The way X,Y,Z axis are portrayed in the way that is most common in computer graphics. X is left-right, Y is up-down, Z is front-back. That's convenient because X,Y are your screen coordinates for 2D work, if required, Z is stored in a separate buffer, aptly called the Z-buffer.

Orientation of the base vectors can vary between tools, engines and APIs but the Z axis is almost always perpendicular to the screen, and having the Z axis perpendicular to the mirror follows this convention.

And a mirror certainly flips things. In a mirror image, parity is reversed, right hands become left hands, screws turn the other way. A person in front of you doesn't see you flipped, he sees you rotated 180 degrees around the up-down axis. You can achieve the same effect with two vertical mirrors at a right angle from each other. Because there are two mirrors, the image is flipped twice, and because of the way parity works, it is the same as not flipping.

One thing we can say is that flat mirrors both flip and rotate. The flip is always the same, there are only 2 parities and the only thing you can do is go from even to odd and odd to even. The rotation depends on the position and orientation of the mirror. If the mirror is vertical, the axis of rotation is vertical and therefore, it will flip left-right. If the mirror is horizontal the axis of rotation will be horizontal and it will flip up-down. Funhouse-style distorted mirrors also flip, like all mirrors, but will apply a complex, non-linear transformation instead of a simple rotation.

I think it's pretty reasonable to say the image is flipped, but it's flipped along the 3rd axis: Front-to-back.

Exactly. The image in a mirror is physically symmetrical to the direct image from objects in the real world, with the mirror itself as the plane of symmetry.

I find the front-to-back explanation to give a better intuition than the typical "but left and right are relative to your body", which only serves to explain the paradox of "left-right are reversed but up-down ar not", but not the fact that everything looks flipped.

Well, it flips front-to-back. But this side of the mirror, we can't physically do that, so it's not in our brain's list of expected possibilities. We can, however, rotate ourselves 180 degrees. And because we're bilaterally symmetrical, our brain finds it easy to interpret the front-to-back flip as a 180 degree rotation. But that leaves left-to-right weird, because what happened wasn't actually a 180 degree rotation.

Don't beat yourself up about Z. The Z axis is both a convention and commonly used for height in many fields, such as civil engineering, vehicles, and geology. All areas where the horizontal ground is important. It's computer graphics with its vertical screens that mainly has Z for depth.

There does seem to be an underlying commonality to these conventions which might be that Z is normal to some important reference plane, the direction without homogeneity, or the most unique direction.

Agree with your second point, but for the first criticism, many fields actually use z as the "depth" axis.

I haven't come across any but I did carefully choose the word "commonly" as an acknowledgement that it's not mandatory to be this way. :)

The usage of the z-axis is absolutely correct in the article.

The author has essentially defined the x and the y axes. Useful physics (or math), as opposed to what appears to be an arbitrary common convention in whatever field you're familiar with, would suggest placing the z-axis in the direction that is co-perpendicular to the defined x and y axes.

That a z-axis represents height and not depth is the least physics thing I've ever heard. Frankly, I dont think that's a thing at all.

Computer graphics use Z as the depth axis.

I've only ever known the Z axis to represent depth. Be it maths, physics or software development (web dev: "z-index", Direct3D, etc).

Also your second point is reiterating exactly what the video said. She repeatedly says "the mirror isn't flipping anything [along the horizontal axis], you are."

The physics of what she's discussing is correct, you've just been a bit rash to judge it.

> I've only ever known the Z axis to represent depth. Be it maths, physics or software development

A standard math textbook will usually show the x-axis pointing toward the reader, the y-axis pointing right, and the z-axis pointing up. Something like this:

    z
    |_
    /  y
   x

Similarly, if you're defining a cone or a spiral or what have you, you'll usually do it in terms of an r/θ/z coordinate system, where z is height. So the convention exists.

But obviously where the x and y axes are defined, the z axis will be perpendicular to the x-y plane.

Yes. Usually, the right-hand rule is followed. A positive rotation is from the positive x axis toward the positive y axis. If you curl the fingers of your right hand in that direction, then the thumb points along the positive z axis.

Your second point is saying the same thing that the article says. There's no "terrible physics" here.