Just a 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....

Nooooo, a hypercube is drawn in 3d.. We are talking about a 4d object passing through a 3d plane.. A sphere passing through 2d is seen as a circle increasing in diameter and then decreasing and then disappearing.. I want an example of a 4d object passing through our 3d plane which we can actually see everyday.. A shadow perhaps.. I don't know how to explain it..

Answer 1

I think you've missed the point of the Flatland story. It's trying to help us imagine how incomprehensible to us in 3d WOULD BE the shadow of a 4d object. However, we never see such things. There is no example of the 3d shadow of a 4d object. You can imagine it, with the help of the Flatland story, but don't expect to ever actually see it.

Answer 2

I don't think I can give you an example of a "4D shadow" in our everyday experience. Searching hypercube does provide some good ways of visualizing 4D space, but keep in mind that in all cases, one is projecting (mathematically) the 4D to a 3D and then to a 2D space. So they're just tools to allow you to visualize the space. Same thing with the Flatlanders. They might live in a 3D space, but the point is, to them, it'll look 2D. They can't really see the 3rd dimension because it'll look like the shadow of the 2nd (if i'm understanding the analogy right).

When I think of a universe with greater than 3 spacial dimensions (time is dimension, but it has different properties than the spatial dimensions), I think of our 3D space with each point of our space containing the other dimensions. So say if I wanted to visualize a 5D space. Each point in our 3D space would have an invisible sphere at it (assuming the other 2D are curved/closed) where the 2D surface of the sphere are the other 2 dimensions. If I wanted 6D, I would allow the interior of the sphere to be considered. We cannot see this sphere, but gravitons can (and perhaps the other particles too depending on the model). We can measure this sphere only if our measurements are sensitive enough to measure forces (the fundamental interactions) at distances of about the same size as the radius of that sphere.

I said all that as an alternative way of viewing small or warped extra dimensions. But again, it's a mathematical projection, not necessarily what the world *actually* looks like.

The point is, that mathematically, one can describe a many-dimensional universe and then project it to our 3D experience using a variety of visual tools. The extra-dimensions would really exist, but we'd have no way of knowing it unless we took data that was sensitive to the other dimensions (like gravitational experiments on a very small scale).

Answer 3

Hi. Do a search on "hypercube". Not the programming part. Also check out "hypersphere". Have fun!

Edit. OK. There was another story about a creature who could visualize in 4D. This creature's vision of a human being was a very long object that started small (birth) at one end, moved and twisted through space (life), then just ended (death). Would this be a shadow?

Answer 4

You are able to ask this question because you are assuming the existance of 2d universe (flatland) that really exists as a subset of a 3d universe (with spheres, etc.). You are able to ANSWER this question, because you live in a 3D universe.

This is not the case with 4D -> 3D. There are no objects with 4 spatial dimensions which we can project onto our 3 dimensional space. Therefore it's nonsensical to ask what they would look like.

In short, YOU would have to live in a 4D universe to answer this question.

-T

Answer 5

Here is an example of a 4d object passing through our world:

A baby is concieved and grows, lives and dies as an adult, and rots away to virtual nothing. Someone who lived longer than the baby would be able to view this long process, over time. But if you could video tape it all, you could lay each of the frames out in a line, and see them all at once.

Yes, you're completely misisng the point. Mr. Square doesn't see anything at all. Since he lives inside of that 2d world, neither he nor his environment have any depth. So he owuld be viewing them from the side. from our view, Mr. Square's house would have some squares and rectangles, but from his view, if he could see anything, it would simply be a line. But since lines have no 3rd dimension, he really wouldn't see anything. A plane disappears when viewed exactly from the side. So if a 3d cube slides through his world, he would still not see anything, but if you want to be visual, he would still simply see a line, because he would be viewing planal sections exactly from the side. The same thing would happen to the sphere, except that as it passed through, he would be seeing different sized sections of the sphere, so he would see a line(circle from the side) that appeared small at first and then grew as it passed through.

Now, here's the kicker. We live in a 3d world, but only see in 2d. If you were to take a snapshot of your view of the world, what does it become? A photograph. It is exactly what you saw, but now frozen in time. You can't see around objects, without another dimension added in--Distance and time(or spacetime). The reason 3d objects appear 3d to you is because your eyes have distance between them and are combining two different views of the world. If you were to close one eye, everything would appear suddenly 2d(you lose depth perception). Now, the only way you know you're still in a 3d world is because of your own distance and time--you can move around in your world, creating a 3d map of your environment in your mind-memory. So I believe time is the 4th dimension...not another direction from center.

I've decided that the Hypercube is a stupid way of looking at 4d. We already live in the 4th dimension. If you were to draw a 2d creature on a piece of paper, and then move him up and down in the air, you're giving him the 4th dimension, but he cannot control the dimension himself. Just as we cannot control our 4th dimension. We can only move one direction in that dimension, and we are not in control, as of yet, of the speed, or direction. We can only control, to a degree, our 3 dimensional propterties. I believe the hypercube is thinking way too far into the science of it. Here is how I explain it--

0d: a point
Add an infinite number of points in equal and opposite directions -->
1d: a line
Add an infinite number of lines in equal and opposite directions -->
2d: a plane
add an infinite number of planes in equal and opposite directions -->
3d: the universe
Add an infinite number of universes in equal and opposite directions -->
4d: the universe in time on a timeline.

if you were to view all of the frames of the time line at one time(or for this purpose, just a segment) you would see the earth in the form of a thick, blob of a curve for all the places it's been through time. It's just like looking at pictures where the shutter was left open and cars go by, so their tail lights burn trails along the photo. That would be viewing a 2d world while viewing a small segment of time all at once. Understand?

Here is my full explanation:

http://answers.yahoo.com/question/index;_ylt=AtKKNYruLnM0SRvAPZOWHj_sy6IX?qid=1006041605743