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)
We present an axiomatic framework for nonstandard analysis-the Nonstandard Class Theory (NCT) which extends von Neumann-Gödel-Bernays Set Theory (NBG) by adding a unary predicate symbol St to the language of NBG (St(X) means that the class X is standard) and axioms-related to it- analogs of Nelson's idealization, standardization and transfer principles. Those principles are formulated as axioms, rather than axiom schemes, so that NCT is finitely axiomatizable. NCT can be considered as a theory of definable classes of Bounded Set (...) Theory by V. Kanovei and M. Reeken. In many aspects NCT resembles the Alternative Set Theory by P. Vopenka. For example there exist semisets (proper subclasses of sets) in NCT and it can be proved that a set has a standard finite cardinality iff it does not contain any proper subsemiset. Semisets can be considered as external classes in NCT. Thus the saturation principle can be formalized in NCT. (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)
A decade ago, Isham and Butterfield proposed a topos theoretic approach to quantum mechanics, which meanwhile has been extended by Doering 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 (see 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 x n matrices. This leads to an explicit expression for the pointfree quantum phase space 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 P(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 of functions from the poset of all unital commutative C*-subalgebras of M_n(C) to P(M_n(C)). The latter lattice is essentially the (pointfree) topology of the quantum phase space mentioned above, and as such defines a Heyting algebra. Each element of the lattice corresponds to a ``Bohrified'' proposition, in the sense that to each classical context it associates a yes-no question pertinent to this context, 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)
_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)
The overaraching goal of this paper is to elucidate the nature of superselection rules in a manner that is accessible to philosophers of science and that brings out the connections between superselection and some of the most fundamental interpretational issues in quantum physics. The formalism of von Neumann algebras is used to characterize three different senses of superselection rules (dubbed, weak, strong, and very strong) and to provide useful necessary and sufficient conditions for each sense. It is then shown (...) how the Haag–Kastler algebraic approach to quantum physics holds the promise of a uniform and comprehensive account of the origin of superselection rules. Some of the challenges that must be met before this promise can be kept are discussed. The focus then turns to the role of superselection rules in solutions to the measurement problem and the emergence of classical properties. It is claimed that the role for “hard” superselection rules is limited, but “soft” (a.k.a. environmental) superselection rules or N. P. Landsman’s situational superselection rules may have a major role to play. Finally, an assessment is given of the recently revived attempts to deconstruct superselection rules. (shrink)
The projection lattices T(Mr), T(M2) of two von Neumann subalgebras Mr, M2 of the von Neumann algebra M are defined to be logically independent if A A B g 0 for any 0 g A E P(&r), 0 g B E 7 (M2). After motivating this notion of independence it is shown that 7 (Mr), 7 (M2) are logically independent if Mr is a subfactor in a finite factor M and T(&r),V'(M2) commute. Also, logical independence is related to (...) the statistical independence conditions called C*-independence W*- independence and strict locality. Logical independence of T(Mr), T(M2) turns out to be equivalent to the C*- independence of (Mr, M2) for mutually commuting Mr, M2, and it is shown that if (Mr, M2) is a pair of (not necessarily commuting) von Neumann subalgebras, then T(&r),V'(M2) are logically independent if (Mr, M2) is a W*-independent pair or if Mr, M2 have the property of strict locality. (shrink)
Ethical mysticism, by S. Coit.--The ethical import of history, by D. S. Muzzey.--The tragic and heroic in life, by W. M. Salter.--Distinctive features of the ethical movement, by A. W. Martin.--Ethical experience as the basis of religious education, by H. Neumann.--"All men are created equal," by G. E. O'Dell.--How far is art an aid to religion? by P. Chubb.--Evolution and the uniqueness of man, by H. J. Bridges.--The spiritual outlook on life, by H. J. Golding.--The ethics of Abu'l Ala (...) al Ma'arri, by N. Schmidt.--Life's unused moral force, by H. Snell.--Is the ideal real? by G. A. Smith.--Some ethical tendencies in the professions, by R. D. Kohn.--On the art of living, by W. Boerner.--The relation of the ethical ideal to social reform, by J. L. Elliott.--Concerning tolerance, by R. F. Dewey.--Ethical culture in Germany after the war, by R. Penzig.--A confession of faith, by S. B. Weston.--"Hearing the witnesses," by J. Gutmann. (shrink)
The relationship between extensive and normal form analyses in non-cooperative game theory seems to be dominated, at least traditionally, by the so-called ‘sufficiency of the normal form principle’, according to which all that is necessary to analyse and ‘solve’ an extensive game is already in its normal form representation. The traditional defence of the sufficiency principle, that Myerson (1991, p. 50) attributes to von Neumann and Morgenstern, holds that, with respect to extensive games, it can be assumed without loss (...) of generality, that players formulate simultaneously and independently their strategic plans at the beginning of the game – a situation which, it is claimed, is exactly described by the normal representation of an extensive game. (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)
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.
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)
Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues, on the basis of his examination of certain arguments that claim to demonstrate the existence of such nonlocal influences, that such influences do not exist. However, his examination was restricted mainly to hidden-variable-based arguments that include in their premises some essentially (...) classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties of a system that are logically incompatible with some premises of the proof. Hence Griffiths’ argument regarding hidden-variable proofs has a secure base. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his ‘consistent quantum theory’ shows that the cited proof is valid within that very restrictive framework. This necessary existence, within the ‘consistent’ framework, of long range essentially instantaneous influences refutes the claim made by Griffiths that his ‘consistent’ framework is superior to the orthodox quantum theory of von Neumann because it does not entail instantaneous influences. (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)
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)
Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules that describe connections between our observations. Many physicist have believed that this renunciation of the attempt describe nature herself was premature, and John von Neumann, in a major work, reformulated quantum theory as a theory of the evolving objective universe. In the course of his work he converted to a benefit what had appeared to be a severe deficiency (...) of the Copenhagen interpretation, namely its introduction into physical theory of the human observers. He used this subjective element of quantum theory to achieve a significant advance on the main problem in philosophy, which is to understand the relationship between mind and matter. That problem had been tied closely to physical theory by the works of Newton and Descartes. The present work examines the major problems that have appeared to block the development of von Neumann’s theory into a fully satisfactory theory of Nature, and proposes solutions to these problems. (shrink)
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)
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)
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)
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)
