The ultimate tactics of self-referential systems

Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can be seen, in a first approach, as a language, it goes beyond this concept. I conjecture that mathematics presents two extreme features, denoted here by {\sl irreducibility} and {\sl insaturation}, representing delimiters for self-referentiality. These features are then related to physical laws by realizing that nature is a self-referential system obeying bounds similar to those respected by mathematics. Self-referential systems can only be autonomous entities by a kind of metabolism that provides and sustains such an autonomy. A rational mind, able of consciousness, is a manifestation of the self-referentiality of the Universe. Hence mathematics is here proposed to go beyond language by actually representing the most fundamental existence condition for self-referentiality. This idea is synthesized in the form of a principle, namely, that {\sl mathematics is the ultimate tactics of self-referential systems to mimic themselves}. That is, well beyond an effective language to express the physical world, mathematics uncovers a deep manifestation of the autonomous nature of the Universe, wherein the human brain is but an instance.Comment: 9 pages. This essay received the 4th. Prize in the 2015 FQXi essay contest: "Trick or Truth: the Mysterious Connection Between Physics and Mathematics

Marx, the labour theory of value and the transformation problem

This article reconsiders what Marx says about the transformation problem in Chapter IX of Capital Volume III, in the light of Marx's claim, made in Capital Volume I, that the value of a commodity is determined by the socially necessary labour time that goes into its production. The article criticises the traditional way of thinking about the transformation problem, according to which what Marx is doing in Chapter IX is considering the transformation of values into prices ('prices of production'). I argue that Marx's prices of production may be thought of as modified values. The discussion in Chapter IX is usually seen as a supplement to the labour theory of value. On this view its purpose is to explain how and why the prices of commodities sometimes deviate from their values. Against this view, the paper argues that Marx's remarks in Chapter IX can be seen as an elaboration on or development of the labour theory of value. It is a refinement of the account offered in Capital Volume I, which takes into consideration what Marx had in mind there when he introduced the notion of socially necessary as opposed to actual labour-time. The paper draws attention to the importance of Marx's distinction between the individual value of a commodity (determined by actual labour-time) and its social value (determined by socially necessary labour-time). It also draws attention to the methodological difficulties that are generated by any attempt to read Marx in this way

Quantum Fluctuations Driven Orientational Disordering: A Finite-Size Scaling Study

The orientational ordering transition is investigated in the quantum generalization of the anisotropic-planar-rotor model in the low temperature regime. The phase diagram of the model is first analyzed within the mean-field approximation. This predicts at $T=0$ a phase transition from the ordered to the disordered state when the strength of quantum fluctuations, characterized by the rotational constant $\Theta$, exceeds a critical value $\Theta_{\rm c}^{MF}$. As a function of temperature, mean-field theory predicts a range of values of $\Theta$ where the system develops long-range order upon cooling, but enters again into a disordered state at sufficiently low temperatures (reentrance). The model is further studied by means of path integral Monte Carlo simulations in combination with finite-size scaling techniques, concentrating on the region of parameter space where reentrance is predicted to occur. The phase diagram determined from the simulations does not seem to exhibit reentrant behavior; at intermediate temperatures a pronounced increase of short-range order is observed rather than a genuine long-range order.Comment: 27 pages, 8 figures, RevTe

Обнаружение частичных разрядов импульсным методом

Выпускная квалификационная работа содержит 124 с., 68 рис., 13 табл., 22 источника, 1 прил. Ключевые слова: импульсный метод, частичный разряд, обнаружение, дефект, науглероживание. Объекты исследования: секции конденсатора (90 пФ, 0,12 мкФ, 700 пФ, 1100 пФ, 1500 пФ), пропитывающий состав (касторовое масло). Цель работы: исследование метода для обнаружения частичных разрядов при помощи подаваемого импульсного напряжения на испытуемый объект. Проведено испытания по обнаружения частичных разрядов путем подачи импульса с крутым фронтом на испытуемый объект, в котором возможно появление частичных разрядов (секция импульсного конденсатора). Установлено, что появление частичных разрядов изменяет форму тока через испытуемый объект путем подачи на объект напряжения с крутым фронтом. Различная емкоIn the production, transportation and processing of biological resources different electrical equipment is used, the integral part of which are DC machines. Energy efficiency and reliability of the production depends on the drives. The breakdown even of one engine may stop the production process and consequently entail losses. One reason for the failure of the DC motors is insulation damage due to exposure to partial discharge, however, a partial discharge detection technique has not been developed yet. For early warning of failure of DC machines and reducing the cost of unplanned stoppage on the replacement of a failed motor it is proposed to detect partial discharge sat an early stage. There are many developments related to the detection of partial discharges. The majority of methods re