A. Macdonald: Sobczyk’s simplicial calculus does not have a proper foundation


Alan Macdonald, Sobczyk’s simplicial calculus does not have a proper foundation, arxiv preprint: https://arxiv.org/abs/1710.08274, submitted on 18 Oct 2017.

Abstract: The pseudoscalars in Garret Sobczyk’s paper \emph{Simplicial Calculus with Geometric Algebra} are not well defined. Therefore his calculus does not have a proper foundation.

Source: Email from A. Macdonald, macdonal_AT_luther.edu, 24 Oct. 2017, https://arxiv.org/abs/1710.08274 .

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2 Comments

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2 responses to “A. Macdonald: Sobczyk’s simplicial calculus does not have a proper foundation

  1. The flaw in my partitioning scheme had already been pointed out in
    F. James, “Surface Area and the Cylinder Area Paradox”, The College Mathematics Journal 8 (1977) 207-211. It is obviously not a trivial problem and it is one that is worth looking into. If MacDonald had done that, he would have made a real contribution.

    • Alan Macdonald

      Zames’ paper (which I cite and describe) has nothing to do with geometric algebra. It describes a similarly failed construction using simplices, that of 2D (surface) area. Google Scholar lists 36 citations to Sobczyk’s paper. As far as I know, the flaw in it had not previously been noted, even by citing Zames.

      There are correct geometric definitions of 2D area using simplices. As far as I know, none generalize to nD volume. So I don’t see much hope for the more difficult task of salvaging Sobczyk’s nD paper while retaining “simplicial” in its title.

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