The dynamical equations of quantum mechanics are rewritten in the form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated, and squeezed quadrature introduced in the so-called “symplectic tomography”. Then the possibility of a purely classical description of a quantum system as well as a reinterpretation of the quantum measurement theory is discussed and a comparison with the well-known quasi-probabilities approach is given. Furthermore, an analysis of the properties of this marginal distribution, which contains all the (...) quantum information, is performed in the framework of classical probability theory. Finally, examples of the harmonic oscillator's states dynamics are treated. (shrink)
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator. The relevant concepts of quantum mechanics are then reconsidered and the epistemological implications of such approach discussed.
The notion of dynamical symmetry is discussed in the framework of the symplectic tomography scheme for the harmonic oscillator. The stationary states are shown to appear as solutions to eigenvalue equation for “classical” probabilities. All the probabilities describing the energy levels are constructed using dynamical-symmetry operators.
The notion of conditional entropy is extended to noncomposite systems. The \-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the noncomposite systems. New entropic inequalities for quantum tomograms of qudit states including the single qudit states are obtained. The Araki–Lieb inequality is found for systems without subsystems.
Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.
V domnevno Platonovem dialogu Alkibiadu I je postavljena trditev, da je del duše, ki skriva naše pravo sebstvo, naš jaz, podoben Bogu: nekdo, ki ga uvidi in je spoznal božansko – boga in razumnost, bo tako najbolje dojemal tudi samega sebe. Vprašanje sebstva v dialogu nastopi kot smiselno nadaljevanje poprejšnjih izpeljav, po katerih se določa, da mi nismo ne telo, ne naše lastne stvari, temveč duša. S tem, ko sebstvo poistovetimo z Bogom, nekako uidemo problemu samonanašanja in postavimo vprašanje samovédenja (...) v novo dimenzijo. Članek obravnava nekatere nejasnosti definicije sebstva , torej vključujočega telo in dušo, ali le kot duše, kot v Alkibiadu Prvem , ki uporablja telo in mu vlada , v odnosu do božanskega.In Alcibiades I, for many interpreters still a spurious dialogue, Plato claims that our true self resembles the divine. Someone who looked at it and grasped everything divine, God and intelligence, would have the best grasp of himself as well. The question of the self comes as the natural consequence of previous claims showing we are neither our possessions nor our bodies, but our souls. By making the self similar to God, we can tackle the problem of reflexivity differently, putting the question of self-knowledge into new perspective. The article discusses some unclear questions concerning the definition of the self, defined as »the whole man« in Charmides , i.e. including body as integral part, or as excluding it in Alcibiades I, where the self is the soul , since the soul uses the body and rules it , and its relations to the divine. (shrink)
Der Gedanke, der sich in der modernen Idee der Autonomie verdichtet, ist ein doppelter: Die Figur der Autonomie enthält zugleich eine neue Auffassung von Normativität und eine eigene Konzeption von Freiheit. Dem Gedanken der Autonomie zufolge ist ein Gesetz, das wahrhaft normativ ist, eines, als dessen Urheber wir uns selbst betrachten können; und eine Freiheit, die im vollen Sinne wirklich ist, drückt sich in Gestalt eben solcher selbstgegebener Gesetze aus. Die Idee der Autonomie artikuliert so die Einsicht, dass man Freiheit (...) und Gesetz nicht durch ihre Entgegensetzung bestimmen kann, sondern durcheinander erläutern muss. Wirkliche Freiheit ist nicht Freiheit von Gesetzen, sondern Freiheit in Gesetzen; verbindliche Normen sind nicht das, was Freiheit äußerlich beschränkt, sondern das, was Freiheit innerlich verwirklicht. Die Idee der Autonomie, die für die moderne praktische Philosophie seit Rousseau und Kant grundlegend ist, zielt so darauf, Freiheit und Verbindlichkeit in einem Zuge zu artikulieren: durch die Form selbstgegebener Gesetze. Mit Beiträgen von Robert Brandom, Judith Butler, Thomas Khurana, Christoph Menke, Terry Pinkard und Sebastian Rödl. (shrink)
Because the investigation of things and the extension of knowledge is a method of thinking, Ch'eng Tzu dealt with it first. In Erh Ch'eng i-shu [Legacy of the Two Ch'engs], section 25, it is said: "The Ta hsueh [Great Learning] states: A thing has its essentials and nonessentials, an affair has a beginning and an end. Knowledge of what is primary and what is secondary approximates the truth." Ch'eng Tzu maintained that the most important thing in study is to know (...) what is essential and what is nonessential - the beginning and the end. The extension of knowledge lies in the investigation of things; it is essential and constitutes the beginning. Governing the world and the state is nonessential and constitutes the end. Chu Tzu [Chu Hsi] said: "Ch'eng Tzu discussed the theory of the investigation of things in detail." But what is the extension of knowledge and the investigation of things? Chu Tzu maintained that "to investigate" [ko] means "to study thoroughly" [ch'iung]; the term "thing" [wu] means "principle" [li]. To investigate the thing is to study its principle thoroughly. A thorough study of principle leads to an extension of knowledge; without a thorough study there can be no extension. Consequently, he thought that the investigation of things is the beginning of truth and that the student who undertakes the investigation of things is already near the truth. Why? Because the student who undertakes the investigation of things can control his mind completely. Although the key to governing the state and pacifying the world lies in the person — as in the saying "governing the world and the state must begin with the person" — one who would govern the state and pacify the world must first cultivate himself. Cultivating the self is the key to governing the state and pacifying the world, and the means of cultivating the self are the investigation of things, the extension of knowledge, sincere thought, and a correct mind. Perhaps the reader will ask, what the relationship is between cultivating the self, on the one hand, and the investigation of things and the extension of knowledge, on the other hand? Cultivating the self belongs to the realm of ethics; investigating things and the extension of knowledge belong to the realm of knowledge. Given the fact that the cultivation of the self belongs to the realm of ethics and the investigation of things and the extension of knowledge belong to the realm of knowledge, how can an intrinsic relationship between these two dissimilar realms develop? We know that Ch'eng Tzu emphasized two kinds of knowledge, moral knowledge and empirical knowledge. He maintained that if there were only empirical knowledge, there would be only the physical person dependent upon external things without knowing truth. Moral knowledge is true knowledge; therefore, it is necessary to transform empirical knowledge into moral knowledge. Only when external, empirical knowledge and internal, moral knowledge are combined is there true knowledge. But how are empirical knowledge and moral knowledge combined? Chu Tzu elaborated on this point. In the collected writings of Chu Tzu there is an explanation of the couplet "Heaven gave birth to the people/There are things and there are laws" from the Shihching [Book of Poetry]: "Ta ya cheng min." Chu Tzu maintained that in the line "There are things and there are laws" from the Shih-ching, the word "thing" [wu] means "form" [hsing] and the word "laws" [tse] means principle [li]. "Form" is a metaphysical concept, and "law" is what is called metaphysics. Man certainly cannot be without this thing, but unless we understand the "principle" of this "thing," we have no way of knowing whether it conforms to the correct form of life or of deciding the appropriateness of the thing. We must, therefore, seek the principle of this thing. But even if we know the thing and seek its principle, we still have not reached "the limits of the thing"; "the principle of the thing" has not been thoroughly studied and our knowledge of it is not complete. Consequently, we must strive "to reach its limits." This is the meaning of the statement:Only by investigating the thing and arriving at the thing itself can the principle of the thing be known completely. When the principle of the thing is known completely, our knowledge of it is extended and focused. Without obscuration, weaknesses and insurmountable barriers, the intention cannot but be sincere and the mind cannot but be up-right. (shrink)
Contents: INTRODUCTION. Kazimierz TWARDOWSKI: The Majesty of the University. I. Zygmunt ZIEMBI??N??SKI: What Can Be Saved of the Idea of the University? Leszek KO??l??AKOWSKI: What Are Universities for? Leon GUMA??N??SKI: The Ideal University and Reality. Zygmunt BAUMAN: The Present Crisis of the Universities. II. Kazimierz AJDUKIEWICZ: On Freedom of Science. Henryk SAMSONOWICZ: Universities and Democracy. Jerzy TOPOLSKI: The Commonwealth of Scholars and New Conceptions of Truth. Klemens SZANIAWSKI: Plus ratio quam vis. III. Leon KOJ: Science, Teaching and Values. Klemens SZANIAWSKI: (...) The Ethics of Scientific Criticism. Jerzy BRZEZI??N??SKI: Ethical Problems of Research Work of Psychologists. IV. Janusz GO??L??KOWSKI: Tradition in Science. Jerzy KMITA: Is a "Creative Man of Knowledge" Needed in University Teaching? Leszek NOWAK: The Personality of Researchers and the Necessity of Schools in Science. RECAPITULATION. Jerzy BRZEZI??N??SKI: Reflections on the University. (shrink)
The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...) bound for the domains of type , and has a #P lower bound for the domains of type. (shrink)
Through an interdisciplinary approach, I attempt to construct a partial ethno-agronomy of the Seneca people in late pre-contact times and examine it for relevance to modern agriculture.Diohe'ko, the Three Sisters, had been cultivated for at least five hundred years prior to contact by the Seneca, an Iroquoian tribe inhabiting western New York State. The Three Sisters, corn, beans and squash (pumpkins, gourds), were planted together in hills in fields, cultivated and harvested by work parties of women.Changes of village sites and (...) patterns of village movement respond to the adoption of agriculture as well as other factors. Evaluating land use, crop yields and carrying capacity, I question the accuracy of Seneca population estimates.The Three Sisters was an important cultural complex. The Sisters are protagonists of a number of Seneca tales, myths, ceremonies and legends.As an agricultural strategy, Three Sisters embodies several efficiencies in growth patterns, nutrient, solar and water use, harvest and nutritional use. Microhabitat manipulation was practiced by the Seneca. The plants exhibit a high degree of cooperation, or commensality, in the association.Some preliminary judgments can be made about specific varieties of the Sisters in use among the Seneca prior to contact. Northern Flint Corn, Cutshort or Cornhill Beans, and Cucurbita pepo such as Crookneck Squashes are likely the eldest varieties in the area.Three Sisters agriculture demonstrates qualities of permanence and sustainability, especially as related to the Seneca cultural fabric. A conservative ethic, like Handsome Lake's teaching, it binds together people in culture and people and nurture in nature. Mary Jemison, who farmed both the colonial and Three Sisters ways, seems to have favored the latter's “leisurely” approach. (shrink)
In connection with the discussion on the problem of logic, both within our country and abroad , it has already turned from the general, comparatively abstract, and difficult-to-resolve problem of the "relationship between formal logic and dialectics" to the more concrete problem of the functional scope of formal logic. Some people have even utilized special articles to inquire about a certain law in formal logic: the functional scope of the law of identity or the law of contradiction. The purpose of (...) these philosophers or logicians is to try to define the functional scope of a certain law in formal logic as a starting point, and then to proceed to study the functional scope of formal logic in the entire thinking process of mankind. If the functional scope of formal logic in mankind's entire thinking process is clearly and precisely defined, the solution of this complicated problem of the "relationship between formal logic and dialectics" would certainly not be very difficult. The basic purpose of Comrade Chu-ko Yin-t'ung's article on the problem of "whether or not formal logic's law of contradiction can be contravened in the dialectical thinking process" of men, which appeared in issue No. 82 of the "Philosophy" supplement of Kuang-ming Daily on April 24, is like this. It should be considered as a rather practical method. But I do not quite agree with his basic points of argument and with his analysis of certain examples of dialectics. I intend to present my superficial views here and to study them with Comrade Chu-ko. (shrink)
The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...) bound for the domains of type, and has a #P lower bound for the domains of type. (shrink)
There are three results in this study. First, redefinition of "Being". I've classified and redefined the concept of "being" into "Being", "Existence", "Reality" which have been used confusingly. And the definition of God has been also renewed. So we came to understand what "a triangle exists", "a sharp pencil exists", "the God exists" mean. Also I proved that the mean of "I will be who I will be" which is the name of God in Bible equals to the mean of (...) almightiness. Second, trinitarianism. I proved that the essence of God does not belong to the "the world of idea" which the essence of triangle belongs to and also to the "the physical world" which the essence of sharp pencil belongs to. This is the same to physical rules like "E=mc²". And I refer to the world which includes "the God" and"physical rules" as "the world of causes". In this way, a view of world suggested in this study is not dualism but trinitarianism. Third, the new cosmological argument. I've suggested "the new cosmological argument" using modern science's imperfection which inferred from "Werner Karl Heisenberg's uncertainty principle". The conclusion of this proof is that a man who recognizes the reality of "physical rules" should recognize the reality of "God". In other word a rational man who believes causality should recognize the reality of "The cause which is cause of every causes but don't need any cause" "the God". (shrink)
This thesis reviews Haam Seok Heon‘s See-al philosophy, the main philosophy about life in terms of women. The See-al philosophy was created by Haam, who went through the turbulent times of Korea. So far, we have had papers that dealt with his philosophy under the political, historical and religious contexts, but there has been no paper focused on women. Actually, Haam confessed that it was his mother who structured the foundation of his philosophy. He also said that he learned from (...) his mother about freedom, equality, and the basics of See-al ideas. He developed his philosophy of life, See-al, through the image of his motherwho devoted her whole life to bring him up with love and willingly sacrificed her life for her beloved son. Haam regarded women as a link of all lives in history. He also thought mothers, women in other words, have that power that gives birth, breeds lives and infuses new structure into eternal life; in addition, he stated that women have energy which pulls clear and new things out of filthy and dirty things. Through his image about women, Haam's See-al philosophy extends itself as an ecological life movement. In this paper, Haam's philosophy about women is not reviewed and analyzed by the western point of view because Haam is not a man who spent his life in so-called the "times of women" in the western view. Since his philosophy emphasizes self-reflective, independent life, freedom andequality, we might find out that there are some discrepancies between his philosophy and the lives of his mother and wife who had sacrificed their lives under the patriarchal social system. However, the meaning of Haam's independent life is totally different from the western concept of if. That is, his idea of independent life is closely related to sacrifice. In the current society under the influence of Neo-liberalism, only competition and economic logic matter; however, Haam's philosophy, which states "Life is no different between you and I, and only love can save you and I as one existence" and cherishes every single life as one organism that connects all existing things--sky, earth, human beings, etc.--is of great importance for us to reconsider. (shrink)
I examine Leonhard Euler’s original solution to the Königsberg bridges problem. Euler’s solution can be interpreted as both an explanation within mathematics and a scientific explanation using mathematics. At the level of pure mathematics, Euler proposes three different solutions to the Königsberg problem. The differences between these solutions can be fruitfully explicated in terms of explanatory power. In the scientific version of the explanation, mathematics aids by representing the explanatorily salient causal structure of Königsberg. Based on this analysis, I defend (...) a version of the so-called “Transmission View” of scientific explanations using mathematics against objections by Alan Baker and Marc Lange, and I discuss Lange’s notion of “distinctively mathematical explanations” and Christopher Pincock’s notion of “abstract explanations”. (shrink)