Tony Paletta wrote on Sat, Dec 13, 2003 03:55 AM UTC:
Fergus,
In one of 12-12 comments ('As it turns out, the dictionary ...') you
brought up statistics and suggested that a different meaning
('specialized sense') was being given to orthogonal by statisticians. I
responded by indicating that these statistical senses were not different
in their root meaning. You criticized this as involving equations between
sets of coordinates rather than geometry.
Many fields of mathematics are extensions of the concepts of classical
(Euclidean) geometry, in a variety of directions -- including quite a few
fields which tend to deal with planes and vector spaces. The consistency
with the geometric sense of orthogonal (where orthogonal lines are lines
at right angles to each other) is maintained, even when not superficially
apparent.
How does one get three 'orthogonal' paths to pass through a point in a
plane? We could Humpty-Dumpty up a meaning of orthogonal that directly
conflicts with the established meaning, but that doesn't impress me as
exactly dazzling the world with our brilliance. Choosing our terms more
carefully to convey our intended meaning seems like a better way to
communicate.
Fergus, In one of 12-12 comments ('As it turns out, the dictionary ...') you brought up statistics and suggested that a different meaning ('specialized sense') was being given to orthogonal by statisticians. I responded by indicating that these statistical senses were not different in their root meaning. You criticized this as involving equations between sets of coordinates rather than geometry. Many fields of mathematics are extensions of the concepts of classical (Euclidean) geometry, in a variety of directions -- including quite a few fields which tend to deal with planes and vector spaces. The consistency with the geometric sense of orthogonal (where orthogonal lines are lines at right angles to each other) is maintained, even when not superficially apparent. How does one get three 'orthogonal' paths to pass through a point in a plane? We could Humpty-Dumpty up a meaning of orthogonal that directly conflicts with the established meaning, but that doesn't impress me as exactly dazzling the world with our brilliance. Choosing our terms more carefully to convey our intended meaning seems like a better way to communicate.