On Thu, 19 Aug 2010 11:03:53 -0700, Russ P. wrote: > For those who insist that zero-based indexing is a good idea, why you > suppose mathematical vector/matrix notation has never used that > convention? I have studied and used linear algebra extensively, and I > have yet to see a single case of vector or matrix notation with zero- > based indexing in a textbook or a technical paper. Also, mathematical > summation is traditionally shown as "1 to N", not "0 to N-1".
In my experience, it's more likely to be "0 to N" than either of the above, thus combining the worst of both notations. > Are > mathematicians just too simple-minded and unsophisticated to understand > the value of zero-based indexing? No, mathematicians are addicted to tradition. Unlike computer scientists, who create new languages with radically different notation and syntax at the drop of a hat, mathematicians almost never change existing notation. Sometimes they *add* new notation, but more often they just re-use old notation in a new context. E.g. if you see (5, 8), does that mean a coordinate pair, a two-tuple, an open interval, or something else? Additionally, mathematical notation isn't chosen for its ability to encourage or discourage errors. It seems often to be chosen arbitrarily, or for convenience, but mostly out of tradition and convention. Why do we use "x" for "unknown"? Why do we use i for an integer value, but not r for a real or c for a complex value? Mathematicians are awfully lazy -- laziness is one of the cardinal virtues of the mathematician, as it is of programmers -- but they value brevity and conciseness over notation that improves readability and robustness. That's why they (e.g.) they use implicit multiplication, a plethora of "line noise" symbols that would boggle even Perl programmers, and two-dimensional syntax where the meaning of tokens depends on where they are written relative to some other token. (E.g. subscript, superscript, and related forms.) There is one slightly mainstream language that uses mathematical notation: APL. The result isn't pretty. -- Steven -- http://mail.python.org/mailman/listinfo/python-list