The authors present the main ideas of the computer-assisted proof of Mischaikow and Mrozek that chaos is really present in the Lorenz equations. Methodological consequences of this proof are examined. It is shown that numerical calculations can constitute an essential part of mathematical proof not only in the discrete mathematics but also in the mathematics of continua.
The ontology of Bohmian mechanics includes both the universal wave function and particles. Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated—replaced by a set of single-particle pilot-wave fields living in (...) ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields which influence the particles’ motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the program of trying to replace the configuration space wave function with a set of fields in ordinary physical space. (shrink)
Parallel language activation in bilinguals leads to competition between languages. Experience managing this interference may aid novel language learning by improving the ability to suppress competition from known languages. To investigate the effect of bilingualism on the ability to control native-language interference, monolinguals and bilinguals were taught an artificial language designed to elicit between-language competition. Partial activation of interlingual competitors was assessed with eye-tracking and mouse-tracking during a word recognition task in the novel language. Eye-tracking results showed that monolinguals looked (...) at competitors more than bilinguals, and for a longer duration of time. Mouse-tracking results showed that monolinguals’ mouse movements were attracted to native-language competitors, whereas bilinguals overcame competitor interference by increasing the activation of target items. Results suggest that bilinguals manage cross-linguistic interference more effectively than monolinguals. We conclude that language interference can affect lexical retrieval, but bilingualism may reduce this interference by facilitating access to a newly learned language. (shrink)
This work proposes a realistic solution to the control problem of sensorless induction motors. Due to some important aspects related to their construction and reliability, the induction motors are extensively used in many modern industrial applications. Considering that the system is facing the lack of hardware sensors, the proposed complex control strategies are based on the estimation of unavailable system variables and parameters. In order to control the rotor speed, two robust control strategies are proposed: a modified super-twisting adaptive technique (...) and a model predictive technique. The tests performed under several practical assumptions show that the closed loop behaviour of the system is adequate, and the output variable follows the imposed time varying reference, despite the considered uncertainties and disturbances acting on the process. (shrink)
The author presents Einstein's viewpoint on the issue of the relation between mathematics and the world. Mathematics, as Einstein seems to suggest, cannot model the structure of the world in an absolutely adequate way since, if mathematical theorems are certain, they don't apply to the reality. However from the fact that something cannot be done in an adequate way, it doesn't follow that it can't be done at all. Mathematics can and should be applied to desrcibe the reality, but in (...) such a case its theorems are not certain. Mathematics is a formal science. To be able to state something about the world it must be filled with real meaning - which for Einstein means that mathematical asertions, after a suitable interpretation, must be linked through a network of experimental procedures with the world of nature. Einstein, as it appears, applied these general suggestions to approach the problem of geometry of real space. (shrink)
In the paper there are presented two proposals of the interpretations of the applications of mathematics in the natural sciences - realistic and instrumentalistic. The realistic conception, in accordance with the successes of science, maintains that there exists some kind of correspondence between the mathematical structures and the internal structure of the world. It is expressed in the thesis of the mathematicality of nature. The instrumentalistic approach separates the cognitive content of the scientific theory from the mathematical means of expression (...) of the content. In this approach the mathematical categories do not represent any aspect of the modelled reality. In the final part of the paper the author undertakes such an attempt of approaching the applications of mathematics which, while combining the advantages of the above discussed conceptions, would be devoid of their disadvantages. (shrink)
The paper is an attempt to present the cognitive functions of mathematics in relation to empirical sciences. Firstly - mathematics is a 'generator' of mathematical categories used in natural sciences. In this sense mathematics is a science about the tools of cognition which it creates or perfects. Secondly - mathematics plays the role of 'prism' through which we view the world because some phenomena e.g. from the micro- and macro-world can only be seen through the prism of mathematical structures and (...) notions. And thirdly - mathematics is also a 'selector' of cognitive content. It eliminates from the cognitive field these phenomena which presently can't be grasped by the existing mathematical structures. It is worth noticing that the functions of mathematics: 'selector' and 'prism' are complementary in some sense; although they are opposites ('prism' lets you 'see' something, and 'selector' restricts this 'seeing'), they don't exclude each other. (shrink)
This paper is an attempt to review the historically existing types of demonstration of mathematical theorems. The author shows how the notion of mathematical proof has changed through the time from the moment when mathematicians realised (thanks to the philosophical method) the necessity to justify their theses until a precise notion of proof has appeared in the framework of the formal method. Next, the author considers the possibility of modifying the notion of mathematical proof under the influence of the development (...) of computer sciences. (shrink)
The aim of this paper is a presentation, specification and criticism of the thesis proclaiming the mathematicality of nature. The author distinguishes between the structural and the functional aspects of this thesis. With such an interpretation this thesis has a strong methaphysical interpretation. However such thesis is linked with some problems, concerning the issue of its verification. Therefore the author proposes to consider a neutral thesis proclaiming that nature is amathematical. Then we avoid strong assumptions concerning the structure of the (...) world and better understand not only the successes but also failures of mathematical methods. Besides we gain a new view of the issue of efficacy of mathematical methods in natural sciences. (shrink)
The paper presents philosophical views which have been propagated in the first decade of the 20 th -century by Austrian experimental physicist Franz-Serafin Exner. According to Exner all apparently deterministic laws are only a kind of the macroscopic limit of the indeterministic random events and processes in nature. The paper attempts to show whether Exner’s ideas have influenced the views on randomness and probability developed by renowned Polish physicist Marian Smoluchowski who belonged to informal circle of Exner’s students and (...) assistants. (shrink)
The main purpose of this paper is to investigate and reconstruct the philosophical thoughts in Marian Smoluchowski’s papers. He was an outstanding Polish physicist, who lived at the turn of the XIX and XX century. Smoluchowski was particularly interested in theoretical physics. His achievements in this discipline, some even very significant, have caused him to be perceived mainly as a physicist. His work in the theory of fluctuations and kinetic theory of gases, especially in the theory of Brownian motions, (...) is well known to physicists. My attention in this paper is focused on the metascientific problems which dominated his philosophical reflections. His analysis in the fields on philosophy of science ought to be perceived in light of physics. Philosophical reflections were at the margins of science which he practiced – physics was always the background to his deliberations. An important limit to our deliberations was set by concentrating on issues typical of the philosophy of science. In Smoluchowski’s case, however, it is difficult to say that his branch of philosophy is characterized by systematic reflection. It is difficult to classify his reflection in the framework of any given philosophical trend. (shrink)
Author looks into the problem of Marian Zdziechowski’s cooperation with the journal „Nový život”, the newsletter for Czech Catholic modernists. The background for author’s considerations is a historical outline of The Modernist Crisis, its intellectual origins and historic consequences. From 1902 to 1905 five Zdziechowski’s essays were translated and published in „Nový život”. The ideas of the Polish philosopher significantly influenced the development of the Catholic modernism in Bohemia. Zdziechowski discussed such issues as: the crisis and the revival of (...) religion at the turn of the 19th and 20th centuries, the significance of the Catholic Modernism for the renewal of Roman Catholic Church and the relation between religion and modern art. (shrink)
The main goal of this paper is to present the Marian Smoluchowski’s work on thermal and primordial fluctuations which are the main cause of Brownian motion and one of the first empirical evidences for molecular structure of matter.
The aim of tis article is to present the selected Marian Smoluchowski's manuscripts to be published in this volume. At the beginning, a history and current state of research of his manusript legacy was showed. Next there were characterized a philosophical significance of his unpublished manuscripts and a short analysis of the manuscripts published in this volume. At the end of the article the details about the current edition of Smoluchowski's manuscripts were described.
For centuries pilgrimages are present in Christianity. For Catholics, the importance of devotions and visits to the Marian sanctuaries is indisputable. The number of visitors and pilgrims to these temples make the local economy an important destination of religious tourism. In order to understand the economic determinants of religious tourism, two sanctuaries were studied, namely, Aparecida and Fatima. Given the large collection of statistical information of the Portuguese Sanctuary, it was verified through the Vector Autoregressive model that Gross Domestic (...) Product and Unemployment have a causal unidirectional relation with the pilgrimages. The Autoregressive Distributed Lag model revealed that an increase in Gross Domestic Product and international arrivals in the short term positively impacts the number of pilgrims. Through the Ordinary Least Squares regression, significant statistical relationships between climatic factors and visitors in the Sanctuary of Fatima were found. The Seasonal Autoregressive Integrated Moving Average forecast method was applied to the number of monthly visitors to the Sanctuary of Aparecida and to the number of pilgrims in the Sanctuary of Fatima, the results show a strong seasonality and that the first and last months of the year are periods of low demand. The results of this study allow a new look at religious tourism in the Marian context, the empirical results allow those responsible for establishing public policies, tourism agents and the administration of the Sanctuaries to direct their actions. Measures planned and executed jointly between the various agents can benefit residents, visitors, pilgrims, the tourism sector, the local economy and the Sanctuaries themselves. (shrink)
Marian Smoluchowski solved the greatest scientific problem of his time. It was the explanation of the phenomenon of the Brownian motion. In the article, I show that Smoluchowski in fact in this explanation used an ontological interpretation of the causality principle, although in his writings he applied it also in the epistemological interpretation. This is understandable because in the scientific practice some kinds of ontological commitment are required.
Marian Wesoły devoted a considerable part of his life and research to studying the philosophical thought of antiquity. He is, therefore, widely known to scientific community as an admirer of Hellas, outstanding scholar and expert on ancient philosophy, which is reflected in his many publications in the field. Importantly, however, Marian Wesoły, has also been a pioneer of research into a much lesser known field of research, namely Greek philosophy in Byzantium. While this neglected and often disdained area (...) of research has been the subject of Marian Wesoły’s numerous publications, this article presents an over view of his most important findings. (shrink)