Visualizing 4 Dimension Objects - Length, Breadth, Height & Time

[deoxys22]

i know there are 4 dimensions the fourth one being time.

I had recently seen some images which claimed to be 4 dimension. How do you visualize them, the fourth dimension is time so how can you represent time on a paper or in drawing

are those figures even related to the 4 dimensions of relativity(length,breath, height and time) or are they 4 dimensional in another sense.

 

[ZapperZ]

I had recently seen some images which claimed to be 4 dimension. How do you visualize them, the fourth dimension is time so how can you represent time on a paper or in drawing

Next time, when you write something like this, it is imperative that you cite the exact source. Without that, we have no clue on what you saw, or whether such a thing has any validity as far as physics is concerned. If you don't do that, then you will run into a discussion involving nothing more than guess work. This tends to not solve anything and are often candidates to becoming a locked thread on PF.

Zz.

 

[George Jones]

i know there are 4 dimensions the fourth one being time.

I had recently seen some images which claimed to be 4 dimension. How do you visualize them, the fourth dimension is time so how can you represent time on a paper or in drawing

You can imagine a hypothetical world that has four spatial dimensions. Just as a 3-dimensional cube can be represented using projection (and maybe perspective) by a drawing a on a 2-dimensional sheet of paper, a 4-dimensional cube can be represented by a drawing a on a 2-dimensional sheet of paper, or a by model in 3-dimensional space.

Take a look at the applet at http://www.maa.org/editorial/knot/tesseract.html" .

are those figures even related to the 4 dimensions of relativity(length,breath, height and time) or are they 4 dimensional in another sense.

As ZapperZ said, this depends on the actual stuff at which you were looking.

 

[DaveC426913]

The thing to note here, is that, when referring to 4 dimensions, one must specify which four.

Yes, practically, time is considered the fourth dimension; it is one of the four that make up our real world. But it is possible to explore multiple physical dimensions in mathematics, and it is these that you are surely looking at.

One of the most common ones is the tesseract, or hypercube, as George Jones is pointing you at.

Take a 0 dimensional point, sweep it one inch through dimension X and you have a 1" 1D line.
Sweep that 1D line 1" through dimension Y and you have a 1" square.
Sweep that 2D square 1" through dimension Z and you have a 1" cube.
Sweep that 3D cube 1" through dimension W and you have a 1" hypercube.

 

[Math Jeans]

i know there are 4 dimensions the fourth one being time.

I feel I need to clear this up. The concept of the fourth dimension being time is a very common misconception.

Take the book Flatland which is about a two dimensional world. In flatland, one of the characters states that in their schools, they had been taught that the 3rd dimension was time. However, when he is visited by a three dimensional sphere, he learns that it is a direction. You can also tell through the book, that from a 3d perspective, time in flat land is the same for them.

If the fourth dimension was time, then the following would be true: Our 3D universe would be a solid 4D cube, where every infintesimal section is a part of our time. However, in reality, if there was a fourth dimension, they would view us as a three dimensional world, and not a four dimensional block.

The origin of the thought that time is the fourth dimension stems from the belief that time is the only unit in the third dimension that moves an infinite amount of times through any period. However, the fourth dimension is a new direction, and is something that we are unaware of, not a unit that we already experience. Time is common in all dimensions.

You need to think about this from a two dimensional perspective. In a two dimensional world, all of your vision is seen in lines, or basically, the vision of stationary two dimensional person is one dimensional.

For a three dimensional person, if we were stationary, our vision is two dimensional, or in other words, could be printed two dimensionally. However, cannot be printed one dimensionally.

A four dimensional person would see things in a three dimensional way. Mainly, if they were stationary, what they see could not be represented two dimensionally, but can be represented three dimensionally.

There are so many ways to interpret how one would percieve the fourth dimension, and how the fourth dimension perceives us.

It is a very complex topic, however, the fourth dimension is NOT time.

 

[Chris Hillman]

Suggestions for further reading (for more advanced students)

AFAIK, there are no books which attempt to present a unified exposition of the basic phenomena of n-dimensional Euclidean geometry, which I take it is the topic of discussion here (cf. Math Jeans). So the following

D. M. Y. Sommerville, An introduction to the geometry of n dimensions, Dover reprint

M. G. Kendall, A course in the geometry of n dimensions, Dover reprint.

must be supplemented with other important facts these authors omit, such as the canonical form for operators in O(n) given in Herstein, Topics in Algebra. See also good books on real and/or finite dimensional linear algebra (e.g. the books by Fekete or Halmos) and books on tensor algebra.

For those interested in n-dimensional projective geometry, try good textbooks on algebraic geometry such as Harris. For those interested in n-dimensional Riemannian geometry, there are zillions of good books. For those interested in n-dimensional space forms (Riemannian n-manifolds of constant curvature), try Joseph A. Wolf, Spaces of constant curvature, 5th ed., Publish or Perish, 1984. For transformation groups and Kleinian geometry, try various books by Robert Hermann (b. 1931--- don't confuse him with an IMHO cranky mathematician who happens to have a similar name!).

BTW, deoxys22 has once again illustrated the kind of thing I am talking about in [thread=199303]this thread[/thread]. Ditto what ZapperZ wrote

 

[mista_chewey]

Question: When I was in 9th Grade I read a book called "Hyperspace" by a japanese physicst. In there he mentions how there might even be up to 10spatial Dimensions. I believe he also said that when the universe was created the dimensions were "split" up or something. We got 3 spatial dimensions and the other 7 is in another level of space.

Has anyone tried to project a 10 dimensional object into 3 dimensions for visuzlization, like they did for the hypercube?
It's been awhile since I read that book I don't remember if he said it was just 10.

 

[DaveC426913]

Question: When I was in 9th Grade I read a book called "Hyperspace" by a japanese physicst. In there he mentions how there might even be up to 10spatial Dimensions. I believe he also said that when the universe was created the dimensions were "split" up or something. We got 3 spatial dimensions and the other 7 is in another level of space.

Has anyone tried to project a 10 dimensional object into 3 dimensions for visuzlization, like they did for the hypercube?
It's been awhile since I read that book I don't remember if he said it was just 10.

Certainly. What you're remembering sounds like a pretty good description of string theory. 10 dimensions: 3 very large, 6 very small and 1 time.

 

[OJones]

I believe the book in question ('Hyperspace') is indeed on string theory, and was written by Michio Kaku. I have read it myself - an engaging popular account of frontier physics.