Dimensional question?

Question

For the people who have read the example of a creature in Flatland.. It says that a 2d being on Flatland will "see" a 3d sphere as a shadow if place above it.. the shadow will be that of a circle.. again a 2d right? It then says that for a 3d being the 4d also is seen as a shadow.. Can someone give me an example in our world.. An example of a "shadow" which is a 4d in our everyday experience? Or am I completely missing the point here....

Answer 1

When the 3 dimensional sphere intersects with 2 dimensional Flatland the sphere appears as a point, becomes a circle that grows first and becomes smaller again.

In 3 dimensional space the same thing happens, with a 4 dimensional "sphere" starting as a point, expanding to a 3 dimensional sphere that grows.

We have only one example of that.... it's the Big Bang itself.
According to theory our 3D Universe started as a point, became an expanding sphere. And it is still expanding today. 14 billion years later.

Interesting way of looking at it, isn't it ?

Answer 2

In Flatland, when the sphere entered the 2-D world, he appeared as a circle that grew larger then smaller--much like if you looked at a ball floating in water. A cross section of the ball on the surface of the water would be a circle. I'm not sure what you mean by "shadow."

However, the basic principle of the book stated that, mathematically, it is completely feasable and possible for there to be a fourth dimension.

Something "4-D" in our dimension would be as difficult to understand as the square trying to understand the cube. I'm not sure if this is really answerable...at least, not by me, for I am but a 3-D creature myself.

Answer 3

I have not read the book that you have referred to but it is mathematically possible for multiple dimensions to exist. Even if you encountered a 4d object in your life, you would only see those parts of the object that can be perceived in 3d. An example of a shadow of a 4d object in 3d is a 'Tesseract'. It is a nested cube. Nobody knows how it looks like in four dimensions but we can see the shadow of the object in 3d.

Answer 4

That's an interesting question. The fourth dimension is often teken to be time. If you ran toward a camera that took one photo per second and all the photos were developed full size, cut out and stacked on top of each other, they would provide a two-dimensional history of your run with respect to time. A similar set of holographic 3-D snapshots of you stacked on top of each other would provide a 3-D history of your run. Three physical dimensions plus time would equal four dimensions and at this "instant" you can see the fourth dimensional "shadow" with time frozen in a single 3-D snapshot. There must be several other explanations, right?