expect that the question ‘What are the new implications of chaos for unpredictability?’ has already been answered in a satisfactory way. However, (...) this is not the case. I will critically evaluate the existing answers and argue that they do not fit the bill. Then I will approach this question by showing that chaos can be defined via mixing, which has never before been explicitly argued for. Based on this insight, I will propose that the sought-after new implication of chaos for unpredictability is the following: for predicting any event, all sufficiently past events are approximately probabilistically irrelevant. (shrink)
Hempel's proposal of covering laws which explain historical events has a certain plausibility, but can never be actually realized due to the chaotic nature of history. The natural laws that would govern both individual lives and greater history would be nonlinear; consequently, in the terminology of chaos theory, the final states of both are extremely sensitive to initial conditions. Initial conditions would need to be exactly known in order to account correctly for historic phenomena, especially for causes and effects (...) which span long, historically interesting, lengths of time. Covering-law history therefore fails because the details of initial conditions are generally unknowable. Since this constraint diminishes as the time over which covering laws operate is divided into smaller consecutive intervals of scenes, covering-law explanations resolve into those having a narrative temporal structure. (shrink)
This paper explores the possibility that chaos theory might be helpful in explaining free will. I will argue that chaos has little to offer if we construe its role as to resolve the apparent conflict between determinism and freedom. However, I contend that the fundamental problem of freedom is to find a way to preserve intuitions about rational action in a physical brain. New work on dynamic computation provides a framework for viewing free choice as a process that (...) is sensitive and unpredictable, while at the same time organized and intelligent. I conclude that this vision of a chaotic brain may make a modest contribution to an intuitively acceptable physicalist account of free will. (shrink)
This article looks at the strong links between Deleuze's molecular ontology and the fields of complexity and emergence, and argues that Deleuze's work implies a ‘philosophy of technology’ that is both open and dynamic. Following Simondon and von Uexküll, Deleuze suggests that technical objects are ontologically unstable, and are produced by processes of individuation and self-organization in complex relations with their environment. For Deleuze design is not imposed from without, but emerges from within matter. The fundamental departure for Deleuze, on (...) the basis of such an ontology, is to conceive of modes of relating to the evolution of technology. In this way Deleuze, along with Guattari, provides the basis for an ethics and a politics of becoming and emergent control that constitutes an alternative to the hubris of contemporary reductionist accounts of new areas such as nanotechnology. (shrink)
Agent-centered constraints on harming hold that some harmful upshots of our conduct cannot be justified by its generating equal or somewhat greater benefits. In this paper I argue that all plausible theories of agent-centered constraints on harming are undermined by the likelihood that our actions will have butterfly effects, or cause cascades of changes that make the world dramatically different than it would have been. Theories that impose constraints against only intended harming or proximally caused harm have unacceptable implications for (...) choices between more and less harmful ways of securing greater goods. This leaves as plausible only theories that impose constraints against causing some unintended distal harms. But, I argue, given the distal harms our actions are likely to cause through their butterfly effects, these theories entail that any way of sustaining our lives is overwhelmingly likely to involve unjustified killing, and that we are therefore morally required either to allow ourselves to waste away or kill ourselves. (shrink)
In this article we discuss two divergent accounts of non-human animals as analog models of human biomedical phenomena. Using a classical account of analogical reasoning, toxicologists and teratologists claim that if the model and subject modeled are substantially similar, then test results in non-human animals are likely applicable to humans . However, the same toxicologists report that different species often react very differently to the same chemical stimuli . The best way to understand their findings is to abandon the classical (...) view of analogical - i.e., linear - reasoning, and replace it with a version informed by chaos theory. We briefly outline the current understanding of chaos, and trace its implications for toxicology and teratology. (shrink)
This paper discusses the explanatory significance of the equilibrium concept in the context of an example of extremely complicated dynamical behavior. In particular, numerical evidence is presented for the existence of chaotic dynamics on a "strange attractor" in the evolutionary game dynamics introduced by Taylor and Jonker [also known as the "replicator dynamics"]. This phenomenon is present already in four strategy evolutionary games where the dynamics takes place in a simplex in three dimensional space-the lowest number of dimensions in which (...) such a strange attractor is possible. From a dynamical point of view, it is the attractor-rather than the equilibrium-that is of prime interest. (shrink)
Laplacean determinism remains a popular theory among philosophers and scientists alike, in spite of the fact that the Copenhagen Interpretation of quantum mechanics, with which it is inconsistent, has been around for more than fifty years. There are a number of reasons for its continuing popularity. One, recently articulated by Honderich, is that there are too many possible interpretations of quantum mechanics, and the subject is too controversial even among physicists to be an adequate basis for overturning determinism. Nevertheless, quantum (...) mechanics is an enormously successful theory, considering the quantity and variety of its predictions which have been verified under conditions never dreamt of by its originators; and the Copenhagen Interpretation is the only widely accepted interpretation of it. Although a hidden variable theory consistent with the results of quantum mechanics is not impossible, one of its major advocates admits that it is highly speculative, and far from adequately developed. Yet such a theory would be needed to reconcile Laplacean determinism with quantum mechanics; most of the controversies alluded to by Honderich are irrelevant. (shrink)