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
Wednesday, June 20, 2007
The Dimensions of Shadows
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4 comments:
I don't think I played with legos enough as a kid.
Actually, I spent a lot more time with Barbies than with Legos as a kid. But that's another story.
I think the shadow is generally the same dimensions as the space you are in. In 3 dimensions, the shadow is also three dimensional and then the surface (e.g., a wall or side walk) provides a 2 Dimensional cross section of the shadow.
Same thing should happen in 4D. The shadow will be 4D, and if you take a projection on a 3D surface, it would be a 3D object or it could be 2D if you choose to take a cross section on a wall which is 2D.
That makes a lot of sense. But man, I'm so used to 2D surfaces, it's hard to wrap my mind around one that's three dimensional. I can appreciate what math says is possible, but I am fundamentally locked in a 3D reality.
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