3D - 2 - How do you best explain 4D to someone in a 3D world?

How do you best explain 4D to someone in a 3D world?

Explain to me (a 3 spatial dimensional being) what a 4th spatial dimension would be like. How would I be able to interact with my environment differently? What things could I do that wouldn't be possible in this 3 dimensional world? Remember, I am only looking for a SPATIAL dimension, not time or light or anything like that.

Public Comments

Since it is fiction anyway, you can make up an answer yourself and it wouldn't be wrong.
Some people add that 4d is Including time. X, Y, Z are the field properties, but to have the mathematical equivalence of our world, we have to add something else to describe what time is. Since you hear stuff about 3d in games and 3d glasses so much the term gets mixed. We dont say 4d because time can not be emulated into what we now call a virtual 3d screen.
CARL SAGAN! in his book "Cosmos" has an excellent description of this very thing that I JUST read last night. And its on page 262 in my edition of the book....As I messed it up earlier and said Asimov wrote this book...LOL
You actually live in a 4D world. The first three dimensions are X Y Z. The fourth dimension is time. Every X Y Z has a time, although not reversible as far as we know.
Just say that 4D is the same as 3D, but adding time. If they don't understand, it's very confusing to go any further with.
Go to church, they believe anything.
It would probably be best to explain this first in terms of a 2D being (that is, one that lived on a piece of paper) would experience a 3D object (I'll use a sphere): Imagine a piece of paper with a being living on (a "Paperperson", I'll call them) it with a sphere approaching the piece of paper. At first, the Paperpeople would see nothing. Then, at the first instant the ball crossed their piece of paper, they'd see a little dot. Then, as the ball continued moving through the piece of paper, they'd see a circle expand from that point to a larger circle. Finally, as the ball began to leave, they'd see the larger circle collapse back to a point and then disappear. So, people percieving 2 spatial dimensions would experience a 3 spatial dimension object as a series of 2D objects spread out across time. By analogy to three dimensions, suppose you had a hypersphere (a 4 dimensional sphere). If it were to pass through our part of space, we'd experience it as a point, leading into a series of expanding spheres, and finally collapsing back into a point and disappearing again, but the process would occur over time. Make sense? I hope a little! If you're interested you might want to read the Wikipedia article on Tesseracts (Hypercubes, thatis, 4D cubes); specifically the section "Projection on to 2D" or "Projection onto 3D". The URL is as follows: http://en.wikipedia.org/wiki/Tesseract .
Actually, I did a little research on this way back in the 8th grade. The key is to picture what it's like to be a 3 dimensional being and what you can do to puny 2 dimensional creatures. Your digestive system would probably be more efficient. You have a hole in you that starts at one end and passes all the way through you while allowing food to pass through it. Imagine a 2-D creature with the same setup. It doesn't work-- it would split the poor thing in half. 2-D creatures would have to use vacuoles and, to take it back another dimension, vacuoles would split 1-D creatures in two. Thus, whatever digestive system is most efficient for 4-D creatures would probably cut us in half. Now, you may live in a 3-D environment, but your senses only pick up 2 dimensions at best. Think of your eyes as the screens to a projector. Each eye receives a single, 2-D image, and the two are superimposed to create the illusion of depth. So what does it mean to see in 3-D? Imagine a little 2-D creature (like a cell) on your desk. Other 2-D creatures would only be able to see its border, but you can actually see *inside* it. Therefore, 3-D vision is like x-ray vision. More importantly, if you were a 4-D person, you would be able to interact with 3-D environments in strange ways. Look at that imaginary 2-D creature. If you want, you can remove one of its organs without disturbing its border. The 3-D analogy is that you would be able to (pardon the gruesomeness) rip people's hearts out without ever cutting them open. Ripping people's hearts out? I'm sure that's the most thrilling possible answer to your question.
Some people say the 4th dimension is time. This is only sort of true. It's not a dimension in the same sense as space is a dimension. We are always moving forward through time. If we can move backward through time, it certainly can't be done easily. So 4 dimensions. It's best to think of it by analogy. to make a square, you take a line and move it in another direction, shading in its path as you go. To make a cube, you take that square and move it in another direction, shading in bits as you go. To make a hypercube, take a cube and move it in another direction--the 4th dimension, and shade in the bits as you go. A cube is really two squares in each of 3 dimensions. So a hypercube is 2 cubes in each of 4 dimensions. You got a cube on one side, a cube on the other, and 6 cubes connecting. I read a story in high school called "Flatland: A Romance of Many Dimensions". Its main purpose is to explain 4-dimensional space, but it's a neat story too. You can read it here: http://www.geom.uiuc.edu/~banchoff/Flatland/
CONCEPT OF 4TH DIMENSION ------------------------------------------------------ All of the above people have stated their thoughts well. But here's how you will understand the concept of fourth dimension better. Here's a great problem that can start our quest. A man wants to attend a meeting at a place. The address is 50th street, 30th building, floor no 52 and at 4.00 pm. How many dimensions in space are required by the man to reach his destination? Now understand this. Let a street and the building lie in the X-Z plane. So we need the X and Z co-ordinates for travelling to that building. But the floor no 52 comes along the Y-axis. So we need the Y co-ordinate too. So, total three dimensions are required to the normal man. But according to Einstein, space and time are entangled. And to reach the meeting in time, he needs to be there by 4.00 pm. So you see, that time is indeed the fourth co-ordinate required for the man to reach his destination. Thus, in this world, the structure of objects is always defined in three dimensions, i.e. X,Y,Z coordinate system. But when it comes to motion, we get the fourth dimension. So, we conclude finally that our world is made up of four dimensions. So the final question is that can more than four dimensions exist ? I will give you an example. Say, i want to go to a sea shore at 5.00 pm and then dive at a height of of say "g" metres and at a pressure of 'p' pascals. Now how many dimensions are required. Now any guy would say that we require X,Y,Z co-ordinates, time and appropriate pressure. So five dimensions are required. No its wrong. We yet require four dimensions. Pressure is dependant on height and hence one of the co-ordinates. Dimensions in space are fundamental and independent. Time is the greatest independent quantity you can think of. Isn't it a great discovery by Einstein? CHANGES DUE TO SPATILAL 4TH DIMENSION -------------------------------------------------------------- Now all the above was just to give you an idea of 4D. Coming to the fourth spatial dimension, lets see what changes would have occured if there was a 4Dimension. The first change would be the way people referred to their addresses. They would have a complex address. When people saw a building having a fourth dimension say D, they would say how D m big that building is. We would start checking our height and also the 4D factor to see whether we look good or not. With 4D, all the visual effects companies would have been abolished for good and movies would have to take a break for sometime. All this because a 4D software would take years to build since the base of the software is that there are 3Dimensions had to be changed to that there are 4Dimensions. Planes would say that they have coordinates X,Y,Z and D where D is the 4th dimension. Major effects are expected because of this because it will completely change the way a world thinks and also the organisation in Geneva which has developed the SI units would be having serious work on its back. It would be a lot of changes my friend!