The book describes the features that vibrations and waves of all sorts have in commonand includes examples of mechanical, acoustical, and optical manifestations of these phenomena thatunite various parts of physics.

The prevalence of dementia is increasing with the ever-growing population of older adults. Non-pharmacological, music-based interventions, including sensory stimulation, were reported by the Lancet Commission in 2020 to be the first-choice approach for managing the behavioural and psychological symptoms of dementia. Low frequency sinusoidal vibration interventions, related to music interventions through their core characteristics, may offer relief for these symptoms. Despite increasing attention on the effectiveness of auditory music interventions and music therapy for managing dementia, this has not included (...) low frequency vibration. This scoping review, following the JBI methodology guidelines, was conducted to investigate participants’ responses to both sound and mechanical vibration, the characteristics of the delivered interventions, methodological challenges, and the specifics of the research experiments reported. An extensive search was conducted in BMC, CINAHL, Cochrane Central Register of Controlled Trials, EMBASE, ERIC, MEDLINE, Pedro, ProQuest Central, PsycINFO, Scopus, and Web of Science. Current Controlled Trials, Clinical Trials, and Google Scholar were also searched as well as a hand search in relevant journals. Studies on adults with all types of dementia, investigating tactile low frequency sound or mechanical vibration in any context were considered. Data from eight full-length studies were extracted using the data extraction table developed by the authors and were included in the analysis and critical appraisal. Issues in quality related to, for example, control groups and blinding. Few studies addressed participants’ subjective responses to the interventions. Reporting on the intervention characteristics was unclear. It appeared more frequent sessions led to better outcomes and home-based interventions potentially addressing the issue of access and feasibility. Future research should include neuroimaging to measure and confirm the hypothesised mechanism of cerebral coherence. Standardised reporting of intervention characteristics is also needed to ensure replicability of the experiments. Higher quality research is needed to investigate the impact and effect of low frequency vibration for the symptoms of dementia and compare outcomes in meta-syntheses. (shrink)

I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive—just as, following Einstein’s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right.

The contribution describes some aspects related to the representation of special curves; recalling mechanisms created specifically for the design of these curves, which have particular characteristics. Through the construction of a simple apparatus, consisting of two pendulums—which oscillate at the same time- it is possible to graphically reproduce Lissajous’ experiments on the commuting vibrations of the diapasons. This equipment was first built by Samuel Charles Tisley (London 1829-Unknown), under the name of harmonographer. The contribution aslo illustrates the essential characteristics of (...) the harmonograph—born as a means of analysing vibrations—but which, by its principle belongs to mechanics, for its applications to acoustic science and geometry for the ability to draw “harmonious” curves. (shrink)

Here, I outline the idea of a unified hypothesis of sensory perception, developed from the theoretical vibrational mechanism of olfaction, which can be applied across all sensory modalities. I propose that all sensory perception is based upon the detection of mechanical forces at a cellular level, and the subsequent mechanotransduction of the signal via the nervous system. Thus, I argue that the sensory modalities found in the animal kingdom may all be viewed as being mechanoreceptory, rather than being discrete (...) neurophysiological systems which evolved independently of each other. I go on to argue that this idea could potentially explain language evolution, with birdsong being an example of a more simple form of non-Saussurean language that employs ‘frequency-mimicking’ to produce a vocal signal which describes acoustic, chemical and electromagnetic vibrational frequencies detected within in the environment. I also give examples of how this hypothesis could potentially explain phenomena such as vocal mimicry in animals, as well as the human perception of musicality and the occurrence of synaesthesia; a condition found in humans, where the stimulation of one sensory modality results in the stimulation of another. For example, auditory stimuli are detected and are heard as an acoustic signal, as well as being perceived as colour by the visual system. (shrink)

Rotating machinery produces vibrations depending upon the design of the rotor systems as well as any faults or uncertainties in the machine that can increase the vibrations of such systems. This study illustrates the effectiveness of using surrogate modeling based on kriging in order to predict the vibrational behavior of a complex flexible rotor in the presence of uncertainties. The basic idea of kriging is to predict unknown values of a function by using a small size set of known data. (...) The kriging estimation is based on a weighted average of the known values of the function in the neighborhood of the point for which the value of the function has to be calculated. The crucial dependence of a kriging predictor versus the correlation functions and different orders will be illustrated. This paper also shows that reducing the number of samples required to have predictive models can be achieved by performing an initial understanding of the mechanical system of interest and by considering certain characteristics directly deriving from the physics of the problem studied. (shrink)

The vestibular system is critical for human locomotion. Any deteriorated vestibular system leads to gait instability. In the past decades, these alternations in gait patterns have been majorly measured by the spatial-temporal gait parameters and respective variabilities. However, measuring gait characteristics cannot capture the full aspect of motor controls. Thus, to further understand the effects of deteriorated vestibular system on gait performance, additional measurement needs to be taken into consideration. This study proposed using the margin of stability to identify the (...) patterns of dynamic control under different types of mastoid vibrations in walking. This study hypothesized that using the MOS method could facilitate the understanding of another aspect of motor control induced by different types of mastoid vibrations, and applying the mastoid vibrations could induce the asymmetric MOS. Twenty healthy young adults were recruited. Two electromechanical vibrotactile transducers were placed on the bilateral mastoid process to apply different types of vestibular vibrations. A motion capture system with eight cameras was used to measure the MOSap, MOSml, and respective variabilities. The results were in line with the hypotheses that both bilateral and unilateral mastoid vibrations significantly increased MOSap, MOSml, and respective variabilities p = 0.001, p < 0.001; p = 0.001, p < 0.01 when compared to the no vibration condition. Also, significantly larger MOSml, MOSml variability, MOSap, and MOSap variability were observed under the unilateral vibration condition than that observed under the bilateral vibration condition. The above-mentioned result found that different types of mastoid vibrations affected the MOS differently, suggesting different patterns of control mechanisms under different sensory-conflicted situations. Besides, a significant difference between the dominant and non-dominant legs was observed in MOSml. Moreover, applying the unilateral mastoid vibrations induced a greater symmetric index of MOSml, suggesting that more active control in balance was needed in the medial-lateral than in the anterior-posterior direction. (shrink)

The present book takes the discovery that quantum-like behaviour is not solely reserved to atomic particles one step further. If electrons are modelled as vibrating droplets instead of the usually assumed point objects, and if the classical laws of nature are applied, then exactly the same behaviour as in quantum theory is found, quantitatively correct! The world of atoms is strange and quantum mechanics, the theory of this world, is almost magic. Or is it? Tiny droplets of oil bouncing round (...) on a fluid surface can also mimic the world of quantum mechanics. For the layman - for whom the main part of this book is written - this is good news. If the everyday laws of nature can conspire to show up quantum-like phenomena, there is hope to form mental pictures how the atomic world works. The book is almost formula-free, and explains everything by using many sketches and diagrams. The mathematical derivations underlying the main text are kept separate in a -peer reviewed - appendix. The author, a retired professor of Flight Mechanics and Propulsion at the Delft University of Technology, chose to publish his findings in this mixed popular and scientific form, because he found that interested laymen more often than professional physicists feel the need to form visualisations of quantum phenomena. (shrink)

A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be distinctly quantum. To explain this correspondence it has been suggested that the fluid mechanical system provides a single-particle classical model of de Broglie’s idiosyncratic ‘double solution’ pilot wave theory of quantum mechanics. In this paper we assess the epistemic function of the (...) bouncing oil droplet experiments in relation to quantum mechanics. We find that the bouncing oil droplets are best conceived as an analogue illustration of quantum phenomena, rather than an analogue simulation, and, furthermore, that their epistemic value should be understood in terms of how-possibly explanation, rather than confirmation. Analogue illustration, unlike analogue simulation, is not a form of ‘material surrogacy’, in which source empirical phenomena in a system of one kind can be understood as ‘standing in for’ target phenomena in a system of another kind. Rather, analogue illustration leverages a correspondence between certain empirical phenomena displayed by a source system and aspects of the ontology of a target system. On the one hand, this limits the potential inferential power of analogue illustrations, but, on the other, it widens their potential inferential scope. In particular, through analogue illustration we can learn, in the sense of gaining how-possibly understanding, about the putative ontology of a target system via an experiment. As such, the potential scientific value of these extraordinary experiments is undoubtedly a significant one. (shrink)

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv 0 =m 0 c 2 ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon (1) ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to (...) the nonlinear soliton wave U 0 introduced by him in his double solution model of wave mechanics. (2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,” (3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments. (shrink)

Despite growing consumerism and skepticism about authority in the culture as a whole, most patients continue to be pliant. If there is a serious threat to physician autonomy, it is more likely to come from third‐party payers and new forms of medical practice, particularly the rise of for‐profit hospital chains, than from patients. Though physicians are restless, they will learn to adapt to the new conditions of practice.

Timbre is that property of a sound that distinguishes it other than pitch and loudness, for instance the distinctive sound quality of a violin or flute. While the term is obscure, the concept has played an important, implicit role in recent philosophy of sound. Philosophers have debated whether to identify sounds with properties of waves, events, or objects. Many of the intuitive considerations in this debate apply most clearly to timbre qualities. Two prominent forms of timbre physicalism have emerged: one (...) identifying timbre with the spectral composition of proximal waves; the second identifying timbre with the mechanical vibrations at a sound source. I demonstrate that the first possibility is conceptually unsatisfying, while the second fails to meet the standards of rigor established by the color physicalism literature. One response to these worries might be to adopt a more modest, non-reductive realism about timbre, such as the ecological view of J. J. Gibson. (shrink)

This book examines the interface between mathematics and applied sciences. The editor examines the present and future needs for the interaction between various science and engineering areas. This edited book brings together the cutting-edge research on mathematics, combining various fields of science and engineering. The book begins with an introduction to computing and modeling. Next, computation and modeling trends are covered, along with chapters on structural static and vibration problems, heat conduction and diffusion problems, and fluid dynamics problems. Soft (...) computing and machine intelligence based modeling are also discussed, along with bio medical problems. The book concludes with a chapter on modeling in mining, electrical, electronics, and chemical problems. This book is a reference for students and researchers in various fields of engineering such as computer, mechanical, civil, aerospace, electrical, and chemical, as well as and other sciences such as applied mathematics, physics, chemistry, and life sciences. (shrink)

Sound is one of the types of waves that can be felt by the sense of hearing (ears). In physics, the definition of sound is something that is produced from objects that vibrate. Objects that produce sound are called sound sources. The sound source that vibrates will vibrate the molecules into the air around it. Sound is mechanical compression or longitudinal waves that propagate through the medium. This medium or intermediate agent can be liquid, solid, gas. So, sound waves (...) can propagate for example in water, coal, or air. Most sounds are a combination of various vibratory signals composed of harmonic waves, but pure sound can theoretically be explained by oscillating vibrational speed or frequency measured in Hertz (Hz) vibration units and amplitude or loudness of sound with measurements in decibels (dB). The effect sounds can have on us humans is simply astounding. While everyday life becomes stressful, overcrowded and increasingly hectic, we seek ways for inner peace and balance. The power of music, felt through overtone-rich sound therapy and sound massage, can be a solution. No matter how much scientific explanation is behind it, healing through music remains fascinating, even magical. This paper introduces a new field called cymatics and sound healing with their plausible impact to spirituality and consciousness research. (shrink)

This is the first comprehensive translation of the expanded French version of E.F.F. Chladni's Traité d'Acoustique, using Chladni's 1802 Die Akustik for reference and clarification. Chladni's experiments and observations with sound and vibrations profoundly influenced the development of the field of Acoustics. The famous Chladni diagrams along with other observations are contained in Die Akustik, published in German in 1802 and Traité d'Acoustique, a greatly expanded version, published in French in 1809. The present translation was undertaken by Robert T. Beyer, (...) PhD (1920-2008), noted acoustician, Professor of Physics at Brown University, and Gold Medal recipient of the Acoustical Society of America. Along with many other projects completed over the course of his career, Dr. Beyer translated Von Neumann's seminal work, Mathematical Foundations of Quantum Mechanics from the original German, spent 30 years translating Russian physics treatises and journals, served as editor of the English translation of the Soviet Journal of Experimental and Theoretical Physics, and also authored Sounds of our Times: Two Hundred Years of Acoustics. Represents the first comprehensive English translation of a seminal work in acoustics Translated by a prominent acoustician, and former Gold Medal recipient of the Acoustical Society of America In addition to the classic experiments with glass plates and violin bows, covers topics in music, architecture, and anatomy of human and animal hearing Appeals to a wide audience in physics, acoustics, and history of science. (shrink)

Here, in our approximation of polaron theory, we examine the importance of introducing theT product, which turn out to be a very convenient theoretical approach for the calculation of thermodynamical averages.We focus attention on the investigation of the so-called linear polaron Hamiltonian and present in detail the calculation of the correlation function, spectral function, and Green function for such a linear system.It is shown that the linear polaron Hamiltonian provides an exactly solvable model of our system, and the result obtained (...) with this approach holds true for an arbitrary coupling constant which describes the strength of interaction between the electron and the lattice vibrations. Then, with the help of a variational technique, we show the possibility of reducing the real polaron Hamiltonian to a socalled trial or approximate linear model Hamiltonian.We also consider the exact calculation of free energy with a special technique that reduces calculations with the help of the T product, which, in our opinion, works much better and is easier than other analogous considerations, for example, the path-integral or Feynman-integral method.(1,2)Here we furthermore recall our own work,(4) where it was shown that the results of Refs. 7 and 8 concerning the impedance calculation in the polaron model may be obtained directly without the use of the path-integral method.The study of the polaron system's thermodynamics is carried out by us in the framework of the functional method. A calculation of the free energy and the momentum distribution function is proposed.Note also that the polaron systems with strong coupling(9) proved to be useful in different quantum field models in connection with the construction of dynamical models of composite particles. A rigorous solution of the special strong-coupling polaron problem, describing the interaction of a nonrelativistic particle with a quantum field, was given by Bogolubov.(3) The works of Tavkhelidze, Fedyanin, Khrustalev, and others(10–13) are dedicated to the further development and generalization of the Bogolubov method.Notice, too, that the electron-photon interaction effects play an important part in many problems of modern solid state theory (see, e.g., Refs. 7 and 14–19).The present paper summarizes a set of lectures delivered as a special course in the physics department of Moscow State University. (shrink)

The present book of proceedings includes chapters related to the areas of pure, applied and inter-disciplinary mathematics reflecting the potential applications in the domains of sciences and engineering. The main areas include algebra and its applications, analysis and approximation theory, cryptography, computational fluid dynamics, continuum mechanics and vibrations, differential equations and applications, graph theory, fuzzy mathematics and logic, numerical analysis, optimization and its applications, wave propagation, etc. The scientists, engineers, academicians and researchers working in the proposed areas of coding and (...) information theory, computational fluid dynamics, differential equations, fuzzy sets and systems, numerical analysis, optimization, vibrations, etc. looking for new insight and ideas in these areas will be benefitted by the contents of this book. In fact, it will be useful to a large class of readers interested in recent findings related to mathematical sciences and their applications to the diverse domains of knowledge. The book will be a fruitful contribution to all knowledge seekers and researchers in the concerned areas who are looking for new insight and ideas. As it consists of updated research articles on emerging areas of mathematical sciences and their applications, it will be a valued addition to the learning resource centres of various universities, industries, and research and development organizations across the globe. (shrink)

In this paper we study a classical and theoretical system which consists of an elastic medium carrying transverse waves and one point-like high elastic medium density, called concretion. We compute the equation of motion for the concretion as well as the wave equation of this system. Afterwards we always consider the case where the concretion is not the wave source any longer. Then the concretion obeys a general and covariant guidance formula, which leads in low-velocity approximation to an equivalent de (...) Broglie-Bohm guidance formula. The concretion moves then as if exists an equivalent quantum potential. A strictly equivalent free Schrödinger equation is retrieved, as well as the quantum stationary states in a linear or spherical cavity. We compute the energy of the concretion, naturally defined from the energy density of the vibrating elastic medium. Provided one condition about the amplitude of oscillation is fulfilled, it strikingly appears that the energy and momentum of the concretion not only are written in the same form as in quantum mechanics, but also encapsulate equivalent relativistic formulas. (shrink)

The suspension system is referred to as the set of springs, shock absorbers, and linkages that connect the car to the wheel system. The main purpose of the suspension system is to provide comfort for the passengers, which is created by reducing the effects of road bumpiness. It is worth noting that reducing the effects of such vibrations also diminishes the noise and undesirable sound as well as the effects of fatigue on mechanical parts of the vehicle. Due to (...) the importance of the abovementioned issues, the objective of this article is to reduce such vibrations on the car by implementing an active control method on the suspension system. For this purpose, a conventional first-order sliding mode controller has been designed for stochastic control of the quarter-car model. It is noteworthy that this controller has a significant ability to overcome the stochastic effects, uncertainty, and deal with nonlinear factors. To design a controller, the governing dynamical equation of the quarter-car system has been presented by considering the nonlinear terms in the springs and shock absorber, as well as taking into account the uncertainty factors in the system and the actuator. The design process of the sliding mode controller has been presented and its stability has been investigated in terms of the Lyapunov stability. In the current research, road surface variations are considered as Gaussian white noise. The dynamical system behavior for controlled and uncontrolled situations has been simulated and the extracted results have been presented. Besides, the effects of existing uncertainty in the suspension system and actuator have been evaluated and controller robustness has been checked. Also, the obtained quantitative and qualitative compressions have been presented. Moreover, the effect of controller parameters on the basin of attraction set and its extensiveness has been assessed. The achieved results have indicated the good performance and significant robustness of the designed controller to stabilize the suspension system and mitigate the effects of road bumpiness in the presence of uncertainty and noise factors. (shrink)

It is assumed that the motion of a particle in spacetime does not depend on the motion relative to it of any observer or of any frame of reference. Thus if the particle has an internal vibration of the type hypothesized by de Broglie, the phase of that vibration at any point in spacetime must appear to be the same to all observers, i.e., the same in all frames of reference. Each observer or reference frame will have its (...) own de Broglie wave for the particle. The phase of the particle's vibration must, by definition, be the same as that of all possible de Broglie waves at the point where the particle is. By superimposing all these possible de Broglie waves, a wave packet is formed centered in space on the particle. The formation of such a packet is discussed with the help of spacetime diagrams; the packet does not spread with time. The relevance of this packet to the wave mechanics of Schrödinger is discussed; it is also pointed out that any vibration can lead to such a packet. (shrink)

We identify new, rather serious, physical and mathematical inconsistencies of the current formulation of noncanonical or nonunitary string theories due to the lack of invariant units necessary for consistent measurements, lack of preservation in time of Hermiticity-observability, and other shortcomings. We propose three novel reformulations of string theories for matter of progressively increasing complexity via the novel iso-, geno-, and hyper-mathematics of hadronic mechanics, which resolve the current inconsistencies, while offering new intriguing possibilities, such as: an axiomatically consistent and invariant (...) inclusion of gravity, the reduction of macroscopic irreversibility to the most primitive level of vibrations of the universal substratum (ether), or the treatment of multi-valued, irreducible, biological structures. We then identify three corresponding classical formulations of string theories for antimatter via the novel anti-isomorphic isodual mathematics. We finally outline the intriguing features of the emerging new cosmologies (including biological structures, as it should be for all cosmologies), such as: universal invariance (rather than covariance) under a symmetry isomorphic to the Poincaré group and its isodual; equal distributions of matter and antimatter in the universe (as a limit case); continuous creation; no need for the missing mass; significantly reduced dimensions; possibility of experimental identification of antimatter in the universe; identically null total characteristics of time, energy, linear and angular momentum, charge, etc.; and other intriguing features. (shrink)

Differential equations of second order appear in physical applications such as fluid dynamics, electromagnetism, acoustic vibrations, and quantum mechanics. In this paper, necessary and sufficient conditions are established of the solutions to second-order half-linear delay differential equations of the form ς y u ′ y a ′ + ∑ j = 1 m p j y u c j ϑ j y = 0 for y ≥ y 0, under the assumption ∫ ∞ ς η − 1 / a d (...) η = ∞. We consider two cases when a c j, where a and c j are the quotient of two positive odd integers. Two examples are given to show effectiveness and applicability of the result. (shrink)

1. The sequence of the organisation levels is regarded as originating from a sequence of symmetry breakings. Each breaking generates a more improbable structure. In addition to the Euclidian symmetries, homogeneity, isotropy, translation, rotation, helix displacement, neutrality and even indiscernibility can be broken. Here are considered the initial and the subatomic breaking molecular morphogenesis and other higher breakings.2.1 HOMOGENEITY BREAKING OF THE VACUUM SPACE. We studied this as a new model of wave-corpuscle relation. Every noticeable point breaks the space homogeneity. (...) Directed by a momentum this breaking operates as a fissure.2. Postulate of the corpuscle. The quantum mechanical corpuscle is the end of a fissure, the momentum of which characterises direction and velocity.2.2. Postulate of the wave. The associate wave comes from the end of the fissure and works to split the medium.2.3. Corollary to the trajectory. The fissure prefers continuity and a straight line. Nevertheless the fissure can stop at a point and then start from an other point. This discontinuity and any momentum possible discontinuity are limited only by uncertainty relationships; frequency of discontinuity is limited by the first one. Vacuum has no memory of the fissures. 2.4.Corollary to the localisation. The fissure diminishes the medium constraints and allows the medium to vibrate in a domain surrounding the end of the fissure.2.5. Physical analogies. – - Photo-elastic studies of the fissuration of solids show a little sphere and a wavelike perturbation at the end of the fissure. – - A fragile and resonating object can be broken by a sound wave. This crack emits a sound wave. Here we consider one associated wave, emitted and absorbed. – - Broken panes picture an emission of rays. li]2.6. Consequences of the fissure model. (shrink)

For Kant, a body fills out space by means of its causal efficacy. The essential properties of matter are hence dependent on underlying forces and it is one task of the Opus postumum (OP) to reconstruct the system of forces. In order to avoid an infinite regress of causal explanations, this system of forces needs to account for a primitive origin of all mechanical moving forces in something that is constitutive of forces, yet radically different - this is the (...) ether that fills all space that constantly moves or vibrates all the parts of the material bodies internally. I argue that we can read Kant’s argument for the existence of the ether through the lens of dispositions: essential properties of matter, such as ponderability, coercibility, cohesibility, and exhaustibility, should be understood as dispositions. These dispositions are ‘physically conditioned,’ as Kant calls it, on the ether. To display their manifest and perceivable properties, the ether acts as the ubiquitous and universal ‘activation stimulus’ of the dispositions that make up material bodies. He causes them to constantly display their manifest properties that make them continuously perceivable and causally efficient. Thereby Kant offers a solution to a problem formulated by Simon Blackburn, namely that purely dispositional matter would lead us into skepticism. (shrink)

In 1891 Cambridge biologist William Bateson (1861–1926) announced his idea that the symmetrical segmentation in living organisms resulted from energy peaks of some vibratory force acting on tissues during morphogenesis. He also demonstrated topographically how folding a radially symmetric organism could produce another with bilateral symmetry. Bateson attended many lectures at the Cambridge Philosophical Society and viewed mechanical models prepared by eminent physicists that illustrated how vibrations affected materials. In his subsequent research, Bateson utilized analogies and metaphors based upon (...) his observations of nature to build a thought model on the effects of vibrations on living tissue, because he realized that the chemistry and biology of his day lacked technologies to perform actual experiments on the subject. He concluded the production of organic segmentation was both a chemical and mechanical phenomenon. By the time of his death Bateson had incorporated new ideas about embryonic organizer regions to suggest a center from which a rhythmic force emanated and then produced the observed repetitive segmentation as a common feature in living organisms. (shrink)

Music and noise can be considered as a collection of vibrational events which may impinge upon the body and the mind. As such they can induce beneficial or harmful bodily and psychological reactions. Much contemporary music production and consumption, however, produces sensory saturation and/or overload with sounds being manipulated in terms of spectrum and dynamic range. Such manipulation is not harmful by definition, but the manipulations may increase the potential for harm. Much research has been devoted to the risk of (...) auditory overstimulation, but the topic is still relevant as listening to music is a significant form of leisure noise exposure. Listening habits and attitudes toward loud music may even promote behaviors that could cause harm to listeners, both in a direct and indirect way. Listening to loud music, in fact, may be damaging to the cochlea (and possibly also the auditory nuclei and the auditory pathway), and may cause both temporary or permanent hearing loss. On the other hand, loud music may have benefits for us, particularly in terms of social integration and an enhanced sense of wellbeing and fun. Several questions can therefore be raised. What are the physical effects of sound as transferable and vibrational energy? Are there constraints and biases that shape and modify our reactions to the sounds? What are the perceptual and associated behavioral aspects? What are the psychological mechanisms for liking loud music? What are the social factors that contribute to increased preferences for loud music? And how can we assess the beneficial and harmful effects of sounds that are outside of the optimal range of stimulation? (shrink)

continent. 1.3 (2011): 149-155. The world is teeming. Anything can happen. John Cage, “Silence” 1 Autonomy means that although something is part of something else, or related to it in some way, it has its own “law” or “tendency” (Greek, nomos ). In their book on life sciences, Medawar and Medawar state, “Organs and tissues…are composed of cells which…have a high measure of autonomy.”2 Autonomy also has ethical and political valences. De Grazia writes, “In Kant's enormously influential moral philosophy, autonomy (...) , or freedom from the causal determinism of nature, became prominent in justifying the human use of animals.”3 One of the oldest uses of autonomy in English is a description of the French civil war from the late sixteenth century: “Others of the…rebellion entred in counsell, whether they ought to admit the King vpon reasonable conditions, specially hauing their autonomy.”4 Life, and in particular human life, and in particular human politics, is well served by the usages of autonomy . What about the rest of reality, however? Should it be thought of, if it's even considered real and mind-independent, as pure stuff for the manipulation or decorative tastes of truly autonomous beings? We tend to think of things such as paperweights and iPhones as mere tools of human design and human use. To use them is to cause them to exist as fully and properly as they can. But according to Martin Heidegger, when a tool such as a paperweight is used, it disappears, or withdraws ( Entzug ). We are preoccupied with copying the page that the paperweight is holding down. We are concerned with an essay deadline, and the paperweight simply disappears into this general project. If the paperweight slips, or if the iPhone freezes, we might notice it. All of a sudden it becomes vorhanden (present-at-hand) rather than zuhanden (ready-to-hand).5 Yet Heidegger is unable to draw a meaningful distinction between what happens to a paperweight when it slips from the book I'm copying from and what happens to the paperweight when it presses on the still resilient pages of the thick paperback itself. Further still and related to this point, even when I am using the paperweight as part of some general task, I am not using the entirety of the paperweight as such. My project itself selects a thin slice of paperweight-being for the purposes of holding down a book. Even when it is zuhanden the paperweight is withdrawn. Graham Harman is the architect of this way of thinking.6 Harman discovered a gigantic coral reef of withdrawn entities beneath the Heideggerian submarine of Da-sein, which itself is operating at an ontological depth way below the choppy surface of philosophy, beset by the winds of epistemology, and infested with the sharks of materialism, idealism, empiricism and most of the other isms that have defined what is and what isn't for the last several hundred years. At a moment when the term ontology was left alone like a piece of well chewed old chewing gum that no one wants to have anything to do with, object-oriented ontology (OOO) has put it back on the table. The coral reef isn't going anywhere and once you have discovered it, you can't un-discover it. And it seems to be teeming with strange facts. The first fact is that the entities in the reef—we call them “objects” somewhat provocatively—constitute all there is: from doughnuts to dogfish to the Dog Star to Dobermans to Snoop Dogg. People, plastic clothes pegs, piranhas and particles are all objects. And they are all pretty much the same, at this depth. There is not much of a distinction between life and non-life (as there isn't in contemporary life science). And there is not much of a distinction between intelligence and non-intelligence (as there is in contemporary artificial intelligence theory). A lot of these distinctions are made by humans, for humans (anthropocentrism). And the concept autonomy has come into play in policing such distinctions. In this essay I shall to try to liberate autonomy for the sake of nonhumans. I shall do so by parsing carefully the title, which is taken from Hakim Bey's work The Temporary Autonomous Zone .8 First we shall explore the term autonomous . Then we shall explore what the full meaning of zone is. Finally, we shall investigate what temporary means. Each of these terms is of great value. An object withdraws from access. This means that its very own parts can't access it. Since an object's parts can't fully express the object, the object is not reducible to its parts. OOO is anti-reductionist. But OOO is also anti-holist. An object can't be reduced to its “whole” either, “reduced upwards” as it were. The whole is not greater than the sum of its parts. So we have a strange irreductionist situation in which an object is reducible neither to its parts nor to its whole. A coral reef is made of coral, fish, seaweed, plankton and so on. But one of these things on its own doesn't embody part of a reef. Yet the reef just is an assemblage of these particular parts. You can't find a coral reef in a parking lot. In this way, the vibrant realness of a reef is kept safe both from its parts and from its whole. Moreover, the reef is safe from being mistaken for a parking lot. Objects can't be reduced to tiny Lego bricks such as atoms that can be reused in other things. Nor can be reduced upwards into instantiations of a global process. A coral reef is an expression of the biosphere or of evolution, yes; but so is this sentence, and we ought to be able to distinguish between coral reefs and sentences in English. The preceding facts go under the heading of undermining . Any attempt to undermine an object—in thought, or with a gun, or with heat, or with the ravages of time or global warming—will not get at the withdrawn essence of the object. By essence is meant something very different from essentialism . This is because essentialism depends upon some aspect of an object that OOO holds to be a mere appearance of that object, an appearance-for some object. This reduction to appearance holds even if that object for which the appearance occurs is the object itself! Even a coral reef can't grasp its essential coral reefness. In essentialism, a superficial appearance is taken for the essence of a thing, or of things in general. In thinking essentialism we may be able to discern another way of avoiding OOO. This is what Harman has christened overmining .? The overminer decides that some things are more real than others: say for example human perception. Then the overminer decides that other things are only granted realness status by somehow coming into the purview of the more real entity. When I measure a photon, when I see a coral reef, it becomes what it is. But when I measure a photon, I never measure the actual photon. Indeed, since at the quantum scale to measure means “to hit with a photon or an electron beam” (or whatever), measurement, perception ( aisthesis ), and doing become the same. What I “see” are deflections, tracks in a diffusion cloud chamber or interference patterns. Far from underwriting a world of pure illusion where the mind is king, quantum theory is one of the very first truly rigorous realisms, thinking its objects as irreducibly resistant to full comprehension, by anything.9 So far we have made objects safe from being swallowed up by larger objects and broken down into smaller objects—undermining. And so far we have made objects safe from being mere projections or reflections of some supervenient entity—overmining. That's quite a degree of autonomy. Everything in the coral reef, from the fish to a single coral lifeform to a tiny plankton, is autonomous. But so is the coral reef itself. So are the heads of the coral, a community of tiny polyps. So is each individual head. Each object is like one of Leibniz's monads, in that each one contains a potentially infinite regress of other objects; and around each object, there is a potentially infinite progress of objects, as numerous multiverse theories are now also arguing. But the infinity, the uncountability, is more radical than Leibniz, since there is nothing stopping a group of objects from being an object, just as a coral reef is something like a society of corals. Each object is “a little world made cunningly” (John Donne).10 We are indeed approaching something like the political valance of autonomy . The existence of an object is irreducibly a matter of coexistence. Objects contain other objects, and are contained “in” other objects. Let us, however, explore further the ramifications of the autonomy of objects. We will see that this mereological approach (based on the study of parts) only gets at part of the astonishing autonomy of things. Yet there are some more things to be said about mereology before we move on. Consider the fact that since objects can't be undermined or overmined, it means that there is strictly no bottom object . There is no object to which all other objects can be reduced, so that we can say everything we want to say about them, hypothetically at least, based on the behavior of the bottom object. The idea that we could is roughly E.O Wilson's theory of consilience .11 Likewise, there is no object from which all things can be produced, no top object . Objects are not emanations from some primordial One or from a prime mover. There might be a god, or gods. Suppose there were. In an OOO universe even a god would not know the essential ins and outs of a piece of coral. Unlike even some forms of atheism, the existence of god (or nonexistence) doesn't matter very much for OOO. If you really want to be an atheist, you might consider giving OOO a spin. If there is no top object and no bottom object, neither is there a middle object . That is, there is no such thing as a space, or time, “in” which objects float. There is no environment distinct from objects. There is no Nature (I capitalize the word to reinforce a sense of its deceptive artificiality). There is no world, if by world we mean a kind of “rope” that connects things together.12 All such connections must be emergent properties of objects themselves. And this of course is well in line with post-Einsteinian physics, in which spacetime just is the product of objects, and which may even be an emergent property of a certain scale of object larger than 10?¹?cm).13 Objects don't sit in a box of space or time. It's the other way around: space and time emanate from objects. How does this happen? OOO tries to produce an explanation from objects themselves. Indeed, the ideal situation would be to rely on just one single object. Otherwise we are stuck with a reality in which objects require other entities to function, which would result in some kind of undermining or overmining. We shall see that we have all the fuel we need “inside” one object to have time and space, and even causality. We shall discover that rather than being some kind of machinery or operating system that underlies objects, causality itself is a phenomenon that floats ontologically “in front of” them. In so doing, we will move from the notion of autonomy and begin approaching a full exploration of the notion of zone , which was promised at the outset of this essay. Since an object is withdrawn, even “from itself,” it is a self-contradictory being. It is itself and not-itself, or in a slightly more expanded version, there is a rift between essence and appearance within an object (as well as “between” them). This rift can't be the same as the clichéd split between substance and accidents , which is the default ontology. On this view, things are like somewhat boring cupcakes with somewhat less boring sugar sprinkles on them of different colors and shapes. But on the OOO view, what is called substance is just another limited slice of an object, a way of apprehending something that is ontologically fathoms deeper. What is called substance and what is called accidence are just on the side of what this essay calls appearance. The rift (Greek, chorismos ) between essence and appearance means that an object presents us with something like what in logic is known as the Liar: some version of the sentence “This sentence is false.” The sentence is true, which means that it is a lie, which means that it is false. Or the sentence is false, which means that it is telling the truth, which means that it is true. Now logic since Aristotle has tried desperately to quarantine such beasts in small backwaters and side streets so that they don't act too provocatively.14 But if OOO holds, then at least one very significant thing in the universe is both itself and not-itself: the object. An object is p ? ¬p. To cope with this fact, we shall need some kind of paraconsistent or even fully dialetheic logic, one that is not allergic to dialetheias (double-truthed things). Yet if we accept that objects are dialetheic, p ? ¬p, we can derive all kinds of things easily from objects. Consider the fact of motion. If objects only occupy one location “in” space at any “one” time, then Zeno's paradoxes will apply to trying to think how an object moves. Yet motion seems like a basic, simple fact of our world. Either everything is just an illusion and nothing really moves at all (Parmenides). Or objects are here and not-here “at the same time.”15 This latter possibility provides the basic setup for all the motion we could wish for. Objects are not “in” time and space. Rather, they “time” (a verb) and “space.” They produce time and space. It would be better to think these verbs as intransitive rather than transitive, in the manner of dance or revolt . They emanate from objects, yet they are not the object. “How can we know the dancer from the dance?” (Yeats).16 The point being, that for there to be a question, there must be a distinction—or there must not be (p ? ¬p).17 It becomes impossible to tell: “What constitutes pretense is that, in the end, you don't know whether it's pretense or not.”18 In this notion of the emergence of time and space from an object we can begin to understand the term zone . Zone can mean belt , something that winds around something else. We talk of temperate zones and war zones. A zone is a place where a certain action is taking place: the zone winds around, it radiates heat, bullets fly, armies are defeated. To speak of an autonomous zone is to speak of a place that a certain political act has carved out of some other entity. Cynically, Tibet is called TAR, the Tibetan Autonomous Region, for this very reason. In this phrase, Region tries to emulate zone : it sounds as if the place has its own rules, but of course, it is very much under the control of China. What action is taking place? “[N]ot something that just is what it is, here and now, without mystery, but something like a quest…a tone on its way calling forth echoes and responses…water seeking its liquidity in the sunlight rippling across the cypresses in the back of the garden.”19 If as suggested earlier there is no functional difference between substance and accidence; if there is no difference between perceiving and doing; if there is no real difference between sentience and non-sentience—then causality itself is a strange, ultimately nonlocal aesthetic phenomenon. A phenomenon, moreover, that emanates from objects themselves, wavering in front of them like the astonishingly beautiful real illusion conjured in this quotation of Alphonso Lingis. Lingis's sentence does what it says, casting a compelling, mysterious spell, the spell of causality, like a demonic force field. A real illusion: if we knew it was an illusion, if it were just an illusion, it would cease to waver. It would not be an illusion at all. We would be in the real of noncontradiction. Since it is like an illusion, we can never be sure: “What constitutes pretense…” A zone is what Lingis calls a level . A zone is not entirely a matter of “free will”: this concept has already beaten down most objects into abject submission. Objects are far more threateningly autonomous, and sensually autonomous, than the Kantian version of autonomy cited in the first paragraph of this essay. A zone is not studiously decided upon by an earnest committee before it goes into action. One of its predominant features is that it is already happening . We find ourselves in it, all of a sudden, in the late afternoon as the shadows lengthen around a city square, giving rise to an uncanny sensation of having been here before. Objects emit zones. Wherever I find myself a zone is already happening, an autonomous zone. It is the nonautonomous zones that are impositions on what is already the case. Or rather, these zones are autonomous zones that exclude and police. They are brittle. Every object is autonomous, but some objects try to maintain themselves through rigidity and brittleness, like (and such as) a police state. Paradoxically, the more rigidly one tries to exclude contradiction, the more virulent become the dialetheias that are possible. I can get around “This sentence is false” by imagining that there are metalanguages that explain what counts as a sentence. Then I can decide that this isn't a real sentence. This is basically Alfred Tarski's strategy, since he invented the notion of metalanguage specifically to cope with dialetheias.20 For example we might claim that sentences such as “This sentence is false” are neither true nor false. But then you can imagine a strengthened version of the Liar such as: “This sentence is not true”; or “This sentence is neither true nor false.” And we can go on adding to the strengthened Liar if the counter-attack tries to build immunity by specifying some fourth thing that a sentence can be besides true, false, and neither true nor false: “This sentence is false, or neither true nor false, or the fourth thing.” And so on.21 It seems as if language becomes more brittle the more it tries to police the Liars of this world. Why? I believe that this increasing brittleness is a symptom of a deep fact about reality. What is this deep fact? Simply that there are objects, that these objects are withdrawn, and that they are walking contradictions. This means indeed that (as Lacan put it) “there is no metalanguage,” since a metalanguage would function as a “middle object” that gave coherency and evenness to the others.22 Since there is no metalanguage, there is no rising above the disturbing illusory play of causality. This may even have political implications: no global critique is therefore possible, and attempts to smooth out or totalize are doomed to fail. To think the zone is to think the notion of temporary , which we shall now begin to discuss in greater detail. The zone is not in time: rather it “times.” But because a zone is an emanation of an object, it is based on a wavering fragility, since objects are p ? ¬p. When an object is born, that means that it has broken free of some other object. An object can be born because it and other objects are fragile. If not, no movement would be possible. Objects contain the seeds of their own destruction, a dialetheic sentence that says something like “This sentence cannot be proved.” Kurt Gödel argues that every true system of propositions contains at least one sentence that the system cannot prove. In order to be true, the system must have a minimum incoherence. To be real, it has to be fragile. Imagine a record player. Now imagine a record called I Cannot Be Played on This Record Player . When you play it on this record player, it produces sympathetic vibrations that cause the record player to shudder apart. No matter how many defense mechanisms you build in, there will always be the possibility of at least one record that destroys the record player.23 That is what being physical is. An object is inherently fragile because it is both itself and not-itself. When the rift between appearance and essence collapses, that is called destruction, ending, death. When an object breaks, several new objects are born. An opera singer sings a loud note in tune with the resonant frequency of a wine glass. (See the movie included below.) The singing is a zone, an autonomous level of intensity, opening a rift between appearance and essence. The glass ripples—for a moment it is nakedly a glass and a not-glass—almost as if it were having an orgasm, a little death. It is caught in the rift of the singing. Then its structure can't handle the coherence of the sound waves, and it breaks. It is incoherence and inconsistency that is the mark of existence, not consistency and noncontradiction. When things break or die, they become coherent. Essence disappears into appearance. I become the memories of friends. A glass becomes a dancing wave. Instantly, there are glass fragments, new temporary autonomous zones. The fragments have broken free from the glass. They are no longer its parts, but emanate their own time and space, becoming perhaps accidental weapons as they bury themselves in my flesh. Thus Hakim Bey's instructions on creating temporary autonomous zones oscillate disturbingly between performance art and politics, circus clowning and revolution. To play with the aesthetic is to play with causality, to rip from the sensual ether emanating from things new regions, new zones. Anarchist politics is the creation of fresh objects in a reality without a top or a bottom object, or for that matter a middle object: Everything in nature is perfectly real including consciousness, there's absolutely nothing to worry about. Not only have the chains of the Law been broken, they never existed; demons never guarded the stars, the Empire never got started, Eros never grew a beard. … There is no becoming, no revolution, no struggle, no path; already you're the monarch of your own skin—your inviolable freedom waits to be completed only by the love of other monarchs: a politics of dream, urgent as the blueness of sky.24 Bey imagines that this is because chaos is a primordial “undifferentiated oneness-of-being.” A Parmenides or a Spinoza or a Laruelle would read this a certain way. Individual objects, or decisions to talk about this rather than that, are just maggot-like things crawling around on the surface of the giant cheese of oneness.25 Yet he also describes chaos as “Primordial uncarved block, sole worshipful monster, inert & spontaneous, more ultraviolet than any mythology.” This image is of an inconsistent object, not of an undifferentiated field. An object, indeed, that can be distinguished from other things. If not, then the first part of The Temporary Autonomous Zone , subtitled “The Broadsheets of Ontological Anarchism,” is a kind of onto-theology. Onto-theology proclaims that some things are more real than others. Bey, however, is writing poetically, and thus ambiguously. We are at liberty to read “undifferentiated oneness-of-being” as something like the irreducibility of a thing to its parts and so forth (undermining and overmining). This certainly seems closer to the language in the following paragraph: “There is no becoming … already you're the monarch of your own skin.”26 On this view, there is no difference between art and politics: “When ugliness, poor design & stupid waste are forced upon you, turn Luddite, throw your shoe in the works, retaliate.” Since Romanticism this has been the war cry of the vanguard artist.27 To say to is to fall prey to the tired axioms of the avant-garde, and we think we know how the game goes. But OOO is not simply a way to advocate “new and improved” versions of this shock-the-bourgeoisie boredom. Bey's text is certainly full enough of that. Rather, since causality as such is aesthetic, and since nonhumans are not that different from humans, the new approach would be to form aesthetic–causal alliances with nonhumans. These alliances would have to resist becoming brittle, whether that brittleness is right wing (authoritarianism) or left wing (the endless maze of critique). No “ism,” especially not the ultimate forms, nihilism and cynicism, is in any sense effective at this point. All forms of brittleness are based on the mistaken assumption that there is a metalanguage and that therefore “Anything you can do, I can do meta.” I will not be listing any approaches here, as Bey does. Such lists and manifestos belong to the vanguardism that no longer works. Why? Not because of some marvelous revolution in human consciousness, but because nonhumans have so successfully impinged upon human social, psychic and aesthetic space. It is the time after the end of the world. That happened in 1945, when a thin layer of radioactive materials was deposited in Earth's crust. Geology now calls it this era the Anthropocene . Ironically, this period, named after humans, is the moment at which even the most thick headed of us make decisive contact with nonhumans, from mercury in our blood to manta rays to magnesium. Richard Dawkins, Pat Robertson and Lady Gaga all have to deal with global warming and mass extinction, somehow. We now live in an Age of Asymmetry marked by a skewed, spiraling relationship between vast knowledge and vast nonhuman things—both become vaster and vaster because of one another and for the same reasons.28 This means that coming up with the perfect attitude or the perfect aesthetic prescription just won't work any more. Even the most hardened anthropocentrist now has to pay through the nose for basic food supplies, and has to use more sunscreen. Whether he knows it or acknowledges it, he is already acting with regard towards nonhumans. There is nothing special to think, no special critique that will get rid of the stains of coexistence. The problem won't fit into the well-established modern boxes, which is why the “mystical,” “spiritual” quality of Bey's prose is welcome. Of course, when I put it this way, you may immediately close off and decide that I am talking about perfect attitudes after all, or something outside of politics, or other ways that the radical left marshals to police its thinking of the nonhuman. Because that is what is really at stake in all this: the nonhuman in its coexistence with the human—bosons, gods, clouds, spirits, lifeforms, experiences, the sunlight rippling across the cypresses. Bey begins to get at this in a Latour litany in the second part of The Temporary Autonomous Zone , “The Assassins”: Pomegranate, mulberry, persimmon, the erotic melancholy of cypresses, membrane-pink shirazi roses, braziers of meccan aloes & benzoin, stiff shafts of ottoman tulips, carpets spread like make-believe gardens on actual lawns—a pavilion set with a mosaic of calligrammes—a willow, a stream with watercress—a fountain crystalled underneath with geometry— the metaphysical scandal of bathing odalisques, of wet brown cupbearers hide-&-seeking in the foliage—“water, greenery, beautiful faces.”29 This will be conveniently dismissed as orientalism. If we're never allowed to escape the crumbling prison of modernity for fear of imperialism there is truly no hope. In a similar way, the fear of anthropocentrism and anthropomorphism is very often staged from a place that just is anthropocentrism .30 Critique turns into ressentiment . An object radiates a zone that is aesthetic and therefore causal. Because objects “time” they are temporary. Not because they exist “in” time that eventually gets the better of them. Their very existence implies the possibility of their non-existence. Since objects are not consistent, they can cease to exist. But nothing, no one, will ever be able to insert a blade between appearance and existence, even thought there is a rift there. Now that's what I call autonomy. NOTES 1. John Cage, Silence: Lectures and Writings (Middletown, CT: Wesleyan University Press, 1973), 96. 2. P. B. Medawar and J. S. Medawar, The Life Science: Current Ideas in Biology (London: Wildwood House, 1977), 8. 3. David DeGrazia, Animal Rights: A Very Short Introduction (Oxford: Oxford University Press, 2002), 5. 4. Antony Colynet, A True History of the Civil Warres in France (London, 1591), 480. 5. Martin Heidegger, Being and Time , tr. Joan Stambaugh (Albany, N.Y: State University of New York Press, 1996) 62–71. 6. Graham Harman, Tool-Being: Heidegger and the Metaphysics of Objects (Peru, IL: Open Court, 2002). 7. Hakim Bey, The Temporary Autonomous Zone (Brooklyn: Autonomedia, 1991). 8. Graham Harman, The Quadruple Object (Ripley: Zero Books, 2011), 7–18. 9. This is not the place to get into an argument about quantum theory, but I have argued that quanta also do not endorse a world that I can't speak about because it is only real when measured. This world is that of the reigning Standard Model proposed by Niels Bohr and challenged by De Broglie and Bohm (and now the cosmologist Valentini, among others). See Timothy Morton, “Here Comes Everything: The Promise of Object-Oriented Ontology,” Qui Parle 19.2 (Spring–Summer, 2011), 163–190. 10. John Donne, Holy Sonnets 15, in The Major Works: Including Songs and Sonnets and Sermons , ed. John Carey (Oxford: Oxford University Press, 2009). 11. Edward O. Wilson, Consilience: The Unity of Knowledge (New York: Knopf, 1998). 12. Martin Heidegger, What Is a Thing? (Washington: Regnery, 1968), 243. 13. Albert Einstein, Relativity: The Special and the General Theory (London: Penguin, 2006); Petr Horava, “Quantum Gravity at a Lifshitz Point,” arXiv:0901.3775v2 [hep-th]. 14. Graham Priest, In Contradiction (Oxford University Press, 2006), passim: the most notable recent quarantine officers have been Tarski, Russell, and Frege. 15. Priest, In Contradiction , 172–181. 16. William Butler Yeats, “Among School Children,” Collected Poems , ed. Richard J. Finneran (New York: Scribner, 1996). 17. Paul de Man, “Semiology and Rhetoric,” Diacritics 3.3 (Autumn, 1973), 27–33 (30). 18. Jacques Lacan, Le seminaire, Livre III: Les psychoses (Paris: Editions de Seuil, 1981), 48. See Slavoj Zizek, The Parallax View (Cambridge, Mass.: MIT Press, 2006), 206. 19. Alphonso Lingis, The Imperative (Bloomington: Indiana University Press, 1998), 29. 20. Priest, In Contradiction , 9–27. 21. See Graham Priest and Francesco Berto, “ Dialetheism ,” The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), ed. Edward N. Zalta. 22. Jacques Lacan, Écrits: A Selection , tr. Alan Sheridan (London: Tavistock, 1977), 311. 23. The analogy can be found at length in Douglas Hofstadter, “Contracrostipunctus,” Gödel, Escher, Bach: An Eternal Golden Braid (New York: Basic Books, 1999), 75–81. 24. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 25. This is closest to the language of François Laruelle in Philosophies of Difference: A Critical Introduction to Non-Philosophy (New York: Continuum, 2011) 179. 26. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 27. Peter Bürger, Theory of the Avant Garde (Minneapolis: University of Minnesota Press, 1984). 28. For further discussion see Timothy Morton, “From Modernity to the Anthropocene: Ecology and Art in the Age of Asymmetry,” The International Social Science Journal 209 (forthcoming). 29. Bey, “ The Assassins ,” Temporary Autonomous Zone . 30. Timothy Morton, The Ecological Thought (Cambridge, Mass.: Harvard University Press, 2010), 75–76. (shrink)

Robert Hooke’s development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke’s ‘Principles … of Congruity and Incongruity of bodies’ represent a uniquely powerful approach to (...) the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke’s ‘Uniform Geometrical or Mechanical Method’ was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world. (shrink)

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a (...) string and heat conduction. The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit–reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science. (shrink)