What is a dimension?

[niin]

I have been thinking about dimensions lately. People often talk about dimensions like they are real and exist in objective reality. I hope that someone can help me to a greater understanding of this.

What is a dimension?
What is the difference between a direction and a dimension?
Where in objective reality does a dimension exist?

[cabose]

dimension is a direction in physical space. We, as humans, can only work in 3 dimensions plus 1 of time. The Universe is thought to be a 4 dimensional object. Some scientific theories, like string theory, say that there are 10 or as many as 26 dimensions. I hope that helps

[niin]

dimension is a direction in physical space. We, as humans, can only work in 3 dimensions plus 1 of time. The Universe is thought to be a 4 dimensional object. Some scientific theories, like string theory, say that there are 10 or as many as 26 dimensions. I hope that helps

thanks for trying...
Would you say that a dimension exist in objective reality? where?
If a dimension is the same as a direction wouldn't that mean that there are a infinite number of them?
why can humans only work in 3 dimensions? I mean...I can go in more than 30 directions. What do you mean when you say "work"?

[cabose]

I have no idea about objective realities. That will have to be someone else's bag. When I say work, I mean our minds can only comprehend. A great video about dimensions is Carl Sagan's talk about hypercubes and flatland. That is just awesome.

[Neverfly]

thanks for trying...
Would you say that a dimension exist in objective reality? where?
If a dimension is the same as a direction wouldn't that mean that there are a infinite number of them?
why can humans only work in 3 dimensions? I mean...I can go in more than 30 directions. What do you mean when you say "work"?

Imagine a 2 dimensional being living in Flatland.
He can walk forwards and backwards. He can Jump in the Air... But he cannot go "out" into the Third dimension. He can visualize a square- but He cannot visualize a Cube.
He can only see a cube if it is unfolded- as a series of six joined squares. But he would not be able to fold it into a cube.

[astromark]

niin... 3 dimensions are spacial in nature and fact. They are very real. Put one foot wrong and you will fall of the jetty. ( if you are on one.) Your thought of many directions is quite interesting BUT all and every direction you are thinking might be dimensions are covered by those original three, length breadth and depth. Just different ratios of each. Like 175 deg south and 39deg east at 130 feet Alt. I only need those three to put me any where I want. Home.
I can not perceive a point that would be unreachable using the 3 dimensions.
This whole universe is map able with this thinking. Just the size of increment used changes. That is a scale issue not a dimensional one. Mark.

[cabose]

Imagine a 2 dimensional being living in Flatland.
He can walk forwards and backwards. He can Jump in the Air... But he cannot go "out" into the Third dimension. He can visualize a square- but He cannot visualize a Cube.
He can only see a cube if it is unfolded- as a series of six joined squares. But he would not be able to fold it into a cube.

he cant jump. our flatlander can only do forward, backward, left, right and combinations of those. a flatlander cannot get up and down. or more he can't understand it. think of how you would draw a cube, the angles aren't perfect. they aren't real 90 degrees to eachother. thats how a flatlander and see a cube. it's the penalty for losing a dimension.

[niin]

Imagine a 2 dimensional being living in Flatland.
He can walk forwards and backwards. He can Jump in the Air... But he cannot go "out" into the Third dimension. He can visualize a square- but He cannot visualize a Cube.
He can only see a cube if it is unfolded- as a series of six joined squares. But he would not be able to fold it into a cube.

I'm not really interested in imaginary worlds like flatland. I was talking from the presumption that a dimension and a direction was the same thing. This could be wrong of course, but if it's not, then i can move in more than 3 dimensions. Right?

niin... 3 dimensions are spacial in nature and fact. They are very real.

What does that mean? can you point to a dimension in objective reality?

Your thought of many directions is quite interesting BUT all and every direction you are thinking might be dimensions are covered by those original three, length breadth and depth. Just different ratios of each. Like 175 deg south and 39deg east at 130 feet Alt. I only need those three to put me any where I want. Home.
I can not perceive a point that would be unreachable using the 3 dimensions.
This whole universe is map able with this thinking. Just the size of increment used changes. That is a scale issue not a dimensional one. Mark.

I find it irrelevant that you only need 3 variables in a coordinate system to describe reality. If you only look at a single dimension, how is it different from a direction in reality? If there are no difference, how can you say that only 3 dimensions exist.

[Michael Noonan]

Dimensions can be small and within the universe and is how the quantum world is described in a complex series of lines bends curves and re-connections. A simple example is the adding a line at each point and copying the shape for larger dimensions and so a hypercube.

It can also be done with circles like an ice cream cone. The opening is circular and the tip of the cone is a point so circle in two dimensions plus tip is three. This use of dimension uses one linear and two angles to describe.

So dimensions can be higher or lower or a way to describe shape. Then dimensions can be estimated because the are part of the whole universe and have some sort of universal effect. Harder than shapes we can identify easily and so models are used.

[Paul Beardsley]

A dimension is a direction that is at right angles to all the other dimensions.

Suppose you begin with a direction that you choose. Something non-arbitrary such as north-south would be a good one.

Your second dimension needs to be at right angles to the first one. East-west would be a good one

Now your third dimension has to be at right angles to both of the first two. Up-down is the only one that fits the bill.

You can move in an infinite number of directions, but all those directions have components of the three dimensions. For instance, North North East has a lot of the north-south dimension, a little of the east-west dimension, and no up-down at all unless you are walking up a ramp.

[astromark]

Your perception of dimensional space is wrong. Neverfly was just attempting to explain what a two dimensional world might not comprehend a third dimension. As we live in this Universe that has but three dimensions and time.
No you can not move in more than three because there is only three.
To expand on what does that mean, Its just that any movement or location can be accurately referenced by just the three dimensions. Regardless of the scale you use.
Look at how a 'Go to' telescope works on just two axis. every point in the sky is available to that telescope. The third dimension in that case is depth, or distance from you. Why do you see the need to complicate this any more. Direction is not dimension. Three dimensional space is what we live in.

[mugaliens]

dimension is a direction in physical space. We, as humans, can only work in 3 dimensions plus 1 of time. The Universe is thought to be a 4 dimensional object. Some scientific theories, like string theory, say that there are 10 or as many as 26 dimensions. I hope that helps

In addition to a direction in physical space, a dimension is also a direction in time, which is considered by most to be the "fourth dimension."

As for the physical space part, there are several ways of defining dimensions. One is using the x, y, z axis system, where each of these three directions is at right angles to the other two. The centroid, or starting point is where x=y=z=0, This is the most common system. This is referred to as the Cartesian coordinate system, and usually adheres to the right-hand rule syste, such that if you're looking at the x-y plane from a positive altitude along the z axis, positive x will be to your right, and positive y will be upwards.

A second system, called the polar coordinate system, involves the use of a radius, a longitude, and a latitude. Thus, the variables are "(ρ, φ, θ), where ρ is the distance from the origin, φ is the angle from the z-axis (called the colatitude or zenith and measured from 0 to 180°) and θ is the angle from the x-axis (as in the polar coordinates). " (source - Wikipedia)

In this system, φ corresponds to the latitude, and θ corresponds to the longitude.

The benefit of the polar coodinate system is that it makes certain computations, such as celestial navigation, cakework as compared to the Cartesian coordinate system, as everything can be done using triginometry rather than having to convert the x, y, and z into trig, find the solution, then convert back.

Paul Beardsley is correct when he said, " dimension is a direction that is at right angles to all the other dimensions." This holds for both Cartesian as well as polar coordinate systems. The difference is that for the Cartesian coordinate system, the center/centroid is where x, y, and z all equal 0, while for the polar coordinate system, the centroid is simply where r=0. Provided r=0, it doesn't matter what φ and θ are - you're still at the centroid of the coordinate system.

[jokergirl]

What is the difference between a direction and a dimension?

I'll try this once. If we can't agree on the mathematical principles behind it (which were well described in Flatland) a discussion is useless.

Let's start with a straight line.

[...]----a--------b------------c--------[...]

If you connect the dots a, b, and c in different ways, you get vectors along this line. You can go in two directions (a->c or c->a). But you can see every line you draw as a multiple of the "-" with an integer. For example:
ac = ab + bc = 8*"-" + 12*"-" or
ba = 8*"-" *(-1)
We call that - the unit vector of a dimension.

Now if you look at this graph (ascii graphics at its finest!)

--a--------b----------
--------c-------------

you can't connect a->c with just multiples of the unit vector. There is a line break in between
Well, in our example. But technically, that "line break" means that one dimension - our "-"'s - is not enough any more.There must be a different dimension - we went from one-dimensional (line) to two-dimensional (flatland).
Let's try drawing this a->c with dashes and | for columns (because a linebreak is so hard to visualize and I don't want to use the funny "inverted p"):

a------|
------c

(I'm starting to get lazy with drawing here. ASCII graphics on a whitespace-regulated board suck.)
Now a is connected with c by use of two unit vectors, "-" and "|".
You can write the "direction" ac (I simplified now because my patience with ascii has completely run out):

a
-\
--c

as an addition of those two orthogonal units, 6*"-" + 1*"|". So it does not need to be its own dimension, because we already have two that can describe it when used together. So direction does NOT equal dimension

Rinse, repeat, for 3+ dimensions.
Why orthogonal? Because it's the least redundant solution. But I'm not going to write that proof up here.

In a space that has n dimensions, a point is defined by its coordinates in all of those. Consider:

a-------b
--------c

In one dimension ("-"), AB and AC both equal 6*"-". But they are not the same in two:
AB = 6*"-" + 0*"|"
AC = 6*"-" + 1*"|".

You would not say they are the same because you can perceive the two dimensions it needs. But for a being that can only see along the line, but not the column, b and c would appear to be in the same spot:

a------[bc]

because it would lack that dimension.

Clearer now?
I'm so going to get flak from the mathematicians if they find me out. I'm sure this was all almost, but not quite, correct. :P

[mugaliens]

While you're mathematically correct, jokergirl, you're overcomplicating the solution for the laymen.

[John Mendenhall]

Good question, OP. Check here:

http://en.wikipedia.org/wiki/Dimension

Important point: Our universe, so far as we can tell, consists of three spatial dimensions and one time dimension. There is no, zero, nada, zilch evidence for any real additional dimensions, despite all the speculation about dimensions beyond four. As mathematical contstructions additional dimensions are useful; but they are not part of the real physical world, as far as we can tell.

The universe is also flat to within 3%, but that's another discussion.

[Neverfly]

he cant jump. our flatlander can only do forward, backward, left, right and combinations of those. a flatlander cannot get up and down. or more he can't understand it. think of how you would draw a cube, the angles aren't perfect. they aren't real 90 degrees to eachother. thats how a flatlander and see a cube. it's the penalty for losing a dimension.

Of course he can jump. He can jump up- climb down- he cannot Lift himself UP or OUT of the "flat plane." Why wouldn't he be able to jump? Think a little harder on that- you will blush later.

I'm not really interested in imaginary worlds like flatland.

Oh, I'm sorry that I disinterested you.

I'm cryin'.

Get over it- if you want to learn and understand the answer to your question- losing your attitude might help.

[Neverfly]

I was talking from the presumption that a dimension and a direction was the same thing. This could be wrong of course, but if it's not, then i can move in more than 3 dimensions. Right?

It is wrong. But since my previous attempt so disinterested you- I cannot explain it to you until you get interested.

What does that mean? can you point to a dimension in objective reality?

A dimension is not a direction. They are two different things entirely.

I find it irrelevant that you only need 3 variables in a coordinate system to describe reality. If you only look at a single dimension, how is it different from a direction in reality? If there are no difference, how can you say that only 3 dimensions exist.

Can you fold a cube in upon itself into a hypercube that is larger on the inside than it is on the outside?
No. Because you don't understand the forth dimension.

I could explain that- but that would require you to get interested.

[tommac]

I have been thinking about dimensions lately. People often talk about dimensions like they are real and exist in objective reality. I hope that someone can help me to a greater understanding of this.

What is a dimension?
What is the difference between a direction and a dimension?
Where in objective reality does a dimension exist?

From dictionary.com :
Physics. any of a set of basic kinds of quantity, as mass, length, and time, in terms of which all other kinds of quantity can be expressed; usually denoted by capital letters, with appropriate exponents, placed in brackets.

[tommac]

cant anything be used as dimension? Is it only limited to space and time?

I mean the space and time dimensions of space-time are the dimensions of space-time but cant other scalers be called dimensions depending on the situation?

Per the dictionary definition mass can be a dimension.

Good question, OP. Check here:

http://en.wikipedia.org/wiki/Dimension

Important point: Our universe, so far as we can tell, consists of three spatial dimensions and one time dimension. There is no, zero, nada, zilch evidence for any real additional dimensions, despite all the speculation about dimensions beyond four. As mathematical contstructions additional dimensions are useful; but they are not part of the real physical world, as far as we can tell.

The universe is also flat to within 3%, but that's another discussion.

[alainprice]

From dictionary.com :
Physics. any of a set of basic kinds of quantity, as mass, length, and time, in terms of which all other kinds of quantity can be expressed; usually denoted by capital letters, with appropriate exponents, placed in brackets.

This is my general idea of a dimension. Kilograms are a dimension, speed is a dimension, acceleration is a dimension.

Not all dimensions need to be orthogonal, though.

[John Mendenhall]

This is my general idea of a dimension. Kilograms are a dimension, speed is a dimension, acceleration is a dimension.

Not all dimensions need to be orthogonal, though.

Alain, this is less ambiguous.

From Wiki: "In mathematics the dimension of a space is roughly defined as the mimimum number of coordinates needed to specify every point within it. Dimensions can be thought of as the axes in a Cartesian coordinate system, which in a three-dimensional system run left-right, up-down and forward-backward. A set of three co-ordinates on these axes, or any other three-dimensional coordinate system, specifies the position of a particular point in space[3]. In the physical world, according to the theory of relativity the fourth dimension is time, which runs before-after. An event’s position in space and time is therefore specified if four co-ordinates are given."

Calling some physical property a dimension, such as weight, or velocity, or momentum, is acceptable casual usage, but would (pun intended) 'never fly' in physics.

Thinking about the OP's original question, the OP may be confused about the casual and strict usage.

[alainprice]

...
Calling some physical property a dimension, such as weight, or velocity, or momentum, is acceptable casual usage, but would (pun intended) 'never fly' in physics.

Thinking about the OP's original question, the OP may be confused about the casual and strict usage.

No doubt!

[KKHS]

1. What is a dimension?
2. What is the difference between a direction and a dimension?

1. Relation of the stuff of universe (aka mass/energy).

2. Direction is a human way of telling about dimension.

[jokergirl]

While you're mathematically correct, jokergirl, you're overcomplicating the solution for the laymen.

Possibly, but I felt the need for some graphical explanation. Since the conversation before showed that the OP had a problem with some of the definitions of the words used in the explanations.
Probably could have left out the unit vector business, though. :P I was bored.

[Paul Beardsley]

Calling some physical property a dimension, such as weight, or velocity, or momentum, is acceptable casual usage, but would (pun intended) 'never fly' in physics.

Thinking about the OP's original question, the OP may be confused about the casual and strict usage.

Sorry, but I think you are wrong. I remember doing dimensional analysis as a formal part of studying physics, where quantities such as Mass (M), Length (L) and Time (T) were regarded as dimensions. (Constant coefficients were ignored.)

For instance, momentum is mv (mass times velocity) so that would be written as ML/T.

Kinetic energy is (1/2)mv^2 (half mass times velocity squared) so that would be written as MLL/TT (we ignore the half).

Potential energy is mgh, where g is acceleration due to Earth's gravity, and h, height, is a length. Thus it is written as M(L/TT)L = MLL/TT which is dimensionally the same as kinetic energy. This is consistent with the idea that one form of energy can be converted into another form.

[Paul Beardsley]

Of course he can jump. He can jump up- climb down- he cannot Lift himself UP or OUT of the "flat plane." Why wouldn't he be able to jump? Think a little harder on that- you will blush later.

I agree with cabose on this one, I've thought about it, and I'm not blushing. Is your idea of flatland akin to a poster on the wall rather than a tabletop?

In the tabletop scenarion - which is the standard for flatland - he can't jump because his movements are restricted to north-south and east-west, and the directions in between. If he can jump up or climb down, it's hardlyflatland.

[dcl]

A lot of misinformation is being disseminated in this thread. The following statements describe dimensions correctly and concisely:

Dimensions can be defined more broadly than what niin is looking for. He is looking only for those that define position in space. These are called spatial dimensions. If we want to talk about relativity, we must include time, but I see no indication that niin is trying to bring relativity into the discussion. So let's stop confusing the issue by taking about. I also doubt that niin is trying to include string theory in the discussion, so lets not talk about "curled up" dimensions.

The dimensionality of a space is the number of mutually perpendicular lines that can pass through any given point in that space, It follows directly from the definition of dimensionality of a space that the dimensionalities of lines, surfaces, and that of volumes are one, two, and three, respectively. However, there are also spaces of higher dimensionality. Mathematicians envisage spaces of more than three dimensions

I and others envisage the Universe as containing an additional spatial dimension that we cannot experience. It envisages the Universe as expanding not the way a rubber sheet can be stretched uniformly while remaining flat but the way a balloon can be inflated so that its radius increases. The four-dimensional analog of the expanding balloon is the hypersphere. Just as a balloon has a two-dimensional surface all points on which are the same distance from the center of the balloon, all points on the three-dimensional "surface" of the hypersphere are the same distance from the center of the hypersphere,

[Jeff Root]

Neverfly,

Although discussing Flatland might well be a good way to address niin's
questions, you didn't say anything about Flatland that was relevant to
those questions -- whatever they are.

niin,

You've seen how many different and confusing answers you are getting.
That's because nobody really knows what you are trying to ask.

My guess is that what you are trying to understand is why it is said that
space has three dimensions. Is that correct? If so, the other posters can
quit bringing up such things as dimensional analysis, hyperdimensions, and
time as the fourth dimension, because they aren't what niin is looking for.

-- Jeff, in Minneapolis

[alainprice]

A lot of misinformation is being disseminated in this thread. The following statements describe dimensions correctly and concisely:

Dimensions can be defined more broadly than what niin is looking for....

The dimensionality of a space is the number of mutually perpendicular lines that can pass through any given point in that space, It follows directly from the definition of dimensionality of a space that the dimensionalities of lines, surfaces, and that of volumes are one, two, and three, respectively. However, there are also spaces of higher dimensionality. Mathematicians envisage spaces of more than three dimensions

Again, seperate spacial dimensions do not need to be orthogonal(perpendicular). Space is not necessarily cartesian.

[niin]

Thanks to everyone who has replied so far.

A dimension is a direction that is at right angles to all the other dimensions.

If a dimension is the same as a direction then you cant have a direction that is at right angles to all other directions. right?
If a dimension is not the same as a direction, then i stil wonder about what a dimension really is in objective reality.

Your perception of dimensional space is wrong. Neverfly was just attempting to explain what a two dimensional world might not comprehend a third dimension. As we live in this Universe that has but three dimensions and time.

My perceptions could be wrong, I admit that. Thats is why I'm asking questions in this thread.
Regarding to flatland and such...you can imagine all kind of stuff...this doesn't make it real. Sure i can see that we live on a surface (of the earth) but we are not confined to that surface and therefor i can't see the relevance of imagining that we can't comprehend more than that surface. I try to compare things to reality and not be lost in imagination, if that make any sense.

No you can not move in more than three because there is only three.

But i can move in more than 3 directions. Right?

To expand on what does that mean, Its just that any movement or location can be accurately referenced by just the three dimensions. Regardless of the scale you use.
Look at how a 'Go to' telescope works on just two axis. every point in the sky is available to that telescope. The third dimension in that case is depth, or distance from you. Why do you see the need to complicate this any more. Direction is not dimension. Three dimensional space is what we live in.

I like what you are saying here. "Direction is not dimension." Sadly, I don't know what the difference is between them in objective reality. Do you? If yes, what is the difference?

Paul Beardsley is correct when he said, " dimension is a direction that is at right angles to all the other dimensions." This holds for both Cartesian as well as polar coordinate systems. The difference is that for the Cartesian coordinate system, the center/centroid is where x, y, and z all equal 0, while for the polar coordinate system, the centroid is simply where r=0. Provided r=0, it doesn't matter what φ and θ are - you're still at the centroid of the coordinate system.

I see...so dimension is a direction that is at right angles to all other dimensions. How do you find the first dimension? Of all the infinite directions why do one become a dimension?

I'll try this once. If we can't agree on the mathematical principles behind it (which were well described in Flatland) a discussion is useless.

Im more interested in objective reality than a made up mathematical world (like flatland), if that make any sense. Sure, mathematical principles can be very useful, so if you want to mentions a few that would clarify the discussion, that would be great.

Clearer now?

Thanks for the effort, but i don't think my questions has been answered yet. I'm sure your math was logical consistent with regard to itself, but I'm more concerned with what the relation between dimensions and objective reality is.

Good question, OP. Check here:

http://en.wikipedia.org/wiki/Dimension

Thanks
I already checked the wiki entry before starting this thread. Sadly, I didn't get any answers to my questions.

Important point: Our universe, so far as we can tell, consists of three spatial dimensions and one time dimension. There is no, zero, nada, zilch evidence for any real additional dimensions, despite all the speculation about dimensions beyond four. As mathematical constructions additional dimensions are useful; but they are not part of the real physical world, as far as we can tell.

You say that there is not evidence for additional dimensions. That might be true, but i fail to see the relevance to my questions.
I would still like to know what a dimension is in objective reality. I would also like to know what the evidence is for the three spatial dimensions?
Thanks for trying.

Oh, I'm sorry that I disinterested you.

I'm cryin'.

Get over it- if you want to learn and understand the answer to your question- losing your attitude might help.

I'm sorry, but i can't see the relevance of talking about imaginary worlds like this.
If the imaginary world conflict with reality, i just don't see the point of talking about it. It's a flawed model.

A dimension is not a direction. They are two different things entirely.

I am perfectly open for this possibility. That was why i asked for the difference between the two.
Maybe you would like to try to explain this? I would appreciate it.

Can you fold a cube in upon itself into a hypercube that is larger on the inside than it is on the outside?
No. Because you don't understand the forth dimension.

I could explain that- but that would require you to get interested.

No thanks, but if you could explain the normal 3 dimensions, that would be great.

Dimensions can be defined more broadly than what niin is looking for. He is looking only for those that define position in space. These are called spatial dimensions.

I do not dispute the usefulness of using 3 variable to describe physical reality. But people say that dimensions are real and exist in objective reality. I'm not interested in a mathematical model that does not match reality. I am trying to figure out if there is match, if dimensions are real?

If we want to talk about relativity, we must include time, but I see no indication that niin is trying to bring relativity into the discussion. So let's stop confusing the issue by taking about.

Well, one of the reasons that I'm interested in this is that relativity make use of dimensions, but i would like to avoid that subject for the time being.

niin,

You've seen how many different and confusing answers you are getting.
That's because nobody really knows what you are trying to ask.

I guess that could be my fault. I try to be concise and clear, but i guess i failed.

My guess is that what you are trying to understand is why it is said that
space has three dimensions. Is that correct?

Well, that would be a question that i would be interested in the answer to.
But i would still like my original questions answered.
Thanks for asking.