We consider a real-valued function f defined on the set of infinite branches X of a countably branching pruned tree T. The function f is said to be a limsup function if there is a function $u \colon T \to \mathbb {R}$ such that $f(x) = \limsup _{t \to \infty } u(x_{0},\dots,x_{t})$ for each $x \in X$. We study a game characterization of limsup functions, as well as a novel game characterization of functions of Baire class 1.

The paper examines the difference between János Bolyai’s and Lobachevskii’s notion of non-Euclidean parallelism. The examination starts with the summary of a widespread view of historians of mathematics on János Bolyai’s notion of non-Euclidean parallelism used in the first paragraph of his Appendix. After this a novel position of the location and meaning of Bolyai’s term “parallela” in his Appendix is put forward. After that János Bolyai’s Hungarian manuscript, the Commentary on Lobachevskii’s Geometrische Untersuchungen is elaborated in (...) order to see how Bolyai and Lobachevskii’s notions of parallelism differ. The careful examination of the Commentary reveals a seeming incoherence of Bolyai’s translation, and finally the explanation of this incoherence offered by the Received View and that of the novel position will be compared and assessed. L’article examine la différence entre la notion du parallélisme non-Euclidean de János Bolyai et celle de Lobachevskii. Tout d’abord le travail s’occupe de l’opinion répendue parmi les historiens de géometrie (le « Received View » ), selon laquelle János Bolyai précise la notion du parallélisme non-Euclidean dans le premier paragraph de l’Appendix. Ensuite une pointe de vue toute neuve sera présentée concernant la place et le sens du terminus technicus,,paralella” de Bolyai dans l’Appendix. Enfin on va analyser les Commentaires (un manuscrit hongrois) de János Bolyai sur le livre Geometrische Untersuchungen de Lobachevskii àfin de voir jusqu’à quel point la notion de parallelisme de Bolyai se diffère de celle de Lobachevskii. L’analyse bien fondue des Commentaires va nous relever un apparent incohérence de la traduction de Bolyai. On examine et on compare l’opinion répendue dans le vaste public avec la nouvelle interpretation de l’Appendix, et on discute les explications probables de cet incohérence. (shrink)

A tension between content and form can even be said to be essential to the effect of a great deal of rhymed poetry in English. William Wimsatt’s wonderful essay on “One Relation of Rhyme to Reason” argues precisely that rhymes in English poetry work when differences of meaning and of part of speech tend to counterpoint similarities of sound.3 Rhyming nouns together, for example, ought to be avoided, since the salutory tension will arise from the fact that a difference in (...) grammatical function will coexist with sameness of sound. This means that prosodical structure does not mirror content, and that even in rhymed poetry the sense may be variously drawn out. Empson makes the complementary remark that English is blessed with the fact that subjects and verbs cannot in general rhyme:The crucial thing about English, as a language for poetry, is that you cannot rhyme the subject with the verb, because either ‘the cat distracts’ and ‘the nerves swerve’ or ‘the cats distract’ and ‘the nerve swerves’; this bit of grammar has been enormously helpful to English poetry by forcing it away from platitude.4This means that the grammar of rhymed poems will not simply be determined by the rhyme scheme but will tend to be a kind of counterpoint to that scheme, since the predicate is kept from rhyming with the subject. 3. William Wimsatt, “On Relation of Rhyme to Reason,” The Verbal Icon: Studies in the Meaning of Poetry , pp. 152-66. In this essay, anticipating some of the deconstructive claims he came to find too extreme at the end of his life, Wimsatt writes that “verse in general, and more particularly rhyme, make their special contribution to poetic structure … [by imposing] upon the logical pattern of expressed argument a kind of fixative counterpattern of alogical implication” . See also Wimsatt, “Verbal Style: Logical and Counterlogical,” The Verbal Icon, pp. 200-217.4. Empson, “Rhyme,” Argufying, p. 136. William Flesch teaches English at Brandeis University and is the author of The Heart of Generosity: Largess and Loss in Herbert, Shakespeare, and Milton. (shrink)

In “The Origin of Species,” Darwin describes a hypothetical example illustrating that large, slowly reproducing mammals such as the elephant can reach very large numbers if population growth is not affected by regulating factors. The elephant example has since been cited in various forms in a wide variety of books, ranging from educational material to encyclopedias. However, Darwin’s text was changed over the six editions of the book, although some errors in the mathematics persisted throughout. In addition, full details of (...) the problem remained hidden in his correspondence with readers of the Origin. As a result, Darwin’s example is very often misinterpreted, misunderstood or presented as if it were a fact. We show that the population growth of Darwin’s elephant population can be modeled by the Leslie matrix method, which we generalize here to males as well. Darwin’s most often cited figure, about 19 million elephants after 750 years is not a typical outcome, actually a very unlikely result under more realistic, although still hypothetical situations. We provide a recursion formula suggesting that Darwin’s original model corresponds to a tribonacci series, a proof showing that sex ratio is constant over all age classes, and a derivation of a generating function of the sequence. (shrink)

The application of evolutionary perspectives to analyzing sex differences in aggressive behavior and dominance hierarchies has been found useful in multiple areas. We draw attention to the parallel of gender differences in the worsening health status of restructuring societies. Drastic socio-economic changes are interpreted as examples of hierarchy disruption, having differential psychological and behavioral impact on women and men, and leading to different changes in health status.

The paper distinguishes two types of Platonist approach, namely the Traditional one and the Robust one. In relation to this distinction I am going to argue that if the ontology of mathematics is intended to be defended plausibly in a Platonist way then this cannot be done according to the Traditional version. This will draw our attention to the plausibility of the Robust version. The plausibility of the two versions of Platonism will be examined in relation to one of the (...) central problems of the philosophy of mathematics, namely the truth-proof problem. The surveying of the truth-proof problem will bring to the surface the prima facie plausibility of the Platonist approach, as well as the apparent accessibility problem of it. Focusing on the accessibility problem will help us to identify two conditions that have to be met by any particular access theory of Platonism. These will be the reducibility condition, and the matching one. The Traditional version will appear an insufficient philosophical theory in relation to the two former conditions. The insufficiency will be demonstrated in the area of the incompatible mathematical theories, namely in the area of Euclidean and hyperbolic geometries. It will turn out that Robust Platonism can escape the squeeze of these conditions, so can it save the original prima facie plausibility of the Platonist approach. (shrink)

János Kornai, a distinguished Hungarian economist, began his adult life as an ardent believer in socialism and then became a critic of the communist political and economic system. He lost family members in the Holocaust, contributed to the ideological preparation for the 1956 Hungarian Revolution, and became an influential theorist of the post-Soviet economic transition. He has been a journalist, a researcher prohibited from teaching in his home country, and a tenured professor at Harvard. By Force of Thought traces (...) Kornai's lifelong intellectual journey and offers a subjective complement to his academic research.Disenchanted with communism, Kornai published Overcentralization, the first book written by someone living behind the Iron Curtain to be openly critical of Soviet-style economics. Although it was attacked in Hungary, it was hailed by Western economists. The Kornai-Lipták theory on two-level planning captured the attention of mathematical economists. Kornai went on to publish the controversial Anti-Equilibrium, a critique of the general equilibrium theory underpinning mainstream economic analyses of markets, Economics of Shortage, The Road to a Free Economy, and the summary of his lifetime research, The Socialist System. An intellectual emissary between East and West, Kornai commuted between Harvard and Budapest for many years.Kornai's memoir describes his research--including his present-day evaluation of his past work--as well as the social and political environments in which he did his work. The difficulties faced by a critic of central planning in a communist country are made especially vivid by material from newly opened secret police files and informers' reports on his activities. By Force of Thought will be an essential resource for students of economic thought, socialist systems, and postsocialist transition, and for readers interested in Eastern European intellectual life before, during, and after communism. (shrink)

The concept of “acculturation” is closely linked to the history of European colonialism. In spite of all efforts to endow it with a “neutral” or “positive” meaning, the term has never meant anything other than the subjection of indigenous cultures to Western civilization in all its forms.

János Kornai, a distinguished Hungarian economist, began his adult life as an ardent believer in socialism and then became a critic of the communist political and economic system. He lost family members in the Holocaust, contributed to the ideological preparation for the 1956 Hungarian Revolution, and became an influential theorist of the post-Soviet economic transition. He has been a journalist, a researcher prohibited from teaching in his home country, and a tenured professor at Harvard. By Force of Thought traces (...) Kornai's lifelong intellectual journey and offers a subjective complement to his academic research.Disenchanted with communism, Kornai published Overcentralization, the first book written by someone living behind the Iron Curtain to be openly critical of Soviet-style economics. Although it was attacked in Hungary, it was hailed by Western economists. The Kornai-Lipták theory on two-level planning captured the attention of mathematical economists. Kornai went on to publish the controversial Anti-Equilibrium, a critique of the general equilibrium theory underpinning mainstream economic analyses of markets, Economics of Shortage, The Road to a Free Economy, and the summary of his lifetime research, The Socialist System. An intellectual emissary between East and West, Kornai commuted between Harvard and Budapest for many years.Kornai's memoir describes his research--including his present-day evaluation of his past work--as well as the social and political environments in which he did his work. The difficulties faced by a critic of central planning in a communist country are made especially vivid by material from newly opened secret police files and informers' reports on his activities. By Force of Thought will be an essential resource for students of economic thought, socialist systems, and postsocialist transition, and for readers interested in Eastern European intellectual life before, during, and after communism. (shrink)

Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and postselective quantum mechanics, QND measurements, complementarity, and tests of quantum mechanics itself against, e.g., the so-called causal communication constraint. We show how to produce various nonlocal entangled states of multiple cavity fields that are useful for these tests, using cavity QED techniques. First, we discuss the generation of the Bell basis states in two entangled cavities, (...) when there is at most one photon in either of the cavities, and then a straightforward generalization to similar N-cavity states. We then show how to produce a nonlocal entangled state when there is precisely one photon hiding in three cavities. These states can be produced by sending appropriately prepared atoms through the cavities. As applications we briefly review two proposals: one to test quantum mechanics against the causal communication constraint using a two-cavity entangled state and the other to test pre- and postselective quantum mechanics using a three-cavity entangled state. The outcome of the latter experiment can be discussed from the viewpoint of the consistent histories interpretation of quantum mechanics and therefore provides an opportunity to subject quantum cosmological ideas to laboratory tests. Finally, we point out the relation between these schemes and the schemes suggested for quantum computing, teleportation, and quantum copying. (shrink)

This short communication includes comments on a single sentence cited from a recent paper by C. Ricotta. I discuss shortly the relationship between diversity and classification as well as the possibility of expressing diversity for continuous variables.Asimple example shows that the notion of diversity can be expanded to situations without an underlying classification. I suggest an evenness formula based on absolute deviations from the perfectly even distribution. If expressed for species data and multiplied by number of species in the community, (...) this becomes an easily interpretable diversity measure. It is stressed that conventional diversity formulae cannot be informative on community structure, but there is a solution. (shrink)

Die Thematisierung des modernen Verhältnisses zwischen Staat und Gesellschaft ist so ausgerichtet, dass sie von vornherein zu einer Privilegierung der Gesellschaft neigt. Die neuzeitliche sozialphilosophische Diskussion läuft auf eine Zurücknahme des Staates in die Gesellschaft hinaus. An die Stelle der staatlich bestimmten Gesellschaft tritt der gesellschaftlich bestimmte Staat. Die entscheidende Frage ist, wie kann die Gesellschaftlichkeit des Staates begründet werden. Der Staat ist nicht mehr selbstständig, schwebt nicht mehr über der sozialen Wirklichkeit, sondern muss selbst als sozial bestimmt verstanden werden. (...) Die grundsätzliche Frage der neuzeitlichen Sozialphilosophie ist daher: Wie ist der Staat überhaupt möglich? Diese Frage wird durch eine Theorie der Konstitution des Staates beantwortet. (shrink)

Gene-technology was developed in the eighties and stimulated an overmuch heated social debate. Let's think such problems as cloning, transgenic organisms, Human Genom Project, DNA diagnostics and therapy, the geneticalisation of society etc. While the gene manipulation develops rapidly the necessary social control is missing. Regarding the social co-ordination of gene technology, the decision-makers still excessively trust in the institution of market and in the experts' competence.

It is a central claim of György Márkus’s philosophy of culture that the Enlightenment project ended up in deep, apparently irresolvable antinomies. But, unlike the majority of ‘postmodern’ thinkers, Márkus insists that the commitments of the Enlightenment cannot and should not be given up. This tension between the failure of the Enlightenment to produce a society of free and equal persons, each leading their lives autonomously, drawing on the resources of rational high culture, and the impossibility and undesirability of the (...) abandonment of the commitments of the Enlightenment finds an expression in what Márkus calls ‘the antinomies of late modernity’. This paper offers an interpretation of Márkus’s conception; it identifies a certain ambiguity in Márkus’s use of the term ‘antinomies’, and suggests that Márkus’s ambition is compatible with maintaining the first two but is failed by the third one which should, therefore, be abandoned. (shrink)

Linguistic Modelling of Scenarios proposes a paradigm change from the 'systemic VIEW' to 'systems SCIENCE', so as to extend the methodology of conventional science of physics into the domains hitherto beyond the reach of this kind of treatment. The book: I. Identifies the problematic issues in current approaches to the 'systemic or structural view' of parts of the world as opposed to the 'quantitative/qualitative views' of conventional science of physics and the arts whereby introducing the 'third culture'. II. Locates the (...) position of the structural view in the context of 'human intellectual endeavour'. III. Discusses the fundamental questions raised by modelling aspects of human behaviour. IV. Introduces the basic ideas and the symbolism of linguistic modelling which are then applied to turning descriptions of scenarios as a story or narrative into reasoning schemes. V. Describes a methodology of 'problem solving' of which design thinking and the operation of purposive systems are seen as essential ingredients. Problem solving is a universal activity of living in particular human beings through innovation, invention and creativity. Lack of this activity leads to death! Problem solving is regarded as pivotal point which may propel the spread of the modified structural view into social, technical, cultural and educational awareness. VI. Shows the location of aspects of conventional science within the scheme of systems science whereby achieving a 'continuity of the scientific endeavour'. VII. Outlines a teaching scheme for 'linguistic modelling'. Janos Korn explains how a view can be converted into a science which can lead to a possibility of 'organised speculation' or simulation of behaviour, exploring the effects of variation of parameters on performance, and the occurrence of outcomes of operations, beneficial or not, of dynamic structures. Static and dynamic structures are expressed in more rigorous and computable terms so that the results of analysis and design of human activity scenarios could be exposed to at least thought experiments. Linguistic Modelling of Scenarios is an informative read for any professionals, teachers and students of engineering, social science, management, business and production. (shrink)

The goal of constructing artificial photosynthetic assemblies is to use sunlight for the generation of hydrogen from water; the hydrogen obtained should be an ideal energy source. The use of surfactant vesicle entrapped‐catalyst coated colloidal semiconductors and sacrificial electron donors for photosensitized water reduction illustrates how chemists mimic photosynthesis.

Recent neurophysiological observations are giving rise to the expectation that in the near future genuine biological experiments may contribute more than will premature speculations to the understanding of global and cognitive functions. The classical reflex principle — as the basis of neural functions — has to yield to new ideas, like autopoiesis and/or self-organization, as the basic paradigm in the framework of which the essence of the neural can be better understood. Neural activity starts in the very earliest stages of (...) development well before receptors and afferent input become functional. Under suitable conditions, both in nervous tissue cultures and in embryonic tissue recombination experiments, the conditions of such initial autopoietic activity can be studied. This paper tries to generalize this elementary concept for various neural centers, notably for the spinal segmental apparatus and the cerebral cortex. (shrink)

Modem economics relied on the false presupposition that natural resources are free goods. It gave rise to exaggerated expectations on the side of economists concerning the possibilities of economic growth. I try to interpret the terms of natural resources, sustaining capacity, production from a human-ecological platform. The quantity of natural resources may vary within a large spectrum between absolute abundance and total exhaustion. The support capacity can be raised in different ways. Extensive growth is wrong while technological development is a (...) good way. So, certain technological-market processes aiming at extensive growth must be suppressed, processes that could increase effectivity and technical developments, which would draw new resources into production, should be supported. (shrink)

In all kinds of implementations of computing, whether technological or biological, some material carrier for the information exists, so in real-world implementations, the propagation speed of information cannot exceed the speed of its carrier. Because of this limitation, one must also consider the transfer time between computing units for any implementation. We need a different mathematical method to consider this limitation: classic mathematics can only describe infinitely fast and small computing system implementations. The difference between mathematical handling methods leads to (...) different descriptions of the computing features of the systems. The proposed handling also explains why biological implementations can have lifelong learning and technological ones cannot. Our conclusion about learning matches published experimental evidence, both in biological and technological computing. (shrink)

The paper deals with some of the contemporary theories of science which see the latter as an organized cognitive activity. On the background of the controversy concerning the nature of rationality and relativism the author underlines the contribution of the sociology of scientific knowledge, showing its role in reconceptualization of the dichotomy between internalism and externalism. His argumentation is in favor of the institutionalist conception of science as a subsystem of society. The problem of the reliability of knowledge is explained (...) in the context of the globalized science: for science to be cognitively successful it is necessary to optimize the institutional mechanisms producing consensus and working as the controlling and corrective mechanisms. (shrink)