Single Comment

Tony P.,

I already responded briefly to this quotation of yours, but now I will
respond in more detail:

'but that they did not have the same FULL MEANING as on the chessboard
(crossing edges at right angles, but also moving along paths
that are at right angles), which in turn did parallel the more
comprehensive meanings used in mathematics (as opposed to the less
specific 'at right angles' dictionary entry).'

There are certain problems with using orthogonal to describe lines of
movement that are orthogonal to each other. First, it does not describe a
quality that belongs to any line of movement. Rather, it describes a
quality of the relation between two different lines of movement. Second,
it does not distinguish how a Rook moves from how a Bishop moves. On a
standard chessboard, the Bishop's lines of movement are also orthogonal
to each other, for they too are at right angles to each other.

But if we take an orthogonal line of movement to be a line of movement
that intersects the boundaries of a space at right angles, it describes a
quality of the movement itself, and it distinguishes how a Rook moves from
how a Bishop moves. It also fits well with the very first definition given
in Webster's: 'intersecting or lying at right angles.' It is movement
along a line that intersects the boundaries of spaces at right angles.

Now, if we combine these two senses of orthogonal and call it the FULL
MEANING of orthogonal, as you seem to suggest we should do, we have really
just conflated two independent ideas.