How is 4D even possible?

Question

Okay, so I know 3D is three dimensional. This means length, width and height. I don't understand how there can be a fourth dimension, what it is, or how it could be different than 3D!? Help!

Answer 1

Well there is an everyday fourth dimension - Time.    But where as we can move freely about in the 3 dimensions of space, we can only move in one direction of time.

As to other dimensions of space, it is not possible to imagine experiencing them in any meaningful way. (at least to most of our limited 3D minds)   But it is possible to represent them with math.  That is where the higher dimensions are everyday things.

Answer 2

This isn't really correct, but here is one way to think about what four dimensions would "look" like.  In three dimensions, two planes can be parallel or that can intersect in a line.  However, in four dimensions, two planes can intersect at a single point, intersect in a line, or be parallel.  So imagine two parallel planes in three dimensions.  Let the distance between the two parallel planes be a function of time, so that at some time t' the distance between the two planes is zero.  At that time t' in the four-dimensional space defined by x,y,z,t, the two planes intersect at a single point in four dimensions.  Sort of.  

You can use this to visualize a tesseract as eight cubes at different times moving around touching each other, although if I write that out I create a wormhole and my computer will vanish.  Either that or people will think I am writing about a bizarre geometric orgy.

Answer 3

4th dimension is Time.

Answer 4

The standard answer is that the 4th dimension is time. We are free to move in the other three dimensions, but are "doomed" to always move forwards in time (like being on a travelator).

It is possible that there are other spatial dimensions, however. These are usually used in theoretical physics and as mathematical concepts, rather than in "everyday" life - but one example from everyday stuff is the Sci-Fi idea of "hyperspace".

Others have pointed you towards Flatland, so I won't discuss it in too much detail. But here's my take on the concepts:

Picture a flat plane, like sheet of paper. On it, there live stick figure-like "people" who are entirely 2D. They can move left/right and in/out, but not up/down above or below the paper; that dimension doesn't exist for them. If you were to draw a square around them, it would be like a prison they couldn't escape.

They would be unable to hide from any 3D observer, because if they hid inside a square, we could see into it just fine from our third dimension. If a sphere were to cross their dimension, it would start as a dot, grow to a circle, and then shrink to a dot again before vanishing; they might be able to mathematically conceive of such an object, but they'd call it a "hypercircle" or something.

Hyperspace, then, works like this:

If you take that flat plane, and curve it into a sphere, then the 2D inhabitants could still only move north/south or east/west - never into or out of the sphere. If they want to get from one side of the sphere to the other, they have to go around the outside of it. but if they could somehow access the 3rd dimension, they could travel *through* the centre of the sphere to the other side, which is a much shorter distance. As far as the others on the surface were concerned, the traveller would disappear, and re-appear on the other side in an unnaturally (possibly impossibly) quick time.

This would be their hyperspace.

For us, the idea is similar, except we are "stuck" in a 3D space, but might be able to access a 4th spatial dimension that would allow us to travel much more quickly across the middle of a "hypersphere".

Of course, this is still just sci-fi.

Answer 5

Very, very few people in the world can actually imagine what 4D would really "look" like, so instead I'll try to get you to imagine what 3D would look like to a 2D person.

This person, let's call him Flatlander, only knows left, right, forward and backwards. The words "up and "down" are meaningless. To us, his world is paper thin, but to him, thats as much as he can imagine.

Now imagine that Flatlander is on a cube if he walks (crawls?, wiggles?) from one face of the cube to the other, he doesn't realize that there was an edge, it's all flat to him. Do you see why it is so for us hard to imagine 4D now? You could try as hard as you can to imagine a line perpendicular to the x,y,and z axis but good luck.

Some physicists believe we actually live in 11D! As if 4D wasn't mind boggling enough.