Article

Is symmetry identity?

International Studies in the Philosophy of Science 02/2012; 16(2). DOI: 10.1080/02698590220145061
Source: arXiv

ABSTRACT Wigner found unreasonable the "effectiveness of mathematics in the natural
sciences". But if the mathematics we use to describe nature is simply a coded
expression of our experience then its effectiveness is quite reasonable. Its
effectiveness is built into its design. We consider group theory, the logic of
symmetry. We examine the premise that symmetry is identity; that group theory
encodes our experience of identification. To decide whether group theory
describes the world in such an elemental way we catalogue the detailed
correspondence between elements of the physical world and elements of the
formalism. Providing an unequivocal match between concept and mathematical
statement completes the case. It makes effectiveness appear reasonable. The
case that symmetry is identity is a strong one but it is not complete. The
further validation required suggests that unexpected entities might be
describable by the irreducible representations of group theory.

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    ABSTRACT: A group-theoretically motivated investigation of feature extraction is described. A feature extraction unit is defined as a complex-valued function on a signal space. It is assumed that the signal space possesses a group-theoretically defined regularity that the authors introduce. First the concept of a symmetrical signal space is derived. Feature mappings then are introduced on signal spaces and some properties of feature mappings on symmetrical signal spaces are investigated. Next the investigation is restricted to linear features, and an overview of all possible linear features is given. Also it is shown how a set of linear features can be used to construct a nonlinear feature that has the same value for all patterns in a class of similar patterns. These results are used to construct filter functions that can be used to detect patterns in two- and three-dimensional images independent of the orientation of the pattern in the image. Finally it is sketched briefly how the theory developed here can be applied to solve other, symmetrical problems in imaging processing
    Journal of the Optical Society of America. A, Optics and image science 06/1989; 6(6):827-34.

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