Concerning forward/backward or into-page/out-of-page, etc...
It certainly helps to have a picture, which is why I referenced Figure-4 on
the Wiki page. When I discuss this in my classes I already have a labeled
coordinate system drawn on the board, just like the Wiki picture, and I put
my back to the class so I am facing the same way they face, and I have them
stand up and mimic me by putting their right arms out to their right and
calling that positive x. We then walk "forward" a couple steps which is
toward the board (or into the board if you wish) and call that positive y.
Then we walk backward to our original position and say we moved in the
negative y direction. Sometimes I have them stand up tall for positive z
and crouch down low for negative z, but since I am facing away from them I'm
not even sure they're all really doing what I've asked them to do, so
stretching and crouching might be a bit much to ask college students to do.
But many seem to remember this, if for no other reason than because it was
the day I made them act like little kids in elementary school.
I think it is interesting that Dan and John M. (and probably other readers
of my earlier post) initially viewed my use of forward as "out of the page."
I have never viewed it that way. I view forward as "in the direction I am
facing." Therefore, if I am holding a page in front of me, forward is into
the page. I would like to say that thinking of forward as out of the page
surprises me, but the truth is that nothing much surprises me anymore when
it comes to miscommunication.
The Wikipedia wording that accompanies Figure-4 refers to the figure by
saying, "The axes are depicted in a world-coordinates orientation with the
z-axis pointing up." I believe "world coordinates orientation" is a good
way to say it (although John D. has mentioned that aeronautical engineers
say +Z points down). A point I try to make is the things scientists draw on
paper are often representations of real-word situations, and the real-word
convention is that +Z is up, +X is to your right, and if we are adopting the
so-called right-handed coordinate system then +Y extends in front of you
(the way you are facing... forward). For +X move right. For -X move left.
For +Z move up. For -Z move down. For +Y move forward. For -Y move
backward.
If you haven't thought about it, another interesting thing is that most
people make an automatic assumption for paper on the desk being in a
different orientation than world coordinates. This automatic assumption is
sort of wrong. The top of the page isn't really up. It's away from you.
When you draw a line "upward" or toward the top of the page you are really
drawing a horizontal line away from you (or forward) assuming we define the
way you are facing as outward from your chest. Therefore, when you draw a
2D "x-y graph" on paper that is on a desk, the true orientation of the graph
axes are the same as what Wiki refers to as world-coordinates orientation.
I suppose we get "top of the page" and/or "up" from the fact that we
sometimes hold the paper real-world-vertical when we read it, or when we
view it on a computer screen (or in those old things called typewriters).
The other day my wife was holding a flashlight for me while I was working on
something. She was facing me. I needed the light moved a bit toward my
left, so I told her to move the light a little to the right. She made a
similar mental gyration and moved the light to my right. I said, "No! To
the right; to the right." She said, "I did move it to your right." Oops.
Then there was the time I was teaching my daughter to drive. She had just
backed up, came to a stop, and was waiting to move forward, but still had
the car in reverse. I said, "Keep your foot on the brake. Don't go
anywhere. Answer this question. If you were to take your foot off the
brake and give the car some gas, which way will the car move, forward or
backward." She thought about it, saw where the shifter was, and said, "What
is this? A trick question? It won't do either one. It will go in
reverse." Okay... smart aleck.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
1 University Drive
Bluffton, OH 45817
419.358.3270
edmiston@bluffton.edu