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#105: Scalar Coordinates -----------------------------+---------------------------------------------- Reporter: markh | Owner: [email protected] Type: enhancement | Status: new Priority: medium | Milestone: Component: cf-conventions | Version: Resolution: | Keywords: -----------------------------+---------------------------------------------- Comment (by biard): Steve, I like the way you think! In particular, the question regarding the mathematical distinction got my mind going. I don't know if it will generate more heat than light, but here's what your questions led me into. (By the way, I'm an "independent" when it comes to this issue. I see merit in the arguments of both the "Originalist" and "Living CF" parties.) If I think about the concept of scalar vs vector/matrix in linear algebra, I find that a scalar is treated differently than a matrix of dimension 1 x 1. Multiplication of a matrix by a scalar is defined as multiplication of every element of the matrix by the scalar. Multiplication of one matrix by another is only possible when they share a dimension. Following that sort of semantics, a scalar coordinate could well be considered to be different than a vector coordinate in a similar fashion. A scalar coordinate is considered to apply to every element of a variable as an ensemble. A vector coordinate is considered to apply to a variable through a relation over one or more shared dimensions. If I continue to follow the linear algebra analogy, I can decompose a matrix multiplication by a vector into a sum of scalars (taken from the vector) multiplying column vectors (taken from the matrix). Correspondingly, I can compose a set of scalars multiplying column vectors (that all have the same length) into a matrix multiplied by a vector. This corresponds to the multi-file aggregation of variables with scalar coordinates into a single higher-dimension variable with a vector coordinate composed from scalar coordinates. Thinking about the problem this way actually is leading me to smile more on the idea of scalar coordinates being different from vector coordinates of length 1. The semantic difference is specifically honored within linear algebra, and adopting this approach doesn't seem (to me) to constrain anyone in terms of how they may choose to compose (or not compose) higher-dimension relations using multiple files. -- Ticket URL: <https://cf-pcmdi.llnl.gov/trac/ticket/105#comment:2> CF Metadata <http://cf-pcmdi.llnl.gov/> CF Metadata This message came from the CF Trac system. To unsubscribe, without unsubscribing to the regular cf-metadata list, send a message to "[email protected]" with "unsubscribe cf-metadata" in the body of your message.
