An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the (...) chords, that is unique to the maximum entropy principle. (shrink)

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

In recent decades, several theories have claimed to explain the teleological causality of organisms as a function of self-organising and self-producing processes. The most widely cited theories of this sort are variations of autopoiesis, originally introduced by Maturana and Varela. More recent modifications of autopoietic theory have focused on system organisation, closure of constraints and autonomy to account for organism teleology. This article argues that the treatment of teleology in autopoiesis and other organisation theories is inconclusive for three reasons: First, (...) non-living self-organising processes like autocatalysis meet the defining features of autopoiesis without being teleological; second, organisational approaches, whether defined in terms of the closure of constraints, self-determination or autonomy, are unable to specify teleological normativity, that is, the individuation of an ultimate beneficiary; third, all self-organised systems produce local order by maximising the throughput of energy and/or material (obeying the maximum entropy production (MEP) principle) and thereby are specifically organised to undermine their own critical boundary conditions. Despite these inadequacies, an alternative approach called teleodynamics accounts for teleology. This theory shows how multiple self-organising processes can be collectively linked so that they counter each other’s MEP principle tendencies to become codependent. Teleodynamics embraces – not ignoring – the difficulties of self-organisation, but reinstates teleology as a radical phase transition distinguishing systems embodying an orientation towards their own beneficial ends from those that lack normative character. (shrink)

In a preceding publication a fundamentally oriented and irreversible world was shown to be de- rivable from the important principle of least action. A consequence of such a paradigm change is avoidance of paradoxes within a “dynamic” quantum physics. This becomes essentially possible because fundamental irreversibility allows consideration of the “entropy” concept in elementary processes. For this reason, and for a compensation of entropy in the spread out energy of the wave, the duality of particle and wave has (...) to be mediated via an information self-image of matter. In this publication considerations are extended to irreversible thermodynamics, to gravitation and cos- mology with its dependence on quantum interpretations. The information self-image of matter around particles could be identified with gravitation. Because information can also impose an al- ways constant light velocity there is no need any more to attribute such a property to empty space, as done in relativity theory. In addition, the possibility is recognized to consider entropy genera- tion by expanding photon fields in the universe. Via a continuous activation of information on matter photons can generate entropy and release small energy packages without interacting with matter. This facilitates a new interpretation of galactic redshift, emphasizes an information link between quantum- and cosmological phenomena, and evidences an information-triggered origin of the universe. Self-organized processes approach maximum entropy production within their constraints. In a far from equilibrium world also information, with its energy content, can self- organize to a higher hierarchy of computation. It is here identified with consciousness. This ap- pears to explain evolution of spirit and intelligence on a materialistic basis. Also gravitation, here identified as information on matter, could, under special conditions, self-organize to act as a su- per-gravitation, offering an alternative to dark matter. Time is not an illusion, but has to be understood as flux of action, which is the ultimate reality of change. The concept of an irreversible physical world opens a route towards a rational understanding of complex contexts in nature. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective (...) interpretations that are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (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)

According to the second law of thermodynamics, irreversible processes in an isolated system move towards the goal of reaching maximum entropy. In this state, mechanical work is converted to thermal energy and thermodynamic equilibrium occurs; which is determined by the equilibrium in temperature, pressure, etc. Assuming that the universe is an isolated system, the second law of thermodynamics states that the fate of the universe is a state of thermodynamic equilibrium in which all mechanical energies are converted to (...) thermal energy and the heat is dispersed all throughout the universe. In this state, there will be no movement and the universe will expire; an event called the “heat death”. This theory has certain theological implications that can serve as a proof for the perishability of the material world. And since decay implies creation, the heat death theory can be considered an argument in favor of the temporal originatedness of the material world. (shrink)

An indifference principle says that your credences should be distributed uniformly over each of the possibilities you recognise. A chance deference principle says that your credences should be aligned with the chances. My thesis is that, if we are anti-Humeans about chance, then these two principles are incompatible. Anti-Humeans think that it is possible for the actual frequencies to depart from the chances. So long as you recognise possibilities like this, you cannot both spread your credences evenly and defer to (...) the chances. I discuss some weaker forms of indifference which will allow anti-Humeans to defer to the chances. (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)

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)

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)

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)

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)

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.

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)

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean (...) logic of subsets is the normalized counting measure of the subsets (events). Thus logical entropy is a measure on the set of ordered pairs, and all the compound notions of entropy (join entropy, conditional entropy, and mutual information) arise in the usual way from the measure (e.g., the inclusion-exclusion principle)--just like the corresponding notions of probability. The usual Shannon entropy of a partition is developed by replacing the normalized count of distinctions (dits) by the average number of binary partitions (bits) necessary to make all the distinctions of the partition. (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 paper strengthens and defends the pluralistic implications of Einstein's successful, quantitative predictions of Brownian motion for a philosophical dispute about the nature of scientific advance that began between two prominent philosophers of science in the second half of the twentieth century (Thomas Kuhn and Paul Feyerabend). Kuhn promoted a monistic phase-model of scientific advance, according to which a paradigm driven `normal science' gives rise to its own anomalies, which then lead to a crisis and eventually a scientific revolution. Feyerabend (...) stressed the importance of pluralism for scientific progress. He rejected Kuhn's model arguing that it fails to recognize the role that alternative theories can play in identifying exactly which phenomena are anomalous in the first place. On Feyerabend's account, Einstein's predictions allow for a crucial experiment between two incommensurable theories, and are an example of an anomaly that could refute the reigning paradigm only after the development of a competitor. Using Kuhn's specification of a disciplinary matrix to illustrate the incommensurability between the two paradigms, we examine the different research strategies available in this peculiar case. On the basis of our reconstruction, we conclude by rebutting some critics of Feyerabend's argument. (shrink)

This study has demonstrated that entropy is not a physical quantity, that is, the physical quantity called entropy does not exist. If the efficiency of heat engine is defined as η = W/W1, and the reversible cycle is considered to be the Stirling cycle, then, given ∮dQ/T = 0, we can prove ∮dW/T = 0 and ∮d/T = 0. If ∮dQ/T = 0, ∮dW/T = 0 and ∮dE/T = 0 are thought to define new system state variables, such (...) definitions would be absurd. The fundamental error of entropy is that in any reversible process, the polytropic process function Q is not a single-valued function of T, and the key step of Σ[(ΔQ)/T)] to ∫dQ/T doesn’t hold, P-V fig. should be P-V-T fig.in thermodynamics. Similarly, ∮dQ/T = 0, ∮dW/T = 0 and ∮dE/T = 0 do not hold, either. Since the absolute entropy of Boltzmann is used to explain Clausius entropy and the unit (J/K) of the former is transformed from the latter, the non-existence of Clausius entropy simultaneously denies Boltzmann entropy. (shrink)

Metaphors establish connection. Root metaphors--patterns of relational imagery in the language and thought of a culture, in which a diverse group of tenors are related to a single indentifiable class of vehicles--play an important role in organizing our thought, and in bringing a coherence to our vision of the world. This is a political function; root metaphors, as philosopher Stephen Pepper discusses them, are most often found in the works of philosophers remembered as political philosophers. ;The second law of thermodynamics--the (...) law of entropy--holds that in any spontaneous process, usable energy becomes unusable energy. It also suggests that improbable order must succumb, through time, to more probable chaos. The law of entropy has enjoyed a popularity as metaphor unusual for such physics esoterica. In the works of Brooks Adams, Henry Adams, Nicholas Georgescu-Roegen, and Thomas Pynchon, the idea of entropy appears as the fundamental, organizing idea for an economic interpretation of history, a philosophy of history, an ecologically enlightened economic theory, and an encyclopedic novel that apotheosizes modern culture. Analysis of how the entropy metaphor is manifest in the works of these thinkers allows us to judge the strengths and weaknesses of entropy as root metaphor. Analysis of its contemporary popularity affords insight into the politics of the day. Ultimately, the entropy root metaphor serves as the foundation of a refurbished "generating substance" world hypothesis, but the root metaphor itself remains equivocal on the important issue of centralized versus decentralized political organization. (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)

We provide here irrefutable facts that prove the falsehood of the claims published in [1] by Dehmer and Mowshowitz (DM) against our paper published in [2]. We first prove that Dehmer’s definition of node probability [3] is flawed. In addition, we show that it was not Dehmer in [3] who proposed this definition for the first time. We continue by proving how the use of Dehmer’s definition does not reveal all the physico-mathematical richness of the walk entropy of graphs. (...) Finally, we show a few facts about the failure of DM themselves to cite properly the relevant literature in their field. We also show here how the Editors of Complexity have failed to manage the publication of [1] in an appropriate way according to the accepted guidelines given in the Code of Conduct and Best Practice Guidelines for Journal Editors, published by the Committee on Publication Ethics (COPE). (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.

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)

We present a novel approach to quantum theory construction that involves solving a maximization problem on the Shannon entropy of all possible measurements of a system relative to its initial preparation. By constraining the maximization problem with a phase that vanishes 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 vanishing Spin^c(3,1)-valued phase, but with dilations). The first two cases are equivalent to established theory, even naturally yielding the SU(3)xSU(2)xU(1) (...) gauge symmetries of the Standard Model, whereas the latter case additionally yields the pseudo-Riemannian inner product as an observable, constructing the metric tensor as a double-copy of Dirac currents. Finally, the solution is consistent only with 3+1 spacetime dimensions, as it encounters obstructions in all other dimension configurations. This framework integrates quantum mechanics, relativistic quantum mechanics, a candidate for a theory of quantum gravity, spacetime dimensionality, and particle physics gauge symmetries from a simple entropy maximization problem constrained by a vanishing phase. (shrink)

I summarize, in this informal interview, the main approaches to the ‘Past Hypothesis’, the postulation of a low-entropy initial state of the universe. I’ve chosen this as an open problem in the philosophical foundations of physics. I hope that this brief overview helps readers in gaining perspective and in appreciating the diverse range of approaches in this fascinating unresolved debate.

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and (...) a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems. (shrink)

Originally appeared in the field of thermodynamics, the concept of entropy, especially in its statistical acceptation, has found applications in many different disciplines, both inside and outside science. In this work we focus on the possibility of drawing an isomorphism between the entropy of Boltzmann’s statistical mechanics and that of Xenakis’s stochastic music theory. We expose the major technical aspects of the two entropies and then consider affinities and differences between them, both at syntactic and at semantic level, (...) hereto particularly referring to the philosophical problem of the asymmetry of time. (shrink)

The sunspot data seems to indicate that the Sun is likely to enter Maunder Minimum, then it will mean that low Sun activity may cause low temperature in Earth. If this happens then it will cause a phenomenon which is called by some climatology experts as “The Little Ice Age” for the next 20-30 years, starting from the next few years. Therefore, the Earth climate in the coming years tend to be cooler than before. This phenomenon then causes us to (...) ask: what can we do as human being in Earth to postpone or avoid the worsening situation in terms of Earth cooling temperature in the coming years? We think this is a more pressing problem for the real and present danger that we are facing in the Earth. What we are suggesting in this paper is that perhaps it is possible to model Sun-Earth interaction in terms of Shannon entropy. Since Shannon entropy can be expressed as bits of information, then it would mean that perhaps we can do something with Earth temperature by controlling the amount of information transfer and storage in the Earth. This proposal is somewhat in resemblance with message of a 2012 movie “A Thousand words” where we shall strive to love our neighbours and nature, instead of being absorbed in a culture of less-meaningful fast-talk (starred by Eddie Murphy). (shrink)

We propose here to clarify some of the relations existing between information and meaning by showing how meaningful information can be generated by a system submitted to a constraint. We build up definitions and properties for meaningful information, a meaning generator system and the domain of efficiency of a meaning (to cover cases of meaningful information transmission). Basic notions of information processing are used.

The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...) subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement. (shrink)

In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended to yield (...) probability distributions with moderately high entropy levels. In the present article, we present data charting the performance of the four systems when reasoning in environments of various entropy levels. The results illustrate variations in the performance of the respective reasoning systems that derive from the entropy of the environment, and allow for a more inclusive assessment of the reliability and robustness of the four systems. (shrink)

“There’s Plenty of Room at the Bottom”, said the title of Richard Feynman’s 1959 seminal conference at the California Institute of Technology. Fifty years on, nanotechnologies have led computer scientists to pay close attention to the links between physical reality and information processing. Not all the physical requirements of optimal computation are captured by traditional models—one still largely missing is reversibility. The dynamic laws of physics are reversible at microphysical level, distinct initial states of a system leading to distinct final (...) states. On the other hand, as von Neumann already conjectured, irreversible information processing is expensive: to erase a single bit of information costs ~3 × 10−21 joules at room temperature. Information entropy is a thermodynamic cost, to be paid in non-computational energy dissipation. This paper addresses the problem drawing on Edward Fredkin’s Finite Nature hypothesis: the ultimate nature of the universe is discrete and finite, satisfying the axioms of classical, atomistic mereology. The chosen model is a cellular automaton with reversible dynamics, capable of retaining memory of the information present at the beginning of the universe. Such a CA can implement the Boolean logical operations and the other building bricks of computation: it can develop and host all-purpose computers. The model is a candidate for the realization of computational systems, capable of exploiting the resources of the physical world in an efficient way, for they can host logical circuits with negligible internal energy dissipation. (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)

The Kolmogorov-Sinai entropy is a fairly exotic mathematical concept which has recently aroused some interest on the philosophers’ part. The most salient trait of this concept is its working as a junction between such diverse ambits as statistical mechanics, information theory and algorithm theory. In this paper I argue that, in order to understand this very special feature of the Kolmogorov-Sinai entropy, is essential to reconstruct its genealogy. Somewhat surprisingly, this story takes us as far back as the (...) beginning of celestial mechanics and through some of the most exciting developments of mathematical physics of the 19th century. (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)

Suppose that God or a demon informs you of the following future fact: despite recent cosmological evidence, the universe is indeed closed and it will have a ‘final’ instant of time; moreover, at that final moment, all 49 of the world’s Imperial Faberge eggs will be in your bedroom bureau’s sock drawer. You’re absolutely certain that this information is true. All of your other dealings with supernatural powers have demonstrated that they are a trustworthy lot.

Introduction & Objectives: Norwich’s Entropy Theory of Perception (1975 [1] -present) stands alone. It explains many firing-rate behaviors and psychophysical laws from bare theory. To do so, it demands a unique sort of interaction between receptor and brain, one that Norwich never substantiated. Can it now be confirmed, given the accumulation of empirical sensory neuroscience? Background: Norwich conjoined sensation and a mathematical model of communication, Shannon’s Information Theory, as follows: “In the entropic view of sensation, magnitude of sensation is (...) regarded as a measure of the entropy or uncertainty of the stimulus signal” [2]. “To be uncertain about the outcome of an event, one must first be aware of a set of alternative outcomes” [3]. “The entropy-establishing process begins with the generation of a [internal] sensory signal by the stimulus generator. This is followed by receipt of the [external] stimulus by the sensory receptor, transmission of action potentials by the sensory neurons, and finally recapture of the [response to the internal] signal by the generator” [4]. The latter “recapture” differentiates external from internal stimuli. The hypothetical “stimulus generators” are internal emitters, that generate photons in vision, audible sounds in audition (to Norwich, the spontaneous otoacoustic emissions [SOAEs]), “temperatures in excess of local skin temperature” in skin temperature sensation [4], etc. Method (1): Several decades of empirical sensory physiology literature was scrutinized for internal “stimulus generators”. Results (1): Spontaneous photopigment isomerization (“dark light”) does not involve visible light. SOAEs are electromechanical basilar-membrane artefacts that rarely produce audible tones. The skin’s temperature sensors do not raise skin temperature, etc. Method (2): The putative action of the brain-and-sensory-receptor loop was carefully reexamined. Results (2): The sensory receptor allegedly “perceives”, experiences “awareness”, possesses “memory”, and has a “mind”. But those traits describe the whole human. The receptor, thus anthropomorphized, must therefore contain its own perceptual loop, containing a receptor, containing a perceptual loop, etc. Summary & Conclusions: The Entropy Theory demands sensory awareness of alternatives, through an imagined brain-and-sensory-receptor loop containing internal “stimulus generators”. But (1) no internal “stimulus generators” seem to exist and (2) the loop would be the outermost of an infinite nesting of identical loops. (shrink)

A review of Eric Schneider and Dorion Sagan's 2006, "Into the Cool: Energy Flows, Thermodynamics, and Life.".

International Studies in the Philosophy of Science, Volume 27, Issue 3, Page 273-293, September 2013.

From the epistemological posture that we present in this work we sustain the following thesis:-That as subjects we constitute the world we live in through one of the possible conceptual frameworks.-Our cognitive and social practices construct the world in a certain manner, which makes us responsible for the way this world is constituted.

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)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant (...) ''future''), the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (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)

If an asymmetry in time does not arise from the fundamental dynamical laws of physics, it may be found in special boundary conditions. The argument normally goes that since thermodynamic entropy in the past is lower than in the future according to the Second Law of Thermodynamics, then tracing this back to the time around the Big Bang means the universe must have started off in a state of very low thermodynamic entropy: the Thermodynamic Past Hypothesis. In this (...) paper, we consider another boundary condition that plays a similar role, but for the decoherent arrow of time, i.e. the quantum state of the universe is more mixed in the future than in the past. According to what we call the Entanglement Past Hypothesis, the initial quantum state of the universe had very low entanglement entropy. We clarify the content of the Entanglement Past Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify some challenges and open questions for future research. (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)

One finds, in Maxwell's writings on thermodynamics and statistical physics, a conception of the nature of these subjects that differs in interesting ways from the way that they are usually conceived. In particular, though—in agreement with the currently accepted view—Maxwell maintains that the second law of thermodynamics, as originally conceived, cannot be strictly true, the replacement he proposes is different from the version accepted by most physicists today. The modification of the second law accepted by most physicists is a probabilistic (...) one: although statistical fluctuations will result in occasional spontaneous differences in temperature or pressure, there is no way to predictably and reliably harness these to produce large violations of the original version of the second law. Maxwell advocates a version of the second law that is strictly weaker; the validity of even this probabilistic version is of limited scope, limited to situations in which we are dealing with large numbers of molecules en masse and have no ability to manipulate individual molecules. Connected with this is his concept of the thermodynamic concepts of heat, work, and entropy; on the Maxwellian view, these are concepts that must be relativized to the means we have available for gathering information about and manipulating physical systems. The Maxwellian view is one that deserves serious consideration in discussions of the foundation of statistical mechanics. It has relevance for the project of recovering thermodynamics from statistical mechanics because, in such a project, it matters which version of the second law we are trying to recover. (shrink)

Moral reasoning traditionally distinguishes two types of evil:moral (ME) and natural (NE). The standard view is that ME is the product of human agency and so includes phenomena such as war,torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in cyberspace, (...) a new class of interesting and important examples of hybrid evil has come to light. In this paper, it is called artificial evil (AE) and a case is made for considering it to complement ME and NE to produce a more adequate taxonomy. By isolating the features that have led to the appearance of AE, cyberspace is characterised as a self-contained environment that forms the essential component in any foundation of the emerging field of Computer Ethics (CE). It is argued that this goes someway towards providing a methodological explanation of why cyberspace is central to so many of CE's concerns; and it is shown how notions of good and evil can be formulated in cyberspace. Of considerable interest is how the propensity for an agent's action to be morally good or evil can be determined even in the absence of biologically sentient participants and thus allows artificial agents not only to perpetrate evil (and fort that matter good) but conversely to `receive' or `suffer from' it. The thesis defended is that the notion of entropy structure, which encapsulates human value judgement concerning cyberspace in a formal mathematical definition, is sufficient to achieve this purpose and, moreover, that the concept of AE can be determined formally, by mathematical methods. A consequence of this approach is that the debate on whether CE should be considered unique, and hence developed as a Macroethics, may be viewed, constructively,in an alternative manner. The case is made that whilst CE issues are not uncontroversially unique, they are sufficiently novel to render inadequate the approach of standard Macroethics such as Utilitarianism and Deontologism and hence to prompt the search for a robust ethical theory that can deal with them successfully. The name Information Ethics (IE) is proposed for that theory. Itis argued that the uniqueness of IE is justified by its being non-biologically biased and patient-oriented: IE is an Environmental Macroethics based on the concept of data entity rather than life. It follows that the novelty of CE issues such as AE can be appreciated properly because IE provides a new perspective (though not vice versa). In light of the discussion provided in this paper, it is concluded that Computer Ethics is worthy of independent study because it requires its own application-specific knowledge and is capable of supporting a methodological foundation, Information Ethics. (shrink)