Philosophie als -sterben wollen- (Platon) bestimmt die Tradition bis hin zur -Geworfenheit zum Tode- (Heidegger). Die Welt fuhrt sich mit diesem Menschenbild entsprechend auf. Sich absolut setzende Wahrheiten blenden die Wahrnehmung aus, dass wir in einer falschen Welt mit falschem Bewusstsein leben. Der Poet Schiller mokiert sich in seinem Gedicht "Die Taten der Philosophen" (1795) hierzu. In der Schlusszeile spricht er die Krafte an, die aus dem Leben alle Wesen und in besonderer Weise den Menschen bestimmen: HUNGER und LIEBE. Vorliegende (...) Arbeit ist der Versuch einer Theorie des poetischen Menschen aus diesen Urkraften des Lebens. Es ist der Versuch der Wiedervereinigung von KUNST und Mensch und Absage an alle Wahrheits-Ideologien. Der poetische Mensch kennt nur Wahrheiten -auf Zeit-. Einzig im Willen zum Leben kann eine neue Welt gedichtet werden...". (shrink)

This book presents a comprehensive view of an important new field in human geography and interdisciplinary studies of nature-society relations. Tracing the development of political ecology from its origins in geography and ecological anthropology in the 1970s, to its current status as an established field, the book investigates how late twentieth-century developments in social and ecological theories are brought together to create a powerful framework for comprehending environmental problems. Making Political Ecology argues for an inclusionary conceptualization of the field that (...) absorbs empirical studies from urban, rural, First World and Third World contexts and the theoretical insights of feminism, poststructuralism, neo-Marxism, and non-equilibrium ecology. Extracts from the writings of key figures in political ecology provide an empirical grounding for these abstract concepts. Neumann's book will convince readers of political ecology's particular suitability for grappling with the most difficult questions concerning social justice, environmental change, and human relationships with nature. (shrink)

The coronavirus disease 2019 pandemic is altering dynamics in academia, and people juggling remote work and domestic demands – including childcare – have felt impacts on their productivity. Female authors have faced a decrease in paper submission rates since the beginning of the pandemic period. The reasons for this decline in women’s productivity need to be further investigated. Here, we analyzed the influence of gender, parenthood and race on academic productivity during the pandemic period based on a survey answered by (...) 3,345 Brazilian academics from various knowledge areas and research institutions. Productivity was assessed by the ability to submit papers as planned and to meet deadlines during the initial period of social isolation in Brazil. The findings revealed that male academics – especially those without children – are the least affected group, whereas Black women and mothers are the most impacted groups. These impacts are likely a consequence of the well-known unequal division of domestic labor between men and women, which has been exacerbated during the pandemic. Additionally, our results highlight that racism strongly persists in academia, especially against Black women. The pandemic will have long-term effects on the career progression of the most affected groups. The results presented here are crucial for the development of actions and policies that aim to avoid further deepening the gender gap in academia. (shrink)

Objectives:Social isolation is increasing in aging societies and several studies have shown a relation with worse cognition in old age. However, less is known about the association in the oldest-old (85+); the group that is at highest risk for both social isolation and dementia. Methods:Analyses were based on follow-up 5 to 9 of the longitudinal German study on aging, cognition, and dementia in primary care patients (AgeCoDe) and the study on needs, health service use, costs, and health-related quality of life (...) in a large sample of oldest-old primary care patients (AgeQualiDe), a multi-center population-based prospective cohort study. Measurements included the Lubben Social Network Scale (LSNS-6), with a score below 12 indicating social isolation, as well as the Mini-Mental Status Examination (MMSE) as an indicator of cognitive function. Results:Dementia-free study participants (n = 942) were M = 86.4 (SD = 3.0) years old at observation onset, 68.2% were women. One third (32.3%) of them were socially isolated. Adjusted linear hybrid mixed effects models revealed significantly lower cognitive function in individuals with smaller social networks (β = 0.5, 95% CI = 0.3-0.7, p <.001). Moreover, changes in an individual's social network size were significantly associated with cognitive changes over time (β = 0.2, 95% CI = 0.1-0.4, p =.003), indicating worse cognitive function with shrinking social networks. Conclusion:Social isolation is highly prevalent among oldest-old individuals, being a risk factor for decreases in cognitive function. Consequently, it is important to maintain a socially active lifestyle into very old age. Likewise, this calls for effective ways to prevent social isolation. (shrink)

Von Neumann's theory of measurement in quantum mechanics is reinterpreted so that the experimental arrangement specifies the location of the “cut” by calling for the separate observation of the object and the measuring apparatus after the initial measurement interaction. The measurement ascertains which element of the mixture describing the final state of the apparatus is actually present. The relevance and feasibility of observing the final coherent state of the object plus apparatus is criticized and the paradoxes of “Schrödinger's cat” (...) and “Wigner's friend” are discussed. (shrink)

Recognising and responding appropriately to emotions is critical to adaptive psychological functioning. Psychopathic traits (e.g. callous, manipulative, impulsive, antisocial) are related to differences in recognition and response when emotion is conveyed through facial expressions and language. Use of emotional music stimuli represents a promising approach to improve our understanding of the specific emotion processing difficulties underlying psychopathic traits because it decouples recognition of emotion from cues directly conveyed by other people (e.g. facial signals). In Experiment 1, participants listened to clips (...) of emotional music and identified the emotional content (Sample 1, N = 196) or reported on their feelings elicited by the music (Sample 2, N = 197). Participants accurately recognised (t(195) = 32.78, p <.001, d = 4.69) and reported feelings consistent with (t(196) = 7.84, p <.001, d = 1.12) the emotion conveyed in the music. However, psychopathic traits were associated with reduced emotion recognition accuracy (F(1, 191) = 19.39, p <.001) and reduced likelihood of feeling the emotion (F(1, 193) = 35.45, p <.001), particularly for fearful music. In Experiment 2, we replicated findings for broad difficulties with emotion recognition (Sample 3, N = 179) and emotional resonance (Sample 4, N = 199) associated with psychopathic traits. Results offer new insight into emotion recognition and response difficulties that are associated with psychopathic traits. (shrink)

It is the purpose of this note to comment on some important problems which have been already vividly discussed by several authors. Besides the well known former discussions of Schrödinger and J. v. Neumann I should like to mention here especially H. Margenau's article, “Critical Points in Modern Physical Theory,” which strongly influenced my present discussion.

As interpreted by Pattee, von Neumann’s Theory of Self-Reproducing Automata has proved to be a useful tool for understanding some of the difficulties and paradoxes of molecular biosemiotics. But is its utility limited to molecular systems or is it more generally applicable within biosemiotics? One way of answering that question is to look at the Theory as a model for one particular high-level biosemiotic activity, human language. If the model is not useful for language, then it certainly cannot be (...) generally useful to biosemiotics. Beginning with the Universal Turing Machine and continuing with von Neumann’s Theory and Pattee’s interpretation, the properties of universality, programmability, underspecification, complementarity of description/construction, and open-ended evolutionary potential are shown to be usefully applicable to language, thus opening a new line of inquiry in biosemiotics. (shrink)

We comment on and translate Gustav Kirchhoff's important paper of 1857 entitled On the motion of electricity in conductors. The significance of this paper is that Kirchhoff proved with action at a distance that electric disturbances travel along wires of negligible resistance with the velocity of light. He accomplished this with the laws of Newtonian electrodynamics (Coulomb, Ampere, F. Neumann and Weber) before Maxwell had formulated his equations.

_René Descartes proposed an interactive dualism that posits an interaction between the_ _mind of a human being and some of the matter located in his or her brain. Isaac Newton_ _subsequently formulated a physical theory based exclusively on the material/physical_ _part of Descartes’ ontology. Newton’s theory enforced the principle of the causal closure_ _of the physical, and the classical physics that grew out of it enforces this same principle._ _This classical theory purports to give, in principle, a complete deterministic account (...) of the_ _physically described properties of nature, expressed exclusively in terms of these_ _physically described properties themselves. Orthodox contemporary physical theory_ _violates this principle in two separate ways. First, it injects random elements into the_ _dynamics. Second, it allows, and also requires, abrupt probing actions that disrupt the_ _mechanistically described evolution of the physically described systems. These probing_ _actions are called Process 1 interventions by von Neumann. They are psycho-physical_ _events. Neither the content nor the timing of these events is determined either by any_ _known law, or by the afore-mentioned random elements. Orthodox quantum mechanics_ _considers these events to be instigated by choices made by conscious agents. In von_ _Neumann’s formulation of quantum theory each such intervention acts upon the state of_ _the brain of some conscious agent. Thus orthodox von Neumann contemporary physics_ _posits an interactive dualism similar to that of Descartes. But in this quantum version the_ _effects of the conscious choices upon our brains are controlled, in part, by the known_ _basic rules of quantum physics. This theoretically specified mind-brain connection allows_ _many basic psychological and neuropsychological findings associated with the apparent_ _physical effectiveness of our conscious volitional efforts to be explained in a causal and_ _practically useful way.. (shrink)

René Descartes proposed an interactive dualism that posits an interaction between the mind of a human being and some of the matter located in his or her brain. Isaac Newton subsequently formulated a physical theory based exclusively on the material/physical part of Descartes’ ontology. Newton’s theory enforced the principle of the causal closure of the physical, and the classical physics that grew out of it enforces this same principle. This classical theory purports to give, in principle, a complete deterministic account (...) of the physically described properties of nature, expressed exclusively in terms of these physically described properties themselves. Orthodox contemporary physical theory violates this principle in two separate ways. First, it injects random elements into the dynamics. Second, it allows, and also requires, abrupt probing actions that disrupt the mechanistically described evolution of the physically described systems. These probing actions are called Process 1 interventions by von Neumann. They are psycho-physical events. Neither the content nor the timing of these events is determined either by any known law, or by the afore-mentioned random elements. Orthodox quantum mechanics considers these events to be instigated by choices made by conscious agents. In von Neumann’s formulation of quantum theory each such intervention acts upon the state of the brain of some conscious agent. Thus orthodox von Neumann contemporary physics posits an interactive dualism similar to that of Descartes. But in this quantum version the effects of the conscious choices upon our brains are controlled, in part, by the known basic rules of quantum physics. This theoretically specified mind-brain connection allows many basic psychological and neuropsychological findings associated with the apparent physical effectiveness of our conscious volitional efforts to be explained in a causal and practically useful way.. (shrink)

Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules describing connections between our observations. Many physicist have regarded this renunciation of our effort describe nature herself as premature, and John von Neumann reformulated quantum theory as a theory of an evolving objective universe interacting with human consciousness. This interaction is associated both in Copenhagen quantum theory and in von Neumann quantum theory with a sudden change that (...) brings the objective physical state of a system in line with a subjectively felt psychical reality. The objective physical state is thereby converted from a material substrate to an informational and dispositional substrate that carries both the information incorporated into it by the psychical realities, and certain dispositions for the occurrence of future psychical realities. The present work examines and proposes solutions to two problems that have appeared to block the development of this conception of nature. The first problem is how to reconcile this theory with the principles of relativistic quantum field theory; the second problem is to understand whether, strictly within quantum theory, a person's mind can affect the activities of his brain, and if so how. Solving the first problem involves resolving a certain non-locality question. The proposed solution to the second problem is based on a postulated connection between effort, attention, and the quantum Zeno effect. This solution explains on the basic of quantum physics a large amount of heretofore unexplained data amassed by psychologists. (shrink)

For a long while Bayesian techniques in statistics in general, and decision theory in particular, were considered suspect at best, and to be avoided; but now along comes Jeffrey with a system of subjective probability and utility functions determined by the individual's preferences, and a strongly Bayesian approach to decision-making, and by so doing puts the whole matter in a new light and makes it quite important to reassess the prior rejection of Bayesian methods. There are twelve chapters, each with (...) exercises, which begin with the model of deliberation, progress though scaling and ranking desirability, preference and propositional attitudes, thence to probability and measurement of desirability, and finally to induction and confirmation. The author's theory bears some resemblances to that sketched by Ramsey, but it draws somewhat on the later work of Von Neumann and Morgenstern. The author examines probability as viewed both statically—when the agent's attitudes are constant—and dynamically-when desirability and, consequently, probability assignments change. This text is one of the small but growing library of works whose interest is induction and probability theory; in that library, it will occupy an important place.—P. J. M. (shrink)

This article proposes a geostatistical solution for area-to-point spatial prediction (downscaling) taking into account boundary effects. Such effects are often poorly considered in downscaling, even though they often have significant impact on the results. The geostatistical approach proposed in this article considers two types of boundary conditions (BC), that is, a Dirichlet-type condition and a Neumann-type condition, while satisfying several critical issues in downscaling: the coherence of predictions, the explicit consideration of support differences, and the assessment of uncertainty regarding (...) the point predictions. An updating algorithm is used to reduce the computational cost of area-to-point prediction under a given BC. In a case study, area-to-point prediction under a Dirichlet-type BC and a Neumann-type BC is illustrated using simulated data, and the resulting predictions and error variances are compared with those obtained without considering such conditions. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to (...) be families of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to (...) be families of projections indexed by a partially ordered set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski–Mulvey) of the “Bohrification” \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} of A, which is a commutative Rickart C*-algebra in the topos of functors from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}A}$$\end{document} to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns–Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} for A = B(H). (shrink)

Orthodox quantum mechanics is technically built around an element that von Neumann called Process 1. In its basic form it consists of an action that reduces the prior state of a physical system to a sum of two parts, which can be regarded as the parts corresponding to the answers ‘Yes’ and ‘No’ to a specific question that this action poses, or ‘puts to nature’. Nature returns one answer or the other, in accordance with statistical weightings specified by the (...) theory. Thus the standard statistical element in quantum theory enters only after the Process-1 choice is made, while the known deterministic element in quantum theory governs the dynamics that prevails between the reduction events, but not the process that determines which of the continuum of allowed Process-1 probing actions will actually occur. The rules governing that selection process are not fixed by the theory in its present form. This freedom can be used to resolve in a natural way an apparent problem of the orthodox theory, its biocentrism. That resolution produces a rationally coherent realization of the theory that preserves the basic orthodox structure but allows naturally.. (shrink)

It is difficult to describe this book without praising it. Collected here in one volume are some thirty-six high quality translations into English of the most important foreign-language works in mathematical logic, as well as articles and letters by Whitehead, Russell, Norbert Weiner and Post. The contents of the volume are arranged in chronological order, beginning with Frege's Begriffsschrift—translated in its entirety—and concluding with Gödel's famous "On Formally Undecidable Propositions" and Herbrand's "On the Consistency of Arithmetic". The translation of the (...) Gödel article is a small masterpiece, and is especially welcome in view of some of the rather poor efforts which have been made to render this important work into English. But this is more than a paste-pot job of anthologizing. Van Heijenoort and others have written prefaces to each of the included selections, in which are provided background historical and bibliographical information, comments on the intellectual currents which led to the production of the article, and, in many cases, a digest of the important theorems and concepts in the article itself. Each selection is a classic in its own right. In reading through the selections in this volume, one is struck by the extent to which purely mathematical problems and issues have controlled recent logical inquiry and have determined the development of various philosophies of mathematics. In the early stages, Frege and Peano were concerned with the logical reconstruction of arithmetic, and this led to the work of Russell and the logicist philosophy. Already in the development of the new logic there were certain problems which were resolved with Russell's theory of types—a device which many mathematicians felt to be rather artificial. The use of set theory, beginning with Cantor and reaching its maturity in Zermelo's 1904 proof of the well-ordering theorem, gave rise to a new set of difficulties concerning the axioms of choice, the continuum problem, and infinite sets. The two traditions are brought together in a common nexus of foundational problems by Weiner in 1914 and by Skolem's form of the Löwenheim theorem, given in 1920. Hereafter, the way is open for the rise of mathematical inquiry into the foundations of number systems, set theory and logic by Post, Skolem, von Neumann, Hilbert, Bernays, Gödel and many others. The work was far from completed by 1931, but a new and important tradition in mathematical inquiry had been established, and had come into its own. This book is, in effect, the record of an important chapter in the history of thought. No serious student of logic or foundations of mathematics will want to be without it.—H. P. K. (shrink)

Here is a fine semipopular book about the ideas which have motivated the much-talked-about revolution in the theories of information, control and communication. Jagjit Singh is one of those rare science writers who knows how to present intricate technical concepts to the less-than-expert reader without compromising the original sense or significance. The book begins, appropriately enough, with a discussion of the concept of information, culminating in the technical definition which enables us to assign numerical values to its quantity. The following (...) chapters present the conceptual heart of the Shannon-Weaver theory, the theories of automatic computing machines and the intriguing neurological theories of Warren McCulloch and John Von Neumann. The chapter on Turing Machines does not pay enough attention to the purely mathematical applications of these devices for the present reviewer's taste. The closing chapters deal with mathematical theories of intelligence and the brain. The text is accompanied by many good drawings and appropriate mathematical demonstrations. A book of this quality could have been produced only by an author with absolute command of his topic.—H. P. K. (shrink)

There is no prospect of discovering measurable cardinals by radio astronomy, but this does not mean that higher set theory is entirely irrelevant to applied mathematics broadly construed. By way of example, the bearing of some celebrated descriptive-set-theoretic consequences of large cardinals on measurable-selection theory, a body of results originating with a key lemma in von Neumann’s work on the mathematical foundations of quantum theory, and further developed in connection with problems of mathematical economics, will be considered from a (...) philosophical point of view. (shrink)

Quantum mechanics as conceived by Niels Bohr and formulated in rigorous terms by John von Neumann is expressed as quantum neuroscience: a description of the relationship between certain conscious experiences of an observer that are described in terms of the concepts of classical physics and neural processes that are described in terms of the concepts of quantum physics. The theory is applied to recent neuroscience data to determine the rapidity of the observer's probing actions that is needed to account (...) for the capacity of a person's mental intentions to influence that person's bodily actions in the intended way. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}. (shrink)

A simple exactly solvable model is given of the dynamical coupling between a person’s classically described perceptions and that person’s quantum mechanically described brain. The model is based jointly upon von Neumann’s theory of measurements and the empirical findings of close connections between conscious intentions and synchronous oscillations in well separated parts of the brain. A quantum-Zeno-effect-based mechanism is described that allows conscious intentions to influence brain activity in a functionally appropriate way. The robustness of this mechanism in the (...) face of environmental decoherence effects is emphasized. (shrink)

Game trees (or extensive-form games) were first defined by von Neumann and Morgenstern in 1944. In this paper we examine the use of game trees for representing Bayesian decision problems. We propose a method for solving game trees using local computation. This method is a special case of a method due to Wilson for computing equilibria in 2-person games. Game trees differ from decision trees in the representations of information constraints and uncertainty. We compare the game tree representation and (...) solution technique with other techniques for decision analysis such as decision trees, influence diagrams, and valuation networks. (shrink)

David Bourget has raised some conceptual and technical objections to my development of von Neumann’s treatment of the Copenhagen idea that the purely physical process described by the Schrödinger equation must be supplemented by a psychophysical process called the choice of the experiment by Bohr and Process 1 by von Neumann. I answer here each of Bourget’s objections.

Quantum theory has been formulated in several different ways. The original version was ‘Copenhagen’ quantum theory, which was formulated as a practical set of rules for making predictions about what we human observers would observe under certain well-defined sets of conditions. However, the human observers themselves were excluded from the system, in much the same way that Descartes excluded human beings from the part of the world governed by the natural physical laws. This exclusion of human beings from the world (...) governed by the physical laws is an awkward feature of Copenhagen quantum theory that is fixed by “Orthodox” quantum theory, which is the form devised by von Neumann and Wigner. This orthodox form treats the entire world as a quantum system, including the brains and bodies of human beings. Some more recent formulation of quantum theory seek to exclude from the theory all reference to the experiences of human observers, but I do not consider them, both because of their technical deficiencies, and because they are constitutionally unequipped to deal adequately with the causal efficacy of our conscious thoughts.1 The observer plays a central role in both Copenhagen and Orthodox quantum theory. In this connection, Bohr, describing the 1927 Solvay conference, noted that: “…an interesting discussion arose about how to speak of the appearance of phenomena for which only statistical predictions can be made. The question was whether, as to the occurrence of such individual events, we should adopt the.. (shrink)

A criterion for the existence of human free will is specified: a human action is asserted to be a manifestations of human free-will if this action is a specific physical action that is experienced as being consciously chosen and willed to occur by a human agent, and is not determined within physical theory either in terms of the physically described aspects of nature or by any non-human agency. This criterion is tied to the structure of a physical theory. It is (...) noted that the orthodox quantum mechanics that flows from John von Neumann’s analysis of the process of measurement in quantum theory is described in terms of three processes that are effectively based on a three-level conception of reality. Von Neumann’s “Process 2” is the deterministic evolution, via the Schroedinger equation, of a physically described aspect of reality, the quantum state. His “Process 1” is the physically described aspect of a psychophysical probing action whose psychologically described aspect is an increment in the knowledge of a probing agent/observer. Process 3, in Dirac’s words, is “a choice on the part of nature” of the response to such a probing action. It is argued here that all three levels of this quantum structure, the physically described quantum state, the probing knowledge-acquiring agents, and the response-choosing nature, are all best conceived as idea-like in character. Quantum mechanics, though puzzling when viewed from the inappropriate perspective of the mechanistic classical physics, becomes rationally coherent when the underlying reality is conceived to be not a physically described classical monism, but rather an ideabased quantum triality. This idea-based conception of reality evades the pitfalls of nonphysics-based idealism by being erected directly upon the basic concepts of pragmatic empirically validated quantum mechanics. However, the dynamical structure of quantum theory contains certain causal gaps.. (shrink)

The question raised by Shimony and Stein is examined and used to explain in more detail a key point of my proof that any theory that conforms to certain general ideas of orthodox relativistic quantum field theory must permit transfers of information over spacelike intervals. lt is also explained why this result is not a problem for relativistic quantum theory, but, on the contrary, opens the door to a satisfactory realistic relativistic quantum theory based on the ideas of Tomonaga, Schwinger, (...) and von Neumann. (shrink)

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the (...) canonical momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a “mechanical” (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields. (shrink)

Nash is famous for many inventions, but it is less known that he, simultaneously with Marschak, also was the first to axiomatize expected utility for risk. In particular, these authors were the first to state the independence condition, a condition that should have been but was not stated by von Neumann and Morgenstern. Marschak’s paper resulted from interactions with several people at the Cowles Commission. We document unique letters and personal communications with Nash, Samuelson, Arrow, Dalkey, and others, making (...) plausible that Nash made his discovery independently from the others. (shrink)

In the spirit of Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944), we introduce a notion of network stability. We study the structure of stable economic networks and their associated stable payoff allocations by analyzing the conditions under which complete networks and star networks (both with desirable property of inclusiveness) are stable. We also address conditions for existence and uniqueness of stable set of networks.

Generals always prepare for the last war.—Winston ChurchillYet in the 18th century, European thinkers noticed that social transformations had been accelerating for several thousand years; subsequent historical knowledge has made this observation more graphic and global. How long can the acceleration regime continue? In 1958, John von Neumann used the mathematical ‘singularity’ concept apropos of this subject, and the sonorous term was soon accepted in the humanities.The conceptual intrigue has become still more fascinating since a series of independent calculations (...) demonstrated that the acceleration period was not limited by human history and prehistory but embraced 4.5 billion years of biosphere evolution in tune with a simple logarithmic law. This is one of the epoch-making and surprising discoveries in the early 21st century. Continents have been drifting on Earth over billions of years, climate changing repeatedly, meteorites falling down and volcanoes blowing up—yet, the phase tra .. (shrink)

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the (...) concrete example of the C*-algebra M n (ℂ) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ℘(M n (ℂ)) of projections in M n (ℂ) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice $\mathcal{O}(\Sigma_{n})$ of functions from the poset $\mathcal{C}(M_{n}(\mathbb{C}))$ of all unital commutative C*-subalgebras C of M n (ℂ) to ℘(M n (ℂ)). The lattice $\mathcal{O}(\Sigma_{n})$ is essentially the (pointfree) topology of the quantum phase space Σ n , and as such defines a Heyting algebra. Each element of $\mathcal{O}(\Sigma_{n})$ corresponds to a “Bohrified” proposition, in the sense that to each classical context $C\in\mathcal{C}(M_{n}(\mathbb{C}))$ it associates a yes-no question (i.e. an element of the Boolean lattice ℘(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann. (shrink)

The Notebook of Djuthmose, P. Vienna ÄS 10321. By Regina Hölzl, Michael Neumann, and Robert J. Demarée. Probleme der Ägyptologie, vol. 37. Leiden: Brill, 2018. Pp. viii + 72, 23 pls. €145.

In early 1927, Pascual Jordan published his version of what came to be known as the Dirac-Jordan statistical transformation theory. Later that year and partly in response to Jordan, John von Neumann published the modern Hilbert space formalism of quantum mechanics. Central to both formalisms are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in (...) the new theory. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p’s and q’s. Jordan ran into serious difficulties when he tried to extend his approach from quantities with fully continuous spectra to those with wholly or partly discrete spectra. For von Neumann, not constrained by the analogy to classical physics and aware of the daunting mathematical difficulties facing the approach of Jordan ), the solution of a problem in the new quantum mechanics required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p’s and q’s. Related to their disagreement about the appropriate general formalism for the new theory, Jordan and von Neumann stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan was the first to state those rules in full generality, von Neumann rephrased them and then sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan’s approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. (shrink)

Around 1989, a striking letter written in March 1956 from Kurt Gödel to John von Neumann came to light. It poses some problems about the complexity of algorithms; in particular, it asks a question that can be seen as the first formulation of the P=?NP question. This paper discusses some of the background to this letter, including von Neumann's own ideas on complexity theory. Von Neumann had already raised explicit questions about the complexity of Tarski's decision procedure (...) for elementary algebra and geometry in a letter of 1949 to J. C. C. McKinsey. The paper concludes with a discussion of why theoretical computer science did not emerge as a separate discipline until the 1960s. (shrink)