Spatial dimensions above the 3rd

[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?

 

[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.

 

[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.

 

[Felix83]

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

 

[dextercioby]

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

Daniel.

 

[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.

 

[Crosson]

There are no separate "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.

 

[Manchot]

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

 

[funkwort]

In spacetime, the curvature is almost every where locally hyperbolic.

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?

 

[Chronos]

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?

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.

 

[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 equation 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.

 

[abaio]

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

 

[Mute]

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

Are you aware this thread is over six years old?

 

[SteveL27]

Are you aware this thread is over six years old?

Came at us from the fourth dimension.