I think we have reached a semantics impasse. To my eye the shadow is just the lack of light on that part of the plywood. Whatever “depth” there might be to the shadow is not the shadow’s depth, but that of the surface on which the lack of light appears. Please try one more time to explain how the shadow on the plywood has its own depth.
What you see on the ground is technically a two-dimensional projection of a volume of shade… myself, I think it’s equally correct to call the ground projection or the volume as a ‘shadow.’
You can’t see the rest of that volume of shadow as long as the only thing inside it is air, which doesn’t reflect light. If there were a bunch of bright little motes of dust in the air, you’d see them winking out and then brightening again as they follow air currents into and out of the shade. If you stuck your finger into the volume of the shade, you’d see the shadow fall onto it. (And you’d also see the shadow of your finger on the ground, poking into the shadow of whatever else it was.)
All a question of definitions. If we agree on what we define the term ‘shadow’ to mean, there’s nothing to argue over. If we can’t agree on definitions, then we’ll be at it forever.
A shadow gets its depth from the surface it is on so yes the depth is the same as the surfaces depth. Such is the nature of shadows.
Thanks for the answer Laughing Lagomorph. I realize that pretty much anything of substance in our world must exist in 3D, so it makes sense that cells must be completely surrounded by a membrane or cell wall, even if it is just angstroms thick.
I think this is it. What the rest of you are arguing over, the part of the shadow that abuts the surface it’s projected on, is only part of the shadow. The rest of the shadow exists between that projection and the object it emanates from.
Look at it this way:
IIIIIIIIIIII|
The first “I” is the object in question. The straight line at the end is a wall. The “I” right next to the wall is the part of the shadow we see as a silhouette of the object projected.
All the italic "I"s in between are also the shadow. A shadow is the absence of light in an area caused by the interposition of an object in front of the light source. So the shadow has to exist all the way from the object to the projected shape or else there would be no projected shape and no shadow.
Or am I looking at this whole thing the wrong way?
No, you are correct. Shadows are of course 3-dimensional. They only appear to be 2-dimensional in a transparent medium such as air. Shadows can easily be seen to be 3-dimensional in a translucent medium such as mist or cloud.
It is possible to define a shadow in terms of our perceptual system. You might be tempted to say “ahh, but even if we did not have such a perceptual system, there would still be areas of darkness where light was blocked. Ergo, shadows.” The fault in this thinking is that, if we did not have the perceptual apparatuses that we have, a shadow would probably not need a definition. It is an arbitrary category that is defined in terms of the way we perceive the world. If you imagine alternative possible ways of perceiving the world, you’ll find infinitely many of these categories.
An interesting classic on this subject is Nagel’s What is it like to be a bat?
Were you a bat, do you suppose there would be the perceptual analog of a shadow for echolocation? Of course there would be, and it would probably have a character we cannot imagine.
I agree that it is very tempting to think of a shadow as occupying space, but when I do my best to turn off my eyes it is less convincing that shadows really do.