CELKO (4/27/2015)
Calling either a scalar is outrageous: neither is "a quantity having magnitude but no direction, and representable by a single real number" since neither is a quantity and neither has magnitude (neither has direction and each can be represented by a single real number in all sorts of ways, so the rest of the definition is satisfied); and if you are using some other definition of scalar you are completely out of line both with mathematics and with decent English dictionaries.
This used to be measurement theory, but now it is “data theory” to go with “data Science”, etc. I miss being just a statistician sometimes. Look at Joe Celko's Data, Measurements and Standards in SQL [ISBN-13: 978-0123747228].
“Scalar” means measured with a scale in this discipline. In case of identifiers, it is a nominal scale. We could also have categorical, rank, ordinal, interval and ratio scales for other data elements.
Well, an identifier for a position is just as much an identifier as an identifier for a book with a paricular media-type and edition. So if the ISBN, because it's an identifier, can be a scalar, despite being a quartet or a quintet, because it's an identifier, the position identifier too can be a scalar, despite being a pair (or a triplet), because it too is an identifier. So even with that interpretation of scalar it's clear that your claim that ISBNs and position identifiers have an essential difference that an ISBN is scalar while a position identifier can't be a scalar falls down by your own argument.
Tom