This article responds to two unresolved and crucial problems of cognitive science: (1) What is actually accomplished by functions of the nervous system that we ordinarily describe in the intentional idiom? and (2) What makes the information processing involved in these functions semantic? It is argued that, contrary to the assumptions of many cognitive theorists, the computational approach does not provide coherent answers to these problems, and that a more promising start would be to fall back on mathematical communication theory (...) and, with the help of evolutionary biology and neurophysiology, to attempt a characterization of the adaptive processes involved in visual perception. Visual representations are explained as patterns of cortical activity that are enabled to focus on objects in the changing visual environment by constantly adjusting to maintain levels of mutual information between pattern and object that are adequate for continuing perceptual control. In these terms, the answer proposed to (1) is that the intentional functions of vision are those involved in the establishment and maintenance of such representations, and to (2) that semantic features are added to the information processes of vision with the focus on objects that these representations accomplish. The article concludes with proposals for extending this account of intentionality to the higher domains of conceptualization and reason, and with speculation about how semantic information-processing might be achieved in mechanical systems. (shrink)

In this second part of our two-part paper we review and analyse attempts since 1950 to use information theoretic notions to exorcise Maxwell’s Demon. We argue through a simple dilemma that these attempted exorcisms are ineffective, whether they follow Szilard in seeking a compensating entropy cost in information acquisition or Landauer in seeking that cost in memory erasure. In so far as the Demon is a thermodynamic system already governed by the Second Law, no further supposition about information and entropy (...) is needed to save the Second Law. In so far as the Demon fails to be such a system, no supposition about the entropy cost of information acquisition and processing can save the Second Law from the Demon. (shrink)

Information theory presupposes the notion of an epistemic agent, such as a scientist or an idealized human. Despite that, information theory is increasingly invoked by physicists concerned with fundamental physics, physics at very high energies, or generally with the physics of situations in which even idealized epistemic agents cannot exist. In this paper, I shall try to determine the extent to which the application of information theory in those contexts is legitimate. I will illustrate my considerations using the case of (...) black hole thermodynamics and Bekenstein's celebrated argument for his formula for the entropy of black holes. This example is particularly pertinent to the theme of the present collection because it is widely accepted as `empirical data' in notoriously empirically deprived quantum gravity, even though the laws of black hole thermodynamics have so far evaded direct empirical confirmation. (shrink)

The black hole information loss paradox is a catch-all term for a family of puzzles related to black hole evaporation. For almost 50 years, the quest to elucidate the implications of black hole evaporation has not only sustained momentum, but has also become increasingly populated with proposals that seem to generate more questions than they purport to answer. Scholars often neglect to acknowledge ongoing discussions within black hole thermodynamics and statistical mechanics when analyzing the paradox, including the interpretation of Bekenstein-Hawking (...) entropy, which is far from settled. To remedy the dialectical gridlock, I have formulated an overarching, unified framework, which I call ``Black Hole Paradoxes'', that integrates the debates and taxonomizes the relevant `camps' or philosophical positions. -/- I demonstrate that black hole evaporation within Hawking's semi-classical framework insinuates how late-time Hawking radiation is an entangled global system, a contradiction in terms. The relevant forms of information loss are associated with a decrease in maximal Boltzmann entropy and an increase in global von Neumann entropy respectively, which engender what I've branded the ``paradox of phantom entanglement''. Prospective solutions are then tasked with demonstrating how late-time Hawking radiation is either exclusively an entangled subsystem, in which a black hole remnant lingers as an information safehouse, or exclusively an unentangled global system, in which information is evacuated to the exterior. -/- The disagreement between safehouse and evacuation solutions boils down to the statistical interpretation of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy. Safehouse solutions attribute Bekenstein-Hawking entropy to a minority of black hole degrees of freedom, those that are associated with the horizon. Evacuation solutions, in contrast, attribute Bekenstein-Hawking entropy to all black hole degrees of freedom. I argue that the interpretation of Bekenstein-Hawking entropy is the litmus test to vet the overpopulated proposal space. So long as any proposal rejecting Hawking's original calculation independently derives black hole evaporation, globally conserves degrees of freedom and entanglement, preserves a version of semi-classical gravity at sub-Planckian scales, and describes black hole thermodynamics in statistical terms, then it counts as a genuine solution to the paradox. (shrink)

Information, entropy, probability: these three terms are closely interconnected in the prevalent understanding of statistical mechanics, both when this field is taught to students at an introductory level and in advanced research into the field’s foundations. This paper examines the interconnection between these three notions in light of recent research in the foundations of statistical mechanics. It disentangles these concepts and highlights their differences, at the same time explaining why they came to be so closely linked in the literature. In (...) the literature the term ‘information’ is often linked to entropy and probability in discussions of Maxwell’s Demon and its attempted exorcism by the Landauer-Bennett thesis, and in analyses of the spin echo experiments. The direction taken in the present paper is a different one. Here we discuss the statistical mechanical underpinning of the notions of probability and entropy, and this constructive approach shows that information plays no fundamental role in these concepts, although it can be conveniently used in a sense that we shall specify. (shrink)

Functionalism in the philosophy of mind is here criticized from the perspective of a more naturalistic and less compromising form of materialism. Parallels are explored between the problem of cognitive activity and the somewhat more settled problem of vital activity. The lessons drawn suggest that functionalism in the philosophy of mind may be both counterproductive as a research strategy, and false as a substantive position.

We argue that living systems process information such that functionality emerges in them on a continuous basis. We then provide a framework that can explain and model the normativity of biological functionality. In addition we offer an explanation of the anticipatory nature of functionality within our overall approach. We adopt a Peircean approach to Biosemiotics, and a dynamical approach to Digital-Analog relations and to the interplay between different levels of functionality in autonomous systems, taking an integrative approach. We then apply (...) the underlying biosemiotic logic to a particular biological system, giving a model of the B-Cell Receptor signaling system, in order to demonstrate how biosemiotic concepts can be used to build an account of biological information and functionality. Next we show how this framework can be used to explain and model more complex aspects of biological normativity, for example, how cross-talk between different signaling pathways can be avoided. Overall, we describe an integrated theoretical framework for the emergence of normative functions and, consequently, for the way information is transduced across several interconnected organizational levels in an autonomous system, and we demonstrate how this can be applied in real biological phenomena. Our aim is to open the way towards realistic tools for the modeling of information and normativity in autonomous biological agents. (shrink)

Daniel R. Brooks and E. O. Wiley have proposed a theory of evolution in which fitness is merely a rate determining factor. Evolution is driven by non-equilibrium processes which increase the entropy and information content of species together. Evolution can occur without environmental selection, since increased complexity and organization result from the likely capture at the species level of random variations produced at the chemical level. Speciation can occur as the result of variation within the species which decreases the probability (...) of sharing genetic information. Critics of the Brooks-Wiley theory argue that they have abused terminology from information theory and t thermodynamics. In this paper I review the essentials of the theory, and give an account of hierarchical physical information systems within which the theory can be interpreted. I then show how the major conceptual objections can be answered. (shrink)

In this paper I will defend the incapacity of the informational frameworks in thermal physics, mainly those that historically and conceptually derive from the work of Brillouin (1962) and Jaynes (1957a), to robustly explain the approach of certain gaseous systems to their state of thermal equilibrium from the dynamics of their molecular components. I will further argue that, since their various interpretative, conceptual and technical-formal resources (e.g. epistemic interpretations of probabilities and entropy measures, identification of thermal entropy as Shannon information, (...) and so on) are shown to be somehow incoherent, inconsistent or inaccurate, these informational proposals need to 'epistemically parasitize' the manifold of theoretical resources of Boltzmann's and Gibbs' statistical mechanics, respectively, in order to properly account for the equilibration process of an ideal gas from its microscopic properties. Finally, our conclusion leads us to adopt a sort of constructive skepticism regarding the explanatory value of the main informationalist trends in statistical thermophysics. (shrink)

The physical singularity of life phenomena is analyzed by means of comparison with the driving concepts of theories of the inert. We outline conceptual analogies, transferals of methodologies and theoretical instruments between physics and biology, in addition to indicating significant differences and sometimes logical dualities. In order to make biological phenomenalities intelligible, we introduce theoretical extensions to certain physical theories. In this synthetic paper, we summarize and propose a unified conceptual framework for the main conclusions drawn from work spanning a (...) book and several articles, quoted throughout. (shrink)

Integrating concepts of maintenance and of origins is essential to explaining biological diversity. The unified theory of evolution attempts to find a common theme linking production rules inherent in biological systems, explaining the origin of biological order as a manifestation of the flow of energy and the flow of information on various spatial and temporal scales, with the recognition that natural selection is an evolutionarily relevant process. Biological systems persist in space and time by transfor ming energy from one state (...) to another in a manner that generates structures which allows the system to continue to persist. Two classes of energetic transformations allow this; heat-generating transformations, resulting in a net loss of energy from the system, and conservative transformations, changing unusable energy into states that can be stored and used subsequently. All conservative transformations in biological systems are coupled with heat-generating transformations; hence, inherent biological production, or genealogical proesses, is positively entropic. There is a self-organizing phenomenology common to genealogical phenomena, which imparts an arrow of time to biological systems. Natural selection, which by itself is time-reversible, contributes to the organization of the self-organized genealogical trajectories. The interplay of genealogical (diversity-promoting) and selective (diversity-limiting) processes produces biological order to which the primary contribution is genealogical history. Dynamic changes occuring on times scales shorter than speciation rates are microevolutionary; those occuring on time scales longer than speciation rates are macroevolutionary. Macroevolutionary processes are neither redicible to, nor autonomous from, microevolutionary processes. (shrink)

Many mechanisms, functions and structures of life have been unraveled. However, the fundamental driving force that propelled chemical evolution and led to life has remained obscure. The second law of thermodynamics, written as an equation of motion, reveals that elemental abiotic matter evolves from the equilibrium via chemical reactions that couple to external energy towards complex biotic non-equilibrium systems. Each time a new mechanism of energy transduction emerges, e.g., by random variation in syntheses, evolution prompts by punctuation and settles to (...) a stasis when the accessed free energy has been consumed. The evolutionary course towards an increasingly larger energy transduction system accumulates a diversity of energy transduction mechanisms, i.e. species. The rate of entropy increase is identified as the fitness criterion among the diverse mechanisms, which places the theory of evolution by natural selection on the fundamental thermodynamic principle with no demarcation line between inanimate and animate. (shrink)

Quite often the compatibility of the EPR correlations with the relativity theory has been questioned; it has been stated that “the first in time of two correlated measurements instantaneously collapses the other subsystem”; it has been suggested that a causal asymmetry is built into the Feynman propagator. However, the EPR transition amplitude, as derived from the S matrix, is Lorentz andCPT invariant; the correlation formula is symmetric in the two measurements irrespective of their time ordering, so that the link of (...) the correlations is the Feynman zigzag, and that causality isCPT invariant at the microlevel; finally, although the Feynman propagator has theP andCT symmetries, no causal asymmetry follows from that. As for Stapp's views concerning “process” and “becoming,” and his Whiteheadean concept of an advancing front, I object that they belong to “factlike macrophysics,” and are refuted at the microlevel by the EPR phenomenology, which displays direct Fokker-like space-time connections. The reason for this is a radical one. The very blending of a space-time picture and of a probability calculus is a paradox. The only adequate paradigm is one denying objectivity to space-time—but this, of course, is also required by the complementary of the x and the k pictures, which only “look” compatible at the macrolevel. Therefore, the classical “objectivity” must yield in favor of “intersubjectivity.” Only the macroscopic preparing and measuring devices have “factlike” objectivity; the “transition” of the “quantal system” takes place beyond both thex and thek 4-spaces. Then, the intrinsic symmetries between retarded and advanced waves, and statistical prediction and retrodiction, entails that the future has no less (but no more) existence than the past. It is the future that is significant in “creative process,” the “elementary” forms of which should be termed “precognition” or “psychokinesis”—respectively symmetric to the factlike taboos that “we can neither know into the future nor act into the past.” It is gratifying that Robert Jahn, at the Engineering School of Princeton University, is conducting (after others) conclusive experiments demonstrating “low level psychokinesis”—a phenomenon implied by the very symmetry of the negentropy-information transition. So, what pierces the veil of “maya” is the (rare) occurrence of “paranormal phenomena.” The essential severance between “act” and “potentia” is not a spacelike advancing front, but the “out of” and the “into” factlike space-time. Finally, I do not feel that an adequate understanding of the EPR phenomenology requires going beyond the present status of relativistic quantum mechanics. Rather, I believe that the potentialities of this formalism have not yet been fully exploited. (shrink)

The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double interpretation of the state vector as a representation of physical states as well as ofinformation about physical states. The concept of relevance being used in all statistical theories of irreversible thermodynamics is demonstrated to be based on the same observer-relatedness. Quantum theories of irreversible processes implicitly use an objectivized process (...) of state vector reduction. The conditions for the reduction are discussed, and it is concluded that the final (subjective) observer system may be carried by a space point. (shrink)

This article distinguishes two different senses of information-theoretic approaches to statistical mechanics that are often conflated in the literature: those relating to the thermodynamic cost of computational processes and those that offer an interpretation of statistical mechanics where the probabilities are treated as epistemic. This distinction is then investigated through Earman and Norton’s ([1999]) ‘sound’ and ‘profound’ dilemma for information-theoretic exorcisms of Maxwell’s demon. It is argued that Earman and Norton fail to countenance a ‘sound’ information-theoretic interpretation and this paper (...) describes how the latter inferential interpretations can escape the criticisms of Earman and Norton ([1999]) and Norton ([2005]) by adopting this ‘sound’ horn. This article considers a standard model of Maxwell’s demon to illustrate how one might adopt an information-theoretic approach to statistical mechanics without a reliance on Landauer’s principle, where the incompressibility of the probability distribution due to Liouville’s theorem is taken as the central feature of such an interpretation. (shrink)

Cartesian mind body dualism and modern versions of this viewpoint posit a mind thermodynamically unrelated to the body but informationally interactive. The relation between information and entropy developed by Leon Brillouin demonstrates that any information about the state of a system has entropic consequences. It is therefore impossible to dissociate the mind's information from the body's entropy. Knowledge of that state of the system without an energetically significant measurement would lead to a violation of the second law of thermodynamics.

The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, i.e. (...) geodesics are obtained from the principle of least action for mechanics, electrodynamics and quantum mechanics. The arrow of time, associated with the expansion of the Universe, identifies with grand dispersal of energy when high-energy densities transform by various mechanisms to lower densities in energy and eventually to ever-diluting electromagnetic radiation. Likewise, time in a quantum system takes an increment forwards in the detection-associated dissipative transformation when the stationary-state system begins to evolve pictured as the wave function collapse. The energy dispersal is understood to underlie causality so that an energy gradient is a cause and the resulting energy flow is an effect. The account on causality by the concepts of physics does not imply determinism; on the contrary, evolution of space–time as a causal chain of events is non-deterministic. (shrink)

Study represents an application of the neutrosophic method, for solving the contradiction between communication and information. In addition, it recourse to an appropriate method of approaching the contradictions: Extensics, as the method and the science of solving the contradictions. The research core is the reality that the scientific research of communication-information relationship has reached a dead end. The bivalent relationship communicationinformation, information-communication has come to be contradictory, and the two concepts to block each other. After the critical examination of conflicting (...) positions expressed by many experts in the field, the extensic and inclusive hypothesis is issued that information is a form of communication. The object of communication is the sending of a message. The message may consist of thoughts, ideas, opinions, feelings, beliefs, facts, information, intelligence or other significational elements. When the message content is primarily informational, communication will become information or intelligence. The arguments of supporting the hypothesis are: a) linguistic (the most important being that there is "communication of information" but not "information of communication"; also, it is clarified and reinforced the over situated referent, that of the communication as a process), b) systemic-procedural (in the communication system is developing an information system; the informing actant is a type of communicator, the information process is a communication process), c) practical (the delimitation eliminates the efforts of disparate and inconsistent understanding of the two concepts), d) epistemological arguments (the possibility of intersubjective thinking of reality is created), linguistic arguments, e) logical and realistic arguments (it is noted the situation that allows to think coherently in a system of concepts - derivative series or integrative groups) f) and arguments from historical experience (the concept of communication has temporal priority, it appears 13 times in Julius Caesar’s writings ). In an axiomatic conclusion, the main arguments are summarized in four axioms: three are based on the pertinent observations of specialists, and the fourth is a relevant application of Florentin Smarandache’s neutrosophic theory. (shrink)

The paper offers the foundations of the theory of information media. Information media are dynamical systems with additional macrostructure of information-carrying states and information-preserving transformations. The paper also defines the notion of information media network as a system of information media connected by information transformations. It is demonstrated that many standard examples of information-containing and processing systems are captured by the general notion of information medium. The paper uses the theory (and informal discussion) of information media to motivate a structural (...) approach to the information in media. The idea is that the notion of information transformation should be regarded as more primitive than the notion of informational state. Thus in information systems, especially in the context of information technology, information is secondary while information transformation is primary. (shrink)

. The origin and history of Landauer’s principle is traced through the development of the thermodynamics of computation at IBM from 1959 to 1982. This development was characterized by multiple conceptual shifts: memory came to be seen not as information storage, but as delayed information transmission; information itself was seen not as a disembodied logical entity, but as participating in the physical world; and logical irreversibility was connected with physical, thermodynamic, irreversibility. These conceptual shifts were characterized by an ambivalence opposing (...) strong metaphysical claims to practical considerations. Three sorts of practical considerations are discussed. First, these conceptual shifts engaged materials central to IBM’s business practice. Second, arguments for metaphysical certainties were made with reference to the practical functioning of typical computers. Third, arguments for metaphysical certainties were made in the context of establishing the thermodynamics of information as a sub-discipline of physics. (shrink)

Within continental philosophy of biology the work of Michel Serres has not received a lot of attention. Nonetheless, this chapter wants to argue that Serres was part of a group of thinkers – together with Jacques Monod and Henri Atlan – that started to think about biology in terms of second-order cybernetics and information theory. Therefore, this chapter aims to do four things. First of all, it maps the relation between Serres and Canguilhem, one that was mediated by authors such (...) as Louis Althusser or Jacques Monod. Secondly, it fleshes out Serres’s own ‘biophilosophy’. I label this alternative tradition as a ‘biophilosophy without a subject’. Finally, this chapter explores the consequences of this alternative biophilosophy through a brief examination of two authors whose work lies in the line of this tradition: René Girard and Bruno Latour. Though at first sight different, they both draw inspiration from this biophilosophy to develop a framework that, paradoxically, ‘jumps over’ the subject. Hence, the reason why biology is neither a prominent theme in Girard’s nor in Latour’s work. This is not because of a lack of biophilosophy, but because of an implicit one: a biophilosophy without a subject. (shrink)

It is assumed that experiments yield results that are not isomorphic with reality, but represent a distorted image of reality. Reality is related to observation via a communication channel of finite capacity. Quantum uncertainties are due to the bound on the amount of information available. Use is made of recent results from information and communication theories.

The physical process of observation is considered from a specific information theoretical viewpoint. Using the modified concept of an information based on infinite alternatives, a formalism is derived describing the elementary transfer of one bit of information. This bit of information is produced on a virtual (nonreal) sub-quantum level of physical description. The interpretation of the formalism yields the following, complementary points: (i) the effect of spatiotemporal delocalization on the sub-quantum level, and (ii) a possible access to the concept of (...) chaos as an intrinsic property of quantum systems. As a brief example, elementary information transfer is illustrated in a cosmological context. Finally, a formal approach to information production on the sub-quantum level is sketched on the basis of complex time. (shrink)

The living forms represented in this paper are sets of parts that spontaneously increase in organization. Their organizations are measured by an information-theoretic function derived from the work of Boltzmann and Shannon. We briefly review its derivation in the context of the troubled role of mathematics in biology, and then define the function. We illustrate its nature by measuring the 22 different organizations of a set of eight things; and we facilitate its use by defining the parameters that determine an (...) amount of organization. The measure is then applied to show that the organization of limb pairs on free-living arthropods, based on data given by Cisne, confirms a pattern of increasing organization in their evolution from the Cambrian era to the present. Further applications measure the changes in organizations of ideal (theoretical) life forms, and contrasting changes in inanimate systems. Our main results represent the reproduction of unicellular organisms, and the formation of hierarchies, as processes of increasing organization. (shrink)

"Complexity" is a catchword of certain extremely popular and rapidly developing interdisciplinary new sciences, often called accordingly the sciences of complexity. It is often closely associated with another notably popular but ambiguous word, "information"; information, in turn, may be justly called the central new concept in the whole 20th century science. Moreover, the notion of information is regularly coupled with a key concept of thermodynamics, viz. entropy. And like this was not enough it is quite usual to add one more (...) at present extraordinarily popular notion, namely chaos, and wed it with the abovementioned concepts. It is my aim in this paper to critically analyse this conceptual mess from a logical and philosophical point of view concentrating on the concepts of complexity and information and the question concerning the true relation between them. (shrink)

We consider, from a physical perspective, the case where the interface between an organism and its environment becomes large enough that it acts as a buffer regulating their matter and energy exchanges. We illustrate the physiological and evolutionary role of buffers through the example of lungfish estivation. Then we ponder the relevance of buffers of this kind to the quest for a general definition of concepts like niche construction, the extended phenotype, and related ones, whose meaning is conveyed at present (...) mostly through particular examples. Finally, we comment on the potential significance of buffers to organism—environment codetermination in the sense originally suggested by Lewontin. (shrink)

We present an analysis of Szilard's one-molecule Maxwell's demon, including a detailed entropy accounting, that suggests a general theory of the entropy cost of information. It is shown that the entropy of the demon increases during the expansion step, due to the decoupling of the molecule from the measurement information. It is also shown that there is an entropy symmetry between the measurement and erasure steps, whereby the two steps additivelv share a constant entropy change, but the proportion that occurs (...) during each of the two steps is arbitrary. Therefore the measurement step may be accompanied by an entropy increase, a decrease, or no change at all, and likewise for the erasure step. Generalizing beyond the demon, decorrelation between a physical system and information about that system always causes an entropy increase in the joint system comprised of both the original system and the information. Decorrelation causes a net entropy increase in the universe unless, as in the Szilard demon, the information is used to decrease entropy elsewhere before the correlation is lost. Thus, information is thermodynamically costly precisely to the extent that it is not used to obtain work from the measured system. (shrink)

All the attempts to find the justification of the privileged evolution of phenomena exclusively in the external world need to refer to the inescapable fact that we are living in such an asymmetric universe. This leads us to look for the origin of the “arrow of time” in the relationship between the subject and the world. The anthropic argument shows that the arrow of time is the condition of the possibility of emergence and maintenance of life in the universe. Moreover, (...) according to Bohr’s, Poincaré’s and Watanabe’s analysis, this agreement between the earlier-later direction of entropy increase and the past-future direction of life is the very condition of the possibility for meaningful action, representation and creation. Beyond this relationship of logical necessity between the meaning process and the arrow of time the question of their possible physical connection is explored. To answer affirmatively to this question, the meaning process is modelled as an evolving tree-like structure, called “Semantic Time”, where thermodynamic irreversibility can be shown. (shrink)

Brillouin sees order as generated by tapping negentropy sources existing upstream, while Prigogine sees it as generated by dumping entropy downstream. Joining both ideas yields a picture of the computer closely paralleling that of Carnot's heat engine. The difference is that the one delivers information and the other, work. In either case the irretrievable (that is, by definition) loss occurs at the last step. Bennett and Landauer very rightly emphasize this, but their fixation on the condenser blinds them to the (...) necessity of the furnace; thus they are led to believe in the possibility of “perpetual duplication of the second kind,” which Brillouin explicitly denies. (shrink)

In the course of a study of elementary particles, an analysis is given of a fundamental presupposition of many research programs, namely the belief in the ultimate unity of physics. It is argued tht this unity-idea is incorrect. By classical physics, relativity theory and quantum theory three distinct structures of nature are revealed. Next, the essential aspect of measurement, that a measurement always results in a record, is analysed. Recording implies irreversibility and entropy production. In modern elementary particle physics the (...) record itself is all important, and therefore the entropy production due to measurement is essential. It is argued that this aspect of measurement will play a central role in a distinct theory concerning fundamental characteristics of elementary particles, revealing a fourth structure of physical reality. Some basic notions of this new theory are proposed. Finally the meaning of irreversibility on the micro-level of elementary particles is discussed, in connection with the concept of time. (shrink)