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
Subscribe to:
Post Comments (Atom)
8 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.
Actually shadows are three dimensional. During a Solaw Eclipse, for example, when the moon blocks out the sun it casts a shadow on Earth. If you were to look at this from a perfect right angle, a side view, you would see the "umbra". The Umbra is like the "cut" or void in between the light, the space where the light is absent. This is shadow occupying three dimensional space.
When the shadow hits a surface, the surface displays a cross section of the shadow. The cross section is 2 dimensional, but the shadow itself is 3dimensional.
If a 4-D hypercube were hit with visible light, it would also cast a 4 dimensional shadow, but the cross sections of the shadow would be three dimensional.
If it's too difficult to imagine, just think of it this way:
0D= point
1D= line
2D= square
3D= cube
4D= tesserect (hypercube)
The points are the surface of the line. The line is the surface of a square. The square is a surface of a cube. And a cube would be the surface of a tesserect.
Dear Sir,
I think all shadows are in 3 dimension because we are living in a 3 deminsional world. And I don't think it's possible to create a 4th dimensional object. Our eyes can only see in 3 dimension. However, I have one question. Is our reflection in a mirror in 3D ? Because we can't feel our refection. But maybe it is also in 3D because it is similiar to a shadow.
And I want to say something which is also a wish. Why won't God himself answer all of our questions so that we won't have to think too hard to come to an answer?
Dear Sir,
I made a mistake by assuming all shadows are in 3D. A fog shadow is in 3D. A shadow on a wall must be in 2 diminsional because you can't look at it behind it. And a reflection in a mirror is in 2D because you can't see it behind it.
You might as well ignore my previous comment I made at 2:47 AM.
And I don't think God will bother to answer any of our questions. It's as if he doesn't exist.
even in a well lit room a shadow cast exists in 3 dimensions. if the shadow is dark enough to project an image on a flat surface (which you view as a 2d image) it is limiting ALL light in between point A (light source) and point b (flat surface)
Since this is a constant it must be true to say the dim space between point A, and point B, is 3 dimensional.
Post a Comment