# Spatial dimensions above the 3rd

1. Feb 25, 2005

### Felix83

what do spatial dimensions higher than the third dimension mean? what do they represent. any object can be described in 3 dimensions, how are higher dimensions possible? how can you even comprehend them?

2. Feb 25, 2005

### jcsd

What they represent is the minimum amount of parameters needed to continiously parameterize space. So in 3 diemsnioanl space you need 3 numbers to describe each point (in a manner that respects the relationship between points), in Cartesian coordiantes we use x,y and z for example.

3. Feb 25, 2005

### dextercioby

We cannot picture (effectively draw in 2 dimensions,or imagine in our mind) objects with more than 3 dimensions.That's the sad truth...

However,we know that mathematics is the queen of abstractness and it can definitely work even with an infinite # of dimensions...Modern physics (Relativity and QM,for example) shows that these extra-dimensions EXIST AND HAVE A VERY PRECISE MEANING,they're no longer mathematical abstractions...

Daniel.

4. Feb 25, 2005

### Felix83

can u lead me to anywhere with some info on how and why these dimensions exist?

5. Feb 25, 2005

### dextercioby

Yes,any book on Special and General Relativity would convince you.

Daniel.

6. Feb 26, 2005

### Moo Of Doom

I found http://www.geocities.com/jsfhome/Think4d/think4d.html to be quite an interesting read. I thought those articles helped me immensely to envision the 4th dimension.

The 4th dimension is often taken to be time (really, the dimensions have no inherent 'order' - it might as well be the 2nd or the 3rd, but it doesn't matter). One can measure hypervolume (the 4D equivalent to volume) by measuring length x width x height x how long an object has been around, heh.

What's your hyperdepth? Mine's around 18.5 years.

7. Feb 26, 2005

### Crosson

There are no seperate "temporal" and "spatial" dimensions, that is just a human idea attached to our 4-space. Why does time seem very different from the other three dimensions in our universe?

In spacetime, the curvature is almost every where locally hyperbolic. Think of a hyperbola, a cone. In a 3 dimensional cone, two of the dimensions are interchangeable and one of them occupies a special place, the axis of revolution for the cone. In spacetime, time is the central axis and that is why we percieve it differently then the other three dimensions. By the way, we know that spacetime is hyperbolic because a hyperbolic metric is the only one that leads to a lorentz invariant way of measuring intervals in spacetime.

8. Feb 26, 2005

### Manchot

I certainly can't find my hypervolume. Doing the integration is way too hard. :)

9. Feb 27, 2005

### funkwort

What exactly does spacetime curvature mean. I understand that space must be curved, I guess, because of circular motion or gravity?? But how is it that time is curved?

10. Feb 27, 2005

### Chronos

You could say time is curved, instead of spatial dimensions. But that would be even more difficult to conceptualize. It's a lot easier to imagine the universe being curved around you, than you being curved around the universe.

11. Feb 28, 2005

### Crosson

Flatness and Curvature are intuitive concepts that can be mathematically characterized in a number of ways. One such way is to examine the distance between two nearby points in terms of some coordinates i.e.

ds^2 = dx^2 + dy^2 (the pythagorean formula holds in flat space)

In spaces that are not flat, we measure distances according to a different metric than the pythagorean (using the fact that all smooth spaces look euclidean = flat = pythagorean when we get very close up).

Here is the metric of flat spacetime: ds^2 = dx^2 + dy^2 +dz^2 - (cdt)^2

The reason that this is the metric is because the lorentz transformation does not vary this quantity (the distance in space time is invariant to the motion of the observe). If you are familiar with conic sections, you will recognize the spacetime metric as the eqation of a hyperbola curled around the t axis.

Cones are mathematically flat (i.e. the pythagorean theorem works because it is a rolled up sheet of flat paper) so hyperbolic spacetime is flat spacetime (no gravity). This is the geometry of the special theory of relativity.

12. Jul 22, 2011

### abaio

Your mind wasnt designed to perceive higher dimensions. In order to survive it needed only 3 spacial dimensions to perceive a predator coming toward him/her. That doesnt mean the dimensions arent there, it just means our minds cannot perceive them.

13. Jul 22, 2011

### Mute

Are you aware this thread is over six years old?

14. Jul 22, 2011

### SteveL27

Came at us from the fourth dimension.