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In this work a new approach to multidimensional geometry and multidimensional physics based on smooth infinitesimal analysis (SIA) is proposed. Reality may be considered as the process of time evolution of holistic energetically very weak macro objects - elastic membranes with the geometry based on smooth infinitesimal analysis. An embedded membrane in this multidimensional world will look different for the external and internal observers: from the outside it will look like a material object with smooth infinitesimal geometry, while from the inside our Universe-like space-time fabric. It is shown that our perception may be considered as the result of elastic oscillations of two dimensional elastic membranes with closed topology embedded in our bodies. Only one elastic membrane responsible for its perceptions will correspond to the selected organism, but there may be other membranes, even at the cell level. Elastic membranes stretch and propagate along the direction of attentive focus and occupy energetically favorable positions around microtubules involved into ORch OR. According to the model ORch OR and the elastic membrane corresponding to the living organism are closely connected and support each other. INTRODUCTION Undoubtedly the Penrose-Hameroff Orch OR model may be considered as a good theory for describing information processing mechanisms and holistic phenomena in the human brain [1-3]. The theory explains both physical and biological aspects of consciousness such as 1. Non-computability of consciousness; 2. Relation of consciousness to space-time geometry; 3. The role of microtubules as suitable candidates for information processing; 4. Mechanisms for macroscopic quantum computing – dendritic webs. But the theory doesn’t give us satisfactory explanation of human perception. Perception cannot be explained in terms of elementary particles: interactions between separate entities - the elementary particles of our bodies cannot establish a feeling of having perceptual experience, because the notion of “elementary particle” is very abstract and is derived from our perceptions. And there may be objects of higher priority around us. Obviously, such fundamental processes as the processes of perception should be explained using objects of the highest priority. A more fundamental object which incorporates all physical objects around us is our Universe. We explore it from inside and, therefore, our knowledge about it is incomplete. The empty space we see from the inside may be only the result of internal observation. Einstein’s full theory of space-time, called General Relativity can be extended easily to higher space dimensions. This fact is a good argument in favor of the multidimensional science concept. Modern physics is not truly multidimensional – we don’t know how universes of different dimensionalities (I mean here the number of large dimensions) and different physical parameters can be embedded one into another. In order to create multidimensional physics we firstly should create multidimensional geometry. This will be done in the next section. 2 DUAL METRIC MODEL OF MULTIDIMENSIONAL GEOMETRY The concept of multidimensional geometry itself has a dualistic meaning: each surface may be embedded into a higher dimensional bulk and at the same time it may contain lower dimensional surfaces embedded in it. Multidimensional geometry is tightly connected with the basic rules of human perception and depends on how we explain the terms "dimension", "embeddance" and "space". Traditionally, under the term "space" we imply a set of zero-size points on which a metric can be defined. Under the term "dimensionality" we understand a minimal number of real numbers needed to describe this set unequally. An elementary geometrical object "point" itself has no dimensionality and is the same for all dimensions. This understanding of dimensions tells nothing about their true nature. Why do compositions of points have different number of dimensions? In this work a new approach to multidimensional geometry based on smooth infinitesimal analysis (SIA) is proposed. An embedded surface must be considered from two sighting points, namely, for internal and external observers. For the internal observer we have a picture we are used to (for example, the space-time we are living in), but for the external observer the picture is quite different (when we try to imagine a 2-dimensional surface we act like external observers). According to this approach n-dimensional spaces and surfaces are composed of n-dimensional elementary objects "point-connections." The number of dimensions of a manifold depends on how its points are connected. So, an ndimensional object "point-connection" has a dual nature: in addition to being a point of a manifold, it plays a role of connection within a certain set of points of a manifold. In other words, an n-dimensional "point-connection" has two elements: first – a "point" to be connected, and second – a "connection" which connects the "points." 网站原创范文除特殊说明外一切图文作品权归所有；未经官方授权谢绝任何用途转载或刊发于媒体。如发生侵犯作品权现象，英语论文题目，保留一切法学追诉权。()，英语论文 |
