On Spatial Dimensions

[The Sum of Awe]

I have been curious about spatial dimensions. I have a few questions:

Are spatial dimensions different perspectives of this one reality? Or are they separate planes of existence?

Does this sound right to describe a 4th dimensional being: In the forth dimension, time can be traveled through like we travel through space, but only in a linear direction (while fifth extends to non-linear movement in time, so pretty much different timelines). To see a 4th dimensional being from a 3rd dimensional perspective would be like to see a body forming out of link with chronological order. Let's say a 4th dimensional being is walking back through time, from our point of view it'd appear in reverse. You'd see a person spawn and with every passing second it deforms, you'd see it degrade from an entire body to a ball of flesh that eventually simply vanishes. If you were seeing him walk forward in time, you'd see him form normally, not in reverse, until he fully becomes a body and moves instead through space as he's arrived at the point in time he wanted to travel to (thus fully formed). Does that sound right?

Some say that time can't work as a spatial dimension. I don't understand why. From our perspective, time is linear, but that is only from our perspective. Perhaps time is truly another proponent of space? Why couldn't it be?

With that understanding, that the 4th is existence in linear time and the 5th is existence in different timelines, what would be the sixth dimension and above?

Is there a zeroth dimension perhaps you could describe?

Why are we perceiving 2 dimension and not 3? Why are we in this specific dimension not another one? Is it even possible for something to be 4 dimensional in our existence?

 

[Yerda]

It's not too clear what you are asking. What is a plane of existence?

 

[LegionOnomaMoi]

Are spatial dimensions different perspectives of this one reality?

Although the word "dimensions" is plural, the space "described" by n-dimensional space can't be so easily considered in terms of separate dimensions. The simplest example is to consider a point or line in R2 (or 2-D Euclidean space) vs. R3. A point or line in R2 can't exist in R3 (and vice-versa). Every single point in R, R2, R3, to Rn is characterized entirely and only by the dimensional coordinates of that space.

If we are really "four-dimensional hunks of matter" (a phrase taken from the title of The Ontology of Physical Objects: Four-Dimensional Hunks of Matter (Cambridge Studies in Philosophy), then we exist wholly and only in 4D. Every point in our cosmos is a point in 4D, there is no time independent of space, and movement in this space is movement in spacetime.

Does this sound right to describe a 4th dimensional being: In the forth dimension, time can be traveled through like we travel through space

It can't. Every system's spatial position in 4D is always and everywhere characterized by four-coordinates. When I move in "space" I necessarily move in time, and consequently we find paradoxes: movement in a four-dimensional cosmos means that time isn't linear and in a very real sense doesn't exist.

while fifth extends to non-linear movement in time

Adding dimensions doesn't bear on linearity.

To see a 4th dimensional being from a 3rd dimensional perspective would be like to see a body forming out of link with chronological order.

Actually it's more like seeing certain Escher drawings we see as appearing in 3D as if we "lived" on their surfaces.

Let's say a 4th dimensional being is walking back through time, from our point of view it'd appear in reverse.

Simultaneity doesn't exist according to spacetime physics and modern relativity.

Perhaps time is truly another proponent of space? Why couldn't it be?

A more important question is what we mean by space and how, for example, spacetime geometry differs from the Euclidean space we seem to experience in ways that have nothing to do with dimensions.

Is there a zeroth dimension perhaps you could describe?

Yes. Every dimensional space necessarily contains the "null" ("0-dimensional") subspace.

Why are we perceiving 2 dimension and not 3?

For the same reason we can't really even understand what it would mean to perceive 1,000th dimensional space (although we can and do treat such spaces formally all the time).

Why are we in this specific dimension not another one?

You may be confusing "dimension" in the sci-fi sense with the term as it is used in physics.

 

[Riverwolf]

You may be confusing "dimension" in the sci-fi sense with the term as it is used in physics.

While I sort of understand the distinction, perhaps a primer on what "dimension" means in terms of physics could be provided, especially as contrasted with the sci-fi concept? (Such as where the sci-fi concept might have come from).

 

[Iti oj]

Read flat land

 

[LegionOnomaMoi]

While I sort of understand the distinction, perhaps a primer on what "dimension" means in terms of physics could be provided, especially as contrasted with the sci-fi concept? (Such as where the sci-fi concept might have come from).

"Time is sometimes referred to as 'the fourth dimension.' This is misleading. A point in R4 is simply four numbers. If the first three numbers give the x, y, z coordinates, the fourth number might give time. But the fourth number could also give temperature, or density, or some other kind of information. In addition...there is no need for any of the numbers to denote a position in physical space; in higher dimensions, it can be more helpful to think of a point as a 'state' of a system. If 3356 stocks are listed on the New York Stock Exchange, the list of closing prices for those stocks is an element of [point in] R3356 and every element of R33556 is one theoretically possible state of closing prices on the stock market."

from Hubbard & Hubbard's Vector Calculus, Linear Algebra, & Differential Forms. I emailed this quote to my father several years ago after I first read it because he had informed me as a child that time was the fourth dimension. However, I was about 5 and unlike him I didn't have a degree in physics from Cornell, so it made no sense and took me years to wrap my head around. Naturally, when it turned out mostly inaccurate, I gloated. It didn't go as well as I'd hoped as he remembered the context better than I.

The main point is that dimensions can be thought of as "directions" or coordinate variables. In one dimension, like the real number line, a single variable can take on any value in R. If we recall high school algebra, we may remember the x,y-coordinate plane (or Cartesian coordinate plane) with variables x & y that can take on any values in R. Add a 3rd variable (z) and you have our 3D Euclidian space. Add 2 million additional variables in R, and you have 2 million and 3 dimensional space. Dimensions are simply the number of variables that determine a "point" in some space.

This "space" need not be Euclidean. Spacetime coordinates exist in Minkowski space, a 4D space which is not Euclidean. However, it is fourth-dimensional because every point in that space is entirely and only determined by four variables.

In sci fi, "dimensions" refer to other universes or to alternate reality. In physics, as in mathematics, they simply refer to variables. Sometimes physical systems that exist in what appears to be 3D are represented as existing in 1D phase space. In QM, most systems are represented in potentially infinite-dimensional spaces because they are represented as probability functions.

Adding another dimension to our apparently 3D reality doesn't mean adding something to the cosmos we perceive. It means that the cosmos we perceive is something else.

Imagine that we were really entities in a 2D space as in that excellent literary adventure Flatland. In such a cosmos, there would be no 1D entities, just as seemingly "flat" or 2D entities in our reality, like paper, are really 3D. Most dimensions are entirely abstractions. Those few that directly relate to the "space" we inhabit cannot be reduced to some set of dimensions. Anything that exists in a 3D space cannot exist in a 4D space, and nothing which exists in a 4D space can have only 3-dimensions.

 

[ScottySatan]

I make 3D color movies. That made me think of dimensions differently.
1)X position
2)Y position
3)Z position
4)time
5)brightness
6)Red channel
7)Green channel
8)Blue channel
a 3D movie is an 8-dimensional graph. Your can make it 9 dimensions by making it a CMYK color scheme instead of RGB. You can make it 7 dimensions by doing it as a snapshot, not over time. You can make it 5 dimensions by making it greyscale, not color.

A more basic way to think of dimensions is in the mathematical/informational sense. the number of dimensions are really the number of distinct variables in the equation that you're thinking about. How many dimensions are there? as many as you'd like. Are they dependent on one another? sometimes.

 

[The Sum of Awe]

Read flat land

I've watched a movie based on the book and they didn't exactly answer questions that i don't already know