We present a novel approach to quantum theory construction that involves maximizing the Shannon entropy of quantum measurements relative to their initial preparation. By constraining the maximization problem with a phase that vanish under measurements, we obtain quantum mechanics (vanishing U(1)-valued phase), relativistic quantum mechanics (vanishing Spin^c(3,1)-valued phase), and quantum gravity (also a vanishing Spin^c(3,1)-valued phase, but with a non-vanishing dilation part). The first two cases are equivalent to established theory, whereas the later case yields a quantum theory of (...) accelerated reference frames, in which a quantized version of the Einstein field equation lives. Specifically, the spacetime interval is promoted to an observable, effectively building the metric tensor from the underlying quantum structure. Moreover, the SU(3)xSU(2)xU(1) gauge symmetries of the Standard Model arise naturally without additional assumptions. Finally, the solution is consistent only with 3+1 spacetime dimensions, as it encounters obstructions in all other dimensional configurations. This framework integrates quantum mechanics, relativistic quantum mechanics, quantum gravity, spacetime dimensionality, and particle physics gauge symmetries from a simple entropy maximization problem constrained by a vanishing phase. (shrink)

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...) paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states. (shrink)

[Accepted for publication in Lakatos's Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, special issue of Kriterion: Journal of Philosophy. Edited by S. Nagler, H. Pilin, and D. Sarikaya.] Lakatos’s analysis of progress and degeneration in the Methodology of Scientific Research Programmes is well-known. Less known, however, are his thoughts on degeneration in Proofs and Refutations. I propose and motivate two new criteria for degeneration based on the discussion in Proofs and Refutations (...) – superfluity and authoritarianism. I show how these criteria augment the account in Methodology of Scientific Research Programmes, providing a generalized Lakatosian account of progress and degeneration. I then apply this generalized account to a key transition point in the history of entropy – the transition to an information-theoretic interpretation of entropy – by assessing Jaynes’s 1957 paper on information theory and statistical mechanics. (shrink)

Purpose – The purpose of this paper is to ask whether a first-order-cybernetics concept, Shannon’s Information Theory, actually allows a far-reaching mathematics of perception allegedly derived from it, Norwich et al.’s “Entropy Theory of Perception”. Design/methodology/approach – All of The Entropy Theory, 35 years of publications, was scrutinized for its characterization of what underlies Shannon Information Theory: Shannon’s “general communication system”. There, “events” are passed by a “source” to a “transmitter”, thence through a “noisy channel” to a “receiver”, (...) that passes “outcomes” (received events) to a “destination”. Findings – In the entropy theory, “events” were sometimes interactions with the stimulus, but could be microscopic stimulus conditions. “Outcomes” often went unnamed; sometimes, the stimulus, or the interaction with it, or the resulting sensation, were “outcomes”. A “source” was often implied to be a “transmitter”, which frequently was a primary afferent neuron; elsewhere, the stimulus was the “transmitter” and perhaps also the “source”. “Channel” was rarely named; once, it was the whole eye; once, the incident photons; elsewhere, the primary or secondary afferent. “Receiver” was usually the sensory receptor, but could be an afferent. “Destination” went unmentioned. In sum, the entropy theory’s idea of Shannon’s “general communication system” was entirely ambiguous. Research limitations/implications – The ambiguities indicate that, contrary to claim, the entropy theory cannot be an “information theoretical description of the process of perception”. Originality/value – Scrutiny of the entropy theory’s use of information theory was overdue and reveals incompatibilities that force a reconsideration of information theory’s possible role in perception models. A second-order-cybernetics approach is suggested. (shrink)

The principle of maximal entropy (further abbreviated as “MaxEnt”) can be founded on the formal mechanism, in which future transforms into past by the mediation of present. This allows of MaxEnt to be investigated by the theory of quantum information. MaxEnt can be considered as an inductive analog or generalization of “Occam’s razor”. It depends crucially on choice and thus on information just as all inductive methods of reasoning. The essence shared by Occam’s razor and MaxEnt is for the (...) relevant data known till now to be postulated as an enough fundament of conclusion. That axiom is the kind of choice grounding both principles. Popper’s falsifiability (1935) can be discussed as a complement to them: That axiom (or axiom scheme) is always sufficient but never necessary condition of conclusion therefore postulating the choice in the base of MaxEnt. Furthermore, the abstraction axiom (or axiom scheme) relevant to set theory (e.g. the axiom scheme of specification in ZFC) involves choice analogically. (shrink)

A generalized information theory is proposed as a natural extension of Shannon's information theory. It proposes that information comes from forecasts. The more precise and the more unexpected a forecast is, the more information it conveys. If subjective forecast always conforms with objective facts then the generalized information measure will be equivalent to Shannon's information measure. The generalized communication model is consistent with K. R. Popper's model of knowledge evolution. The mathematical foundations of the new information theory, (...) the generalized communication model , information measures for semantic information and sensory information, and the coding meanings of generalized entropy and generalized mutual information are introduced. Assessments and optimizations of pattern recognition, predictions, and detection with the generalized information criterion are discussed. For economization of communication, a revised version of rate-distortion theory: rate-of-keeping-precision theory, which is a theory for datum compression and also a theory for matching an objective channels with the subjective understanding of information receivers, is proposed. Applications include stock market forecasting and video image presentation. (shrink)

Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by (...) means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo-Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement and exploit it to define entanglement measures in the general probabilistic framework. In addition, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted). (shrink)

This paper reveals errors within Norwich et al.’s Entropy Theory of Perception, errors that have broad implications for our understanding of perception. What Norwich and coauthors dubbed their “informational theory of neural coding” is based on cybernetics, that is, control and communication in man and machine. The Entropy Theory uses information theory to interpret human performance in absolute judgments. There, the continuum of the intensity of a sensory stimulus is cut into categories and the subject is shown exemplar (...) stimuli of each category. The subject must then identify individual exemplars by category. The identifications are recorded in the Garner-Hake version of the Shannon “confusion matrix”. The matrix yields “H”, the entropy (degree of uncertainty) about what stimulus was presented. Hypothetically, uncertainty drops as a stimulus lengthens, i.e. a plot of H vs. stimulus duration should fall monotonically. Such “adaptation” is known for both sensation and firing rate. Hence, because “the physiological adaptation curve has the same general shape as the psychophysical adaptation curve”, Norwich et al. assumed that both have the same time course; sensation and firing rate were thus both declared proportional to H. However, a closer look reveals insurmountable contradictions. First, the peripheral neuron hypothetically cannot fire in response to a stimulus of a given intensity until after somehow computing H from its responses to stimuli of various intensities. Thus no sensation occurs until firing rate adapts, i.e. attains its spontaneous rate. But hypothetically, once adaptation is complete, certainty is reached and perception ends. Altogether, then, perception cannot occur until perception is over. Secondly, sensations, firing rates, and H’s are empirically not synchronous, contrary to assumption. In sum, the core concept of the cybernetics-based Entropy Theory of Perception, that is, that uncertainty reduction is the basis for perception, is irrational. (shrink)

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author’s semantic information G theory with (...) the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shannon’s MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon’s MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks’ latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development. (shrink)

Within the field of quantum gravity, there is an influential research program developing the connection between quantum entanglement and spatiotemporal distance. Quantum information theory gives us highly refined tools for quantifying quantum entanglement such as the entanglement entropy. Through a series of well-confirmed results, it has been shown how these facts about the entanglement entropy of component systems may be connected to facts about spatiotemporal distance. Physicists are seeing these results as yielding promising methods for better understanding the (...) emergence of (the dynamical) spacetime (of general relativity) from more fundamental quantum theories, and moreover, as promising for the development of a nonperturbative theory of quantum gravity. However, to what extent does the case for the entanglement entropy-distance link provide evidence that spacetime structure is nonfundamental and emergent from nongravitational degrees of freedom? I will show that a closer look at the results lends support only to a weaker conclusion, that the facts about quantum entanglement are constrained by facts about spatiotemporal distance, and not that they are the basis from which facts about spatiotemporal distance emerge. (shrink)

For scatterplots with gaussian distributions of dots, the perception of Pearson correlation r can be described by two simple laws: a linear one for discrimination, and a logarithmic one for perceived magnitude (Rensink & Baldridge, 2010). The underlying perceptual mechanisms, however, remain poorly understood. To cast light on these, four different distributions of datapoints were examined. The first had 100 points with equal variance in both dimensions. Consistent with earlier results, just noticeable difference (JND) was a linear function of the (...) distance away from r = 1, and the magnitude of perceived correlation a logarithmic function of this quantity. In addition, these laws were linked, with the intercept of the JND line being the inverse of the bias in perceived magnitude. Three other conditions were also examined: a dot cloud with 25 points, a horizontal compression of the cloud, and a cloud with a uniform distribution of dots. Performance was found to be similar in all conditions. The generality and form of these laws suggest that what underlies correlation perception is not a geometric structure such as the shape of the dot cloud, but the shape of the probability distribution of the dots, likely inferred via a form of ensemble coding. It is suggested that this reflects the ability of observers to perceive the information entropy in an image, with this quantity used as a proxy for Pearson correlation. (shrink)

Many researchers suppose that the forward direction of time as a consequence of increasing entropy. But the human brain, including the human brain with memories, and life in general, are regarded as pockets of decreasing entropy, so as to accommodate the continual addition of memories and abilities. But then humans and life in general should see time going ‘backward’ in some sense. But we do not. Therefore, time is not entropic in origin. -/- The purpose of this note (...) is to bring attention to this idea. (shrink)

Maxwell’s Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to “exorcise” the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, (...) but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell’s Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer’s thesis, are not general. In this paper we demonstrate that Maxwell’s Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of “macrostates”, thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere. (shrink)

In this article, the notion of entropology introduced by Claude Lévi-Strauss is applied and developed in the context of Georges Bataille’s anthropological philosophy: Bataille’s project is defined as entropological. Four philosophical vectors are chosen for this: the theory of general economy, the concept of decay, the idea of extinction and the notion of inhumanism. The theory of general economy allows us to understand the immanent terrestrial nature of humanity and the negative – entropic – side of the capitalist economy. The (...) concept of decay gives access to the thought of bodily disintegration and decomposition, which is temporality and mortality that split the subject. The idea of extinction speculates on the consequences of humanity’s destructiveness, libidinally charged inertia, and the extreme perspective of entropy’s impact on the planet. The notion of inhumanism suggests a radical rethinking of the human relationship with alienation and exteriority: Bataille’s philosophy is reinterpreted as inhumanist. I conclude that the Lévi-Strauss’s neologism – entropology – can be productively articulated and actualised within the framework of Bataille’s philosophy. (shrink)

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some (...) theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. (shrink)

Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang. A theory in which most observers are of the Boltzmann Brain type is generally thought to be unacceptable, although opinions differ. I argue that such theories are indeed unacceptable: the real problem is with fluctuations into observers who are locally identical to ordinary observers, and their existence cannot be swept under the (...) rug by a choice of probability distributions over observers. The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there (...) are two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

The paper provides an axiological analysis of the concepts of respect for information and of information dignity from the vantage point provided by Information Ethics and the conceptual paradigm of object-oriented analysis (OOA). The general perspective adopted is that of an ontocentric approach to the philosophy of information ethics, according to which the latter is an expansion of environmental ethics towards a less biologically biased concept of a ‘centre of ethical worth’. The paper attempts to answer the following question: what (...) is the lowest possible common set of attributes which characterises something as intrinsically valuable and an object of respect, and without which something would rightly be considered intrinsically worthless or even positively unworthy and therefore rightly disrespectable in itself? The thesis developed and defended in the paper is that the minimal condition of possibility of an object’s least intrinsic worthiness can be identified with its abstract nature as an information entity. Thus, all entities, interpreted as clusters of information, have a minimal moral worth qua information objects (i.e. qua information), that deserves to be respected. The principles elaborated in the course of the analysis are those of ‘reflective respect’ (A’s respect towards all members of A’s class motivated by A’s respect towards A not qua individual, but qua instantiation of a class of entities), ‘ontic uniformity’ (A’s recognition of A’s membership to the class of information entities) and ‘ontic solidarity’ (A’s recognition of any information entity’s dignity). (shrink)

What is the most general common set of attributes that characterises something as intrinsically valuable and hence as subject to some moral respect, and without which something would rightly be considered intrinsically worthless or even positively unworthy and therefore rightly to be disrespected in itself? This paper develops and supports the thesis that the minimal condition of possibility of an entity's least intrinsic value is to be identified with its ontological status as an information object. All entities, even when interpreted (...) as only clusters of information, still have a minimal moral worth qua information objects and so may deserve to be respected. The paper is organised into four main sections. Section 1 models moral action as an information system using the object-oriented programming methodology (OOP). Section 2 addresses the question of what role the several components constituting the moral system can have in an ethical analysis. If they can play only an instrumental role, then Computer Ethics (CE) is probably bound to remain at most a practical, field-dependent, applied or professional ethics. However, Computer Ethics can give rise to a macroethical approach, namely Information Ethics (IE), if one can show that ethical concern should be extended to include not only human, animal or biological entities, but also information objects. The following two sections show how this minimalist level of analysis can be achieved. Section 3 provides an axiological analysis of information objects. It criticises the Kantian approach to the concept of intrinsic value and shows that it can be improved by using the methodology introduced in the first section. The solution of the Kantian problem prompts the reformulation of the key question concerning the moral worth of an entity: what is the intrinsic value of x qua an object constituted by its inherited attributes? In answering this question, it is argued that entities can share different observable properties depending on the level of abstraction adopted,and that it is still possible to speak of moral value even at the highest level of ontological abstraction represented by the informational analysis. Section 4 develops a minimalist axiology based on the concept of information object. It further supports IE's position by addressing five objections that may undermine its acceptability. (shrink)

The essential difficulty about Computer Ethics' (CE) philosophical status is a methodological problem: standard ethical theories cannot easily be adapted to deal with CE-problems, which appear to strain their conceptual resources, and CE requires a conceptual foundation as an ethical theory. Information Ethics (IE), the philosophical foundational counterpart of CE, can be seen as a particular case of environmental ethics or ethics of the infosphere. What is good for an information entity and the infosphere in general? This is the ethical (...) question asked by IE. The answer is provided by a minimalist theory of deseerts: IE argues that there is something more elementary and fundamental than life and pain, namely being, understood as information, and entropy, and that any information entity is to be recognised as the centre of a minimal moral claim, which deserves recognition and should help to regulate the implementation of any information process involving it. IE can provide a valuable perspective from which to approach, with insight and adequate discernment, not only moral problems in CE, but also the whole range of conceptual and moral phenomena that form the ethical discourse. (shrink)

The essential difficulty about Computer Ethics’ (CE) philosophical status is a methodological problem: standard ethical theories cannot easily be adapted to deal with CE-problems, which appear to strain their conceptual resources, and CE requires a conceptual foundation as an ethical theory. Information Ethics (IE), the philosophical foundational counterpart of CE, can be seen as a particular case of ‘environmental’ ethics or ethics of the infosphere. What is good for an information entity and the infosphere in general? This is the ethical (...) question asked by IE. The answer is provided by a minimalist theory of deserts: IE argues that there is something more elementary and fundamental than life and pain, namely being, understood as information, and entropy, and that any information entity is to be recognised as the centre of a minimal moral claim, which deserves recognition and should help to regulate the implementation of any information process involving it. IE can provide a valuable perspective from which to approach, with insight and adequate discernment, not only moral problems in CE, but also the whole range of conceptual and moral phenomena that form the ethical discourse. (shrink)

Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to the (...) largest macro-region. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. (shrink)

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of (...) time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite (...) probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |U|² from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions.". (shrink)

This paper develops a Fragmentalist theory of Presentism and shows how it can help to develop a interpretation of quantum mechanics. There are several fragmental interpretations of physics. In the interpretation of this paper, each quantum system forms a fragment, and fragment f1 makes a measurement on fragment f2 if and only if f2 makes a corresponding measurement on f1. The main idea is then that each fragment has its own present (or ‘now’) until a mutual quantum measurement—at which time (...) they come (‘become’) to share the same ‘now’. The theory of time developed here will make use of both McTaggart’s A-series (in the form of future-present-past) and B-series (earlier-times to later-times). An example of an application is that a Bell pair of electrons does not take on definite spin values until measurement because the measuring system and the Bell pair do not share the same present (‘now’) until mutual quantum measurement, i.e. until they ‘become’ to share the same A-series. Before that point the ‘now’ of the opposing system is not in the reference system’s fragment. Relativistic no-signaling is preserved within each fragment, which will turn out to be sufficient for the general case. Several issues in the foundations of quantum mechanics are canvassed, including Schrodinger’s cat, the Born rule, modifications to Minkowski space that accommodate both the A-series and the B-series, and entropy. (shrink)

Although the concept of uncertainty is as old as Epicurus’s writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. (...) Of course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution. (shrink)

My article began as a very short 250 words inspired by astrophysicist Jeff Hester's (pro-evolution) pages on entropy (Astronomy magazine - Oct. and Nov. 2017 - http://www.astronomy.com/magazine/jeff-hester/2017/09/entropys-rainbow and http://www.astronomy.com/magazine/jeff-hester/2017/10/entropy-redux). The letter I wrote pointed out evolution's pluses (eg adaptations) and minuses (regarding origins). It went on to speak of a human, scientific, entirely natural explanation for what is called God. It proposes that the true human condition after death and before birth is as a member of the Elohim (...) - a name used for God in the Old Testament which, according to World Book Encyclopedia, means the PLURAL MAJESTY OF THE ONE GOD. This led to a few hundred more words about why some people call an entirely natural process "supernatural". I speculate that it must be because of the applications in thousands of years of finding a successful theory of quantum gravity (union of quantum mechanics and Einstein's theory of gravity - general relativity). Like quantum mechanics and gravitation, those apps would include all space and all time, and would undoubtedly be as mysterious to us as our technology would initially be to the builders of Egypt's first pyramids. In years past, the denial of divine beings by science may have been logical. But times sometimes change radically. Such a paradigm shift seems to be upon us now, with the recent discovery of gravitational waves and the anticipation of quantum gravity. In changing times, scientists and philosophers and everyone must always keep open minds. Of course, proposing that the human condition after death and before birth is as a member of the Elohim means that humans of the far distant future must be capable of the creation attributed to God by many people throughout the centuries. Therefore, a subsection entitled "Creation Of The Infinite, Eternal Cosmos Using Electronic BITS, Pi And Imaginary Time" has been added to the end of this article. -/- . (shrink)

In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee (...) that every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect occurring with unit probability on some state. For theories satisfying our four axioms, we show a constructive algorithm for diagonalizing every given state. The diagonalization result allows us to formulate a majorization criterion that captures the convertibility of states in the operational resource theory of purity, where random reversible transformations are regarded as free operations. (shrink)

I propose that, in addition to the commonly recognized increase of entropy, two more time arrows influence living beings. The increase of damage reactions, which produce aging and genetic variation, and the decrease of the rate of entropy production involved in natural selection are neglected arrows of time. Although based on the statistical theory of the arrow of time, they are distinguishable from the general arrow of the increase of entropy. Physiology under healthy conditions only obeys the (...) increase of entropy arrow. But aging, death, and evolution are determined by the other time arrows as well. Paradoxes emerge from conflicts among the specific determinisms associated with each arrow. These conflicts, along with uncertainties intrinsic to the low-number statistics of the arrows of damage reactions and decrease of the rate of production of entropy, highlight the limits of determinism at different levels of biology and its dependence on time span and number of organisms. The recognition of the three time arrows opens new perspectives for the problem of compatibility of the flow of time in physics and psychology. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

Starting from a philosophical perspective, which states that the living structures are actually a combination between matter and information, this article presents the results on an analysis of the bipolar information-matter structure of the human organism, distinguishing three fundamental circuits for its survival, which demonstrates and supports this statement, as a base for further development of the informational model of consciousness to a general informational model of the human organism. For this, it was examined the Informational System of the Human (...) Body and its components from the perspective of the physics/information/neurosciences concepts, showing specific functions of each of them, highlighting the correspondence of these centers with brain support areas and with their projections in consciousness, which are: Center of Acquisition and Storing of Information (CASI) reflected in consciousness as memory, Center of Decision and Command (CDC) (decision), Info-Emotional Center (IES) (emotions), Maintenance Informational System (MIS) (personal status), Genetic Transmission System (GTS) (associativity/genetic transmission) and Info Genetic Generator (IGG) related by the body development and inherited behaviors. The Info Connection (IC), detected in consciousness as trust and confidence can explain the Near-Death Experiences (NDEs) and associated phenomena. This connection is antientropic and informational, because from the multitude of uncertain possibilities is selected a certain one, helping/supporting the survival and life. The human body appears therefore as a bipolar structure, connected to two poles: information and matter. It is argued that the survival, which is the main objective of the organism, is complied in three main ways, by means of: (i) the reactive operation for adaptation by attitude; (ii) the info-genetic integration of information by epigenetic processes and genetic transmission of information for species survival, both circuits (i) and (ii) being associated to the information pole; (iii) maintenance of the material body (defined as informed matter) and its functions, associated to the matter pole of the organism. It results therefore that the informational system of the human body is supported by seven informational circuits formed by the neuro-connections between the specific zones of the brain corresponding to the informational subsystems, the cognitive centers, the sensors, transducers and execution (motor/mobile) elements. The fundamental informational circuits assuring the survival are the reactive circuit, expressible by attitude, the epigenetic/genetic circuit, absorbing and codifying information to be transmitted to the next generations, and the metabolic circuit, connected to matter (matter pole). The presented analysis allows to extend the informational modeling of consciousness to an Informational Model of Consciousness and Organism, fully describing the composition/functions of the organism in terms of information/matter and neurosciences concept. (shrink)

This book is the result of a collective research effort performed during many years in both Sweden and Spain. It is the result of attempting to develop a new field of research that could we denominate «human act informatics.» The goal has been to use the technologies of information to the study of the human act in general, including embodied acts and disembodied acts. The book presents a theory of the quantification of the informational value of human acts as order, (...) opposing the living order against entropy. We present acting as a set of decisions and choices aimed to create order and to impose Modernity. Karl Popper’s frequency theory of probability is applied to characterize human acts regarding their degree of freedom and to set up a scale of order in human decisions. The traditional theory of economics and social science characterize the human act as rational, utilitarian and ethical. Our results emphasize that the unique significance of an act lies in its capacity to generate order. An adequate methodology is then presented to defend such hypothesis according to which, the rationality respective irrationality of acting, is in fact only a function of the act’s organizational capacity. From this perspective, it has been necessary to define «order» respective «disorder» as operative concepts that allowed the comparison of the organizational differences generated by each kind of act. According to the presented conclusions, the spontaneity of living, as unconscious thinking, dreaming, loving, etc. and the mainstream of the human acts, are utilitarian, but in an irrational way; they are rooted in unconscious drifts and therefore must be considered irrational-utility acts. (shrink)

Macroscopic irreversible processes emerge from fundamental physical laws of reversible character. The source of the local irreversibility seems to be not in the laws themselves but in the initial and boundary conditions of the equations that represent the laws. In this work we propose that the screening of currents by black hole event horizons determines, locally, a preferred direction for the flux of electromagnetic energy. We study the growth of black hole event horizons due to the cosmological expansion and accretion (...) of cosmic microwave background radiation, for different cosmological models. We propose generalized McVittie co-moving metrics and integrate the rate of accretion of cosmic microwave background radiation onto a supermassive black hole over cosmic time. We find that for flat, open, and closed Friedmann cosmological models, the ratio of the total area of the black hole event horizons with respect to the area of a radial co-moving space-like hypersurface always increases. Since accretion of cosmic radiation sets an absolute lower limit to the total matter accreted by black holes, this implies that the causal past and future are not mirror symmetric for any spacetime event. The asymmetry causes a net Poynting flux in the global future direction; the latter is in turn related to the ever increasing thermodynamic entropy. Thus, we expose a connection between four different “time arrows”: cosmological, electromagnetic, gravitational, and thermodynamic. (shrink)

Many religions and religious philosophies say that ultimate reality is a kind of primal energy. This energy is often described as a vital power animating living things, as a spiritual force directing the organization of matter, or as a divine creative power which generates all things. By refuting older conceptions of primal energy, modern science opens the door to new and more precise conceptions. Primal energy is referred to here as ‘spirit’. But spirit is a natural power. A naturalistic theory (...) of spirit is developed using ideas from information theory and thermodynamics, such as the maximum entropy production principle. Spirit drives the evolution of complexity at all levels of existence. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being (...) true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

Our intuition tells us that there is a general trend in the evolution of nature, a trend towards greater complexity. However, there are several definitions of complexity and hence it is difficult to argue for or against the validity of this intuition. Christoph Adami has recently introduced a novel measure called physical complexity that assigns low complexity to both ordered and random systems and high complexity to those in between. Physical complexity measures the amount of information that an organism stores (...) in its genome about the environment in which it evolves. The theory of physical complexity predicts that evolution increases the amount of ‘knowledge’ an organism accumulates about its niche. It might be fruitful to generalize Adami’s concept of complexity to the entire evolution (including the evolution of man). Physical complexity fits nicely into the philosophical framework of cognitive biology which considers biological evolution as a progressing process of accumulation of knowledge (as a gradual increase of epistemic complexity). According to this paradigm, evolution is a cognitive ‘ratchet’ that pushes the organisms unidirectionally towards higher complexity. Dynamic environment continually creates problems to be solved. To survive in the environment means to solve the problem, and the solution is an embodied knowledge. Cognitive biology (as well as the theory of physical complexity) uses the concepts of information and entropy and views the evolution from both the information-theoretical and thermodynamical perspective. Concerning humans as conscious beings, it seems necessary to postulate an emergence of a new kind of knowledge - a self-aware and self-referential knowledge. Appearence of selfreflection in evolution indicates that the human brain reached a new qualitative level in the epistemic complexity. (shrink)

The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially, this means that an algorithm can only preserve information about an input, rather than generate new information. This uncertainty arises from characteristics such as arithmetic logical irreversibility, Landauer's principle, and memory erasure, which ultimately lead to a loss of information and an increase in entropy. To measure this uncertainty and (...) loss of information, the concept of arithmetic logical entropy can be used. The Turing machine and its equivalent, general recursive functions can be understood through the λ calculus and the Turing/Church thesis. However, there are certain recursive functions that cannot be fully understood or predicted by other algorithms due to the loss of information during logical-arithmetic operations. In other words, the behaviour of these functions cannot be completely determined at every stage of the computation due to a lack of information in their definition. While there are some cases where the behaviour of recursive functions is highly predictable, the lack of information in most cases makes it impossible for algorithms to determine if a program will halt or not. This inability to predict the outcome of the computation is the essence of the halting problem of the Turing machine. Even in cases where more information is available about the program, it is still difficult to determine with certainty if the program will halt or not. This also highlights the importance of the Turing oracle machine, which introduces information from outside the computation to compensate for the lack of information and ultimately decide the result of the computation. (shrink)

Abstract The Greek composer and architect Iannis Xenakis has shown in Formalized Music (1963) how it is possible to compose or describe music and sound by means of probabilistic laws from mathematics, information theory and statistical mechanics. In his theory, scientific concepts and properties such as entropy take on a musical meaning in that they become also properties structurally instantiable by music. Philosophically speaking, this raises many important questions about the relation between science and the arts. One of these (...) questions concerns in particular the possibility for aesthetic symbols (like musical compositions) to convey scientific understanding, and understanding in general. In the present work, I claim that this question can be answered positively. In general, understanding does not necessarily depend on truth, explanation and propositionality (non-factualism, non-reductivism). Understanding can be conveyed also in non-propositional domains, in particular by means of exemplification. Since aesthetic and musical symbols are non-propositional, they can advance understanding possibly by exemplification, and in particular scientific understanding as long as they exemplify scientific concepts and properties. I moreover substantiate my claim by taking a case study: the concept of entropy in music. On the basis of Xenakis’ stochastic theory of music, I show how by exemplifying this concept, music can advance understanding of it. (shrink)

State features are affected by the connection with digital coins. Social systems create their own limits and remain alive according to their internal logic, which does not derive from the system environment. So, social systems are operationally and autonomously closed - interacting with their environment and there is a general increase in entropy, but individual systems work to maintain and preserve their internal order. Autopoietic systems (like the state, with the tendency to maintain the inner order with a remarkable (...) degree of independence from the outside world) may contrast with allopoietic ones. It results in a state with a finite influence area, but recently troubled by the new forms of digital money and the corresponding infrastructure. DOI: 10.13140/RG.2.2.28007.80803 . (shrink)

Ediţia a doua (revăzută şi îmbunătăţită) O introducere în teoriile şi conceptele, forţele fundamentale şi particule, metode şi tabele utilizate în fizică, subdomenii şi domenii ştiinţifice înrudite, cu accent pe înţelegerea fenomenelor fizice. Fizica clasică se ocupă, în general, cu materia și energia la scară normală de observație, în timp ce o mare parte a fizicii moderne se ocupă de comportamentul materiei și energiei în condiții extreme sau pe o scară foarte mare sau foarte mică. De exemplu, pentru fizica atomică (...) și nucleară contează scara cea mai mică la care elementele chimice pot fi identificate. Fizica particulelor elementare are o scară chiar mai mică, deoarece se referă la unitățile de bază ale materiei; această ramură a fizicii este, de asemenea, cunoscută sub numele de fizica energiilor înalte, din cauza energiilor extrem de ridicate necesare pentru a produce mai multe tipuri de particule, în acceleratoare de particule mari. La această scară, de obicei, noțiunile obișnuite de spațiu, timp, materie și energie nu mai sunt valabile. Cele două teorii principale ale fizicii moderne prezintă o imagine diferită a conceptelor de spațiu, timp, și materie, faţă de fizica clasică. Teoria cuantică studiază natura mai degrabă discretă decât continuă a multor fenomene la nivel atomic și subatomic, și aspectele complementare ale particulelor și undelor în descrierea unor astfel de fenomene. Teoria relativității studiază descrierea fenomenelor care au loc într-un cadru de referință, care este în mișcare faţă de un observator. Teoria specială a relativității studiază mișcarea relativ uniformă în linie dreaptă, iar teoria generală a relativității mișcarea accelerată și legătura sa cu gravitația. Atât teoria cuantică cât și teoria relativității îşi găsesc aplicații în toate domeniile fizicii moderne. CUPRINS: Fizica - Scurtă istorie - Fizica şi filozofia - Teorii de bază în fizică - - Fizica clasică - - Fizica modernă - - Diferenţa între fizica clasică şi fizica modernă - Cercetarea în fizică - - Metode ştiinţifice - - Teorie şi experiment - Domenii de aplicare şi obiective - - Domenii de cercetare - - Direcţii de dezvoltare - - Direcţii actuale de cercetare Teorii - Fizica teoretică - - Teorii recunoscute - - Teorii propuse - - Teorii marginale Teorii recunoscute - Termodinamica - - Legile termodinamicii - - Concepte în termodinamică - - Substanţe care se pot descrie doar prin temperatură - - Substanţe care se pot descrie doar prin temperatură şi presiune - - Substanţe care se pot descrie prin temperatură, presiune şi potenţial chimic - - Substanţe care se pot descrie prin temperatură şi câmp magnetic - - Sisteme termodinamice - - Stări termodinamice - Mecanica statistică - Relativitatea specială - - Motivaţia pentru teoria relativităţii speciale - - Invarianţa vitezei luminii - - Lipsa unui cadru de referinţă absolut - - Echivalenţa dintre energie şi masă - - Simultaneitatea - - Evoluţia teoriei relativităţii speciale - Teoria relativităţii generale - - Dezvoltarea relativităţii şi a relativităţii speciale - - Gaura de vierme - - - Călătorii cu viteze mai mari decât viteza luminii şi călătorii în timp - - - Universul nostru, într-o gaură neagră - - - Concluzii - Mecanica cuantică - - Descrierea teoriei - - Formularea matematică - - Interacţia cu alte teorii ale fizicii - - Istoria, filozofia şi viitorul mecanicii cuantice - - - Istoria - - - Filozofia - - - Viitorul - - Optica cuantică - - - Electronica cuantică - - Laser - - - Concepte de bază - - - Terminologie - - - Construcţia unui laser - - - Fizica laserilor - - - Extreme Light Infrastructure - - - Arme cu laser - Teoria câmpului cuantic - - Probleme ale mecanicii cuantice obişnuite - - Câmpuri cuantice - Modelul Standard - - Teste, predicţii şi provocări Teorii propuse - Teoria finală (Theory of everything) - - Idei speculative - Teoria marii unificări - Teoria M - - Relaţia teoriei M cu supercorzile şi supergravitaţia - - Caracteristici ale teoriei M - Gravitaţia cuantică în buclă - - Incompatibilitatea dintre mecanica cuantică şi relativitatea generală - - Buclele Wilson şi reţelele de spin - - Gravitaţia cuantică în buclă şi cosmologia cuantică - - Testele experimentale de GCB - Emergenţa Teorii marginale - Fuziunea la rece - - Fuziunea cu bule - Tesla şi Teoria dinamică a gravitaţiei - Eter luminifer - - Dezavantaje şi critici - Energia orgonică - - Dezvoltarea de către Reich a teoriilor sale orgonice - - Cărţile lui Reich Concepte - Mecanica clasică - - Istoria - - Statica - - - Vectori - - - Forţa - - - Momentul forţei - - - Ecuaţiile de echilibru - - - Momentul de inerţie - - - Solide - - - Fluide - - Dinamica - - - Principii - - - Dinamica liniară şi de rotaţie - - - Forţa - - - Legile lui Newton - - Frecarea - - - Legile frecării uscate - - - Reducerea frecării - Materia - - Antimateria - Energia - - Legile conservării în fizică - - - Filosofia legilor de conservare - - Masa - - - Masa inerţială - - - Masa gravitaţională - - - Echivalenţa maselor inerţială şi gravitaţională - - - Consecinţele relativităţii - - Cantitatea de mişcare (impulsul) - - - Cantitatea de mişcare în mecanica clasică - - - Cantitatea de mişcare în mecanica relativistă - - - Cantitatea de mişcare în mecanica cuantică - - Momentul cinetic - - Spinul - - - Istoria - - - Aplicaţii - Dimensiuni - - Timpul - - - Măsurarea timpului - - - Timpul în inginerie şi fizica aplicată - - - Timpul în filosofie şi fizica teoretică - - Spaţiu-timp - - - Cadrul de referinţă - - - Câteva fapte generale despre spaţiu-timp - - - Este spaţiul-timp cuantificat? - - Viteza - - Forţa - - - Relaţiile dintre unităţile de forţă şi unităţile de masă - - - Unităţi imperiale de forţă - - Momentul forţei - Sisteme fizice - Unde - - Exemple de unde - - Proprietăţi caracteristice - - Unde transversale şi longitudinale - - Polarizarea - - Descriere fizică a unei unde - - Unde de deplasare - - Ecuaţia undelor - - Entanglementul cuantic - - Magnetism - - - Dipoli magnetici - - - Modele de materiale magnetice - - Electricitatea - - - Istorie - - - Puterea electrică - - - Curentul electric - - - Fenomene electrice în natură - - Radiaţia electromagnetică - - Temperatura - - - Unităţi de temperatură - - - Bazele teoretice - - - Capacitatea termică - - - Temperatura în gaze - - - Măsurarea temperaturii - - - Temperaturi negative - - Entropia - - - Schimbarea de entropie în motoarele termice - - - Definiţia statistică a entropiei: Principiul lui Boltzmann - - - Măsurarea entropiei - - Informaţia în fizică - - - Informaţia clasică vs informaţia cuantică - - - Informaţii clasice - - - Informaţiile fizice şi entropia - Tranziţii - - Tranziţii de fază - - - Clasificarea tranziţiilor de fază - - - - Clasificarea Ehrenfest - - - - Clasificarea modernă a tranziţiilor de fază - - - Proprietăţi ale tranziţiilor de fază - - - - Puncte critice - - - - Simetria - - - - Exponenţi critici şi clase de universalitate - - Supraconductibilitatea - - - Istoria - - - Teorii ale supraconductibilităţii - - - Aplicaţii tehnologice ale supraconductibilităţii - - - Proprietăţile elementare ale supraconductorilor - - Superfluiditatea Forţe fundamentale - Gravitaţia - - Despre legea gravitaţiei universale a lui Newton - - - Forma vectorială - - - Istorie - - - Reticenţele lui Newton - - - Comparaţie cu forţa electromagnetică - - Teoria relativităţii generale a lui Einstein - - - Mecanica cuantică şi ondulatorie - - Situaţii specifice - - - Gravitaţia Pământului - - - Ecuațiile pentru un corp în cădere în apropiere de suprafața Pământului - - - Gravitaţia și astronomia - - - Radiația gravitațională - - - Viteza gravitaţiei - Electromagnetism - - Descrierea matematică - - Câmp electric E - - Metoda electromagnetică - - Electrostatica - - - Serii triboelectrice - - - Generatoare electrostatice - - - Neutralizarea sarcinilor - - - Inducţia sarcinilor - - - Electricitatea "statică" - Forţa nucleară slabă - Forţa nucleară tare Particule - Particule elementare - - Proprietăţi conceptuale - - - Dimensiunea - - - Compoziţia - - Modelul Standard în fizica particulelor elementare - - - Fermioni fundamentali - - - - Antiparticule - - - - Cuarci - - - Bosoni fundamentali - - - - Gluoni - - - - Bosoni electroslabi - - - - Bosonul Higgs - - Extensii ale Modelului Standard în fizica particulelor elementare - - - Marea unificare - - - Supersimetria - - - Teoria corzilor - - - Teoria preonilor - Atomi - - Modele istorice de atomi - - Nucleul atomic - Protoni - Neutroni - - Istoric - - - Evoluţia actuală - Electroni - - Istoria - - Detalii tehnice - - Electricitate - Cuarci - Fotoni - Gluoni - Bosoni W şi Z - - Bosonul Higgs - Gravitoni - Neutrino - - Neutrino, noul sistem de comunicaţii - - Telefonul – particulă - - Comunicaţii cu submarinele - - Mesaje pentru călătoria în timp - Cvasiparticule - - Relaţia cu mecanica cuantică multi-corp - - Distincţia între cvasiparticule şi excitaţii colective - - Efectul asupra proprietăţilor colective - - Istoria - Fononi - - Unde de reţea - - Fononi acustici şi optici Subdomenii - Acustica - - Concepte fundamentale ale acusticii - - - Propagarea undelor: nivele de presiune - - - Propagarea undelor: frecvenţa - - - Transducţia în acustică - Astrofizica - - Erupţii solare - - - Evoluţia exploziilor solare - - - Impactul exploziilor solare asupra omenirii - - - - Ejecţia masei coronariene - - - - Misiunile spaţiale - - - - Întreruperi de energie electrică - Fizica atomică, moleculară, şi optică - - Apa grea - - Osmoza - Fizica computaţională - Fizica materiei condensate - Criogenia - Mecanica fluidelor - Optica - - Optica clasică - - Optica modernă - Fizica plasmei - Fizica particulelor - - Istoria - - Modelul Standard - - Fizica particulelor experimentală - - Obiecţii - - Politici publice Metode - Metode ştiinţifice - - Elementele metodelor ştiinţifice idealizate - - Aspecte ale metodelor ştiinţifice - - - Observaţia - - - Ipoteza - - - Predicţia - - - Verificarea - - - Evaluarea - - - Alte aspecte ale metodelor ştiinţifice - Mărimi fizice - Măsurători fizice - Analiza dimensională - - Exemplu aplicat - Statistica Tabele - Legile fizicii - Constante fizice - Sistemul Internaţional pentru unităţi de măsură - - Origine - - Scrierea SI - - Unităţi de bază în Sistemul Internaţional SI - - - Lungime (l) - - - Masa (m) - - - Timp (t) - - - Curentul electric (I) - - - Temperatura termodinamică (T) - - - Cantitatea de substanţă (n) - - - Intensitatea luminoasă (I) - - Unităţi SI derivate - - Prefixe SI în fizică - - - Unităţi folosite în afara SI - Unităţi fizice - - Unităţi ca dimensiuni - - Unităţi de bază şi derivate - - Conversia unităţilor - - Prefixele in sistemul SI - - Sfaturi şi reguli pentru calcule cu unităţi fizice Istoria - Fizica în antichitate - Fizica în Evul Mediu - Fizica în sec. XVI-VIII - Fizica în sec. XIX - Fizica în sec. XX Probleme nerezolvate în fizică Domenii interdisciplinare - Fizica aplicată (Fizica tehnologică) - Fizica acceleratorilor - - Accelerarea și interacțiunea particulelor cu structuri RF - - Dinamica fluxului - - Coduri de modelare - - Diagnosticările fluxului - - Toleranţele maşinii Domenii înrudite - Relaţia fizicii cu alte domenii - - Cerinţe preliminare - - Applicaţii şi influenţe - Astronomia - - Scurtă istorie - - Subdomenii ale astronomiei. Cum se obţin informaţiile în astronomie. - - - După subiect - - - Modalităţi de obţinere a informaţiilor - - Telescoape - - - Tipuri de telescoape - - Planetele rătăcitoare - Biofizica - - Subiecte în biofizică şi domenii conexe - - Biofizicieni celebri - Chimia fizică - - Concepte-cheie - Cosmologia - - Subiecele din cosmologie includ: - - - Cosmologia fizică - - - Cosmologii alternative - - - Cosmologia filosofică - - - Cosmologia religioasă - Electronica - - Exemplu - Geofizica - - Metode - - - Geodezie - - - Sonde spaţiale - - Cutremure - Fizica chimică - Ingineria - - Sarcina ingineriei - - Rezolvarea problemelor - - Utilizarea calculatoarelor - - Etimologia - - Conexiunile cu alte discipline - Ştiinţa materialelor Pseudofizica - Anti-gravitaţia - - Efecte convenţionale care imită efectele anti-gravitaţiei - - Soluţii ipotetice - - - Scuturi gravitaţionale - - - Cercetări în relativitatea generală în anii 1950 - - - A cincea forţă - - - "Unităţi distorsionate" în relativitatea generală - - - Breakthrough Propulsion Physics Program - - Încercări experimentale şi comerciale - - - Dispozitive giroscopice - - - Gravitatorul lui Thomas Townsend Brown - - - Cuplarea gravitoelectrică - - - Premiul Göde - Eter luminifer - - Dezavantaje şi critici - Fuziunea la rece - - Fuziunea cu bule - - Rezultate - - - Producţia de energie şi căldura în exces - - - Heliu, elemente grele, şi neutroni - - Mecanisme propuse Referinţe Despre autor - Nicolae Sfetcu - - Contact . (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the (...) most important notions of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

Four experiments investigated the extent to which abstract quantitative information can be conveyed by basic visual features. This was done by asking observers to estimate and discriminate Pearson correlation in graphical representations where the first data dimension of each element was encoded by its horizontal position, and the second by the value of one of its visual features; perceiving correlation then requires combining the information in the two encodings via a common abstract representation. Four visual features were examined: luminance, color, (...) orientation, and size. All were able to support the perception of correlation. Indeed, despite the strikingly different appearances of the associated stimuli, all gave rise to performance that was much the same: just noticeable difference was a linear function of distance from complete correlation, and estimated correlation a logarithmic function of this distance. Performance differed only in regards to the level of noise in the feature, with these values compatible with estimates of channel capacity encountered in classic experiments on absolute perceptual magnitudes. These results suggest that quantitative information can be conveyed by visual features that are abstracted at relatively low levels of visual processing, with little representation of the original sensory property. It is proposed that this is achieved via an abstract parameter space in which the values in each perceptual dimension are normalized to have the same means and variances, with perceived correlation based on the shape of the joint probability density function of the resultant elements. (shrink)

The paper tries to demonstrate that the process of the increase of entropy does not explain the asymmetry of time itself because it is unable to account for its fundamental asymmetries, that is, the asymmetry of traces (we have traces of the past and no traces of the future), the asymmetry of causation (we have an impact on future events with no possibility of having an impact on the past), and the asymmetry between the fixed past and the open (...) future, To this end, the approaches of Boltzmann, Reichenbach (and his followers), and Albert are analysed. It is argued that we should look for alternative approaches instead of this, namely we should consider a temporally asymmetrical physical theory or seek a source of the asymmetry of time in metaphysics. This second approach may even turn out to be complementary if only we accept that metaphysics can complement scientific research programmes. (shrink)

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set environment.

I assess the thesis that counterfactual asymmetries are explained by an asymmetry of the global entropy at the temporal boundaries of the universe, by developing a method of evaluating counterfactuals that includes, as a background assumption, the low entropy of the early universe. The resulting theory attempts to vindicate the common practice of holding the past mostly fixed under counterfactual supposition while at the same time allowing the counterfactual's antecedent to obtain by a natural physical development. Although the (...) theory has some success in evaluating a wide variety of ordinary counterfactuals, it fails as an explanation of counterfactual asymmetry. (shrink)

Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Hemmo and Shenker (2006) have recently argued against this view by attacking von Neumann's (1955) argument. I argue that Hemmo and Shenker's arguments fail due to several misunderstandings: about statistical-mechanical and thermodynamic domains of applicability, about the nature of mixed states, and about the role of approximations in physics. As a result, their arguments fail in all cases: in the single-particle case, the finite particles case, (...) and the infinite particles case. (shrink)

This careful note is a very initial foray into the issue of the change in entropy with respect to both McTaggart’s A-series and his B-series. We find a possible solution to the Past Hypothesis problem.

In this paper, a special type of polysemantic words, that is, words with multiple meanings for the same part of speech, are analyzed under the name of neutrosophic words. These words represent the most dif cult cases for the disambiguation algorithms as they represent the most ambiguous natural language utterances. For approximate their meanings, we developed a semantic representation framework made by means of concepts from neutrosophic theory and entropy measure in which we incorporate sense related data. We show (...) the advantages of the proposed framework in a sentiment classification task. (shrink)

Background: Emergentism as an ontology of consciousness leaves unanswered the question as to its mechanism. Aim: I aim to solve the Body-Mind problem by explaining how conscious organisms emerged on an evolutionary basis at various times in accordance with an accepted scientific principle, through a mechanism that cannot be understood, in principle. Proposal: The reason for this cloak of secrecy is found in a seeming contradiction in the behaviour of information with respect to the first two laws of thermodynamics. Information, (...) the microstate of particles within an isolated system’s macrostate, can, like first law energy, be neither created nor destroyed, yet the information in the system, like second law entropy, will inevitably increase. To explain information increasing without being created, Laplace’s demon is invoked, able to predict where each particle is destined. This doesn’t work for emerging events like consciousness, which are unpredictable. This can be understood in terms of the derivation of entropy, and the emergence of classical physics, from the Relativistic Transactional Interpretation of Quantum Mechanics. I propose that the increased entropy in a time-irreversible, unpredictable (emergent) isolated system requires the simultaneous deletion of information concerning the steps, or calculations, involved. Conclusion: Thus, the steps leading to consciousness are immediately destroyed and must remain a mystery. Implications include that entropy, not panpsychism, is the Universal principle generative of consciousness, that our being conscious proves that we are not predetermined, and that consciousness requires assuming an “entropy debt” that can only be repaid by living organisms, prohibiting the emergence of conscious machines. (shrink)