Die „Magie des Extrems“ in philosophischen Neuorientierungen. Nietzsches neue extreme Problemstellungen und -lösungen und das alte Beispiel des Sokrates

The later Nietzsche developed the “magic of the extreme” as a special strategy in order to make his philosophical reorientations successful. He needed this strategy not only to be heard at all; also the problems he faced called for it. The article first gives an overview of the most important problems Nietzsche coped with and the extreme solutions he offered. Then, we show how, according to Nietzsche, even Socrates, who stands for the beginning of the European Enlightenment, used the “magic” of extreme irritation and fascination to get this Enlightenment on its way.

Die „Magie des Extrems“ in philosophischen Neuorientierungen. Nietzsches neue extreme Problemstellungen und -lösungen und das alte Beispiel des Sokrates

The later Nietzsche developed the “magic of the extreme” as a special strategy in order to make his philosophical reorientations successful. He needed this strategy not only to be heard at all; also the problems he faced called for it. The article first gives an overview of the most important problems Nietzsche coped with and the extreme solutions he offered. Then, we show how, according to Nietzsche, even Socrates, who stands for the beginning of the European Enlightenment, used the “magic” of extreme irritation and fascination to get this Enlightenment on its way.

Trade-Offs in Choice

To explain trade-offs in choice, researchers have proposed myriad phenomena and decision rules, each paired with separate theories and idiosyncratic vocabularies. Yet most choice problems are ultimately resolved with one of just two types of solutions: mixed or extreme. For example, people adopt mixed solutions for resolving trade-offs when they allow exercising to license indulgence afterward (balancing between goals), read different literary genres (variety seeking), and order medium-sized coffees (the compromise effect). By contrast, when people adopt extreme solutions for resolving these exact same trade-offs, they exhibit highlighting, consistency seeking, and compromise avoidance, respectively. Our review of the choice literature first illustrates how many seemingly unrelated phenomena actually share the same underlying psychology. We then identify variables that promote one solution versus the other. These variables, in turn, systematically influence which of opposite choice effects arise (e.g., highlighting versus balancing). Finally, we demonstrate how several mistakes people purport to make can potentially instead be reinterpreted as mixed solutions for resolving trade-offs. We conclude with guidance for distinguishing mistakes from mixed solutions.

Prime Fermat numbers and maximum determinant matrix conjecture

Purpose: Solution to the problem of optimizing the determinants of matrices with a modulus of entries < 1. Developing a theory of such matrices based on preliminary research results. Methods: Extreme solutions (in terms of the determinant) are found by minimizing the absolute values of orthogonal matrix elements, and their subsequent classification. Results: Matrices of orders equal to prime Fermat numbers have been found. They are special, as their absolute determinant maximums can be reached on a simple structure. We provide a precise evaluation of the determinant maximum for these matrices and formulate a conjecture about it. We discuss the close relation between the solutions of extremal problems with the limitation on the matrix column orthogonality and without it. It has been shown that relative maximums of orthogonality-limited matrix determinants correspond to absolute maximums of orthogonality-unlimited matrix determinants. We also discuss the ways to build extremal matrix families for the orders equal to Mersenne numbers. Practical relevance: Maximum determinant matrices are used extensively in the problems of error-free coding, compression and masking of video information. Programs for maximum determinant matrix search and a library of constructed matrices are used in the mathematical network “mathscinet.ru” along with executable online algorithms.

Between constructivist and pluralistic modernism - a contribution to the understanding of the Slavko Osterc's circle

The theme of this article was inspired by a series of questions that arise to researchers when discussing compositions by musical modernist Slavko Osterc and his pupils from the first half of the 20th century, whose music was neither "tonal" nor extreme "atonal". On the one hand, there is a strong doubt of the Slovenian analysts in the progress (modernity) of the compositional means of the mentioned music, since the works are usually compared with the most extreme solutions of the Second Vienesse School – with atonality, athematicism or twelve-tone technique, and on the other hand the rejection of this music from the Slovenian cultural management in concert performing. The central question that arises is the question of the meaningfulness of such comparison, given that these composers were educated also in Prague and did not want to follow the Schönberg's twelve-tone method.

A Class of Coupled Causal Differential Equations

In this thesis, we consider the existence of extreme solutions to a class of coupled causal differential equations. By utilizing two comparison theorems and a monotone iterative technique, we have obtained sufficient conditions under which the equations have extreme solutions. One practical example is presented.

(Anti)evaporation of dyonic black holes in string-inspired dilaton f(R)-gravity

We discuss dyonic black hole solutions in the case of f(R)-gravity coupled with a dilaton and two gauge bosons. The study of such a model is highly motivated from string theory. Our black hole solutions are extensions of the one firstly studied by Kallosh, Linde, Ortín, Peet and Van Proeyen (KLOPV) in arXiv:hep-th/9205027 . We will show that extreme solutions are unstable. In particular, these solutions have Bousso–Hawking–Nojiri–Odintsov (anti)evaporation instabilities.

CHOICE OF SOLUTIONS ON MANAGEMENT OF STATES OF NAVIGATION OR FISHING SITUATIONS

The problem of the choice of extreme multidimensional solutions of a given finite and admissible set and Pareto optimal, which is received by a person decision maker (PDM) in the dialogue process with the software expert system, was considered. Such a system increasing the level of both navigational safety and the safety of the fishery operates under the condition of "weak" assumptions about the type of structure preferences expressed through a utility function. It is shown that the "weak" assumptions about the form of the utility function in the software product of the expert system can be compensated, if the decision-maker is offered questions formulated on two levels as follows: "For what reduction by one criterion may you agree to receive a predetermined increment on other criteria, provided that other evaluation criteria remain unchanged?" or "What is to choose the reducing in the value of one criterion by a predetermined amount and the increasing the value of the other criterion by a predetermined value or leave the previous criteria values provided that the other evaluation criteria remain unchanged?". It offers the option of mathematical models of "man-machine" dialogues between a decision-maker and software expert system, while ensuring the safety of navigation and the safety of the fishery. As a result of using such dialogues either the only vector estimation, corresponding to the extreme decision of the person decision maker, in terms of its structure of preferences, or some subset of the extreme solutions, which will also contain this estimation, can be obtained.