Scientists, when they want to understand properties of complex systems, they divide them into simple parts and – knowing the parts and their relations – reconstruct the whole. This approach is effective in the case of simple systems: atomic nuclei, atoms, chemical compounds, stars and so on. In biology it is supplemented by the theory of evolution. However the situation is hopeless when one wants to explain the astonishing properties of the Universe generally known as Anthropic Principle. Discussing that problem, (...) philosophers use the metaphor of God as a Mathematician. The aim of the paper is to prove the inadequacy of this metaphor. (shrink)

The purpose of this paper is to compare two conceptions of order. One, based on classical mechanics, identifies order as simplicity of components and their compositions. Within this framework it is difficult to describe and understand system which have rich, dynamical structures. In order to accomplish this, we need non-linear dynamics, and hence a new notion of order. In non-linear dynamics local processes are chaotic, but order emerges on the higher level.

This article is a polemic with the thesis held by J. Bobryk that we will never succeed in giving a unified description of human thinking and physiological processes taking place in human brain. The author rejects this view on the basis of the results achieved by modelling the brain's activities with the help of the theory of chaos. These models treat the brain as an incredibly complex dynamical system in which the order apprears as a result of mutual interactions of (...) big neuron collections. The significant empirical material was gathered, ilustrating chaotic dynamics of the sense of sight, muscles movements, concentration etc. There seems to be no unsurmountable obstacles on the way of creating the unified theory of the brain dynamics and the consciousness. (shrink)

After the rise of the theory of relativity and the quantum theory, the classical mechanics has been recognized as an approximate version of both theories - applicable only within the bounds of macro-phenomena and by relatively low velocities. The theory of chaos - unfolding nowadays, and being amplification of the classical mechanics - reverses this relation: quantum processes are treated as a certain rather simple class of non-linear and non-stable mechanics phenomena. The unexpected revival of the classical mechanics forces the (...) considerable weakening of the thesis about incommensurability of the theories separated by a scientific „revolution”. (shrink)

Elementary particle physics is an intensively developing fundamental branch of physics. It has many important results and the picture of the fundamental level of the structure of matter elaborated by this theory becomes more and more detailed and complete. Physicists call the picture the Standard Model. However, in spite of its great achievements, Standard Model has several serious problems that cannot be solved by its methods. In order to overcome these problems physicists formulate the ultimate physical theory, called the supersymmetry (...) theory. They have big expectations with respect to this theory and they build strong accelerators to perform experiments testing specific predictions of supersymmetry. Till now none of those predictions has been empirically corroborated and this fact leads to the conclusion that the idea of supersymmetry is more fantasy than the empirical scientific theory. The paper is based on the presentation of the supersymmetry theory given by G. Kane in his book Supersymmetry. Squarks, Photinos and the Unveilling of the Ultimate Laws of Nature. (shrink)

The subject of the paper is the presentation and discussion of Lee Smolin's book The Trouble with Physics . Smolin presents in his book the history and the current state of elementary particle physics. He shows that this field of research is now in a very bad situation because no progress has been achieved for last twenty five years. Since the time of Galileo and Newton, fundamental physics has been in the process of permanent progress and the recent lack of (...) success is considered by Smolin as ex-ceptional and dangerous. Superstring theory is, in his opinion, the main cause of this trouble with physics. The theory dominated elementary particle physics in USA, al-most completely eliminating other more fruitful approaches to elementary particles and their interactions. Smolin analyses the situation from sociological point of view and he proposes some preventive measures. He is completely concentrated on phys-ics in USA and he neglects the rest of the world. (shrink)

The central topic of this article is the analyse of a role which modern mathematics plays in developing empirical theories. This is done with the help of an example of how fractal theory is applied to physics.