The Dimensions of Shadows

In honor of the recent Father’s Day, I’m posting about a debate I once had in the car with my dad. We were talking about shadows and dimensions. Okay, so this is more math, but if you like physics, you must at least have some appreciation for the power of math.

Dad believes that a four-dimensional object could cast a three-dimensional shadow. I was convinced that all shadows must be two dimensional.

In my mind, a shadow is just a two-dimensional map of places where light has passed by or been obstructed by an object. So it must be two dimensional. Wikipedia says that I’m just talking about the cross section of a shadow — they’re all essentially three-dimensional.

It’s hard to imagine a four-dimensional object, though. If I was better at math, maybe I could say something about how photons would interact with it, but I don’t have much of a conceptual idea. Some folks at Union College of New York who are better at math made short animations of the shadows of rotating cubes (3D) and hypercubes (4D, projected in 2D for the picture).

In the animation, each face of the hypercube casts a three-dimensional shadow. So I guess the math supports my dad. It’s really hard to argue with math. But if you have an opinion on the matter, I’d love to read it.

Photo Credits: Wikipedia

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