Online research in philosophy

This book provides an introduction to applied statistical mechanics by considering physically realistic models. It provides a simple and accessible introduction to theories of thermal fluctuations and diffusion, and goes on to apply them in a variety of physical contexts. The first part of the book is devoted to processes in thermal equilibrium, and considers linear systems. Ideas central to the subject, such as the fluctuation dissipation theorem, Fokker-Planck equations and the Kramers-Kroenig relations are introduced during the course of the exposition. The scope is then expanded to include non-equilibrium systems and also illustrates simple nonlinear systems. This book will be of interest to final year undergraduate and graduate students studying statistical mechanics, plasma physics, basic electronics, solid state physics and anyone who wants an accessible introduction to the subject.

Fractal geometry offers a new approach to describing the morphology of fern leaves. Traditional morphology is based on the Euclidean concept of shape as an area defined by a boundary. This approach has not proven successful with fern leaves because they are so elaborate. Fractal geometry treats forms as relationships between parts rather than as areas. In fern fronds there are often constant relationships between parts. Four fractal methodologies for describing these relations within leaves are explored in this paper. These include recursive line branching algorithms, iterated function systems (IFS), modifications of IFS, and L-systems. The methods are evaluated by comparing their results with measurements and appearances of various ferns. Fractal methods offer objective, quantifiable and succinct descriptions of fern-leaves. We conclude that fractal geometry offers simple descriptions of some elaborate fern shapes and that it will probably have application in investigating different aspects of ferns and other organisms.

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation process should be statistically similar, i.e. their fractal dimensions and their form factors should be equal. In this paper, we analyze 49 woodlot fragments (Pinus sylvestris L.) in the Belgian Kempen region to study the direct relationship between a transformation process and the concomitant patch geometry. Although the fractal dimension of the woodlots is scattered (i.e. they are not statistically similar), the perimeter-area relation of the fragments is characterized by a single, ‘dimension-like’ exponent. This exponent suggests a certain shape homogeneity among the patches, which is confirmed by the absence of hierarchical levels associated with sharp increases of the fractal dimension at scale transitions. The interaction of different natural (soil factor, vegetation type) and anthropogenic (afforestation, urbanization) processes during patch development is assumed to have generated this feature. Comparison of the area and perimeter fractal dimension with an ecological index for habitat quality, the interior-to-edge ratio, shows that the fractal dimension is suitable for predicting interior habitat presence, which is more likely for patches with smooth perimeters and compact areas. The ratio of the area to the perimeter fractal dimension confirms this observation, with high values for high interior-to-edge ratios, characteristic for regularly shaped patches.

In human consciousness a world of separated objects is perceived by an inner observer who is experienced as an undivided feeling of one-self. A topological correlation of the self to the world, however, entails a paradoxical situation by either merging all separated objects into one or splitting the self into as many subselves as there are objects perceived. This study introduces a model suggesting that the self is generated in a neural network by algorithmic compression of spatial and temporal information into a fractal structure. A correlation of an inner observer to parts of a fractal structure inevitably entails a correlation to the whole, thereby preserving the undividedness of the self. Molecular mechanisms for the generation of a fractal structure in a neural network and the possibility of experimental investigation will be discussed.

A general treatment of stationary Gaussian fractals is presented. Relations are established between the fractal properties of an n-dimensional random field and the form of its correlation function and power spectrum. These relations are used to show that the second-order parameter H commonly used to describe fractal texture is insufficient to characterize all fractal aspects of the field. A larger set of measures -- based on the power spectrum -- is shown to provide a more complete description of fractal texture.

A new event is defined as an intervention in the time reversible dynamical trajectories of particles in a system. New events are then assumed to be quantum fluctuations in the spatial and momentum coordinates, and mental action is assumed to work by ordering such fluctuations. It is shown that when the cumulative values of such fluctuations in a mean free path of a molecule are magnified by molecular interaction at the end of that path, the momentum of a molecule can be changed from its original direction to any other direction. In this way mental action can produce effects through the ordering of thermal motions. Examples are given which show that the ordering of 10^4 10^5 molecules is sufficient to (a) produce detectible PK results and (b) open sufficient ion channels in the brain to initiate a physical action. The relationship of the above model to the arrow of time is discussed.

The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a single power-law relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. This change in fractal scaling, that is, multifractality, provides new insights into changes in energy flow through the cognitive system. We survey recent findings demonstrating the role of multifractality in (a) understanding atypical developmental outcomes, and (b) predicting cognitive change. We propose that multifractality provides insights into energy flows driving the emergence of cognitive structure.