There is Up, then there is Up
When you drop a ball in front of a mirror, its reflection moves up, not down.
I say this under the same pretext as when we say that in our reflection left is right and right is left.
If you were to stand in front of a mirror and hold out your left hand, it would look like your reflection is holding out its right hand. This is because the orientation of reflections in a mirror are exactly the same as the orientation of their original counterparts except that everything is reversed along the z-axis.
If a mirror were a reflective piece of graph paper with the x-axis running across the bottom (horizontal axis) and the y-axis running up the side (vertical axis), then the z-axis would stick directly out of the mirror. When everything is reversed along the z-axis, it means that the z values are reversed from positive to negative while the x and y values remain the same.
Assuming the distance from the mirror would be a positive amount, the perceived distance from the mirror in the reflection would be a negative amount. So you can only be a positive distance from the mirror and your reflection can only be a negative perceived distance from it.
Now, imagine that the mirror is still a reflective piece of graph paper, except instead of having the zero point of the x and y axis at the bottom corner of the mirror, it will be right between your eyes. This way, everything to your left will be represented by negative x values along the x-axis, and everything to your right will be represented by positive x values along the x-axis. Also, everything downwards will be represented by negative y values along the y-axis, and everything upwards will be represented by positive y values.
Hopefully I haven’t confused you in describing the placement of the graph. The graph is still the mirror, so the z-axis still extends out from it, and the mirror surface still represents point 0 on the z-axis (no distance away from the mirror, and no perceived distance within the reflection). The only thing that has changed is that no matter where you are, down is considered negative and up is considered positive, left is considered negative and right is considered positive. So the left side of your body is in the negative half the the x-axis, vice versa for your right side, and only your forehead and the top of your head are in the positive portion of the y-axis while the rest of your body is in the negative portion of the y-axis (unless you’re so excited about this discussion that you’ve flung your arms above your head).
Why is it so important to use graph terms to explain why a falling ball’s reflection moves up, not down? Assuming you know the basics of how a graph works then it will help you understand my argument by simply reading this post.
Back to introducing you to your reflection-
Your left appears to be your reflection’s right just as your reflection’s left appears to be your right. This would mean that since your reflection’s right hand is to the left of you, your reflection’s right hand has a negative x value (remember, to you everything to your left is considered negative). This reversal of value between you and your reflection is a direct result of reversing the orientation of everything along the z-axis into negative values (reflect= reverse z value from + to -).
Your perspective is associated to the positive z value and your reflection is associated to the negative z value.
In this regard, yourt left (positive) is the same as your reflection’s right (negative) and vice versa for your right. So positive left = -right and +right = -left.
Since it’s now understood how the orientation on the z-axis determines our understanding of the two directions on the x-axis (left and right), what about our understanding of the two directions on the y-axis?
Normally we would associate up as one direction on the y-axis and down as the other, the same way that left and right oppose each other on the x-axis.
Since left is the negative right and right the negative left, isn’t it safe to say that up is the negative down, and down the negative up? No?
Maybe because we grew up surrounded by gravity our entire lives we consider up to always point the same way.
As planet dwellers, we associate the upward/downward directions to gravitational force. Whichever direction points to the gravitational pull is considered down. The direction pointing directly away from the gravitational pull is considered up.
These two rules are applied at every angle across the globe, exemplifying the subjection of the definitions of the words up and down. A person on the north pole would describe up as the opposite direction as a person on the south pole would, even though both would be using the same tool to come to their conclusions, gravity.
Since the current definition of up, the direction pointing away from the gravitational pull, is inconsistent, let’s consider a new definition of up.
Up can be defined as the direction in which y-values increase.
By this definition, up is no longer dependent on the location of the observer.
But how do we know in-which direction y-values increase? I might say y-values increase in parallel to the direction from the south pole to the north pole whereas you might say y-values increase the higher one goes, as in elevation.
And yet another argument is that there is no such thing as up since the universe is adirectional, as in, it is without direction. Based on this argument, there may not be a universal up, and ‘up’ may be nothing more than an expression defined by the observer, like forward.
So the y-axis would have to be defined in order to determine which direction is up, and the use of that y-axis would only apply within the argument. With each context, up is considered only an expression, making it consistent through all applications.
So, if you were to rub your finger across the surface of a mirror to the right, your reflection would be rubbing its finger across the mirror to its left, +right = -left. And if you rub your finger upwards across the mirror +up, then your reflection would be rubbing its finger -down, +up = -down, (+down = -up).
A person on the north pole will not contradict the person on the south pole in the argument of which way is up as long as they both agree on which direction y-values are increasing.
The old argument for up used a consistent tool, gravity, to express inconsistent observations. The new argument for up uses a consistent tool to express independent, non-overlapping observations.
We need to reconsider the meaning of up so that, as strange as it sounds, up is not so much a direction as it is an expression; and a falling ball’s reflection is moving up to the floor, instead of down to the floor.