Dual Metric Model of Multidimensional Geometry
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This work deals with the problems of knowledge integration and the role of physics in this process. Physics is the only natural science, which gives us mathematically strict description of reality. It also provides us with technologies and equipment to be applied in other natural sciences. Physics powered by its rich theoretical and experimental technologies is a reliable basis for science integration. Main strategies of knowledge integration such as "reductionism" and "emergentism" are discussed and the integrative character of the works of Albert Einstein is marked. His main scientific tools were universalism when postulating the underlying theoretical principles and generalization through integration of the basic theories. Special and General theories of relativity may be considered as the most significant examples of integrative thinking. From these works we see that Albert Einstein attached great importance to how we understand geometry and dimensions. It is shown how the use of integrative approach allows us to create a model of multidimensional geometry, which gives a new interpretation of such terms as "dimensionality" and "embeddance". The geometry may be useful for predicting and explaining multidimensional and quasi-multidimensional phenomena. The proposed geometry has three features, which distinguish it from the existing geometries:
1. It is holistic. Space is represented as interweaving of connections; each point exists only in the context of the background space, which may be understood as undivided wholeness.
2. It is really multidimensional. Point-connections of different dimensionality have different topology.
3. It is elastic. Embedded surfaces possess dual metric: internal and external. They can change their form in the bulk without changing the internal metric.
The geometry is based on the unity "point-connection" and the duality "zero-infinitesimal" which form its conceptual basis. This geometry may bring to us new ideas about the nature of multidimensional and quasi-multidimensional processes, which are not yet well studied.
