4th Dimension and Beyond

[Bowser]

Been watching videos about possible multiple dimensions, and what I found interesting is the idea that our perception of time is limited. Much like the flatlanders of a 2 dimensional world, our perception of higher dimensions, such as time, are limited. We experience it in cross sections rather than as a whole. How it might look otherwise is beyond me, but it does tickle the imagination.

 

[mathman]

Defining time as the fourth dimension is a part of relativity. Flatland is a story about spatial dimensions. It is dificult to visualize, but mathematics can be used to describe four (or any) spatial dimensions.

 

[NotEinstein]

Been watching videos about possible multiple dimensions, and what I found interesting is the idea that our perception of time is limited. Much like the flatlanders of a 2 dimensional world, our perception of higher dimensions, such as time, are limited. We experience it in cross sections rather than as a whole. How it might look otherwise is beyond me, but it does tickle the imagination.

While it is true that our (biological) perception is quite limited, our understanding is no longer constrained to just that. We have theories and mathematics to describe these dimensions more completely and accurately than even our minds can fathom. So, while we wait for our biology to catch up, the beauty of nature can only be experienced most fully by learning the mathematics and understanding the science.

 

[Bowser]

While it is true that our (biological) perception is quite limited, our understanding is no longer constrained to just that.

Yes, the temptation to try reducing it into the 3 dimensional realm does have limitations. Fascinating stuff nonetheless.

 

[NotEinstein]

Yes, the temptation to try reducing it into the 3 dimensional realm does have limitations.

It's not so much about the reduction to 3 dimensions, it's about the world we grew up (and evolved) in. In our daily lives we encounter sized from millimeters to kilometers, from seconds to years, and we've adapted to such concepts. We are ill-equipped to deal with lightyears and millions of years, because that isn't something we had to be able to think about previously. Why evolve a brain capable to visualizing the entire visible universe (about 47 billion lightyears across) when you can spend that energy on surviving better?

Luckily we've been (partially) able to overcome these limitations through science, and lately with the usage of computers as well.

Fascinating stuff nonetheless.

Absolutely!

 

[Dinosaur]

When you assign time to be the 4th dimension, you are describing a static reality. This can be a useful concept because it allows the laws of physics to be modeled using a well developed mathematical discipline called differential geometry.

There are well developed notions & formulas relating to geometry in higher dimensions (not using time as dimension). Google will find formulas for volumes & surface areas of hyper-spheres & other objects in higher dimensional spaces. I think that pi squared is involved the volume of a hyper-sphere in 4 dimensions.

There are some counter intuitive results in higher dimensions. An example relates to hyper-spheres embedded in a hyper-cube with hyper-spheres in the corners of the hyper-cube. For larger dimensions, the hyper-spheres in the corners are larger than the hyper-sphere in the middle.

 

[NotEinstein]

When you assign time to be the 4th dimension, you are describing a static reality.

I may be misunderstanding you, but how does introducing time make the universe static? Isn't it the exact opposite: introducing time makes the universe dynamic?

 

[Dinosaur]

Think of two space dimensions with time treated as a 3rd dimension.

A point moving along a circular path is represented as a helix on the surface of a cylinder.

Id est: The 2D motion is modeled by a static curve in 3D.

Similarly, treating time as a 4th dimension results in motion being represented by a static curve in a 4D space.

This can be useful because there is a well developed mathematical discipline called differential geometry which can be applied to static 4D curves.

 

[NotEinstein]

Think of two space dimensions with time treated as a 3rd dimension.

A point moving along a circular path is represented as a helix on the surface of a cylinder.

Id est: The 2D motion is modeled by a static curve in 3D.

Similarly, treating time as a 4th dimension results in motion being represented by a static curve in a 4D space.

This can be useful because there is a well developed mathematical discipline called differential geometry which can be applied to static 4D curves.

Ah, so you were talking about the worldlines, got it. Yes, those are indeed static.

 

[socratus]

When you assign time to be the 4th dimension, you are describing a static reality.

Minkowski created an absolute 4D spacetime as an absolute-static reference frame
Minkowski said:
''The views of space and time which I wish to lay before you have sprung from the soil
of experimental physics, and therein lies their strength. They are radical. Henceforth,
space by itself, and time by itself, are doomed to fade away into mere shadows,
and only a kind of union of the two will preserve an independent reality.''
Minkowski. (Sep 21, 1908)
And he gave geometrical - cone image of this absolute 4-D
Geometrical-cone image is not real image of Nature.
If we don't know what 2+2=4, then how we can do more complex arithmetic.
If we don't know what 4-D really is, then how we can understand 11-D, 27=D . . . .
. . . the ''string - particle'' . . . the Nature
(https://en.wikipedia.org/wiki/Minkowski_space)
===