On Sun, Oct 26, 1997 at 10:16:03AM -0600, Jim Choate wrote:
Hi,
I believe the first definition for orthogonal is not the vector or Cartesian definition but rather from geometry.
Where, for example, polygonal means a closed shape made up from many line segments, orthogonal means a closed shape made from line segments at right angles to each other. The simplest being the square.
DeCarte used the concept of ortho- to describe the relationship between the axis of his measurement system, hence orthogonal. Strictly speaking orthogonal is a misnomer and should be orthometric or 'measurements at right angles'.
I am interested in how orthogonal obtained its variety of other meanings. I run across it in linguistics, computer science, philosophy, etc. In most of them it means some sort of pure or simple relationship. Unfortunately I can't find any sort of description of how it got expanded this way.
Sorry I misread your prior post. The first context where I am aware of this use of the term orthogonal is from language design -- it was promoted by Niklaus Wirth and other purists, with languages like Pascal, Modula, CLU, and so on. Larry Wall's "perl" language, with its slogan "there's more than one way to do it", is a direct revolt against the language purists. The basic idea is that a computer language should have the minimum number of constructs necessary to span the intended application. So for example, you don't provide hyperbolic trig functions, because the user can implement them using simpler math functions. On the other hand, you do supply commonly used math functions that would otherwise require iterative algorithms. I do believe the use of the term this way was inspired by the notion of a 'basis' in a vector space -- a set of orthogonal vectors that span the space, ideally, unit vectors. -- Kent Crispin "No reason to get excited", kent@songbird.com the thief he kindly spoke... PGP fingerprint: B1 8B 72 ED 55 21 5E 44 61 F4 58 0F 72 10 65 55 http://songbird.com/kent/pgp_key.html